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Localisation des productions agricoles et durabilité des
systèmes d’approvisionnement alimentaire en milieu
urbain.
Anne Fournier
To cite this version:
Anne Fournier. Localisation des productions agricoles et durabilité des systèmes d’approvisionnement
alimentaire en milieu urbain.. Economies et nances. Université Paris Nanterre, 2014. Français.
�tel-02886503�
´
Ecole doctorale no396 : ´
Economie, Organisations, Soci´et´e
T H `
E S E
pour obtenir le grade de
Docteur de l’Universit´
e Paris Ouest Nanterre La D´
efense
Discipline: Sciences ´
Economiques
pr´esent´ee et soutenue publiquement par
Anne FOURNIER
le 01 d´ecembre 2014
Localisation des productions agricoles et
durabilit´
e des syst`
emes
d’approvisionnement alimentaire
en milieu urbain.
sous la direction de : Pierre-Andr´e JOUVET et Carl GAIGN ´
E
Jury
M. St´ephane DE CARA, Directeur de Recherche INRA-Grignon Co-Encadrant
M. Carl GAIGN´
E, Directeur de Recherche INRA-Rennes Co-Directeur
M. Pierre-Andr´e JOUVET, Professeur Universit´e Paris Ouest Nanterre Directeur
M. Fabien MOIZEAU, Professeur Universit´e Rennes 1 Rapporteur
M. Lionel RAGOT, Professeur Universit´e Paris Ouest Nanterre Examinateur
M. St´ephane RIOU, Professeur Universit´e Jean Monnet Rapporteur
Universit´e Paris Ouest Nanterre La D´efense
EconomiX - UMR CNRS
Table des mati`eres
Introduction g´en´erale 1
1 L’approvisionnement alimentaire des villes 5
1.1 Bref historique et ´etat des lieux ........................... 5
1.1.1 S´edentarisation de l’activit´e agricole et naissance des villes ....... 5
1.1.2 D’une agriculture de subsistance `a une agro-industrie mondialis´ee . . . . 6
1.1.3 Caract´eriser le syst`eme agro-alimentaire actuel .............. 7
1.2 Villes et alimentation : d´efinir la nouvelle probl´ematique ............. 8
1.2.1 Contraintes environnementales ....................... 9
1.2.2 Contraintes en ressources humaine et fonci`ere ............... 10
1.2.3 Evolution des pr´ef´erences .......................... 11
1.3 Les syst`emes d’approvisionnement alimentaire alternatifs ............. 12
1.3.1 Des avantages invoqu´es... .......................... 13
1.3.2 ... `a la valid´ee contest´ee ........................... 14
1.4 Espace, agriculture et environnement : une approche th´eorique. ......... 15
1.4.1 La dimension spatiale dans la th´eorie ´economique ............. 16
1.4.2 Economie g´eographique et agriculture ................... 18
1.4.3 Economie spatiale et environnement .................... 20
1.5 R´ef´erences ....................................... 27
2 Urbanization, Agricultural Location, and Greenhouse Gas Emissions 33
2.1 Introduction ...................................... 34
i
2.2 The framework .................................... 38
2.2.1 Spatial structure ............................... 39
2.2.2 Transportation/distribution network .................... 39
2.2.3 Producers ................................... 41
2.2.4 Consumers .................................. 41
2.2.5 Equilibrium .................................. 43
2.2.6 Emissions ................................... 45
2.3 Emissions-minimizing spatial distribution of food production .......... 46
2.4 Welfare-maximizing spatial distribution of food production ........... 50
2.5 Spatial-equilibrium distribution of food production ................ 53
2.6 Discussion and possible extensions ......................... 56
2.7 Concluding remarks ................................. 58
2.8 R´ef´erences ....................................... 60
2.9 Emissions-minimizing distribution of food production ............... 63
2.10 Welfare-maximizing distribution of food production ................ 65
2.11 Spatial-equilibrium distribution of food production ................ 66
2.12 Simulation results .................................. 67
2.13 Discussion and Extensions with Kjelevators and bundling capacity τ. . . . . 69
2.13.1 Equilibrium .................................. 69
2.13.2 Intra-regional transport flows ........................ 70
2.13.3 Ton-mileage .................................. 71
3 Conventional vs. Alternative Farming : Assessing the Sustainability of a
Regional Food Supply Pattern. 73
3.1 Introduction ...................................... 74
3.2 The framework .................................... 76
3.2.1 The spatial structure ............................. 76
3.2.2 Preferences and demand ........................... 77
3.2.3 Technologies and agricultural profits. .................... 78
ii
3.3 The equilibrium pattern of agricultural land use .................. 81
3.3.1 Equilibrium land allocation ......................... 81
3.3.2 Urbanization and agricultural practices .................. 83
3.3.3 Soil quality and fertilizer use at the equilibrium .............. 85
3.4 Agricultural pattern and regional welfare ..................... 86
3.4.1 Urban households utility and alternative farming. ............. 86
3.4.2 The welfare-maximizing solution ...................... 87
3.5 Does alternative farming development lead to a decrease in GHG emissions ? . 89
3.5.1 Synthetic fertilizer use and agricultural production ............ 90
3.5.2 Intra-regional food transportation and trade ................ 91
3.5.3 Emissions from the regional food supply chain .............. 93
3.6 Assessing the impact of an energy price rising. .................. 95
3.6.1 The impact of a fertilizer price rising .................... 95
3.6.2 The impact of an agricultural transport cost rising ............ 96
3.7 Conclusion ...................................... 96
3.8 R´ef´erences ....................................... 98
4 Direct Selling Farming Under Varying Spatial Externalities 107
4.1 Introduction ......................................108
4.2 The framework ....................................110
4.2.1 The spatial structure .............................110
4.2.2 Preferences and demand ...........................111
4.2.3 The direct selling sector ...........................113
4.3 The short-run equilibrium. ..............................119
4.3.1 The land market ...............................119
4.3.2 Direct selling goods market .........................123
4.3.3 Direct selling profit and spatial externalities. ...............125
4.4 The long run equilibrium. ..............................126
4.4.1 The equilibrium number of direct selling varieties. ............126
iii
4.4.2 Direct selling varieties and the city size. ..................127
4.5 Direct selling farming and regional welfare. ....................132
4.5.1 Urban households utility ...........................132
4.5.2 Regional welfare ...............................135
4.6 Conclusion ......................................136
4.7 R´ef´erences .......................................138
Conclusion 143
iv
Liste des figures
1.1 Dynamiques et interrelations ´economiques entre secteurs ............. 7
1.2 Principales forces d’agglom´eration et de dispersion. ................ 18
1.3 Economie spatiale et prise en compte de l’environnement. ............ 21
2.1 Spatial structure and transportation flows (dashed lines) of the agricultural
good within (left side) and between (right side) regions. In this example, regions
1 and 2 are importers ; regions 3, 4, and 5 are exporters. ............. 40
2.2 Emissions-minimizing distribution of the rural population (diamonds, left axis)
and cumulative distribution function of the urban population across regions (red
crosses, right axis). Self-sufficient regions are signaled by squares and importing
regions by triangles. Parameter values : m= 50, λu≈0.53, λr≈0.47, λu1≈
0.0796, λuj =λu1/(j0.79) for all j,µ≈0.026, eb≈0.08, ν= 4. .......... 50
2.3 Welfare-maximizing (dots) and spatial equilibrium (asterisks) for two values
of within-region transport costs (ta). Parameter values : m= 50, λu≈0.53,
λr≈0.47, λu1≈0.0796, λuj =λu1/(j0.79) for all j,µ≈0.026, eb≈0.08, ν= 4,
φ= 1, δ= 1, and d= 0.5. .............................. 56
3.1 The sectoral organization .............................. 76
3.2 Farming conversion and regional use of synthetic fertilizer ............ 80
3.3 Bid-rent functions and regional land allocation .................. 82
3.4 Alternative farming share (λ∗
a) and urban population’ size (λu) for different
level of goods’ substituability. ............................ 84
3.5 The regional farming pattern at the equilibrium .................. 85
v
3.6 Urban households’ utility under fully-alternative and fully-conventional farming
patterns. ........................................ 87
3.7 Equilibrium and Optimal farming pattern in function of the urban population’
size ........................................... 88
3.8 GHG emissions from food transportation ..................... 93
3.9 Total GHG emissions from the regional food supply ............... 94
3.10 The impact of a fertilizer price rising on the equilibrium farming pattern. . . . 96
3.11 Variation of synthetic fertilizer use in space .................... 99
3.12 Net incomes differential and equilibrium ......................102
4.1 The regional land allocation .............................123
4.2 The long-run equilibrium ..............................127
4.3 Direct selling varieties and urbanization (without spatial externalities) . . . . . 128
4.4 Direct selling varieties and urbanization (with low pollution effect) . . . . . . . 131
4.5 Direct selling farming and welfare components. ..................135
vi
Liste des tableaux
2.1 Total ton-mileage and average shipment distance of agricultural commodities
and food products by transport mode in the U.S. (2007). Source : Adapted
from from BTS and U.S. Census Bureau [2010] .................. 36
2.2 Summary of the simulation results in the various spatial configurations and for
two values of within-region transport costs (ta). Relative changes in emissions
are computed for each category relatively to emission levels in the emissions-
minimizing configuration. The shares of the respective emission categories in
total emissions for each spatial configuration are given in parentheses. Parameter
values : m= 50, λu≈0.53, λr≈0.47, λu1≈0.0796, λuj =λu1/(j0.79) for all j,µ≈0.026,
eb≈0.08, ν= 4, φ= 1, δ= 1, and d= 0.5. ........................ 68
3.1 Variations of transportation flows with respect to alternative farming share (λa)
and urbanization (λu). ...............................103
3.2 Variations of transportation flows with respect to alternative farming share (λa)
for low-urbanized regions ..............................104
3.3 Variations of transportation flows with respect to alternative farming share (λa)
for high-urbanized regions ..............................104
4.1 Factors influencing the number of direct selling varieties .............127
vii
viii
Remerciements
4h21, l’heure id´eale pour entreprendre la partie plus importante de ce travail ; pas pour
sa pertinence scientifique ou intellectuelle, ni de par sa longueur, je tenterai de rest´ee br`eve.
Importante parce qu’elle me demande un effort consid´erable : parvenir `a vous dire de la
mani`ere la plus sinc`ere qu’il soit, tout ce que Vous ˆetes pour moi.
A Vous deux tout d’abord, Merci pour ce que vous faites de moi au quotidien. Parce que
l’´education que l’on re¸coit et l’environnement dans lequel on grandit sont l’essence mˆeme de
ce que l’on devient. ¸Ca ne fait pas tout, le libre-arbitre vient un jour `a reprendre le dessus et
contribue au passage de “enfant de” `a individu `a part enti`ere, capable de former ses propres
jugements, de faire ses propres choix. Mais le point de d´epart contraint tout de mˆeme le
champ des possibles. Rien de n´egatif ni de malheureux `a cela, au contraire ; je mesure ma
chance, d’avoir grandi puis mˆuri `a vos cˆot´es, toujours guid´es par des valeurs saines, vraies,
justes. Parfois trop altruistes `a mon sens, ce qui force mon respect et mon admiration. Je suis
extrˆemement fi`ere d’ˆetre votre fille, ce qui n’a aucun sens en soi parce que cela ne provient ni
d’un choix, ni d’un acte. Mais je le suis quand mˆeme. . . Et aussi absurde que cela puisse ˆetre,
je le revendique. Vous ˆetes mon exemple, pas simplement l’un ou l’autre, votre combinaison.
D’o`u mon effort depuis le d´ebut de ce paragraphe pour ne pas vous nommer explicitement.
Parce que “psychologiquement perturb´ee” comme je le suis, j’aurais toujours peur que vous
interpr´eteriez l’ordre dans lequel je vous cite comme un signe de pr´ef´erence, d’admiration
relative, etc. . . Chacun de vous m’ap(/im)porte autant. Au final, on ne choisit pas ses parents
mais je n’aurais pas pu esp´erer mieux.
A toi ensuite, ma sœur (on fait la mˆeme taille !). Il n’existe aucun mot pouvant fid`element
exprimer `a quel point tu m’apportes, m’animes, m’inspires et me motives chaque jour un
peu plus. Tu m’agaces aussi! ! Relativement moins avec l’ˆage... Heureusement, on grandit. Je
t’aime, pas parce que tu es ma sœur. Tu le sais, pour moi partager un patrimoine g´en´etique
commun n’implique aucun sentiment inn´e, r´eciproque ou inconditionnel. Je t’aime pour la
personne que tu es, Marie. De mani`ere irrationnelle et anormale pourraient dire certains mais
inutile de te rappeler l’importance que j’accorde `a la normalit´e... Plus que jamais au cours
de ces derniers mois, tu as ´et´e – et le reste en partie– mon soutien premier, ma raison de
poursuivre `a vos cˆot´es. Seule, je n’en avais ni la force, ni l’envie.
A vous autres enfin. Vos deux points communs : m’avoir cˆotoy´e au moins une minute au
cours de ces 26 derni`eres ann´ees et avoir contribu´e de mani`ere suffisamment significative `a
mon bonheur pour avoir connaissance de cette ghost track. Individuellement, vous savez (du
moins je l’esp`ere !) tout le bien que je pense de vous. Je vous appr´ecie profond´ement et si vous
permettre d’atteindre l’un de vos rˆeves devait n´ecessiter un sacrifice de mon cˆot´e, je n’aurais
mˆeme pas `a r´efl´echir. . . Chacun d’entre vous avez su m’apporter ´ecoute et r´econfort, tout en
respectant mon besoin vital de r´eclusion. De cela, je vous en serai ´eternellement reconnaissante.
La suite, c’est mon travail, ce pour quoi je me suis investie parfois sans m´enagement au
cours de ces quatre derni`eres ann´ees. Reste l’´etape de la soutenance. Ce jour-l`a, je serai inca-
pable de vous t´emoigner la moindre marque d’affection ni mˆeme de vous adresser publiquement
tous mes remerciements, me sachant observer par d’autres personnes certes, toutes sympa-
thiques (j’en ai fait la s´election ! :) ), mais contrairement `a vous, ´etrang`eres `a ma vie. A l’avenir
cependant, en cas de doute sur mes sentiments, r´ef´erez-vous simplement `a cet ´ecrit : Inscrit
`a vie, stock´e bien au chaud dans la BU de Nanterre, accessible `a tous, mais d´efinitivement
lisible que par les rares concern´es.
Introduction g´en´erale
Au cours des soixante derni`
eres ann´
ees, la population mondiale a connu un sur-
saut spectaculaire, passant de 2,5 milliards d’habitants `a la fin de la Seconde Guerre
mondiale `a 7 milliards en 2011. Cette croissance d´emographique se distingue des pr´ec´edents
´episodes tant par son importance que par l’apparition conjointe d’une tendance nouvelle et
soutenue `a la concentration des populations au sein des villes. Processus fortement port´e par
deux si`ecles de mutations ´economiques et sociales, l’urbanisation se pr´esente comme l’un des
faits majeurs du 21`eme si`ecle. Ainsi, sur les 9 milliards de personnes que comptera le monde
d’ici 2050, plus des deux tiers seront urbains [United Nations,2014].
Appel´ee `a se renforcer partout dans le monde, cette tendance au grossissement des villes
lance un v´eritable d´efi `a la communaut´e internationale en mati`ere de durabilit´e de notre
syst`eme ´economique : “comment parvenir `a concilier croissance ´economique, d´eveloppement
et pr´eservation de l’environnement, tout en faisant face `a des contraintes de rar´efaction de
ressources ?”
Parmi les grands enjeux qui se profilent, celui de la s´ecurit´e alimentaire revˆet une impor-
tance capitale, `a la fois par son statut de besoin primaire, mais ´egalement par la complexit´e
du d´efi qu’elle impose. Cette probl´ematique n’est pas nouvelle ; bien qu’aujourd’hui essentiel-
lement cantonn´ee aux seuls pays du Sud, elle a longtemps ´et´e une priorit´e pour l’ensemble
des soci´et´es de l’`ere pr´eindustrielle. Sous l’effet des bouleversements induits par l’accroisse-
ment d´emographique, elle pourrait redevenir centrale, y compris dans les pays industrialis´es `a
´economie de march´e. Comme soulign´e par Morgan [2014], les grandes villes des pays du Nord
seront in´eluctablement impact´ees par cette transition, certaines d’entre elles se retrouvant
mˆeme en premi`ere ligne de cette “nouvelle ´equation alimentaire”.
1
En concentrant d´esormais plus de la moiti´e de la population mondiale, les villes doivent
aujourd’hui trouver r´eponse `a la question : “comment nourrir durablement une population ur-
baine en constante progression ?” Cette probl´ematique est au cœur de cette th`ese. De mani`ere
g´en´erale, l’ensemble des travaux regroup´es au sein de ce manuscrit interroge la durabilit´e en-
vironnementale et sociale de la localisation des productions agricoles par rapport aux grands
centres de consommations. Cette th`ese a pour ambition de proposer un traitement th´eorique
de la question de l’approvisionnement alimentaire des villes dans un contexte de r´eflexion
g´en´erale sur le changement climatique et le d´eveloppement durable. A la fronti`ere entre ´econo-
mie g´eographique et ´economie de l’environnement, elle a pour objectif principal d’analyser de
mani`ere formalis´ee les arbitrages environnementaux et sociaux dans un cadre spatial explicite.
En outre, l’id´ee selon laquelle aucune r´eponse ne saurait ˆetre satisfaisante sans qu’une atten-
tion sp´ecifique soit port´ee aux interactions spatiales, ´economiques et ´ecologiques entre espaces
urbains et agriculture constitue l’un des positionnements cl´es d´efendus dans ce travail.
Le premier chapitre de cette th`ese est consacr´e tout d’abord `a une pr´esentation factuelle
du contexte. Celle-ci nous am`ene `a avancer l’id´ee que la g´eographie urbaine telle qu’observ´ee
aujourd’hui est pour l’essentiel le r´esultat d’une construction jointe et mutuellement entretenue
de l’agriculture et des villes. La localisation des grands pˆoles urbains dans l’espace a en effet ´et´e
significativement guid´ee par la nature des terres disponibles, l’h´et´erog´en´eit´e des sols combin´ee
aux contraintes de temps et de coˆut ayant naturellement conduit les populations `a organiser
l’ensemble des activit´es de production autour des terres les plus fertiles. Ce rapide aper¸cu de
l’´evolution des relations entre ville et agriculture nous permet `a la fois de mieux cerner les
contours de la nouvelle probl´ematique alimentaire et de faire ressortir les principaux facteurs
`a prendre en compte dans notre mod´elisation.
Suite `a cette introduction, nous proposons trois travaux th´eoriques abordant la question
de l’approvisionnement alimentaire des villes sous diff´erents aspects. Le chapitre 2 questionne
dans un premier temps la pertinence en termes de b´en´efices ´economiques et environnementaux
d’un syst`eme d’approvisionnement exclusivement local, reposant sur l’autosuffisance alimen-
taire de l’ensemble des villes appartenant `a une mˆeme entit´e g´eographique donn´ee. L’objectif
de ce chapitre n’´etant pas d’´etayer les th´eories de localisation de l’activit´e agricole, mais de
2
rendre compte de l’impact de la structuration d’un territoire sur la qualit´e ´ecologique du
syst`eme pris dans son ensemble, les hypoth`eses retenues pour le mod`ele se veulent volontai-
rement “simplificatrices” car n´ecessaires pour r´epondre `a cette probl´ematique d’allocation des
biens dans un cadre spatial multir´egional.
Les chapitres 3 et 4 proposent un traitement davantage “micro spatial” de la probl´ema-
tique, s’int´eressant tout deux aux conditions ´economiques n´ecessaires `a l’´emergence d’une
fili`ere agricole alternative en p´eriph´erie des grandes villes. De mani`ere plus pr´ecise, le cha-
pitre 3 s’interroge sur la capacit´e d’une agriculture de proximit´e `a s’implanter durablement en
l’absence d’intervention publique. Dans ce mod`ele, agriculture conventionnelle et alternative
proposent des biens imparfaitement substituables et se distinguent ´egalement de par leurs
pratiques de production.
Le chapitre 4 entre quant `a lui plus dans le d´etail en consid´erant de mani`ere plus fine
les pr´ef´erences des consommateurs (introduction de diff´erenciation verticale et horizontale des
produits agricoles), et en tenant compte de l’interaction entre activit´es urbaine et agricole
avoisinantes (introduction d’une externalit´e environnementale).
Le cinqui`eme et dernier chapitre de ce manuscrit dresse finalement le bilan des enseigne-
ments pouvant ˆetre tir´es des travaux propos´es et ouvre la discussion sur les perspectives et
les extensions envisageables.
3
Chapitre 1
L’approvisionnement alimentaire
des villes
1.1 Bref historique et ´etat des lieux
1.1.1 S´edentarisation de l’activit´e agricole et naissance des villes
Le syst`eme agro-alimentaire dans sa forme actuelle est le r´esultat d’une construction de
tr`es long terme. Pour bˆatir leur croissance, les villes ont historiquement eu `a assurer leur
s´ecurit´e alimentaire, menant progressivement agriculture et ´elevage `a se substituer aux acti-
vit´es de cueillette et de chasse. L’offre alimentaire se fixant au sol, les premi`eres cultures ont
logiquement pris place sur les terres les plus fertiles. Ces derni`eres avaient alors pour fonction
de nourrir les agriculteurs, population encore dominante dans les pays d´evelopp´es au 18eme
si`ecle, mais ´egalement de fournir un exc´edant alimentaire suffisant pour approvisionner les
actifs nouvellement install´es dans les cit´es.
De par le jeu conjoint des gains en productivit´e dans le secteur agricole et de la dynamique
insuffl´ee par le d´eveloppement industriel, les villes mut`erent progressivement en pˆoles majeurs
d’activit´e. Leur localisation g´eographique trouve, quant `a elle, sa principale explication dans le
coˆut particuli`erement ´elev´e du transport, celui-ci amenant naturellement une grande majorit´e
des villes `a se d´evelopper `a proximit´e des zones agricoles afin de limiter les pertes li´ees `a
l’acheminement des denr´ees.
5
1.1.2 D’une agriculture de subsistance `a une agro-industrie mondialis´ee
Pour les pays d´evelopp´es, le 19eme si`ecle, et en particulier la p´eriode comprise entre 1820-
1830 et 1914, constitue le tournant entre une soci´et´e encore essentiellement rurale, et une
soci´et´e urbanis´ee dans laquelle pr`es de 90% de la population ne se retrouve plus directement
impliqu´ee dans l’agriculture [Bairoch and Goertz,1986].
Parmi les facteurs ayant contribu´e `a l’urbanisation, l’accroissement de la productivit´e
agricole joue un rˆole ind´eniable. En se basant sur des donn´ees relatives `a vingt pays sur la
p´eriode 1830-1920, Bairoch and Goertz [1986] mettent en ´evidence une corr´elation positive et
fortement significative entre niveau d’urbanisation et productivit´e agricole, expliquant cette
relation par un ph´enom`ene de migration sectorielle ; l’am´elioration de l’efficacit´e productive
a permis de lib´erer une part de plus en plus importante de la main d’œuvre agricole, cette
derni`ere ´etant alors disponible pour travailler dans l’industrie localis´ee en milieu urbain.
Parall`element aux gains de productivit´e enregistr´es dans le secteur agricole, les progr`es
techniques r´ealis´es dans le domaine des transports ont progressivement contribu´e `a gommer la
contrainte de distance qui pesait sur l’organisation de la fili`ere d’approvisionnement alimen-
taire. L’espace et plus encore la localisation relative des diff´erents acteurs de la chaine perdent
en importance. S’op`erent alors de profondes modifications dans la logistique d’acheminement
des produits alimentaires, aboutissant un si`ecle et demi plus tard `a la mondialisation des flux
d’´echange que nous connaissons aujourd’hui.
Bien que de plus en plus diffus, les liens entre ville et campagne demeureront tout de
mˆeme fortement pr´esents jusqu’au d´ebut du 20eme si`ecle ; au-del`a de l’approvisionnement
alimentaire qui se p´erennise en tant que relation marchande, d’autres formes d’activit´es n´e-
cessitant d’´etroits liens d’´echange entre zones urbaines et rurales se d´eveloppent. Ces derni`eres,
r´eunies sous la d´enomination de “proto-industrie” par Mendels [1972], permettent entre autre
de fournir des ressources compl´ementaires aux populations rurales, corrigeant le d´es´equilibre
entre rar´efaction de l’emploi agricole et surcharge d´emographique. La fili`ere textile des pays
du Nord Ouest de l’Europe notamment apparaˆıt comme l’un des exemples les plus aboutis de
proto-industrie, les ateliers ruraux se chargeant des op´erations simples ne n´ecessitant pas ou
peu de capitaux, et celles requ´erant plus de technicit´e ´etant transf´er´ees vers les manufactures
6
urbaines.
Figure 1.1 – Dynamiques et interrelations ´economiques entre secteurs
1.1.3 Caract´eriser le syst`eme agro-alimentaire actuel
Amorc´e d`es la fin du 18eme si`ecle pour les pays du Nord, le renversement du rapport de
force entre villes et campagnes s’est poursuivi tout au long du 19eme si`ecle, se concr´etisant
d´efinitivement au d´ebut du si`ecle dernier ; auparavant“leader” au sens o`u elle conditionnait lo-
calisation, nature, et rythme du d´eveloppement urbain, l’agriculture doit d´esormais s’adapter
aux exigences d’une nouvelle soci´et´e urbaine. Toutefois, bien qu’elle ne soit plus per¸cue prin-
cipale initiatrice de croissance et de d´eveloppement, l’agriculture conserve un rˆole essentiel,
fournissant notamment l’alimentation n´ecessaire `a la main d’œuvre non nourrici`ere localis´ee
dans les pˆoles urbains.
Le panorama actuel des relations villes-campagnes est le r´esultat des trois derniers si`ecles
de mutations conjointes. D’une ´economie o`u activit´es agricoles et non agricoles ´etaient g´eogra-
phiquement regroup´ees et relativement ´equilibr´ees, les pays d´evelopp´es sont d´esormais pass´es
`a une ´economie caract´eris´ee par une offre alimentaire dispers´ee devant satisfaire une demande
nette croissante et fortement concentr´ee.
7
Les avanc´ees technologiques r´ealis´ees dans le domaine du transport expliquent en grande
partie l’´emergence de cette nouvelle forme d’organisation des syst`emes d’approvisionnement
alimentaire. Le poids des coˆuts de transport devenu n´egligeable, les flux d’´echange ont pro-
gressivement ´echapp´e `a la logique de rationalisation du volume et la multiplication des trajets
s’est alors impos´ee, r´epondant davantage aux exigences des consommateurs (goˆut prononc´e
pour la diversification de la nature et de la provenance des biens). Ce passage d’´economie de
stocks `a ´economie de flux conceptualis´e sous la d´enomination “stock roulant” est commun `a
l’ensemble des pays industrialis´es [Oudin,2001]. Dans les faits, cette nouvelle forme de gestion
des flux s’illustre par un recours de plus en plus fr´equent aux parcours de type “navette” et
au principe du “juste-`a-temps” [Leglise,2007]. Ainsi, s’il reste principalement inter-r´egional, le
trafic de denr´ees alimentaire a toutefois consid´erablement cru sous l’effet de la multiplication
des fr´equences d’envoi et d’un allongement des distances li´e `a la polarisation de l’´economie.
Cette tendance `a la globalisation de l’approvisionnement alimentaire a par ailleurs contri-
bu´e au rapide d´eclin de nombreuses productions vivri`eres peu rentables, accompagn´e d’une
sp´ecialisation g´eographique de la production. Dans la p´eriph´erie des grandes villes notamment,
l’agriculture a poursuivi son adaptation `a l’environnement urbain, se transformant progres-
sivement en exploitations de petites tailles, sp´ecialis´ee dans des cultures `a hauts revenus par
hectare, et ayant recours `a des techniques de production plus intensives [Heimlich,1989].
1.2 Villes et alimentation : d´efinir la nouvelle probl´ematique
De mani`ere simple, la question de la r´eorganisation de la chaine d’approvisionnement ali-
mentaire peut ˆetre appr´ehend´ee comme une r´eflexion sur les moyens `a mettre en œuvre pour
permettre `a terme, la r´ealisation d’´economies de flux sous contraintes environnementales, so-
ciales, et `a localisation fixe et donn´ee de la demande. Par opposition aux pr´ec´edents enjeux qui
s’inscrivaient presqu’exclusivement dans une logique de r´eponse quantitative `a une demande
nette croissante, il s’agit d´esormais d’une probl´ematique plus fine d’allocation d’une produc-
tion entre plusieurs points g´eographiquement fix´es, de sorte que l’espace – ou plus pr´ecis´ement
la localisation relative de l’ensemble des acteurs de la chaˆıne – redevient central.
Nourrir les villes n´ecessite donc de trouver et de maintenir un sch´ema coh´erent et organis´e
8
entre espaces urbains et ruraux. Il s’agit aujourd’hui de r´epondre `a une demande alimentaire
caract´eris´ee par une forte concentration g´eographique et de nouvelles exigences sociales, en-
vironnementales et sanitaires de la part des consommateurs. Bien que le principe demeure
similaire - produire suffisamment pour garantir l’´equilibre entre offre et demande -, il est
d´esormais de nouvelles contraintes `a int´egrer, ces derni`eres pouvant ˆetre regroup´ees en trois
grands items.
1.2.1 Contraintes environnementales
Le mod`ele agricole actuellement pr´epond´erant – intensif, sp´ecialis´e et mondialis´e - g´en`ere
des externalit´es n´egatives qui, `a terme, menacent l’´equilibre ´ecologique de la plan`ete. Au
sens large, les implications environnementales des syst`emes d’approvisionnement alimentaire
portent sur deux champs majeurs que sont la production et le transport.
Contrˆoler les impacts li´es `a la production Reposant sur l’optimisation de la production par rap-
port `a la surface cultiv´ee, le syst`eme agricole moderne se caract´erise principalement par une
utilisation accrue d’engrais chimiques et de pesticides. Les cons´equences environnementales
de cette intensification productive sont aujourd’hui largement montr´ees du doigt. Les dom-
mages caus´es par l’azote et les menaces qu’il fait peser `a terme sur la qualit´e des ´ecosyst`emes
soul`event, en premier lieu, de v´eritables d´efis techniques en mati`ere de choix de production
[Sutton et al.,2011]. `
A cela s’ajoute la question de l’effet de serre et du changement climatique,
les ´emissions directement li´ees `a la production agricole repr´esentant environ un cinqui`eme des
´emissions fran¸caises de GES. Enfin, les ´energies fossiles ´etant utilis´ees comme source d’´energie
pour le carburant des machines ou le chauffage des bˆatiments, et comme mati`ere premi`ere
pour la fabrication des intrants chimiques, l’agriculture est et sera directement impact´ee par
la crise ´energ´etique latente, renfor¸cant par la mˆeme les arguments plaidants en faveur d’un
changement dans les pratiques de production.
Maitriser les flux de transports Premiers ´emetteurs de gaz `a effet de serre en France, les
transports produisent pr`es d’un tiers des ´emissions de dioxyde de carbone (CO2) [CITEPA,
2010]. `
A l’´echelle mondiale, la combustion des carburants fossiles provoque des ´emissions de
9
CO2de l’ordre de 7 milliards de tonnes, soit 27% de l’ensemble des ´emissions du syst`eme
´energ´etique plan´etaire (Enerdata). Les transports constituent par ailleurs l’unique activit´e `a
avoir vu sa contribution au bilan des rejets nationaux croˆıtre aussi rapidement au cours des
30 derni`eres ann´ees (+13,5% sur la p´eriode 1990-2008). Sous l’hypoth`ese de constance dans
nos habitudes de consommation, ces ´emissions pourraient atteindre 9 milliards de tonnes `a
horizon 2030 [Dessus and Girard [2009]].
Puisqu’il est largement admis que l’am´elioration de l’efficacit´e ´energ´etique sera insuffi-
sante pour r´eduire les ´emissions `a un niveau compatible avec les engagements internationaux,
d’autres politiques en lien notamment avec l’am´enagement du territoire seront n´ecessaires
[EEA,2009] ; en tenant compte des ajustements dans la localisation des productions agricoles,
les modes d’approvisionnement des bassins de consommation, et de leurs cons´equences sur les
distances parcourues par les marchandises, la planification urbaine pourrait compter parmi
les leviers d’action efficaces.
1.2.2 Contraintes en ressources humaine et fonci`ere
Avec l’´emergence des villes, une transition dans le rapport de l’Homme `a l’espace s’est
amorc´ee ; du point de vue de la logique urbaine, les terres disponibles trouvent d´esormais de
la valeur `a travers la surface physique qu’elles offrent et non plus de par la qualit´e biologique
intrins`eque de leur sol. Activit´es urbaines et agricoles sont donc en concurrence pour l’usage
des sols : d’un cˆot´e, terre et qualit´es des sols demeurent un facteur essentiel et difficilement
compressible `a la production de biens agricoles. De l’autre, l’urbanisation et le d´eveloppement
d’infrastructures, synonymes de consommation d’espace, sont appel´es `a renforcer leur emprise
fonci`ere.
Cette comp´etition qui plus est d´efavorable aux activit´es agricoles du fait de leur faible ren-
tabilit´e relative, est `a l’origine de tensions croissantes sur le march´e foncier, qui, en l’absence
d’intervention publique, se soldent majoritairement par une extension de la ville aux d´epens
de l’agriculture. Cet ´etalement urbain compromet fortement la cohabitation ville-campagne et
rend d’autant moins probable la relocalisation d’une activit´e agricole `a proximit´e des grandes
m´etropoles. Par cons´equent, dans l’optique de l’instauration d’une forme plus durable d’ap-
10
provisionnement alimentaire, les mesures garantissant la pr´eservation d’espace d´edi´ee `a la
production doivent faire l’objet d’un examen approfondi.
De mani`ere analogue, la population vue `a travers sa fonction de facteur de production
offre une probl´ematique sensiblement proche. Au sein d’une entit´e spatiale combinant espaces
urbains et espaces ruraux, la question de l’emploi revˆet un int´erˆet tout particulier. La concur-
rence que se livrent villes et campagnes est l`a encore particuli`erement d´es´equilibr´ee, le milieu
rural souffrant d’une d´esaffection relative par rapport au milieu urbain fortement attractif.
Par cons´equent, mˆeme si l’opportunit´e de cr´eation d’emplois en milieu rural est r´eelle, les
conditions ´economiques sont peu favorables `a leur concr´etisation sans intervention publique.
Ainsi, au mˆeme titre que la ressource fonci`ere, mobiliser la main d’œuvre de mani`ere efficace
–c’est-`a-dire de sorte `a pouvoir r´epondre aux besoins anticip´es des populations tout en garan-
tissant une qualit´e de vie proche sinon ´egale entre urbains et ruraux—est un enjeu `a prendre
en consid´eration dans la r´eflexion sur la durabilit´e des futurs syst`emes d’approvisionnement
alimentaire.
1.2.3 Evolution des pr´ef´erences
Le passage d’une soci´et´e rurale `a une soci´et´e essentiellement urbaine s’est accompagn´e
d’une transformation des pr´ef´erences de consommation. La demande alimentaire urbaine pr´e-
sente en effet des caract´eristiques sp´ecifiques et diff´erentes de celles traditionnellement obser-
v´ees. Ces caract´eristiques comprennent entre autre un renforcement des exigences en mati`ere
de qualit´e nutritive des biens et de tra¸cabilit´e des produits ; les crises sanitaires publique-
ment r´ev´el´ees depuis la fin des ann´ees 90 combin´ees `a la diffusion des connaissances m´edicales
ont sensiblement contribu´e `a renforcer la m´efiance des consommateurs `a l’´egard de l’industrie
agro-alimentaire au sens large, les amenant progressivement `a penser leurs achats alimentaires
davantage en terme “d’investissement sant´e”.
Les consommateurs urbains se distinguent ´egalement par l’importance croissante qu’ils
tendent `a accorder aux impacts indirects sociaux et environnementaux induits par leur consom-
mation. D´esormais soucieux de contribuer `a la p´erennisation de l’activit´e ´economique en milieu
rural, ils peuvent pour certains prendre en consid´eration le caract`ere ´equitable de la redistri-
11
bution de la valeur ajout´ee parmi les acteurs de la chaˆıne.
La demande de plus en plus fr´equente d’acc`es `a une information moins opaque sur l’origine
des produits, l’empreinte carbone associ´ee `a leur commercialisation ou encore un indice de re-
distribution de la valeur ajout´ee, constitue l’un des signes d’un changement de pr´ef´erences de
consommation. Ces derni`eres combinent par ailleurs des ´el´ements parfois difficilement conci-
liables voire incompatibles, ajoutant un degr´e suppl´ementaire de complexit´e. Le cas des biens
exotiques compte parmi les exemples les plus ´evidents de souhaits a priori contradictoires; en
raison des contraintes m´et´eorologiques et climatiques qui ´eliminent de fait la possibilit´e d’une
production locale et durable, l’acc`es `a ce type de biens suppose donc le maintien d’´echanges
marchands potentiellement coˆuteux en terme d’´emissions de GES.
D´efinis par la combinaison de ces trois types de contraintes, les nouveaux contours de
la probl´ematique alimentaire apparaissent comme extrˆemement complexes, et le deviennent
encore davantage si l’on prend en compte l’existence d’externalit´es environnementales entre
milieux urbain et agricole.
1.3 Les syst`emes d’approvisionnement alimentaire alternatifs
L’´emergence de syst`emes d’approvisionnement alimentaire dits “alternatifs” (Alternative
Food Network ou AFN dans la litt´erature anglo-saxonne) est un mouvement commun `a l’en-
semble des pays industrialis´es. Multiples de par leur nature, ils forment toutefois une entit´e
relativement coh´erente au sens o`u l’ensemble de ces initiatives rel`event d’efforts consentis `a la
re-spacialisation et la re-socialisation conjointes des chaines d’approvisionnement alimentaire
et partagent des moyens d’actions proches. Dans son article consacr´e `a l’approvisionnement
alimentaire des grandes m´etropoles, Jarosz [2008] retient entre autres quatre caract´eristiques
permettant de conceptualiser plus finement les AFNs :
R´eduire la distance entre producteurs et consommateurs. Les agriculteurs produisent leurs biens
`a proximit´e des centres o`u ils seront consomm´es, l’objectif premier ´etant de diminuer la dis-
tance parcourue et la consommation ´energ´etique associ´ee au transport des aliments. La r´educ-
tion du nombre d’interm´ediaires impliqu´es dans la chaˆıne afin d’instaurer un lien plus direct
entre agriculteurs et consommateurs y est ´egalement centrale (La Trobe and Acott [2000],
12
O’Hara and Stagl [2001], ou Renting et al. [2003]). En passant par ce canal de distribution,
les producteurs captent et conservent une part plus importante de leur revenu.
Minimiser l’impact environnemental de l’activit´e de production. Les fili`eres alternatives reposent
en grande partie sur une offre agricole provenant d’exploitations de petite taille ayant recours
`a des techniques de production respectueuses de l’environnement. Par opposition `a l’indus-
trie agro-alimentaire conventionnelle, ces exploitants s’orientent vers des pratiques o`u engrais
synth´etiques et pesticides sont totalement absents de la production [Kloppenburg et al.,2000].
Ancrer la relation d’´echange entre producteurs et consommateurs durablement dans le temps en
privil´egiant des circuits de vente exclusivement consacr´es `a la fili`ere alternative (coop´eratives
alimentaires, vente directe, AMAP . . . ) et en misant sur le d´eveloppement de partenariats
avec les administrations publiques (groupes scolaires, cantines centrales) 1[Hendrickson and
Heffernan,2002].
Inscrire les pratiques de l’ensemble des acteurs de la chaˆıne dans le respect de normes sociales, ´eco-
nomiques et environnementales communes. Une attention particuli`ere est notamment port´ee
sur les aspects justes et ´equitables des relations d’´echanges entre producteurs, consommateurs,
et interm´ediaires dans l’acheminement et la distribution des denr´ees.
Un syst`eme alternatif se d´efinit alors selon son positionnement le long d’un axe gradu´e de
faible `a important, pour chacun des items susmentionn´es [Watts et al.,2005].
1.3.1 Des avantages invoqu´es...
Nombre d’arguments sont invoqu´es pour promouvoir le d´eveloppement de ces fili`eres d’un
genre nouveau. Sur le plan ´ecologique d’abord, les AFNs sont souvent per¸cus comme pro-
mouvant des pratiques et une organisation plus favorables `a l’environnement. L’absence de
pesticides et d’engrais de synth`ese dans les pratiques culturales, et le rapprochement g´eogra-
phique des lieux de production et de consommation semblent en effet jouer dans le sens d’une
diminution de l’impact environnemental de la chaˆıne d’approvisionnement dans son ensemble.
1. Voir notamment le rapport de MacLeod and Scott [2007] qui examine les avantages environnementaux,
´economiques et sociaux de l’approvisionnement alimentaire local et offre une revue pr´eliminaire de la litt´erature
sur les initiatives li´ees `a la production alimentaire locale.
13
D’un point de vue social ensuite, les AFNs permettent de restaurer un lien d’´echange direct
et durable entre consommateurs et producteurs.
Economiquement enfin, les AFNs cr´eeraient plus d’emplois et la r´ealisation d’´economies
tout au long de la chaˆıne de distribution via la suppression d’interm´ediaires pourraient avoir
des retomb´ees r´egionales cons´equentes 2.
1.3.2 ... `a la valid´ee contest´ee
La viabilit´e des AFNs comme r´eponse `a la nouvelle probl´ematique alimentaire est encore
sujette `a trop d’incertitudes. Si l’ensemble des objectifs affich´es par ces syst`emes alternatifs
semblent s’inscrire dans une d´emarche coh´erente de d´eveloppement durable, nous disposons
toutefois de peu de recul sur ces initiatives et d’un manque de retours et d’analyses sur leurs
bienfaits effectifs [Edwards-Jones et al.,2008].
L’empreinte ´ecologique des AFNs et leur capacit´e `a r´eduire les ´emissions de GES est l’un
des points les plus controvers´es, notamment du fait de l’association souvent abusive entre
diminution du nombre de kilom`etres-aliments et r´eduction des ´emissions. Born and Purcell
[2006] rel`event `a ce propos que le caract`ere “local” des AFNs n’est pas un gage intrins`eque
de b´en´efice environnemental, le mode de transport ainsi que la logique d’acheminement des
produits pouvant dans certains cas jouer de mani`ere tr`es d´efavorable dans le bilan ´energ´etique
total.
Par ailleurs, le transport ne constitue qu’une seule des ´etapes dans le cycle de vie d’un ali-
ment et n’est pas forc´ement responsable d’une part pr´epond´erante des ´emissions. Ceci am`enent
Pirog et al. [2001]etGarnett [2003] `a souligner l’importance de continuellement garder une
vision d’ensemble de la chaˆıne d’approvisionnement alimentaire afin de r´eduire globalement
les ´emissions de CO2, plutˆot que de cibler un seul aspect au d´etriment des autres.
Parmi les critiques les plus virulentes, Desrochers and Shimizu [2012] vont jusqu’`a affirmer
qu’une politique de souverainet´e alimentaire passant par un retour `a l’agriculture de proxi-
mit´e, ne ferait qu’exacerber les probl`emes. D’un point de vue de la s´ecurit´e alimentaire tout
d’abord, ils soulignent qu’historiquement, les ´echanges internationaux ont permis de r´epartir
2. A titre d’illustration, les fermes mettant en pratique un syst`eme alternatif en France ont une moyenne
de 1,8 employ´es `a plein temps contre 1,5 dans le circuit conventionnel [Chambres d agriculture,2012]
14
les risques inh´erents aux productions agricoles et relatifs aux al´eas climatiques, en permettant
un r´e´equilibrage permanant entre r´egions. Les auteurs critiquent ´egalement la p´erennisation
artificielle de productions locales potentiellement non concurrentielles, allant `a l’encontre de la
logique ´economique de sp´ecialisation r´egionale des productions agricoles, et se traduisant par
un gain ´economique de l’agriculteur prot´eg´e aux d´epens des consommateurs. D’un point de vue
environnemental, Desrochers and Shimizu [2012] invalident l’argument selon lequel produire
localement r´eduirait les ´emissions de GES, les segments li´es `a la production ayant un impact
souvent plus important que le transport sur longues distances, et recommandent au contraire
de produire autant que possible dans les r´egions les plus appropri´ees. En conclusion, ces au-
teurs soutiennent qu’en d´ecourageant l’utilisation efficace et optimale des ressources agricoles
mondiales, la promotion du local ne peut ˆetre garante d’une souverainet´e alimentaire durable.
Marsden [2009]etFranklin et al. [2011] enfin, apportent un avis plus nuanc´e sur la question.
Rejetant l’id´ee selon laquelle les AFNs seraient la version moderne d’une posture protection-
niste, Marsden [2009] avance que la viabilit´e `a long terme de ces syst`emes reposent essentiel-
lement sur leur capacit´e `a interagir intelligemment avec le march´e mondial conventionnel. En
se basant sur une ´etude de cas en Grande-Bretagne, Franklin et al. [2011] soulignent quant `a
eux que, bien qu’encore imparfaits et fragiles, les AFNs seront amen´es `a se modifier dans le
temps de mani`ere `a mieux cadrer avec les enjeux alimentaires globaux et offriront alors des
leviers d’action non n´egligeables.
1.4 Espace, agriculture et environnement : une approche th´eorique.
Pour apporter un ´eclairage th´eorique `a la probl´ematique de l’approvisionnement alimen-
taire en milieu urbain, deux ´el´ements sont n´ecessaires :
– les processus de localisation doivent ˆetre endog`enes afin de permettre `a l’´economie consi-
d´er´ee de prendre une forme spatiale propre `a ses caract´eristiques
– la nature de la concurrence pour repr´esenter l’agriculture alternative doit ˆetre imparfaite
afin de capter l’effet des diff´erents rapports de force du cˆot´e de l’offre et de la demande
Cette quatri`eme et derni`ere sous-partie offre un rapide aper¸cu des travaux faisant explicite-
ment le lien entre ´economie g´eographique, ´economie agricole, et ´economie de l’environnement.
15
1.4.1 La dimension spatiale dans la th´eorie ´economique
La prise en compte de l’espace dans la th´eorie ´economique reste relativement r´ecente. A
l’exception de quelques travaux parmi lesquels ceux de Von Th¨
unen [1827], Christaller [1933]
ou L¨
osch [1940], il faudra v´eritablement attendre la seconde moiti´e du 20eme si`ecle pour voir se
d´evelopper un courant exclusivement consacr´e `a l’´etude des dynamiques spatiales. Les travaux
th´eoriques se rapportant `a ce courant peuvent ˆetre class´es en deux sous-champs :
– les mod`eles d’allocation des sols
– les mod`eles de nouvelle ´economie g´eographique (NEG)
Economie urbaine et allocation des sols : une dimension micro-spatiale Largement inspir´es par la
ville-march´e de Von Th¨
unen [1827], les mod`eles d´evelopp´es dans ce sous-champ de l’´economie
spatiale ont pour structure commune une ville monocentrique form´ee d’un axe unidimensionnel
et d’un “Central Business District” (CBD) [Alonso,1964]. Le CBD, point de l’espace fix´e de
mani`ere exog`ene, regroupe l’ensemble des unit´es de production. Les agents r´esidant dans cette
ville s’installent le long de l’axe, chaque point constituant une localisation caract´eris´ee par sa
distance au centre (accessibilit´e au march´e centre). Ces derniers se rendent quotidiennement
dans le CBD pour y travailler, engendrant des coˆuts de transport suppos´es proportionnels `a
leur distance au centre 3. Leur disponibilit´e individuelle `a payer pour chaque emplacement de
l’espace d´etermine leur fonction d’ench`ere fonci`ere. L’allocation des sols est alors d´efinie par
la confrontation de l’ensemble de ces courbes d’ench`ere sur le march´e foncier ; `a l’´equilibre,
chaque emplacement de l’espace est occup´e par l’agent ayant propos´e l’ench`ere la plus ´elev´ee.
Ces mod`eles proposent ainsi une vision“intra-” ou “micro-spatiale” de l’´economie au sens o`u
ils rendent simplement compte de la r´epartition des agents au sein d’une ville, sans chercher
`a justifier la taille ni mˆeme l’existence de cette ville. Ils offrent par ailleurs une base de
mod´elisation int´eressante dans le cadre de notre probl´ematique o`u la r´epartition des sols entre
usages urbains et agricoles est un aspect essentiel.
3. L’hypoth`ese de proportionnalit´e des coˆuts implique la lin´earit´e des fonctions d’ench`ere fonci`ere. Cette
derni`ere peut ˆetre relˆach´ee, donnant alors lieu `a des fonctions d’ench`ere non lin´eaires pouvant ˆetre monotones
d´ecroissantes dans le cas d’une force centrip`ete toujours dominante, ou croissantes puis d´ecroissantes en pr´esence
de forces centrifuges qui amoindriraient dans un premier temps la force de rappel.
16
Nouvelle ´economie g´eographique et ´equilibre inter-r´egional L’article de Krugman [1991], cou-
ramment cit´e comme papier fondateur de la NEG, fait apparaˆıtre pour la premi`ere fois une
formalisation capable de rendre compte des mutations spatiales `a une ´echelle inter-r´egionale.
Le mod`ele propos´e dans cet article associe une structure de concurrence monopolistique de
type Dixit and Stiglitz [1977] `a une fonction d’utilit´e `a ´elasticit´e de substitution constante
(CES).
De mani`ere g´en´erale, la localisation des agents dans les mod`eles d’inspiration NEG r´esulte
d’arbitrages plus ou moins complexes entre avantages (rendements croissants) et inconv´e-
nients (coˆuts de transport) associ´es `a chaque point de l’espace. Krugman [1991] montre en
particulier que par un processus de causalit´es cumulatives et circulaires entre des relations
en aval (forward linkages) qui incitent les travailleurs `a se localiser pr`es des firmes, et des
relations en amont (backward linkages) qui incitent les firmes `a se concentrer `a proximit´e des
consommateurs, une structure spatiale de type “centre-p´eriph´erie” tend `a ´emerger 4:
“Manufactures production will tend to concentrate where there is a large market, but the
market will be large where manufactures production is concentrated ” p. 486
Ce r´esultat tient `a l’introduction simultan´ee de concurrence imparfaite qui ravive l’im-
portance `a la taille de march´e (Home Market Effect ou HME ), et d’´economies d’´echelle qui
incitent les firmes `a regrouper leur production dans une seule et mˆeme r´egion. La pr´esence
de coˆuts de transport vient parall`element renforcer cette incitation, poussant les firmes `a se
localiser dans la r´egion qui offre le plus grand march´e.
A la suite de Krugman [1991], de nombreux travaux s’appuieront sur ce mˆeme sch´ema
qui, aujourd’hui encore, constitue le cadre de r´ef´erence des travaux cherchant `a expliquer la
formation d’agglom´erations de taille plus ou moins importante.
Vers une formalisation spatiale multiscalaire Bien que proposant chacun une vision diff´erente
de la dimension spatiale en tant qu’objet d’´etude, ces deux sous-champs n’en demeurent pas
moins compl´ementaires, et ouvrent la voie `a des perspectives int´eressantes d’unification de la
4. Plus pr´ecis´ement, Krugman [1991] note que l’´economie tendra vers un ´equilibre d’agglom´eration compl`ete,
`a condition que ces liens en amont et en aval soient suffisamment puissants pour dominer la force centrifuge
g´en´er´ee par l’immobilit´e d’un facteur de production ou d’une ressource.
17
th´eorie spatiale.
Les d´eveloppements propos´es par Fujita [1989], Fujita and Krugman [1995], ou encore
Ottaviano et al. [2002] s’inscrivent dans cette logique 5. Les cadres analytiques obtenus `a
partir de ces travaux offrent un traitement plus complet de la dimension spatiale, permettant
de d´ecrire simultan´ement les dynamiques de migration `a l’´echelle inter-r´egionale et le processus
d’allocation des sols `a l’´echelle intra-r´egionale.
Ind´ependamment des formes fonctionnelles utilis´ees, ces mod`eles de localisation de l’acti-
vit´e ´economique reposent tous sur un mˆeme principe de confrontation entre forces centrip`etes
et forces centrifuges : `a l’issue d’un processus impliquant des mouvements de natures et d’inten-
sit´es vari´ees, l’espace ´economique se structure et donne naissance `a une organisation sp´ecifique
de l’activit´e. L’avanc´ee majeure de ce courant th´eorique tient ainsi en la reconnaissance du
caract`ere organis´e des choix de localisation : le territoire ne se fa¸conne pas de mani`ere al´ea-
toire mais r´epond `a une v´eritable logique d’arbitrage entre coˆuts et b´en´efices que procure un
emplacement donn´e.
Forces centrifuges Forces centrip`etes
- Immobilit´e d’un facteur de production - Existence d’un grand march´e du travail
- Coˆuts de transport faibles ou ´elev´es - Coˆuts de transport interm´ediaires
- Diff´erence de salaire - Relations verticales
- Rentes fonci`eres - Diff´erenciation des biens importante
Figure 1.2 – Principales forces d’agglom´eration et de dispersion.
1.4.2 Economie g´eographique et agriculture
Dans les mod`eles d’inspiration NEG, le secteur agricole fait traditionnellement l’objet
d’un traitement peu satisfaisant car relativement minimaliste ; la nature de la concurrence y
est g´en´eralement parfaite, la production pr´esente des rendements constants, et les produits
sont le plus souvent suppos´es homog`enes et pouvant ˆetre ´echang´es sans coˆut de transport.
5. Ottaviano et al. [2002] retiennent une fonction d’utilit´e quasi-lin´eaire (plutˆot qu’une CES) plus ais´ement
manipulable.
18
Si ces hypoth`eses simplificatrices se justifient pour les travaux se focalisant plutˆot sur les
cons´equences pour le secteur manufacturier, elles ne peuvent en revanche plus tenir lorsque
l’agriculture devient un ´el´ement cl´e de l’objet d’´etude.
Parmi les travaux th´eoriques ayant cherch´e `a redonner du poids au secteur agricole, Fu-
jita et al. [1999] fournit une synth`ese assez compl`ete des cons´equences de l’introduction d’un
coˆut de transport agricole non nul, montrant en substance que ce dernier a pour effet de
ralentir l’effet d’agglom´eration ; de la mˆeme mani`ere que les coˆuts de transport dans le sec-
teur manufacturier, les coˆuts agricoles donnent aux agents une incitation `a se disperser dans
l’espace.
En supposant que le transport agricole est coˆuteux, Davis [1997] aboutit, lui, au r´esultat
que le HME tend `a disparaitre, donnant `a l’hypoth`ese de coˆut de transport agricole nul un
caract`ere d´ecisif pour la formation d’agglom´eration. Il faudra attendre les travaux de Zeng
and Kikuchi [2005] et Picard and Zeng [2005] pour comprendre que la conclusion de Davis
[1997] tient en r´ealit´e au caract`ere homog`ene du bien agricole ; revenant sur cette hypoth`ese et
introduisant de la diff´erenciation dans les biens agricoles, ces auteurs parviennent `a d´emontrer
que le r´esultat de Krugman [1991] perdure mˆeme en pr´esence de coˆut de transport pour le
bien traditionnel.
Au final, Zeng and Kikuchi [2005]etPicard and Zeng [2005] soulignent `a travers leurs
travaux respectifs qu’une meilleure prise en compte des caract´eristiques du secteur agricole
conduit `a introduire de nouvelles forces de dispersion ayant pour effet de mod´erer le ph´enom`ene
de concentration et rendant alors les configurations d’agglom´eration et de forte sp´ecialisation
r´egionale moins probables. Picard and Zeng [2005] montrent en particulier que l’existence
d’un coˆut de transport agricole non nul qui tend `a renforcer la d´ependance des r´egions `a
leur production locale, associ´ee `a la concurrence entre secteurs manufacturier et agricole pour
l’emploi de la main d’œuvre non qualifi´ee, concourent `a l’augmentation simultan´ee des prix des
biens et des salaires agricoles dans la r´egion la plus industrialis´ee qui devient, par cons´equent,
moins attractive pour les firmes du secteur manufacturier.
19
1.4.3 Economie spatiale et environnement
L’´economie spatiale dans son ensemble offre un cadre particuli`erement bien adapt´e `a la
prise en compte de probl´ematiques environnementales. En t´emoigne l’important corpus de
litt´erature liant espace et environnement. Ces travaux abordent des th´ematiques vari´ees telles
que commerce et dumping environnemental, choix de localisation en pr´esence de pollution ou
d’am´enit´es, ou encore planification urbaine durable.
Bien que l’introduction des pr´eoccupations ´ecologiques dans les mod`eles d’´economie spa-
tiale puisse prendre des formes extrˆemement diverses, il est possible de proc´eder `a une clas-
sification en retenant comme double crit`ere de diff´erentiation (i) le cadre analytique choisi et
(ii) la motivation premi`ere du papier.
20
Mod`ele d’inspiration NEG Mod`ele d’allocation des sols
Facteur d’h´et´erog´en´eit´e spatiale l’en-
vironnement agit sur les d´ecisions de loca-
lisation
R´esultante de la dynamique spatiale les
d´ecisions de localisation agissent sur l’environ-
nement
Pollution et changement cli-
matique Van Marrewijk [2005], Lange and Quaas
[2007], Calmette and Pechoux [2007], Rau-
scher [2009]
Grazi et al. [2007], Gaign´e et al. [2012], Borck
and P߬
uger [2013]
Hardie et al. [2004], Lichtenberg et al.
[2007]Glaeser and Kahn [2010]
Biodiversit´e et conflits fon-
ciers Barbier and Rauscher [2007], Eppink and
Withagen [2009]
Grazi et al. [2007], Barbier and Rauscher
[2007]
Polinsky and Shavell [1976], Lee and Fu-
jita [1997], Wu and Plantinga [2003], Irwin
and Bockstael [2002], Lewis and Plantinga
[2007]
Figure 1.3 – Economie spatiale et prise en compte de l’environnement.
21
L’environnement comme facteur d’h´et´erog´en´eit´e spatiale 6L’objectif commun aux travaux re-
group´es dans ce premier ensemble est d’apporter une contribution `a la litt´erature d’´economie
g´eographique en introduisant l’environnement sous forme d’une externalit´e susceptible de mo-
difier les comportements de localisation des agents. La pollution locale agit en somme comme
un param`etre d’h´et´erog´en´eisation de l’espace.
De fait, tous ces mod`eles postulent que les m´enages attribuent une valeur h´edonique `a
la qualit´e environnementale de leur milieu de vie; la pollution li´ee `a l’activit´e productive
des firmes a alors un effet r´epulsif, incitant les habitants d’une r´egion caract´eris´ee par une
concentration excessive du secteur industriel, `a ´emigrer.
Globalement, ces recherches permettent de faire apparaitre des ´equilibres stables de concen-
tration partielle de l’activit´e ´economique. S’appuyant sur un mod`ele d’inspiration NEG `a deux
secteurs (manufacture et agriculture) et deux facteurs de production (main d’œuvre qualifi´ee
et non-qualifi´ee), Van Marrewijk [2005] montre notamment qu’une configuration d’agglom´e-
ration compl`ete devient moins probable en pr´esence de pollution, et d´erive une condition
n´ecessaire et suffisante `a l’apparition d’un ´equilibre stable de dispersion de l’activit´e.
Suivant une approche similaire, Lange and Quaas [2007] examinent la mani`ere dont une
source de pollution locale affecte les configurations spatiales et soulignent que le degr´e d’ag-
glom´eration des activit´es d´epend essentiellement de la valeur marginale des dommages en-
vironnementaux ; plus les agents valorisent la d´esutilit´e li´ee `a la pollution, plus la force de
dispersion induite par le crit`ere de qualit´e ´ecologique est puissante.
Rauscher [2009] enfin ´etudie les configurations spatiales de localisation de l’activit´e indus-
trielle pouvant ´emerger en pr´esence de pollution et met en ´evidence un possible ph´enom`ene
de type “chase-and-flee” : les m´enages cherchant un environnement peu pollu´e fuient l’agglo-
m´eration mais sont poursuivis par les firmes d´esireuses de s’installer `a proximit´e du march´e.
Proposant une approche davantage orient´ee vers l’analyse de l’efficacit´e des politiques
publiques, Calmette and Pechoux [2007] d´emontrent quant `a elles que des mesures de lutte
6. Bien que l’ensemble des papiers ayant pour th´ematique commune “commerce et environnement” puissent
entrer dans cette cat´egorie, nous avons fait le choix de ne pas d´evelopper cette litt´erature, par soucis d’´equilibre
dans la pr´esentation des diff´erentes approches. Mentionnons toutefois l’ouvrage de Copeland and Taylor [2013]
qui propose un aper¸cu d´etaill´e des travaux r´ealis´es dans ce domaine.
22
contre les ´emissions polluantes peuvent dans certains cas s’av´erer contre-productive en renfor-
¸cant l’incitation des m´enages `a s’agglom´erer davantage (mise en ´evidence d’un al´ea moral).
Une litt´erature tout aussi vaste traite des questions de biodiversit´e et observe la mani`ere
dont sa prise en compte modifie les configurations spatiales atteintes `a l’´equilibre. Partant
de l’observation que les syst`emes ´economique et ´ecologique sont en comp´etition permanente
pour l’usage de l’espace, Barbier and Rauscher [2007] examinent notamment l’efficacit´e d’ins-
truments de politique environnementale dans la lutte pour la conservation de la biodiversit´e
et d´emontrent qu’une taxe Pigouvienne ne conduit pas toujours `a une allocation spatiale
optimale.
Eppink and Withagen [2009] poursuivent un travail relativement proche en introduisant
une utilit´e marginale `a la pr´esence de biodiversit´e, et trouvent que l’´equilibre spatial le plus
susceptible d’´emerger correspond `a une configuration sym´etrique de sp´ecialisation r´egionale.
L’environnement comme r´esultante de la dynamique spatiale S’il s’inscrit toujours dans la li-
gn´ee des mod`eles de type NEG, ce deuxi`eme ensemble de travaux poursuit n´eanmoins un
objectif diff´erent, celui de rendre compte de l’impact environnemental de la structuration
d’un territoire sur la qualit´e ´ecologique du syst`eme pris dans son ensemble ; il s’agit `a pr´esent
de comprendre la mani`ere dont la r´epartition de l’activit´e conditionne les flux de transport,
les consommations ´energ´etiques, ou encore la qualit´e et l’utilisation d’une ressource naturelle.
Grazi et al. [2007] par exemple d´eveloppent un mod`ele `a deux r´egions leur permettant
de r´ealiser un classement des configurations spatiales selon deux indicateurs : l’empreinte
´ecologique et une mesure de bien-ˆetre social. En s’appuyant sur des simulations num´eriques,
ils montrent que ces deux crit`eres m`enent `a des classements souvent tr`es diff´erents l’un de
l’autre.
Gaign´e et al. [2012] ´etudient les implications environnementales (´emissions de GES prove-
nant des flux de transport) et sociale (bien-ˆetre des m´enages) d’une politique de densification
urbaine et soulignent qu’en permettant la relocalisation des activit´es ´economiques `a la fois au
sein des villes et entre les villes, augmenter la densit´e n’aboutit pas forc´ement `a un r´esultat
´ecologiquement ni socialement d´esirable.
23
Enfin, en s’appuyant sur un mod`ele proche de Gaign´e et al. [2012] mais en consid´erant une
gamme plus large d’´emissions et un degr´e de densit´e urbaine variable et endog`ene, Borck and
P߬
uger [2013] confirment le caract`ere ambigu de la taille de la ville, l’agglom´eration ayant des
effets de nature et d’ampleur diff´erents selon la source d’´emission consid´er´ee.
L’environnement dans les mod`eles d’allocation des sols Ce troisi`eme ensemble de travaux se
distingue des deux pr´ec´edents par l’utilisation d’un cadre davantage “micro-centr´e”. Leurs
objectifs peuvent ˆetre vari´es mais ils n´ecessitent tous la mobilisation d’outils permettant de
d´ecrire l’organisation spatiale au niveau intra-sp´ecifique.
Les recherches entreprises dans cet ensemble portent principalement sur deux aspects :
l’´evaluation de l’efficacit´e des politiques publiques et des mesures de planification, et l’influence
de la prise en compte d’am´enit´es environnementales sur la formation des courbes d’ench`eres
fonci`eres. Il est `a noter l`a encore que les travaux mentionn´es par la suite n’´etant qu’une
s´erie d’exemples permettant d’illustrer toute la diversit´e de ce champ d’´etude, ils ne sauraient
donner un panorama exhaustif des r´esultats ´etablis dans le domaine.
Parmi les papiers abordant la question de l’efficacit´e des politiques publiques dans un
contexte spatial, Hardie et al. [2004] centrent leurs recherches sur les mesures ayant un impact
direct sur le changement d’utilisation des sols et indiquent que, selon l’interface consid´er´ee
(fronti`ere entre usage urbain et usage agricole ou fronti`ere entre usage agricole et espace
naturel), le choix des instruments diff`ere ; une approche de type “commande et contrˆole”
tend `a ˆetre privil´egi´ee pour influer sur la d´elimitation urbain-rural, tandis qu’`a la fronti`ere
entre agriculture et nature, il est plus fr´equent de recourir `a des mesures de r´egulation et de
subvention afin de contrecarrer les possibles effets non d´esir´es induits par le march´e.
Toujours en relation avec l’´evaluation des politiques publiques, Lichtenberg et al. [2007]
examinent les effets de mesures r`eglementaires d’aide `a la conservation des forets sur l’appari-
tion d’espaces verts en milieu p´eriurbain. Ils ´etablissent de mani`ere th´eorique que ces mesures
peuvent conduire `a une sur-repr´esentation des espaces forestiers aux d´epens des autres formes
d’espaces naturels, et confirment ce r´esultat par une analyse empirique portant sur l’espace
de jonction entre les villes de Washington et Baltimore.
24
`
A partir d’un mod`ele ´econom´etrique d’utilisation des terres permettant de pr´edire la r´epar-
tition spatiale des changements d’affectation, Lewis and Plantinga [2007] examinent l’impact
de politiques incitatives visant `a r´eduire la fragmentation de l’habitat dans la r´egion de la
plaine cˆoti`ere de Caroline du Sud. Ils constatent que les coˆuts li´es `a la r´eduction de la frag-
mentation varient grandement selon les conditions naturelles initiales du milieu et montrent
qu’une subvention uniforme peut produire des r´esultats satisfaisants compar´e `a une politique
plus complexe spatialement cibl´ee.
Parmi la longue liste de travaux abordant la th´ematique des villes durables, Glaeser and
Kahn [2010] proposent une ´etude empirique sur les villes am´ericaines dans laquelle ils s’in-
terrogent sur la localisation optimale des nouvelles constructions de logements. Hormis les
r´esultats sp´ecifiques conduisant `a un classement des soixante-six villes consid´er´ees selon leur
niveau d’´emission relatif, les auteurs mettent ´egalement en ´evidence une corr´elation forte et
n´egative entre niveau d’´emissions et r´eglementation de l’usage des sols.
Concernant les travaux se focalisant sur la relation entre am´enit´es environnementales et
allocation des sols entre usages urbains, agricoles et naturels, nous pouvons finalement relever
les contributions de Polinsky and Shavell [1976], Lee and Fujita [1997], Irwin and Bockstael
[2002], ou encore Wu and Plantinga [2003].
Polinsky and Shavell [1976] tout d’abord ´etendent le cadre classique de ville monocentrique
en introduisant des am´enit´es caract´eris´ees par leur distance au centre, et examinent la mani`ere
dont elles modifient les ench`eres fonci`eres. Ils ´etablissent notamment comme r´esultat que, selon
le cas de figure, le prix de la terre `a une localisation donn´ee peut ne d´ependre que du niveau
de l’am´enit´e en cet emplacement (cas d’une petite ville ouverte), ou du niveau de l’am´enit´e
sur l’ensemble de la ville (cas d’une ville ferm´ee).
En s’interrogeant sur l’efficacit´e ´economique d’un d´eveloppement urbain au-del`a d’une
ceinture verte, Lee and Fujita [1997] montrent que lorsque cette derni`ere g´en`ere des am´enit´es
dont le niveau est ind´ependant de la distance, son emplacement hors de la frange urbaine
constitue l’option la plus efficace. A l’inverse, si le niveau d’am´enit´es g´en´er´e d´ecroit avec la
distance, un d´eveloppement discontinu de l’espace urbain peut s’av´erer d’autant plus efficace
que le salaire r´eel des m´enages et/ou leur satisfaction tir´ee de la pr´esence de cet espace naturel
25
sont grands.
Irwin and Bockstael [2002] s’int´eressent ´egalement aux sch´emas spatiaux de d´eveloppe-
ment discontinu des activit´es urbaines en p´eriph´erie. Elles avancent comme explication `a
ce ph´enom`ene l’existence d’externalit´es n´egatives provenant des interactions entre agents de
l’´economie, et cr´eant en certains points de l’espace un effet r´epulsif ou contre-incitatif `a la
localisation d’une activit´e.
Wu and Plantinga [2003] enfin d´eveloppent un mod`ele de ville monocentrique `a deux
dimensions et ´etudient l’impact de l’am´enagement d’espaces verts publics sur la structure
spatiale des zones urbaines. Ils montrent notamment que la pr´esence d’espaces verts peut ˆetre
`a la source d’un d´eveloppement urbain discontinu (d´eveloppement de type “saute-mouton”).
26
1.5 R´ef´erences
Alonso, W. (1964). Location and land use. toward a general theory of land rent. Location and
land use. Toward a general theory of land rent. 16
Bairoch, P. and Goertz, G. (1986). Factors of urbanisation in the nineteenth century developed
countries a descriptive and econometric analysis. Urban Studies, 23(4) :285–305. 6
Barbier, E. B. and Rauscher, M. (2007). Biodiversity and Geography. CESifo Working Paper
Series 2022, CESifo Group Munich. 21,23
Borck, R. and P߬
uger, M. (2013). Green cities ? urbanization, trade and the environment. 21,
24
Born, B. and Purcell, M. (2006). Avoiding the local trap scale and food systems in planning
research. Journal of Planning Education and Research, 26(2) :195–207. 14
Calmette, M.-F. and Pechoux, I. (2007). Are environmental policies counterproductive? Eco-
nomics Letters, 95(2) :186–191. 21,22
Chambres d agriculture (2012). Les exploitations en circuits courts : Des pourvoyeuses d
emplois. 14
Christaller, W. (1933). Die Zentralen Orte in Suddeutschland.16
CITEPA (2010). Rapport national d’inventaire des ´emissions de polluants atmosph´eriques en
France. Technical report. 9
Copeland, B. R. and Taylor, M. S. (2013). Trade and the environment : Theory and evidence.
Princeton University Press. 22
Davis, D. (1997). The home market, trade, and industrial structure. Technical report, National
Bureau of Economic Research. 19
Desrochers, P. and Shimizu, H. (2012). The locavore’s dilemma : In praise of the 10,000-mile
diet. PublicAffairs. 14,15
Dessus, B. and Girard, P. (2009). L’´etat des lieux. Les Cahiers de Global Chance, 26. 10
27
Dixit, A. K. and Stiglitz, J. E. (1977). Monopolistic competition and optimum product
diversity. The American Economic Review, pages 297–308. 17
Edwards-Jones, G., Mila i Canals, L., Hounsome, N., Truniger, M., K. G., Hounsome, B.,
Cross, P., York, E., Hospido, A., Plassman, K., Harris, I., Edwards, R., Day, G., Tomos,
A., Cowell, S., and Jones, D. (2008). Testing the Assertion that Local Food Is Best :
The Challenges of an Evidence-Based Approach. Trends in Food Science and Technology,
19 :265–274. 14
EEA (2009). Transport at a crossroads term 2008 : indicators tracking transport and envi-
ronment in the european union. Technical report, European Environment Agency. 10
Eppink, F. V. and Withagen, C. A. (2009). Spatial patterns of biodiversity conservation in a
multiregional general equilibrium model. Resource and energy economics, 31(2) :75–88. 21,
23
Franklin, A., Newton, J., and McEntee, J. C. (2011). Moving beyond the alternative : sustai-
nable communities, rural resilience and the mainstreaming of local food. Local Environment,
16(8) :771–788. 15
Fujita, M. (1989). Urban economic theory : land use and city size. Cambridge university press.
18
Fujita, M. and Krugman, P. (1995). When is the economy monocentric ? : von th¨
unen and
chamberlin unified. Regional Science and Urban Economics, 25(4) :505–528. 18
Fujita, M., Krugman, P., and Venables, A. (1999). The Spatial Economy : Cities, Regions,
and International Trade. MIT Press. 19
Gaign´e, C., Riou, S., and Thisse, J.-F. (2012). Are compact cities environmentally friendly?
Journal of Urban Economics, 72(2) :123–136. 21,23,24
Garnett, T. (2003). Wise Moves. Exploring the relationship between food, road transport and
CO2. Technical report, Transport2000. 14
28
Glaeser, E. L. and Kahn, M. E. (2010). The greenness of cities : carbon dioxide emissions and
urban development. Journal of Urban Economics, 67(3) :404–418. 21,25
Grazi, F., van den Bergh, J. C., and Rietveld, P. (2007). Spatial welfare economics versus
ecological footprint : modeling agglomeration, externalities and trade. Environmental and
Resource Economics, 38(1) :135–153. 21,23
Hardie, I. W., Parks, P. J., and Van Kooten, G. C. (2004). Land use decisions and policy
at the intensive and extensive margins. The International Yearbook of Environmental and
Resource Economics 2004/2005 : A Survey of Current Issues, pages 101–38. 21,24
Heimlich, R. E. (1989). Metropolitan agriculture : Farming in the city’s shadow. Journal of
the American Planning Association, 55(4) :457–466. 8
Hendrickson, M. K. and Heffernan, W. D. (2002). Opening spaces through relocalization :
locating potential resistance in the weaknesses of the global food system. Sociologia Ruralis,
42(4) :347–369. 13
Irwin, E. G. and Bockstael, N. E. (2002). Interacting agents, spatial externalities and the
evolution of residential land use patterns. Journal of economic geography, 2(1) :31–54. 21,
25,26
Jarosz, L. (2008). The city in the country : Growing alternative food networks in metropolitan
areas. Journal of Rural Studies, 24(3) :231–244. 12
Kloppenburg, Jr, J., Lezberg, S., De Master, K., Stevenson, G. W., and Hendrickson, J. (2000).
Tasting food, tasting sustainability : Defining the attributes of an alternative food system
with competent, ordinary people. Human organization, 59(2) :177–186. 13
Krugman, P. (1991). Increasing returns and economic geography. Journal of Political Eco-
nomy, 99(3). 17,19
La Trobe, H. L. and Acott, T. G. (2000). Localising the global food system. International
Journal of Sustainable Development & ; World Ecology, 7(4) :309–320. 12
29
Lange, A. and Quaas, M. F. (2007). Economic Geography and the Effect of Environmental
Pollution on Agglomeration. The B.E. Journal of Economic Analysis & Policy.21,22
Lee, C.-M. and Fujita, M. (1997). Efficient configuration of a greenbelt : theoretical modelling
of greenbelt amenity. Environment and Planning A, 29(11) :1999–2017. 21,25
Leglise, M. (2007). La logistique en france : ´evolutions et enjeux. Minist`ere de l’´ecologie du
d´eveloppement durable et de l’am´enagement durables.8
Lewis, D. J. and Plantinga, A. J. (2007). Policies for habitat fragmentation : combining
econometrics with gis-based landscape simulations. Land Economics, 83(2) :109–127. 21,
25
Lichtenberg, E., Tra, C., and Hardie, I. (2007). Land use regulation and the provision of
open space in suburban residential subdivisions. Journal of Environmental Economics and
Management, 54(2) :199–213. 21,24
L¨
osch, A. (1940). Die r¨
aumliche Ordnung der Wirtschaft.16
MacLeod, M. and Scott, J. (2007). Politiques dapprovisionnement alimentaire local : Une
revue de la littture. Technical report, Minist de lergie de la Nouvelle-osse. 13
Marsden, T. (2009). Mobilities, vulnerabilities and sustainabilities : exploring pathways from
denial to sustainable rural development. Sociologia Ruralis, 49(2) :113–131. 15
Mendels, F. F. (1972). Proto-industrialization : the first phase of the industrialization process.
The journal of economic history, 32(01) :241–261. 6
Morgan, K. (2014). Nourishing the city : The rise of the urban food question in the global
north. Urban Studies.1
O’Hara, S. U. and Stagl, S. (2001). Global food markets and their local alternatives : a
socio-ecological economic perspective. Population and Environment, 22(6) :533–554. 13
Ottaviano, G., Tabuchi, T., and Thisse, J.-F. (2002). Agglomeration and Trade Revisited.
International Economic Review, 43 :409–436. 18
30
Oudin, J. (2001). Politique des transports : l’Europe en retard. Technical report, D´el´egation
du S´enat pour l’Union Europ´eenne. 8
Picard, P. M. and Zeng, D.-Z. (2005). Agricultural Sector and Industrial Agglomeration.
Journal of Development Economics, 77(1) :75–106. 19
Pirog, R., Van Pelt, T., Enshayan, K., and Cook, E. (2001). Food, fuel, and freeways : An iowa
perspective on how far food travels, fuel usage, and greenhouse gas emissions. Technical
report, Leopold Center for Sustainable Agriculture. 14
Polinsky, A. and Shavell, S. (1976). Amenities and property values in a model of an urban
area. Journal of Public Economics, 5(1) :119–129. 21,25
Rauscher, M. (2009). Concentration, Separation, and Dispersion : Economic Geography and
the Environment. Thunen-Series of Applied Economic Theory. Working Paper, Universitat
Rostock. 21,22
Renting, H., Marsden, T. K., and Banks, J. (2003). Understanding alternative food networks :
exploring the role of short food supply chains in rural development. Environment and
planning A, 35(3) :393–412. 13
Sutton, M. A., Oenema, O., Erisman, J. W., Leip, A., van Grinsven, H., and Winiwarter, W.
(2011). Too much of a good thing. Nature, 472(7342) :159–161. 9
United Nations (2014). World Urbanization Prospects : The 2014 Revision. Technical report,
United Nations, Department of Economic and Social Affairs, Population Division. 1
Van Marrewijk, C. (2005). Geographical Economics and the Role of Pollution on Location.
Journal of Environmental Economics, 3 :28–48. 21,22
Von Th¨
unen, J. H. (1827). Der isolierte Staat in Beziehung auf Landwirtschaft und Natio-
nal¨
okonomie. Perthes Verlag. 16
Watts, D. C. H., Ilbery, B., and Maye, D. (2005). Making reconnections in agro-food geogra-
phy : alternative systems of food provision. Progress in Human Geography, 29(1) :22–40.
13
31
Wu, J. and Plantinga, A. J. (2003). The influence of public open space on urban spatial
structure. Journal of Environmental Economics and Management, 46(2) :288–309. 21,25,
26
Zeng, D.-Z. and Kikuchi, T. (2005). Home market effect and the agricultural sector. In ERSA
conference papers, number ersa05p135. European Regional Science Association. 19
32
Chapitre 2
Urbanization, Agricultural
Location, and Greenhouse Gas
Emissions
In this chapter, we argue that ’buying local’ does not necessarily reduce greenhouse gas
emissions, even if transport modes, production technologies, and natural endowment are
homogeneous in space. We develop a model of rural-urban systems where the spatial
distribution of food production within and between regions is endogenously determined.
We exhibit cases where locating a significant share of the food production in the least-
urbanized regions results in lower transport-related emissions than in configurations where
all regions are self-sufficient. In addition, the optimal spatial allocation of food production
does not exclude the possibility that some regions should rely solely on local production,
provided their urban population sizes are neither too large nor too small.
Keywords : Urban pollution, Peri-urban Farming, Land allocation
JEL Classification : F12 ; Q10 ; Q54 ; Q56 ; R12
Ce chapitre reprend un article r´ealis´e en collaboration avec
St´ephane DE CARA et Carl GAIGNE.
33
2.1 Introduction
More than half of the world population lives in cities. With this share expected to keep
growing [United Nations,2010], urbanization may have major consequences for the sustai-
nability of food chains [Wu et al.,2011], notably because of larger quantities of food to be
brought into cities and spatial extension of residential areas at the expense of agricultural
land. 1In addition, only firms with high value-added per unit of land can operate profitably in
the most urbanized regions because of agglomeration economies and fierce competition over
land [Fujita and Thisse,2002]. As a result, lower value-added activities–such as those in the
food and agricultural sectors–may be displaced further away from urban centers [Bagoulla
et al.,2010]. Agricultural products are thus expected to be transported in larger quantities
and over longer distances. Evidence of such a trend can be found in recent US transportation
data, which indicate that, for instance, the average mileage per shipment for grains has almost
doubled between 2007 and 2012 [BTS and U.S. Census Bureau,2010,2013].
In this context, the environmental impact of food transportation, in particular with regard
to energy use and greenhouse gas (GHG) emissions, has emerged as a growing concern for pu-
blic authorities. Promoting ‘local-food’ and reducing ‘food-miles’ [Paxton,1994] have become
recurring themes in Climate Change Action Plans [Kampman et al.,2010]. Support for shor-
ter and ‘alternative’ food networks has gained momentum [Sonnino and Marsden,2006]. The
rationale is that the mitigation of GHG emissions requires that food production be located
closer to consumption centers so as to reduce reliance on food imports from distant regions.
This view is often justified by the comparison of transport-related emissions of locally-
grown vs. imported food products. One such example (among many) can be found in a study
by BioIS [2007], which concludes that GHG emissions from the transportation of one ton
of apples consumed in France are 14 times larger when imported from Chile than when
locally grown. However, the conventional wisdom that shorter food chains are necessarily
environmentally-friendlier has been challenged by several empirical studies based on lifecycle
1. As an illustration, residential land use in the US grew 47.5% between 1976 and 1992, while population
only rose by 17.8% over the same period [Overman et al.,2008]. Europe faces a similar trend ; between 1990
and 2000, built-up areas increased by 12% whereas population grew just 2% [EEA,2004].
34
analysis. These studies argue that, in presence in differences in production technologies in
importing and exporting regions and depending on the transport modes used, the overall
impact on GHG emissions might be larger for domestic products than for imported ones. For
example, lambs produced and consumed in Europe may be responsible for more emissions
than imported lambs from New Zealand, which are shipped to Europe by boat and are less
dependant on energy inputs and industrial feed [Saunders et al.,2006]. This debate highlights
that the sign of the overall environmental impact is very much dependent on the type of
product, the transport modes, and the production technologies prevailing in importing and
exporting regions.
The contribution of the present chapter is to provide a novel and more general argument
supporting that shorter food chains are not necessarily good for the environment. We argue
that, even though transport modes, production technologies, and natural endowment do not
vary in space, buying local may increase emissions due to food transportation. When assessing
the impact of food systems on GHG emissions, the existing literature overlooks two major
issues.
First, GHG emissions from intra-regional transport are usually not considered explicitly.
Yet, an important share of the value and tonnage in the transportation of agricultural and
food products is characterized by short-distance shipments. In the US, for instance, cereal
grains–the largest consumer of transportation services–are shipped 139 miles on average (see
Table 2.1). US data also show that, with few exceptions, freight flows occur predominantly
within the same state or with immediate neighboring states : for nine states out of ten,
within-state haulages account for at least 50% of total flows [78% when including flows with
surrounding states, FHWA,2011]. As intra-regional transport is often handled by trucks, this
may have a significant impact on GHG emissions.
Second, the environmental assessment of food systems should be conducted at the entire
urban system level rather than at the city level. This is particularly important to account
for the relocation of agricultural activities in response to urbanization in the long run. The
relocation of food production in the most populated regions may reduce inter-regional trade,
but at the same time increase the need for intra-regional transport in other regions. Whether
35
the net environmental impact is positive or negative remains an open question. Addressing
this question requires a full-fledged analysis that endogenously accounts for the location of
agricultural production within and between regions.
Ton-mileage Average distance [miles]
[109t.miles] All Truck Rail Water
Live animals and live fish 3.9 739 236 1463 n/a
Cereal grain 203.4 139 84 800 1008
Other agricultural products 88.2 354 207 998 1024
Animal feed 76.1 499 136 884 2241
Meat, fish, seafood 48.5 247 128 980 952
Milled grain and bakery products 50.7 403 103 1065 n/a
Other prepared foodstuffs 171.4 268 95 1092 n/a
Tableau 2.1 – Total ton-mileage and average shipment distance of agricultural commodities and food products
by transport mode in the U.S. (2007). Source : Adapted from from BTS and U.S. Census Bureau [2010]
In the spatial model developed in this chapter, the spatial allocation of food produc-
tion across regions depends on land rents, transport costs, and the distribution of the urban
population. The model takes into account the damage caused by emissions from the food-
transportation sector (both within and between regions), as well as the welfare implications
for urban and rural households. This framework extends the model proposed by Gaign´e et al.
[2012] by including an agricultural sector and considering a more general m-region spatial
configuration. Although the multi-region case adds some complexity, the model remains ana-
lytically tractable when considering that trade flows are organized according to a ‘hub and
spoke’ method, a widespread system in the logistics of food supply chains [Konishi,2000].
Our framework differs from the models proposed by Fujita et al. [1999], Picard and Zeng
[2005] and Daniel and Kilkenny [2009] since the location of agricultural production is not
exogenously treated but determined by a social planner or market mechanisms through bid
rent. Our approach also differs from Daniel and Kilkenny [2009] in several dimensions. First, we
36
consider that land is also used by the urban population, so that the spatial allocation of land
between urban activities and agricultural production is endogenously determined. Second, we
derive a complete analytical characterization of the location equilibrium and provide some
comparative statics results. Because the results are not based on numerical simulations, the
chapter offers a fair level of generality. Third, a welfare analysis is developed.
Our results confirm that the assessment of environmental and welfare implications of
the spatial allocation of food production cannot rely solely on the distance between food
production areas and the location of end consumers. The main intuition lies in the trade-off
between intra- and inter-regional transportation flows. The distance traveled by food products
within a region depends on the size of the urban and rural areas. As food production is
determined by agricultural area, an increase of agricultural output in any given region induces
a more than proportional increase in the average distance within the region of production.
As a consequence, intra-regional flows are minimized when food production is distributed
mainly among the least-urbanized regions. By contrast, inter-regional flows are minimized
when the regions with the largest urban population also host the largest agricultural areas.
Therefore, the relocation of food production closer to large cities increases intra-regional trade
in proportions that may offset the decrease in inter-regional flows.
A direct consequence is that configurations in which all regions are self-sufficient –referred
to as ‘pure local-food’– do not necessarily minimize emissions due to food transportation
even if there is no difference in technology and productivity across regions. In other words,
the existence of (some) interregional trade does not necessarily conflict with environmental
objectives. We characterize cases in which locating a significant share of food production in
the least (rather than the most) urbanized regions results in lower emissions than in the
pure local-food configuration. Of course, this is more likely when the mode of transport for
inter-regional shipments is less emissions-intensive than that used for intra-regional shipments
(e.g. rail vs. truck). Our analysis also unveils the role played by agricultural yields and the
distribution and size of urban populations in the relationship between the location of food
production and GHG emissions.
In addition, we find that the optimal allocation of food production does not exclude the
37
possibility that some regions should rely solely on local food. However, this possibility is
restricted to regions with urban populations that are neither too large nor too small. The m-
region model proposed here makes it possible to characterize urban population size threshold
values for which a region should be self-sufficient. We also show that market forces alone do
not lead to a pure local-food configuration unless the urban population is evenly distributed
across regions and/or except for very particular values of the parameters.
In order to disentangle the various effects on welfare, we proceed in three main steps. After
presenting the model (Section 2.2), we analyze the emissions-minimizing spatial distribution
of food production and highlight the trade-off between intra- and inter-regional trade related
emissions (Section 2.3). In Section 2.4, we examine the effects on welfare by combining the
impacts on urban and rural households’ surpluses, and on the environment. In Section 2.5,
we focus on the market forces driving the location of agricultural production and analyze
the resulting spatial equilibrium. Section 2.6 discusses the robustness of the results to some
alternative assumptions. Section 2.7 concludes.
2.2 The framework
Consider an economy with two sectors (agriculture and services) and three primary goods
(labor, land, and a composite good as the num´eraire). The agricultural sector produces a
homogeneous good using land and (rural) labor, while the service sector produces a differen-
tiated good using only (urban) labor. The agricultural market is integrated across regions so
that the price of the agricultural product is unique under perfect competition. The service
sector operates under monopolistic competition. The total population is normalized to 1, and
split into λuand λrurban and rural inhabitants, respectively. This economy comprises m
regions, indexed by j={1, .., m}. Each region hosts an urban and rural population of λuj
and λrj , respectively (Pjλuj +Pjλrj =λu+λr= 1). The spatial distribution of the urban
population across regions is characterized by the m-vector λu= (λu1, . . . , λum ). Similarly,
λr= (λr1, . . . , λrm) denotes the profile of the rural population across regions.
38
2.2.1 Spatial structure
The largest city is assumed to be located in the ‘core’ region, indexed by j= 1. The
m−1 remaining regions are hereafter referred to as ‘peripheral’. Without loss of generality,
peripheral regions are ordered by decreasing urban population, so that λu1≥λu2≥ ··· ≥ λum.
For simplicity, they are assumed to be all located at the same distance νfrom region 1. Each
region is formally described by a one-dimensional space encompassing both urban and rural
areas. Natural amenities are homogeneously supplied within and between regions. Within each
region, locations are denoted x, and are measured from the center of the region. Without loss
of generality, we focus on the right-hand side of the region, the left-hand side being perfectly
symmetrical.
Each city has a central business district (CBD) 2, located at x= 0, where firms in the
service sector are located. All urban inhabitants work for these firms. The space used by
the service sector is considered negligible, so that urban area is used entirely for residential
purposes. Each urban inhabitant consumes a residential plot of a fixed size, normalized to
unity for simplicity.
Farmers live and produce in rural areas. With some additional assumptions regarding
commuting and transport costs (see section 2.2.5), farmers are located in the periphery of
the urban area. Each farmer is assumed to use 1/µ units of land to produce one unit of
the agricultural good, so that µcan be interpreted as the agricultural yield. Each region is
assumed to be endowed with enough land to host all agricultural activities in equilibrium.
The right endpoint of region jis thus :
¯xj=λuj
2+λrj
2µ.(2.1)
2.2.2 Transportation/distribution network
Agricultural goods are first shipped from the farm gate to a collecting point (e.g. an
elevator), and then from the collecting point to the CBD (see left side of Figure 2.1, left). For
simplicity, assume that there is one elevator at each side of the region, located at the center of
the respective rural area. (In Section 2.6, we consider the case where the number of elevators
2. See the survey in Duranton and Puga [2004] for the reasons for the existence of a CBD
39
depends on the mass of farmers). The right-hand side elevator in region jis located at :
xc
j=λuj
2+λrj
4µ.(2.2)
The agricultural good may then be exported to another region. Inter-regional trade is assumed
to follow a ‘hub and spoke’ transportation/distribution method, whereby each peripheral
region is connected to the ‘hub’ (located in the core region) by a ‘spoke’ of length ν(see
right side of Figure 2.1). This system is frequent in the logistics and freight of commodities.
Economic justification for the existence of these systems can be found in Konishi [2000] and
Furusawa and Konishi [2007]. As a modeling strategy, this assumption keeps the analysis of
the m-region case tractable by reducing the number of trade flows to be considered.
¯xj
0
CBD
¯xuj xc
j
ElevatorElevator
Urban area
Pop. : λuj
Pop. : λrj
2Pop. : λrj
2
Rural area
Plot size : 1
Plot size : 1
µPlot size : 1
µ
Size : λuj
Size : λrj
2µSize : λrj
2µ
Rural area Rural area
Region j
ν
ν
j= 1
ν
j= 3
j= 2
j= 4
ν
j= 5
Figure 2.1 – Spatial structure and transportation flows (dashed lines) of the agricultural good within (left
side) and between (right side) regions. In this example, regions 1 and 2 are importers ; regions 3, 4, and 5 are
exporters.
To save on notation, we make the simplifying assumption that unit transport costs for
the farm-to-elevator and elevator-to-CBD segments are both equal to ta. (This assumption
is relaxed in Section 2.6). Following Behrens et al. [2009], we assume also that the inter-
regional transport market is not segmented. Inter-regional transportation and distribution
involves a fixed fee (f) which does not depend on distance. This assumption is justified by
the fact that, in practice, an important share of inter-regional transportation cost is related
to distance-independent cost items (logistics, loading/unloading infrastructure, etc.). Thus,
40
transport costs are given by :
Caj (x) = tax−xc
j+taxc
j+f(2.3)
2.2.3 Producers
Each farmer is assumed to supply inelastically one unit of labor, and to produce at constant
returns to scale. For clarity of exposition, we assume also that producing one unit of an
agricultural good requires one unit of labor. A farmer located at xin region jbears the costs
of transportation of his/her production to the end consumer and the (rural) land rent Rj(x).
Thus, the profit for this farmer is given by
πaj (x) = pa−Rj(x)
µ−Caj (x) (2.4)
2.2.4 Consumers
Preferences over the three consumption goods are the same across urban and rural house-
holds. The first good is homogeneous, can be traded costlessly, and is chosen as the num´eraire.
The second good is the agricultural product, which is homogeneous and can be shipped from
one region to another. The third good (services), which is non-tradable across regions, is a
differentiated good made available under the form of a continuum of varieties. Variety support
may vary between regions (vranging from 0 to ¯vj). We assume also that the utility function
is additive with respect to the quantity of the agricultural good (qa) and services (qs(v) for
variety v∈[0,¯vj]) :
U(q0, qa, qs(v)) =q0+a−bqa
2qa
+αZ¯vj
0
qs(v)dv −β−γ
2Z¯vj
0
[qs(v)]2dv −γ
2¯vjZ¯vj
0
qs(v)dv2(2.5)
To abstract from income effects, the marginal utility with respect to the num´eraire is constant
and each consumer’s initial endowment (¯q0) is sufficient to ensure strictly positive consumption
(q0) in equilibrium. As a consequence, as in e.g. Ottaviano et al. [2002] , our modeling strategy
is akin to a partial equilibrium approach. Nevertheless, note that, due to equilibrium conditions
on labor and regional land markets, this assumption does not remove the interactions between
the agricultural and service sectors. The simple linear-quadratic specification (parameterized
41
by a > 0 and b > 0) of the second term in Eq. (2.5) eases tractability by leading to linear
demand functions for the agricultural good. As for services, we follow Tabuchi and Thisse
[2006] and use the specification proposed by Vives [1990]. Parameters α,β, and γare all
positive. We assume that β > γ to ensure the quasi-concavity of the utility function. γ
measures the substitutability between varieties, while β−γexpresses the intensity of taste
for variety. This specification ensures that the parameters defining the demand function are
independent of the number of varieties supplied in the region. Note that utility is increasing
with respect to ¯vj. This will play a major role as an agglomeration force, as agents are better
off when given access to a wider range of services.
To abstract from redistribution effects, we assume that land is owned by absentee landlords.
Agricultural sector profits (2.4) are assumed to be completely absorbed by farmers. The budget
constraint faced by a rural household located at xin region jis thus :
q0+qapa+Z¯vj
0
qs(v)psj (v)dv = ¯q0+πaj (x) = ¯q0+pa−Rj(x)
µ−Caj (x) (2.6)
Urban costs, defined as the sum of the commuting costs and land rents, are borne by urban
households. The budget constraint faced by an urban household resident at xin region jis :
q0+qapa+Z¯vj
0
qs(v)psj (v)dv = ¯q0+wj−Rj(x)−tux(2.7)
where psj (v) is the price of service vin region j,pais the price of the agricultural product,
wjis the service sector wage in region j, and tuis the per-mile commuting cost.
Maximizing utility (2.5) subject to budget constraints (2.6) and (2.7) leads to the inverse
demand function for the agricultural good :
pa(qa) = max {a−bqa,0}(2.8)
and the inverse demand for service of variety v:
psj (v) = max αβ−γ
β−(β−γ)qsj (v) + γ
β
Psj
¯vj
,0(2.9)
where Psj =R¯vj
0psj (v)dv is the price index of services for the range supplied in region j.
42
2.2.5 Equilibrium
Given our assumptions related to the supply-side of the farming sector, agricultural out-
put in region jis equal to λrj . Combined with Eq. (2.8), the market clearing price for the
agricultural good then is :
p∗
a=a−bX
j
λrj =a−bλr(2.10)
Our assumptions related to the agricultural market (integrated inter-regional market, per-
fect competition, homogeneity of the agricultural commodity) imply that the price received
by all farmers is the same (p∗
a) regardless of the region of production. Therefore, total agricul-
tural output does not depend on the spatial allocation of food production and the agricultural
price does not play a role in farmers’ location choices. 3Food imports in region jare given
by (λuj +λrj )qa−λrj . Replacing qawith its equilibrium value and using simple algebraic
manipulations, imports in region jbecome λuj λr−λrj λu.
In the service sector, each variety is supplied by a single firm producing under increasing
returns as in Tabuchi and Thisse [2006]. Hence, ¯vjis also the number of firms active in region j.
Producing any variety vof services requires 1/φ > 0 units of labor (the marginal requirement
in labor being equal to 0). The profits of a services firm operating in region jare given by
πsj (v) = qsj (v)psj (v)−wj/φ (2.11)
Each firm sets its price so as to maximize its profits taking into account the response of
demand to the price of the service it supplies (given by Eq. (2.9)) and taking the price index
Psj as given. Hence, Psj and wjare treated as parameters Ottaviano et al. [2002]. Since all
firms are identical, profit maximization leads to an equilibrium price that is common to all
varieties and all regions :
p∗
s=α(β−γ)
β+ (β−γ)>0.(2.12)
The labor market clearing conditions imply that there are ¯vj=φλuj firms in region j
(up to the integer problem). We assume local urban labor markets. The equilibrium wage is
determined by a bidding process in which firms compete for workers by offering them higher
wages until no firm can profitably enter the market. Therefore, operating profits are completely
3. Note that these assumptions rule that product differentiation based on the region of origin framework.
43
absorbed by the wage bill and the equilibrium wage paid by service firms established in city
jis equal to :
w∗
j=φ
β−γp∗2
s(λuj +λrj ).(2.13)
Eq. (2.13) indicates that wages in the service sector differ across regions only according to
regional population size, which determines the size of the market since services are sold ex-
clusively in the region of their production.
We next turn to the equilibrium land rent for both urban and rural households. Let Vuj (x)
and Vrj (x) denote the indirect utility of urban and rural households, respectively, obtained
by plugging the respective budget constraints (2.6) and (2.7) and equilibrium quantities and
prices into (2.5) :
Vuj (x) = p∗
aqa(p∗
a) + Zvs
0
p∗
sj (v)qsj (p∗
sj )dv+q0+w∗
j−Rj(x)−tux. (2.14)
Similarly, for rural households :
Vrj (x) = p∗
aqa(p∗
a) + Zvs
0
p∗
sj (v)qsj (p∗
sj )dv+q0+p∗
a−Rj(x)
µ−Caj (x).(2.15)
Because of the fixed lot size assumption, the value of consumption of non-spatial goods at the
residential equilibrium (sum of the first three terms in (2.14) and (2.15)) is the same regardless
of the household’s location.
For urban workers, the equilibrium land rent must solve ∂Vuj (x)/∂x = 0 or, equivalently,
∂Rj(x)
∂x+tu= 0, which solution is Rj(x) = ¯ruj −tux, where ¯ruj is a constant. Similarly, the
equilibrium land rent for rural households must satisfy ∂Vr j (x)/∂x = 0. As a consequence, the
bid rents of rural workers are such that Rj(x) = ¯rrj −µtax−xc
j. Assuming that tu> µta,
the (right-hand side) urban workers reside around the CBD in the land strip (0, xuj ] where
xuj =λuj /2 is the (right-hand side) city limit. Rural households live in (xuj , xj]. Because
the opportunity cost of land is equal to zero, the land rent at the region limit is zero, i.e.
R∗
j(xj) = 0. This implies that ¯rr j =taλrj /4. In addition, urban and rural land rents at the
city limit ¯xuj must be equal, so that ¯ruj =tuxuj +Rj(xuj ). As a result, the equilibrium land
rent is equal to :
R∗
j(x) =
tuλuj
2−xif x≤xuj (urban households)
µtaλrj
4µ−x−xc
jif xuj < x ≤xj(rural households)
(2.16)
44
2.2.6 Emissions
Emissions from the food-transportation sector stem from both intra- and inter-regional
trade. Within each region, the total distance traveled by agricultural goods depends on the
distance (i) from each farm gate to the elevator, and (ii) from the elevator to the CBD (see left
side of Figure 2.1). The total ton-mileage traveled by agricultural commodities within regions
(Tw) can be expressed as a function of the profiles of the urban and rural populations :
Tw(λr,λu) =
m
X
j=1
2"Z¯xj
¯xuj
µ|x−xc
j|dx+λrj
2xc
j#=
m
X
j=1 3
8µλ2
rj +1
2λuj λrj (2.17)
Tw(λr,λu) is an increasing and convex function of λrj. As a consequence, any marginal
change in food production in region jleads to a more than proportional change in the intra-
regional distance traveled by food items.
Because of the ‘hub-and-spoke’ assumption, total between-region ton-mileage (Tb) can be
deduced from the sum of incoming and outgoing trade flows to and from peripheral regions
(see right side of Figure 2.1) :
Tb(λr,λu) =
m
X
j=2
ν|λrj λu−λuj λr|(2.18)
Comparing Eqs (2.17) and (2.18) highlights the trade-off between intra- and inter-regional
flows. For a given rural population λr, total intra-regional ton-mileage is minimized when
λrj =λr
m+2µ
3λu
m−λuj , while inter-regional flows are minimized–and equal to 0–when
λrj λu=λuj λrfor all j.
The emission intensity, i.e. the quantity of GHG emissions per ton-mile, generally differs
for intra- and inter-regional trade transport modes [Weber and Matthews,2008]. Without loss
of generality, the units used to measure are scaled such that the emission factor associated with
intra-regional trade is normalized to 1. Let ebdenote the (relative) emission factor associated
with inter-regional transportation of the agricultural product. Values of eblower than unity
indicate that the transport mode used for inter-regional trade is less emissions-intensive (per
ton-mile) than that exploited for intra-regional trade, such as if agricultural commodities are
transported predominantly by rail or water between regions, but transported by truck within
45
regions. 4Total emissions (E) are thus :
E(λr,λu) = Tw(λr,λu) + ebTb(λr, λu) (2.19)
2.3 Emissions-minimizing spatial distribution of food production
What is the spatial distribution of food production best suited to curb transport-related
emissions ? In the context of the above described framework, three food systems can be envisa-
ged : (i) a ‘pure local-food’ system where all regions are self-sufficient in food (λuλrj =λrλuj
for all j), (ii) a global food system where all regions export or import agricultural products
(λuλrj 6=λrλuj for all j), and (iii) a mixed system where some regions are self-sufficient while
other regions export or import food.
For a given distribution of the urban population across regions, the emissions-minimizing
spatial allocation of food production is defined as :
ˆ
λr≡arg min
λr
E(λr;λu) subject to X
j
λrj = 1 −λuand λrj ≥0 for all j(2.20)
Because of the absolute values in Eq. (2.18), solving (2.20) requires a distinction between sets
of importing (M), exporting (X), and self-sufficient (S) regions. Let mM,mX, and mSdenote
the sizes of M,X, and S, respectively (mM+mX+mS=m). For interior solutions such that
ˆ
λrj >0 for all j, the emissions-minimizing rural population located in any peripheral region
j= 2, . . . , m is characterized by (see 2.9 for details) :
ˆ
λrj =
λr
λuλ+2µ
3λ−λuj if region jimports, i.e. if λuj > λ
λr
λuλ+2µ
3(λ−λuj ) if region jexports, i.e. if λuj < λ
λr
λuλuj if region jis self-sufficient, i.e. if λ≤λuj ≤λ
(2.21)
where λand λare defined as (for mM+mX6= 0) :
λ≡1
mM+mX X
k∈M
λuk +X
k∈X
λuk −4λ2
uµνeb
3λr+ 2λuµ(2mM−1)!(2.22)
λ≡1
mM+mX X
k∈M
λuk +X
k∈X
λuk +4λ2
uµνeb
3λr+ 2λuµ(2mX+ 1)!(2.23)
4. As an illustration, Weber and Matthews [2008, p. 3509] report U.S. emission factors for rail or water
transportation that are 8 to 16 times smaller than those for trucks.
46
As an inter-regional trade hub, region 1 plays a special role in the system. It is easily shown
that region 1 either imports or is self-sufficient. The emissions-minimizing rural population in
region 1 (for interior solutions, see 2.9) is given by :
ˆ
λr1=
λr
λuλ+λ
2+2µ
3λ+λ
2−λu1if region 1 imports, i.e. if λu1>λ+λ
2
λr
λuλu1if region 1 is self-sufficient, i.e. if λu1≤λ+λ
2
(2.24)
Note that, in Eqs. (2.21)-(2.24), ˆ
λrj depends on λand λ, which depend on the sets of
importing and exporting regions at the optimum which, in turn, are determined–through
the inequalities in (2.21)–by the values taken by the cumulative distribution function of the
urban population at λand λ. Therefore, in the absence of further specification of the dis-
tribution of urban population across regions, Eqs. (2.21)-(2.24) do not provide a closed-form
characterization of the emissions-minimizing rural population profile. This characterization
nevertheless offers some interesting insights. In particular, notice that λ−λdoes not depend
on the distribution of the urban population across regions :
λ−λ=8λ2
uµνeb
3λr+ 2λuµ(2.25)
Since λ−λis positive, the inequalities defining the existence of self-sufficient regions in
Eq. (2.21) are not trivial. More importantly, λ−λembeds the terms of the trade-off between
intra- and inter-regional trade related emissions. The (relative) emission factor associated with
inter-regional transportation (eb) plays an obvious role in this trade-off, as does the distance
between the CBDs of the core region and any peripheral region (ν). 1/µ is the field-plot size
required to produce one unit of the agricultural good. Hence, the greater µ(agricultural yield),
the smaller the spatial extension of rural areas for a given level of agricultural output, and
the shorter the distance that the agricultural good has to be transported within the region of
production. The overall urban population rate in the economy (λu) has two opposite effects.
A larger value of λuincreases the average spatial extension of cities, which involves longer
distances from the elevator to the CBD within the region of production. But, as λr= 1 −λu,
this also reduces the average spatial extension of rural areas, implying shorter distances from
farms to the elevator, and from the elevator to the CBD in the region of production. Given our
assumptions about the location and number of elevators, the latter effect dominates. Based
47
on Eq. (2.25), it can be readily shown that λ−λis increasing with respect to eb,ν,µ, and
λu. Hence, the larger λ−λ, the greater the weight of inter-regional transportation relative to
intra-regional transportation in total emissions. 5
Proposition 1 A ‘pure local-food’ configuration (where all regions are self-sufficient in food)
minimizes emissions due to food transportation if and only if the range of urban population
across regions is such that : λu1−λum ≤λ−λ
2=4λ2
uµνeb
3λr+2λuµ. Whenever this condition does not
hold, the emissions-minimizing distribution of agricultural production across regions requires at
least some inter-regional trade between the most urbanized (importers) and the least urbanized
(exporters) regions.
Proof : See 2.11.
The intuition behind Proposition (1) is as follows. Consider a pure local food configuration
such that λrλuj =λuλrj for all j. In this configuration, emissions are only due to intra-regional
food transportation. If the difference in urban population between the most (j= 1) and the
least (j=m) urbanized regions is large enough relatively to the ratio of the corresponding
marginal effects on emissions due to inter- relative to intra-regional flows, it is possible to
reduce total emissions by shifting some food production from region 1 to region m. This
increases interregional trade flows (region mbecomes an exporter) but decreases within-region
ton-mileage (because distances are shorter in region m, see 2.9). Since, in this case, the decrease
in within-region ton-mileage more than offsets the increase in interregional trade flows, a pure
local food system cannot minimize emissions.
Proposition (1) conveys two important messages. First, contrary to the usual recommen-
dation based on the ‘food-miles’ argument [Garnett,2003], a pure local-food system does not
necessarily minimize the emissions due to food transportation. The proposition highlights the
importance of taking into account the relative intensity and magnitude of intra- vs. inter-
regional transportation related emissions. Second, the proposition underscores the role played
by the distribution of the urban population across regions. The wider the range of the urban
population (λu1−λum), the less likely that a pure local-food system minimizes emissions.
5. Note that when inter-regional emissions are negligible (ebν→0), the difference between the threshold
values tends to 0, and λand λboth tend to λu
m, which implies that ˆ
λrj =λr
m+2µ
3(λu
m−λuj )
48
Unless the urban population is uniformly distributed across regions (i.e. unless λuj =λu/m
for all j), locating a significant share of food production in the least urbanized regions, and
allowing these regions to export to the most urbanized ones, may lead to lower emissions than
in the situation where all regions are self-sufficient.
The above configuration is depicted in Figure 2.2. Consider an example with m= 50
regions and assume that the distribution of the urban population follows a (generalized) Zipf
law (λuj =λu1/jζfor all j). The parameter values chosen for this example are such that
the condition given in Proposition 1is not met. In the example, the emissions-minimizing
distribution of agricultural production implies that 68% of the regions are such that λuj < λ
(see Figure 2.2, right axis). These regions export food to the five most urbanized regions
(such that λuj > λ). Self-sufficiency is limited to the remaining eleven regions characterized
by urban populations that are neither too small nor too large (λ≤λuj ≤¯
λ). Note that
although the parameter values were chosen mostly for illustrative purposes, they capture
some essential stylized features of current global land use. The urban and rural population
for the year 2012 are approximately 3.7 bn and 3.3 bn, respectively [World Bank,2013]. We
thus set λu= 3.7/7≈0.53 and λr≈0.47. The World Bank dataset also indicates that 15.1%
of urban inhabitants live in the largest city in their respective countries. The exponent of the
Zipf distribution is calibrated to ζ≈0.79 so that λu1= 0.151×0.53. µis set assuming a world
agricultural area of about 4.9 Gha [World Bank,2013], and a world urban area of 0.066 Gha
[Schneider et al.,2009]. Thus, average urban plot size is approximately 0.018 ha per capita
(0.066/3.7), while the average area needed to feed one person is about 0.7 ha (4.9/7). This
means that average field size is roughly 39 (0.7/0.018) times larger than the average urban
residential plot. We thus set µ= 1/39 ≈0.026. The value of ebis based on the emission
factors of international water and truck transportation reported by Weber and Matthews
[2008] : eb= 14/180 ≈0.08. Lastly, νis chosen to be large enough (ν= 4) for regions not to
overlap, i.e. ν > ¯x1+ ¯xjfor all j6= 1 6.
6. In solving the problem numerically, importing/exporting regions are determined iteratively by incremen-
ting mMand mXand updating the values of λand λaccordingly until the conditions given in Eq. (2.21) are
met.
49
In this example, imposing that all regions be self-sufficient would significantly increase
emissions (by 67%, see Table 2.2 in 2.12) compared to the emissions-minimizing configuration.
Urban population (λuj)λu1
λum
0 0.05
λ
^r1
λ
^rm
Emission−minimizing rural population (λ
^rj)
λλ
0
0.025
CDF of urban population
0.68
0.92
0
1
Figure 2.2 – Emissions-minimizing distribution of the rural population (diamonds, left axis) and cumulative
distribution function of the urban population across regions (red crosses, right axis). Self-sufficient regions are
signaled by squares and importing regions by triangles. Parameter values : m= 50,λu≈0.53,λr≈0.47,
λu1≈0.0796,λuj =λu1/(j0.79)for all j,µ≈0.026,eb≈0.08,ν= 4.
2.4 Welfare-maximizing spatial distribution of food production
The spatial distribution of food production influences not only emissions, but also the
utility of urban and rural households though its effect on transport costs and land rents. We
therefore turn to the spatial distribution of food production that maximizes the welfare of the
whole region’s population. Let W(λr,λu) be a measure of the social welfare in the economy :
W(λr,λu)≡X
j
λrj Vrj (λrj , λuj ) + X
j
λuj Vuj (λrj , λuj )−dE(λr,λu) (2.26)
where d > 0 measures the marginal environmental damage, which is expressed in units of
num´eraire and is assumed constant for simplicity.
Using the number of varieties (¯vj=φλuj) and equilibrium wage (given by Eq. (2.13)) at
50
the equilibrium of the urban labor market into Eq. (2.14), we obtain :
Vuj (λrj , λuj ) = ¯q0+b
2λ2
r+φδλuj +2φδ(β−γ)
β(λuj +λrj )−tu
λuj
2(2.27)
The fourth term in Eq. (2.27) reflects the effect of market size on service sector wages. This
effect reinforces inter-sectoral agglomeration because it increases the interest in locating food
production in the most urbanized regions.
Similarly, the indirect utility of a rural household established in region j(Eq. (2.15))
becomes :
Vrj (λrj , λuj ) = ¯q0+b
2λ2
r+α2β
2(2β−γ)2φλuj + (a−bλr)−f−taλuj
2+λrj
2µ(2.28)
The second and third terms in Eq. (2.28) represent the surplus associated with the consump-
tion of the agricultural good, and services, respectively. The last term captures the effect of
land rent (through transportation costs) on the utility of a rural household.
We can now characterize the welfare-maximizing distribution of agricultural production
across regions for a given distribution of the urban population :
λo
r≡arg max
λr
W(λr;λu) subject to X
j
λrj = 1 −λuand λrj ≥0 for all j(2.29)
Since W(λr;λu) integrates the environmental damage due to emissions, the resolution of
(2.29) closely follows that of (2.20). It requires the sets of importing, exporting, and self-
sufficient regions to be distinguished. The structure of the solution is similar to that given by
Eqs. (2.21)–(2.24), and detailed in 2.10. The interior solutions (λo
rj >0) for peripheral regions
(j6= 1) are given by :
λo
rj =
λr
λuλo+2µ
3d+4tahd+ta−2φδ 3β−2γ
βi(λo−λuj ) if region jimports
λr
λuλo+2µ
3d+4tahd+ta−2φδ 3β−2γ
βi(λo−λuj ) if region jexports
λr
λuλuj if region jis self-sufficient
(2.30)
As in Eq. (2.21), the importer/exporter status of any region j6= 1 is determined by the
position of λuj relative to the threshold values λoor λo(provided in 2.10). Since λoand λo
depend on the set of importing and exporting regions, the resolution does not provide a general
closed-form solution. However, similar to what was described in Section 2.3, it is possible to
51
further characterize the welfare-maximizing distribution of food production by examining the
difference :
λo−λo=8λ2
uµνebd
(3d+ 4ta)λr+ 2λuµd+ta−2δφ 3β−2γ
β(2.31)
This difference summarizes the net social-welfare effect of all the aforementioned trade-offs
(intra- vs. inter-regional trade related emissions, within-region transport costs vs. access to
services, and market-size effect on urban wages). The difference is unambiguously increasing
with respect to the emission factor (eb) and distance (ν) associated with inter-regional trade.
Note that if marginal damage is low (if d→0), then λo−λoalso tends to zero. Standard
calculations show that, in this case, λoand λoboth tend to λu/m implying that only the
regions with an urban population sufficiently close to the overall average urban population
should be self-sufficient. In contrast to our findings in Section 2.3,λo−λois not necessarily
positive. In particular, if the inter-sectoral agglomeration forces related to the service sector
are sufficiently large (e.g. if δis sufficiently large), cases where λo< λoare possible. In such
cases, the welfare-maximizing solution implies that rural areas in the most urbanized regions
should be large enough for these regions to export to the least urbanized ones. Last, note
that for a specific value of the transport costs (ta=λuµ
2λr+λuµ
2φδ(3β−2γ)
β) the agglomeration
and dispersion forces at play in the indirect utility functions cancel out. In that case, the
welfare-maximizing and the emissions-minimizing allocations of food production coincide.
Proposition 2 A pure local-food configuration maximizes social welfare if and only if the
range of urban population across regions is such that λu1−λum ≤|λo−λo|
2. Whenever this
condition does not hold, the welfare-maximizing distribution of agricultural production across
regions requires at least some inter-regional trade. Proof : See 2.10.
The proposition underscores that the welfare-maximizing spatial allocation of food pro-
duction depends on the relative magnitude of various agglomeration and dispersion forces that
extend beyond the sole effect of the distance traveled by food items. Thus, the pure local-food
configuration may not necessarily coincide with the welfare-maximizing spatial food alloca-
tion. The condition given in the proposition emphasizes the role of heterogeneity in the urban
population distribution across regions. In particular, the wider the range of the urban popu-
52
lation (λu1−λum), the less likely that a pure local-food configuration maximizes welfare. As
in the emissions-minimizing case, the optimal allocation of food production may require that
some regions engage in trade while others remain self-sufficient. The size of the urban popula-
tions in the latter regions should be neither too large nor too small (such that λo≤λuj ≤λo
or λo≤λuj ≤λo, depending on the sign of λo−λo).
2.5 Spatial-equilibrium distribution of food production
We now examine the economic drivers of the location of agricultural production among
regions, and analyze the spatial-equilibrium allocation of food production for a given distribu-
tion of the urban population. In our model, the location of agricultural production is driven
by the location of farmers. We recognize that, at the individual level, farmers are tied to their
land. However, empirical evidence shows that the inter-regional distribution of farms varies in
the long run. The question addressed in this chapter is that of the spatial allocation of food
production in the long run. As a result, we adopt the modeling strategy applied in the agglo-
meration and trade literature which studies the location of manufactured good production by
analyzing the spatial allocation of workers [Fujita and Thisse,2002, see for instance]. In our
case, a spatial equilibrium occurs if no farmer is better off by moving to another region. It is
also worth stressing that we disregard the adjustment in the location of urban households to
a change in the location of agricultural production because its effect is not significant.
Based on a well-established tradition in migration modeling if more than two regions are
involved [Tabuchi et al.,2005, see], an interior spatial equilibrium arises at 0 < λ∗
rj <1 when :
∆Vrj (λ∗
r,λu)≡Vrj (λ∗
rj , λuj )−1
m
m
X
k=1
Vrk (λ∗
rk , λuk) = 0 for all j(2.32)
For simplicity, we consider no cost of mobility. An interior equilibrium 7is stable if and only
if the slope of the indirect utility differential is strictly negative in the neighborhood of the
equilibrium (i.e. ∂∆Vrj /∂λrj <0 at λ∗
rj ). Combining Eqs. (2.28) and (2.32), the indirect utility
7. An agglomerated equilibrium (such that all the rural population is concentrated in the same region j,
i.e. such that λ∗
rj =λr) may also exist if ∆Vrj (λ∗
r,λu)>0. Whenever it exists, an agglomerated equilibrium
is stable.
53
differential becomes :
∆Vrj (λr,λu) = λuj −λu
mφδ −ta
2λuj −λu
m+λrj
µ−λr
µm(2.33)
where δ≡α2β
2(2β−γ)2. Since ∆Vrj is decreasing with respect to λrj , the interior equilibrium is
stable. Solving ∆Vrj (λ∗
r,λu) = 0 leads to :
λ∗
rj (λuj ) = λr
m+µλuj −λu
m2φδ
ta−1for all j(2.34)
The spatial equilibrium defined by Eq. (2.34) results from the interactions between various
agglomeration and dispersion forces. The term in square brackets in Eq. (2.34) captures the
net effect of inter-sectoral agglomeration and separation forces. On the one hand, farmers
have an incentive to locate near larger cities so as to enjoy a wider range of services (inter-
sectoral agglomeration). This centripetal force is equivalent to the Home Market Effect. On
the other hand, a larger urban population induces fiercer competition between urban and
agricultural land uses, which tends to increase agricultural land rents. The latter effect favors
the location of food production in the least urbanized regions (inter-sectoral separation).
The spatial equilibrium results from the comparison between the marginal increase in the
utility of rural households (φδ) and the marginal increase in the land rent (ta/2) due to
the presence of one additional urban worker. When these two effects are balanced, the rural
population is evenly distributed across regions (λ∗
rj =λr/m for all j). In addition, for a
given level of agricultural output, the lower the agricultural yield (µ), the larger the spatial
extension of the rural area in any given region, and therefore the more costly is within-region
food transportation. As a result, low agricultural yields (µ→0) favor, ceteris paribus, the
spatial dispersion of food production across regions (λ∗
rj →λr/m for all j). Last, the role of
the heterogeneity in the distribution of the urban population is apparent in Eq. (2.34). The
deviation between the urban population of any given region and the average urban population
acts as a scaling factor on the rural migration flows.
Proposition 3 A pure local-food configuration emerges as a spatial equilibrium if and only if
at least one of the following two conditions is met : (i) λuj =λu
mfor all j or (ii) ta=2φδλuµ
λr+λuµ.
If neither condition holds, then the spatial-equilibrium rural population in any region jis
54
increasing (decreasing) with respect to the urban population in region jif the transportation
cost tais small (large), i.e. if ta≤2φδ (ta>2φδ).
Proof : See 2.11.
The proposition indicates that, in general, the spatial-equilibrium allocation of food pro-
duction leads to a global food system. It coincides with a pure local-food configuration only
under very specific conditions. Moreover, whether food production tends to locate in the most
or in the least urbanized regions depends on the comparison between inter-sectoral agglome-
ration and separation forces. This comparison also determines the direction and magnitude of
trade flows at the spatial equilibrium.
For very low values of intra-regional transport cost (i.e. 0 < ta<2φδλuµ
λr+λuµ), the food pro-
duction locates predominantly in the most-urbanized regions. In this case, the most-urbanized
regions export food to the least-urbanized ones, leading to large intra-regional transportation
flows. As tarises, food production relocates to less urbanized regions, thus simultaneously
reducing intra- and inter-regional flows, and therefore emissions until ta=2φδλuµ
λr+λuµ, the value
at which a pure local-food configuration emerges. For 2φδλuµ
λr+λuµ< ta<2φδ, inter-regional trade
resumes but now, from the least- to the most-urbanized regions. Finally, for any transportation
cost higher than 2φδ, food production locates mainly in the least-urbanized regions, inducing
a substantial increase in inter-regional trade flows. The role of taon the spatial-equilibrium
distribution of food production is depicted in Figure 2.3 for two values of ta(left side :0<
ta<2φδλuµ
λr+λuµand right side : 2φδλuµ
λr+λuµ< ta<2φδ).
The spatial equilibrium differs from the welfare-maximizing allocation of food production
because of the presence of two types of externalities. Farmers’ location choices do not take
account of their impacts on (i) emissions, and (ii) the welfare of urban households. The dis-
crepancy between the two situations is depicted in Figure 2.3 for the same distribution of
the urban population and the same values for µ,eb, and νas in Figure 2.2, and two va-
lues of the within-region transportation cost ta. If tais high (right side of Figure 2.3), the
spatial-equilibrium tends to allocate relatively more (less) food production in the least (most)
urbanized regions than in the welfare-maximizing configuration. In this case, only five re-
gions should be self-sufficient (i.e. such that λo< λuj < λo). The number of self-sufficient
55
regions in the welfare-maximizing configuration rises to eleven for the smaller value of ta(left
side of Figure 2.3). In both examples, the emission level in the welfare-maximizing configura-
tion is close to that in the emissions-minimizing configuration. If tais large, emissions in the
spatial-equilibrium configuration are slightly larger than in the welfare-maximizing case but
still significantly lower than in the pure local-food configuration (See Table 2.2 in 2.12).
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Figure 2.3 – Welfare-maximizing (dots) and spatial equilibrium (asterisks) for two values of within-region
transport costs (ta). Parameter values : m= 50,λu≈0.53,λr≈0.47,λu1≈0.0796,λuj =λu1/(j0.79)for all
j,µ≈0.026,eb≈0.08,ν= 4,φ= 1,δ= 1, and d= 0.5.
2.6 Discussion and possible extensions
In this section, we discuss some of our assumptions and assess how relaxing them might
impact on our findings. First, considering that each region is endowed with enough land
to host all agricultural and urban activities is arguably a strong hypothesis. Relaxing this
assumption would increase the likelihood that more urbanized regions import as soon as their
land constraints become binding. Consequently, introducing a land resource constraint would
restrict the possibility for pure local food configurations to emerge as emissions-minimizing
and/or welfare-maximizing configurations.
Second, some of our assumptions tend to increase within-region transportation costs, and
56
therefore, make the emergence of pure local-food configurations less likely. This is the case
especially for two assumptions regarding the organization of food transportation within each
region, namely that (i) there are only two elevators per region, and (ii) unit transportation
costs from farm-gate to elevator and from elevator to CBD are both equal to ta. Increasing
the number of elevators would reduce the distance traveled by food products within regions.
Moreover, because storage capacities at collecting points may allow for bulk shipment of
several farms’ output to the CBD, it could be argued that unit transport costs associated
with the elevator-to-CBD segment might be lower than farm-to-CBD costs. Assume now that
there are Kj=κλrj /2 elevators (instead of 1) in each rural area and that, once gathered in
the elevators, agricultural production is bundled and sent in bulk shipments to the CBD. The
ability to group commodities is measured by parameter τwith 0 < τ ≤1. This generalization
is explored in 2.13. Allowing for several elevators per rural area reduces the distance that
each farmer has to cover, and therefore reduces transport costs and increases farmers’ profits.
These changes are likely to favor inter-sectoral agglomeration in the spatial equilibrium. The
effect of τon farmers’ profits is more ambiguous (see Eq. (2.58)in2.13). Emissions due to
intra-regional transportation are clearly decreasing with respect to the number of elevators
(Kj) and the bundling capacity (i.e. increasing with respect to τ). However, intra-regional
transport flows are still an increasing convex function of the rural population share λrj and
rise with the urban population share λuj . As a result, our findings hold qualitatively with
an endogenous number of regional elevators, and economies of scale in transportation within
production areas.
Last, all regions are assumed to enjoy the same quality of land (represented by the agri-
cultural yield µ). Considering that land quality could vary from one region to another would
affect both transport related emissions and the distribution of profit in the farming sector
and, hence, the spatial equilibrium. The spatial extension of regions with the highest yields
would be smaller (for a given regional population), thus entailing lower food-mileage and lower
emissions from intra-regional transportation in these regions. There would be environmental
interest in gathering food production in these regions. Allowing for yield heterogeneity would
modify profits, and in turn, spatial distribution of food production in equilibrium. Since far-
57
mers operating in regions with the best-quality land will enjoy a higher income, the incentives
to produce in these regions will increase.
2.7 Concluding remarks
Should local food be promoted on the basis that it contributes to the reduction of the dis-
tance traveled by food items, and therefore, transport-related emissions ? Even from a strictly
environmental perspective, the answer to this question is not as straightforward as conventio-
nal wisdom suggests. It depends, among other things, on the extent to which emissions savings
permitted by less inter-regional trade are offset by potentially larger intra-regional transpor-
tation flows. Thus, food trade does not necessarily conflict with the objective of mitigating
emissions from the food transportation sector. Beyond these purely environmental conside-
rations, social welfare analyses that examine this question should integrate interactions with
other agglomeration and dispersion economic forces through transport costs, land rents, and
other spatial externalities including those affecting non-agricultural markets. In this chapter,
we derive the conditions for a pure local-food system to be socially optimal when combining
these elements. If these conditions are not met, the relocation of some food production closer
to consumption centers may deteriorate both the environment and welfare.
The nature (intra- or inter-regional) and volume of food transportation flows depend stron-
gly on the spatial distribution of the urban population. In the limit case of an urban population
evenly distributed across regions, pure local-food configurations emerge as the spatial equili-
brium, and, simultaneously minimizing emissions and maximizing welfare. However, as soon
as there is some heterogeneity in the distribution of the urban population, market outcome
and the optimal configuration may diverge. Our findings indicate that the greater the diffe-
rence in the populations of the largest and the smallest cities, the less likely that pure-local
food configurations will maximize welfare and minimize emissions. These findings offer a fair
level of generality since they do not require additional specifications for the number of regions
or the distribution of the urban population.
These findings suggest that proximity on its own is not an appropriate basis for policies
aimed at improving the sustainability of food-supply chains. By focusing solely on food-miles,
58
fundamental effects that affect social welfare are ignored, and ultimately, may distort the
economic and environmental assessment of the consequences of the spatial allocation of food
production. However, this is not to say that local-food systems should be systematically ruled
out. Indeed, our results indicate that the welfare-maximizing allocation of food production
might correspond to a configuration that combines trade between some regions and self-
sufficiency for other regions. In this case, the size of the urban population in the self-sufficient
region should be neither too large nor too small.
The presence of environmental and other spatial externalities may justify the use of policy
instruments targeting for example emissions, transport costs, and/or land-use. Our findings
suggest that such instruments should focus on the multi-regional level rather than the level
of individual regions. The analysis proposed in this text lays the groundwork for further
investigation of the design and properties of these policy instruments.
59
2.8 R´ef´erences
Bagoulla, C., Chevassus-Lozza, E., Daniel, K., and Gaign´e, C. (2010). Regional Production
Adjustement to Import Competition : Evidence from the French Agro-Industry. American
Journal of Agricultural Economics, 92 :1040–1050. 34
Behrens, K., Gaign´e, C., and Thisse, J.-F. (2009). Industry location and welfare when trans-
port costs are endogenous. Journal of Urban Economics, 65(2) :195–208. 40
BioIS (2007). Impact environnemental du transport de fruits et l´egumes frais import´es et
consomm´es en France m´etropolitaine. Technical report, ADEME. http://www.ale08.
org/IMG/pdf/Fruits_Legumes.pdf.34
BTS and U.S. Census Bureau (2010). 2007 Commodity Flow Survey. Technical report,
Bureau of Transportation Statistics, DOT, Washington, DC, USA. http://www.bts.gov/
publications/commodity_flow_survey/final_tables_december_2009/index.html.
vii,34,36
BTS and U.S. Census Bureau (2013). 2012 Commodity Flow Survey. Techni-
cal report, Bureau of Transportation Statistics, DOT, Washington, DC, USA.
http://www.rita.dot.gov/bts/sites/rita.dot.gov.bts/files/publications/
commodity_flow_survey/2012/united_states/index.html.34
Daniel, K. and Kilkenny, M. (2009). Agricultural Subsidies and Rural Development. Journal
of Agricultural Economics, 60(3) :504–529. 36
Duranton, G. and Puga, D. (2004). Micro-Foundations of Urban Agglomeration Economies,
chapter 48, pages 2063–2117. Elsevier. 39
EEA (2004). EEA Signals 2004. Technical report, European Environment Agency. 34
FHWA (2011). Freight Analysis Framework. http://faf.ornl.gov/fafweb/FUT.aspx.35
Fujita, M., Krugman, P., and Venables, A. (1999). The Spatial Economy : Cities, Regions,
and International Trade. MIT Press, Cambridge, MA, USA. 36
60
Fujita, M. and Thisse, J.-F. (2002). Economics of Agglomeration. Cambridge University Press,
Cambridge, MA, USA. 34,53
Furusawa, T. and Konishi, H. (2007). Free Trade Networks. Journal of International Econo-
mics , 72(2) :310 – 335. 40
Gaign´e, C., Riou, S., and Thisse, J.-F. (2012). Are Compact Cities Environmentally Friendly ?
Journal of Urban Economics, 72 :123–136. 36
Garnett, T. (2003). Wise Moves. Exploring the relationship between food, road transport and
CO2. Technical report, Transport2000. 48
Kampman, B., van Essen, H., van Rooijen, T., Wilmink, I., and Tavasszy, L. (2010). Infra-
structure and Spatial Policy, Speed and Traffic Management. Paper produced as part of
contract env.c.3/ser/2008/0053 between european commission directorate-general environ-
ment and aea, European Commission. 34
Konishi, H. (2000). Formation of Hub Cities : Transportation Cost Advantage and Population
Agglomeration. Journal of Urban Economics, 48(1). 36,40
Ottaviano, G., Tabuchi, T., and Thisse, J.-F. (2002). Agglomeration and Trade Revisited.
International Economic Review, 43 :409–436. 41,43
Overman, H., Puga, D., and Turner, M. (2008). Decomposing the Growth in Residential Land
in the United States. Regional Science and Urban Economics, 38 :487–497. 34
Paxton, A. (1994). The Food Miles Report : The Dangers of Long Distance Food Transport.
Report, SAFE Alliance, London, UK. 34
Picard, P. M. and Zeng, D.-Z. (2005). Agricultural Sector and Industrial Agglomeration.
Journal of Development Economics, 77(1) :75–106. 36
Saunders, C., Barber, A., and Taylor, G. (2006). Food Miles : Comparative Energy/Emissions
Performance of New Zealand’s Agriculture Industry. Technical report, AERU Research
Report No. 285. Lincoln , New Zealand : Lincoln University. 35
61
Schneider, A., Friedl, M. A., and Potere, D. (2009). A new map of global urban extent from
modis satellite data. Environmental Research Letters, 4(4) :044003. 49
Sonnino, R. and Marsden, T. (2006). Beyond the divide : rethinking relationships between
alternative and conventional food networks in europe. Journal of Economic Geography,
6(2) :181–199. 34
Tabuchi, T. and Thisse, J.-F. (2006). Regional Specialization, Urban Hierarchy, and Commu-
ting Costs. International Economic Review, 47(4) :1295–1317. 42,43
Tabuchi, T., Thisse, J.-F., and Zeng, D.-Z. (2005). On the Number And Size of Cities. Journal
of Economic Geography, 5 :423–448. 53
United Nations (2010). World Urbanization Prospects : The 2009 Revision. Technical report,
United Nations, Department of Economic and Social Affairs, Population Division. http:
//esa.un.org/unpd/wup/Documents/WUP2009_Highlights_Final.pdf.34
Vives, X. (1990). Trade Association Disclosure Rules, Incentives to Share Information, and
Welfare. RAND Journal of Economics, 21 :409–430. 42
Weber, C. and Matthews, H. (2008). Food-Miles and the Relative Climate Impacts of Food
Choices in the United States. Environmental Science & Technology, 42 :3508–3513. 45,46,
49
World Bank (2013). 2013 world development indicators. Dataset, The World Bank, Washing-
ton, USA. http://wdi.worldbank.org/table/ Checked on 08/01/2014. 49
Wu, J., Fisher, M., and Pascual, U. (2011). Urbanization and the Viability of Local Agricul-
tural Economies. Land Economics, 87 (1) :109–125. 34
62
2.9 Emissions-minimizing distribution of food production
To deal with the absolute values in (2.20), we use the change of variables λrj = (Xj−
Mj+λuj λr)/λu, where Xj−Mjdenotes net exports with Xj≥0 and Mj≥0, and rewrite
(2.20) as :
min
(Xj,Mj)E=
m
X
j=1 3
8µλ2
u
(Xj−Mj+λuj λr)2+λuj
2λu
(Xj−Mj+λuj λr)+νeb
m
X
j=2
(Xj+Mj)
s.t.
m
X
j=1
Xj−Mj+λuj λr=λrλu,and Xj≥0, Mj≥0, Mj−Xj≤λuj λrfor all j
(2.35)
For interior solutions such that λrj >0 for all j, the corresponding Lagrangian is :
LE=E−
m
X
j=1
[ρ1(Xj−Mj+λr(λuj −λu)) + ρ2jXj+ρ3jMj] (2.36)
The first-order conditions lead to :
3
4µλ2
u
(X1−M1+λu1λr) + λu1
2λu−ρ1=ρ21 =−ρ31 (2.37)
3
4µλ2
u
(Xj−Mj+λuj λr) + λuj
2λu−ρ1=ρ2j−νeb=ν eb−ρ3jfor j6= 1 (2.38)
We thus have ρ21 +ρ31 = 0, which implies that ρ21 =ρ31 = 0 (as both multipliers are
non-negative) and ρ2j+ρ3j= 2νebfor j6= 1. The complementarity slackness conditions
impose that ρ2j= 0 if Xj>0 (j∈X) and ρ2j= 2νebif Mj>0 (j∈M\{1}). Substituting
into (2.37) and (2.38), eliminating ρ3jand ρ1, and reverting back the change of variables, the
F.O.C. become :
ˆ
λr1=λr
m+2µ
3λu
m−λu1+4µλu
3m"(m+ 1 −2mM)νeb−X
k∈S
ρ2k#(2.39)
ˆ
λrj =λr
m+2µ
3λu
m−λuj +4µλu
3m"mρ2j+ (1 −2mM)νeb−X
k∈S
ρ2k#for j6= 1 (2.40)
Summing the last equation over j∈S(for m−mS=mM+mX6= 0), it comes :
X
k∈S
ρ2k=m
m−mS
3λr+ 2µλu
4µλ2
u X
k∈S
λuk −mS
mλu!+mS
m−mS
(2mM−1)νeb(2.41)
63
Re-injecting in Eqs. (2.39) and (2.40) and using the values of ρ2jfor j∈Xand j∈M, we
obtain :
ˆ
λr1=3λr+ 2λuµ
3λu(mM+mX) λu−X
k∈S
λuk +4λ2
uµνeb(mX−mM+ 1)
3λr+ 2λuµ!−2µ
3λu1(2.42)
ˆ
λrj =3λr+ 2λuµ
3λu(mM+mX) λu−X
k∈S
λuk +4λ2
uµνeb(2mX+ 1)
3λr+ 2λuµ!−2µ
3λuj if j∈M\{1}(2.43)
ˆ
λrj =3λr+ 2λuµ
3λu(mM+mX) λu−X
k∈S
λuk −4λ2
uµνeb(2mM−1)
3λr+ 2λuµ!−2µ
3λuj if j∈X(2.44)
The conditions ˆ
λrj <λr
λuλuj and ˆ
λrj >λr
λuλuj for j∈Mand j∈X, respectively, lead to the
thresholds values given in (2.21) and (2.24).
Proof of Proposition 1Notice that if region 1 does not import, no other region k6= 1 does
since λuk ≤λu1≤(λ+λ)/2≤λ. Since the market must be in equilibrium, this implies
that all regions are self-sufficient. Thus, there is an equivalence between region 1 being self-
sufficient and a pure local-food system. Following a similar reasoning, if region mdoes not
export (λum ≥λ), no other region does, leading to a pure local-food system. Combining these
two conditions, we easily obtain that λu1−λum ≤(λ−λ)/2 provides a necessary and sufficient
condition for a pure local-food system to minimize emissions.
Consider a pure local food configuration such that λrλuj =λuλrj for all j. In this configu-
ration, emissions are only due to intra-regional food transportation. Consider now a marginal
shift in rural population d` from region 1 to region msuch the total rural population λr
is kept constant. In the new configuration, region mexports food to region 1 in quantity
λud`, causing emissions in quantity λuebνd`. At the same time, emissions due to within-
region food transportation (i) decrease in region 1, and (ii) increase in region m. Using
Eq. (2.17), simple calculations indicate that the net change in intra-regional emissions is
[(3λr+ 2λuµ)(λu1−λum)−3λud`](d`/4λuµ). Since d` is positive and arbitrarily small, if the
gap in urban population between the largest and the smallest region is greater than the ratio
of the marginal changes in emissions due to inter- and intra-regional flows, then a pure local
food system cannot minimize emissions. QED.
64
2.10 Welfare-maximizing distribution of food production
The resolution of program (2.29) closely follows that of (2.35) (see 2.9). Using the same
change of variables and omitting the terms that are independent of λrj , the objective function
becomes :
W=
m
X
j=1
Xj−Mj+λuj λr
λuφδ(3β−2γ)
βλuj −λuj +Xj−Mj+λuj λr
µλuta
2−dE (2.45)
For interior solutions, the first-order conditions for the core region lead to :
φδ(3β−2γ)
β−ta
2µλuλu1−3d+ 4ta
4µλ2
u
(X1−M1+λu1λr) + ρ1=−ρ21 =ρ31 (2.46)
Eq. (2.46) implies that ρ21 =ρ31 = 0. As for peripheral regions (j6= 1), the F.O.C. lead to :
φδ(3β−2γ)
β−ta
2µλuλuj −3d+ 4ta
4µλ2
u
(Xj−Mj+λuj λr)+ρ1=dνeb−ρ2j=ρ3j−dνeb(2.47)
Eq. (2.47) implies that ρ2j+ρ3j= 2dνeb. The complementarity slackness conditions impose
that ρ2j= 0 if Xj>0 and ρ2j= 2dνebif Mj>0. Substituting into (2.46) and (2.47),
eliminating ρ3jand ρ1, and reverting back the change of variables, the F.O.C. for region 1
becomes :
λo
r1=λr
m+4µ
3d+ 4ta"d+ta
2µλu−φδ(3β−2γ)
βλu
m−λu1+λu
m (m+ 1 −2mM)dνeb−X
k∈S
ρ2k!#
(2.48)
and for peripheral regions (j6= 1) :
λo
rj =λr
m+4µ
3d+ 4ta"d+ta
2µλu−φδ(3β−2γ)
βλu
m−λuj +λu
m mρ2j+ (1 −2mM)dνeb−X
k∈S
ρ2k!#
(2.49)
As in 2.9,PSρ2kis eliminated by summing Eq. (2.49) over j∈S:
X
k∈S
ρ2k=m
m−mS3d+ 4ta
4µλ2
u
λr+d+ta
2λu−φδ(3β−2γ)
β X
k∈S
λuk −mS
mλu!+mS(2mM−1)
m−mS
dνeb
(2.50)
The values in Eq. (2.30) are obtained by re-injecting the value of PSρ2kinto Eq. (2.49),
and using that ρ2j= 0 for j∈Xand ρ2j= 2dνebfor j∈M\{1}. The threshold values λo
and λoin Eq. (2.30) are then derived from the conditions λo
rj <λr
λuλuj and λo
rj >λr
λuλuj for
j∈Mand j∈X, respectively :
65
λo≡1
mM+mX
X
k∈M
λuk +X
k∈X
λuk −4λ2
uµνebd(2mM−1)
(3d+ 4ta)λr+ 2λuµd+ta−2δφ 3β−2γ
β
(2.51)
λo≡1
mM+mX
X
k∈M
λuk +X
k∈X
λuk +4λ2
uµνebd(2mX+ 1)
(3d+ 4ta)λr+ 2λuµd+ta−2δφ 3β−2γ
β
(2.52)
If λo> λo, then as in 2.9, the most (least) urbanized regions are importers (exporters).
We thus have for j6= 1 : j∈Mif λuj > λo,j∈Sif λo≤λuj ≤λo, and j∈Xif λuj < λo. If
λo< λo, the signs of the above inequalities change.
As for region 1, re-injecting the value of PSρ2kinto Eq. (2.48), using Eqs. (2.51) and
(2.52) and re-arranging leads to (in the case λo> λo) :
λo
r1=
λr
λu
λo+λo
2+2µ
3d+4tahd+ta−2φδ 3β−2γ
βiλo+λo
2−λu1if λuj >λo+λo
2
λr
λuλuj if λuj ≤λo+λo
2
(2.53)
If λo< λo, region 1 can only be an exporter or self-sufficient and the signs of the inequalities
in Eq. (2.53) change.
Proof of Proposition 2If λo> λo, the proof is exactly the same as for Proposition 1. Thus,
in this case we have that λu1−λum ≤(λo−λo)/2 is a necessary and sufficient condition
for a pure local-food system to maximize welfare. If λo< λo, it is necessary to account for
the fact that region 1 either exports or is self-sufficient, and region meither imports or is
self-sufficient. Therefore the condition becomes λu1−λum ≤(λo−λo)/2. QED.
2.11 Spatial-equilibrium distribution of food production
Proof of Proposition 3A pure local-food configuration is characterized by λrj = (λr/λu)λuj
for all j. Using Eq. (2.34), it is easy to see that, for such a configuration to emerge in equili-
brium, we need that λuj −(λu/m) = 0 for all jand/or 2φδ
ta−1µ=λr
λu. The analysis of the
sign of the slope of λ∗
rj with respect to λuj in Eq. (2.34) completes the proof. QED.
66
2.12 Simulation results
67
Relative change in emissions
Spatial configuration Number of regions w.r.t. emissions-minimizing
(share of each emission category)
[%]
Importers Self-suff. Exporters Within Between Total
mMmSmXTwebTbE
Pure local food 0 50 0 +118 -100 +67
(100) (0) (100)
Emissions-minimizing 5 11 34 - - -
(77) (23) (100)
Spatial equilibrium
ta= 0.04 38 0 12 +235 -28 +174
(94) (6) (100)
ta= 1 12 0 38 -11 +81 +10
(62) (38) (100)
Welfare-maximizing
ta= 0.04 5 11 34 +4 -10 +1
(79) (21) (100)
ta= 1 9 5 36 -10 +51 +4
(66) (34) (100)
Tableau 2.2 – Summary of the simulation results in the various spatial configurations and for two values of
within-region transport costs (ta). Relative changes in emissions are computed for each category relatively to
emission levels in the emissions-minimizing configuration. The shares of the respective emission categories in
total emissions for each spatial configuration are given in parentheses. Parameter values : m= 50,λu≈0.53,
λr≈0.47,λu1≈0.0796,λuj =λu1/(j0.79)for all j,µ≈0.026,eb≈0.08,ν= 4,φ= 1,δ= 1, and d= 0.5.
68
2.13 Discussion and Extensions with Kjelevators and bundling capacity τ
2.13.1 Equilibrium
We suppose there are Kjelevators within each agricultural area of region j(thus 2Kj
elevators in region j). They are evenly spaced along the rural area 8and located at xk
j=
{x1
j, x2
j, ..., xK
j}. Without loss of generality, we set ¯xuj < x1
j< x2
j< ... < xK
jso that the
location of elevator kis given by :
xk
j= ¯xuj +¯xj−¯xuj
2Kj
+ (k−1) ¯xj−¯xuj
Kj
=λuj
2+λrj
4µKj
+ (k−1) λrj
2µKj
.(2.54)
For a given distance to an elevator, the transport cost is higher for a farmer located further
away from the city. We also take into account that Kjvaries with λrj since the number of
elevators reacts positively to a change in agricultural production. For simplicity, we assume
that
Kj=κλrj /2 (2.55)
with 0 < κ < 1. Hence, increasing food production in a region induces a rise in the number of
elevators in that region.
Once gathered in the elevators, food production is bundled and sent in bulk shipments to
the CBD. The ability to group commodities is measured by parameter τwith 0 < τ < 1 :
if τ= 1, then the production of each farmer is shipped directly to the city, whereas τ→0
means that all the production received by a collector can be stored and carried in a single
shipment. 9
The individual cost associated with the distribution of farmers’ output is now given by :
Caj (x, k) = f+tax−xk
j+taxk
jτ(2.56)
At given prices and locations of the urban population, each farmer chooses a location that
maximizes his/her utility. Let Vrj (x, k) be the indirect utility of a farmer located at xin region
8. Note that we assume that unit per-mile freight prices between elevator and city are identical regardless
of the elevator and are treated as parameters. Ideally, we would consider a game in which elevators’ owners
act strategically to maximize their profits. This configuration would complexity to the analysis without adding
new significant results.
9. In practice, low values of τare adapted to the case of commodities such as cereals, while values of τclose
to 1 are more adapted to the case of fresh fruits and vegetables.
69
jand carrying his output to elevator k. An equilibrium is reached when no farmer wants to
change his location so that Vrj (x, 1) = ... =Vrj (x, k) = ...Vr j (x, K).
The bid rent at the equilibrium must solve ∂V i
rj (x, k)/∂x = 0 (or equivalently, ∂Rj(x,k)
∂x+
µta= 0) and verify Rj(x, 1) + Caj (x, 1) = ... =Rj(x, K ) + Caj(x, K ). As a consequence, the
land rent capitalizes not only the cost of the distance between farmers and the elevator but
also the transport costsx between the latter and the city. Because the opportunity cost of land
is equal to zero, we have Rj(¯xj) = 0 and the equilibrium agricultural land rent is given by :
R∗
j(x, k) = µtaλrj
4µKj−x−xk
j+τλrj
2µKj
(Kj−k)(2.57)
Finally, using (2.55), (2.56) and (2.57), the net income received by a farmer becomes :
πj(x)=(a−bλr)−f−taτλrj
2µ+λuj
2−(1 −τ)ta
2µκ ≡π∗
j.(2.58)
2.13.2 Intra-regional transport flows
To evaluate the distance traveled by commodities, we need to know the allocation of
farmers between elevators. Farmers choose the elevator minimizing his total cost. Let bxk,k+1
j
be the farmer who is indifferent between elevator kand k+ 1 :
bxk,k+1
j=xk
j+xk+1
j
2+τ(xk+1
j−xk
j)
2=λuj
2+λrj k
2µKj
+τλrj
4µKj
.
The distance to the city differs from one elevator to another. Transportation costs differ
accordingly, implying that farmers cannot be evenly distributed among elevators. The mass
of farmers residing in region jand shipping their output to elevator 1 and Kare respectively
bx1,2
j−¯xuj µ=λr j (2 + τ)
4Kj
and ¯xj−bxK,K−1
jµ=λrj (2 −τ)
4Kj
.
As for the other K−2 elevators, we have
bxk,k+1
j−bxk,k−1
jµ=λrj
2Kj
with k∈ {2, ..., K −1}.
Considering this organization of intra-regional freight, the sum of agricultural flows within
each region becomes :
Twj = 2
K
X
k=1 Zbxk,k+1
j
bxk,k−1
j
µx−xk
jdx+ 2
K
X
k=1
xk
jbxk,k+1
j−bxk,k−1
jµτ
70
2.13.3 Ton-mileage
In region j, the sum of agricultural flows from farms to elevators, and from elevators to
the CBD are given respectively by :
Kj
X
k=1 Zbxk,k+1
j
bxk,k−1
jx−xk
jdx=λrj
4µKj2
+Kj−1
2(λrj (1 + τ)
4µKj2
+λrj (1 −τ)
4µKj2)
=λrj
4µKj2
+ (Kj−1) λrj
4µKj2
(1 + τ2)
=λrj
4µKj2Kj+ (Kj−1)τ2
and
Kj
X
1
xk
jbxk,k+1
j−bxk,k−1
j=λuj
2
λrj
2µ+λrj
4µKj2
(2 + τ) + K−2
2
λrj
2µKj
λrj
2µKj
+(Kj−2)(Kj−1)
2
λrj
2µKj
λrj
2µKj
+λrj
4µKj
+ 2(K−1) λrj
4µKjλrj (2 −τ)
4µKj
=λuj
2
λrj
2µ+λrj
4µKj2
(2 + τ) + 2(Kj−2)Kλrj
4µKj2
+ (2Kj−1)(2 −τ)λrj
4µKj2
=λuj
2
λrj
2µ+λrj
4µKj2
[2K2
j−2τ(Kj−1)]
Hence, the sum of agricultural flows within region jis :
Twj =λ2
rj
4µ"τ2+Kj(1 −τ2)+2τK2
j
2K2
j#+λuj λrj
2τ.
Because Kj=κλrj /2, we finally obtain
Twj =λ2
rj τ
4µ+λrj (1 −τ2)
4κµ +τ2
2κ2µ+λuj λrj
2τ
71
Chapitre 3
Conventional vs. Alternative
Farming : Assessing the
Sustainability of a Regional Food
Supply Pattern.
Feeding the world’s expanding population in a sustainable way is among the main chal-
lenges in the coming decades. In this chapter, we examine whether promoting alternative
farming leads to improve the sustainability of the food supply chain at a regional scale.
Using a spatial model describing the regional land allocation between two types of agri-
cultural practices, we show that alternative farming is more likely to develop and thrive in
regions hosting an intermediate-size city. We highlight that promoting alternative farming
can lead to a welfare improvement compared to the market, provided that the marginal
opportunity cost of urban land remains low enough. However, we find that the conversion
from conventional to alternative farming does not necessarily reduce GHG emissions and
may, as a consequence, offset the positive effect on welfare.
Keywords : Food supply, Agriculture, Land allocation, Sustainability
JEL Classification : F12 ; Q10 ; Q54 ; Q56 ; R12
73
3.1 Introduction
Today’s global food system is characterized by two major features : (i) food production
rests on intensive agricultural practices and (ii) populations depend increasingly on food from
distant sources 1. Long-distance food supply has become the norm in most of the world,
particularly in highly urbanized regions where farmland has greatly declined, forcing the cities
that cannot rely on local production to expand the boundaries of their foodshed [Kloppenburg
et al.,1996].
The sustainability of this system is however questioned. This organization of the global food
system has attracted increasing attention and raises questions with regard to its sustaniability.
The depletion of fossil energy resources and energy-related environmental damages lead the
cities to account for factors that were, until recently, neglected. At the same time, urban
dwellers have more and more demanding expectations with respect to the social and ecological
implications of the food they consume. In affluent cities notably, the primary issue related to
food is no longer one of inadequate supply but rather one of quality, environmental or even
ethical concerns [Deutsch et al.,2013].
In this context, “eating local and organic” has become one of the main watchwords for
food supply planning. Cities are increasingly considering the relevance of developing poli-
cies to explicitly support alternative production and reduce their inter-regional dependencies
[Peters et al.,2009]. From a practical standpoint, improving the sustainability of their current
food supply chain would broadly fall into two sets of measures :
i) Reorienting incentives towards less intensive agricultural practices, including organic
food development and reduced reliance on chemical inputs (Pimentel et al. [2005] and Niggli
et al. [2009]).
ii) Rebuilding the foodshed boundaries so as to reduce the reliance on food imports (local
vs imported production).
Alternative food systems – i.e., systems that rely on both local food production and organic
1. In the United States, food travels between 2,500 and 4,000 kilometers from farm to plate, as much as 25
percent farther than in 1980’s. In the UK, food travels 50 percent farther than it did two decades ago [Halweil,
2002].
74
farming – are, in this respect, commonly viewed to be inherently more sustainable than
conventional ; from the ecological standpoint first, low-input practices and shorter distances
associated with alternative farming are purported to reduce the amount of energy used and
greenhouse gas emissions released in food transportation [Hinrichs,2003]. Regarding the eco-
nomic and the social dimensions then, goods from alternative systems are presumed to be
sold at higher prices, enabling farmers to generate a greater profit and, thereby, improve the
economic viability of rural communities.
In practice however, these assertions are being challenged ; a growing body of research
questions that localness favors food systems that are intrinsically fairer, more sustainable or
more environmentally-friendlier (Bellows and Hamm [2001] ; [Pirog et al.,2001]2;Born and
Purcell [2006]). The debate over the sustainability of alternative systems remains an open
issue [Edwards-Jones et al.,2008].
In this chapter, we develop a theoretical spatial model describing the regional land al-
location between two types of agricultural practices (alternative and conventional) and we
examine whether promoting alternative farming lead to improve the sustainability of the food
supply chain at a regional scale. Exploring the conditions that enable alternative farming
to exist viably, we show that it is more likely to develop and thrive in regions hosting an
intermediate-size city. The intuition is that insufficient market opportunities and expensive
food transportation respectively hinder its development in rural areas surrounding small and
large cities. Regarding the optimality of the market outcome, we highlight that fostering alter-
native farming can lead to a welfare improvement provided that the marginal opportunity cost
of urban land remains low enough. However, when looking at the environmental aspects, we
find that the conversion from conventional to alternative farming does not necessarily reduce
GHG emissions and may, as a consequence, counterbalance the positive effect on the regional
welfare.
The chapter proceeds as follows. Section 3.2 presents the model that we use in Section 3.3
2. Comparing the carbon footprint of local versus imported foodstuffs, Pirog et al. [2001] state that the
higher weight capacities of transportation vehicles used in the global food system are usually more efficient due
to scale. Since farmers involved in local alternatives are most often not part of a distribution network that offers
more organized and efficient transport logistics for delivering food, the environmental benefit is not obvious.
75
to determine the farming pattern that occurs at the equilibrium. In Section 3.4 and 3.5, we
discuss the optimality of the market outcome and we wonder whether fostering alternative
farming can concomitantly improve the regional welfare and the carbon footprint of the food
supply chain. Section 3.6 finally offers a comparative-static analysis focused on the impacts
of rising energy prices.
3.2 The framework
Consider an economy formed by an open region and two sectors (agriculture and urban
sector). The agricultural activity may be of two types : conventional farming, where commo-
dities are gathered to be sold in the global integrated market, and alternative farming where
goods are exclusively sold in the region where they have been grown. The region hosts a popu-
lation exogenously divided into λuurban households and λrfarmers, λu/(λu+λr) measuring
the urbanization rate.
Population
Urban Households
λu
Urban sector
Farmers
λr
Conventional Farming
λr(1 −λa)
Trade-oriented
Alternative Farming
λrλa
Local-oriented
Agricultural sector
Figure 3.1 – The sectoral organization
3.2.1 The spatial structure
The regional space is made of an urban area including a CBD located at x= 0 and urban
households’ lots, and a rural area where farmers live and produce agricultural goods. Soil
quality is assumed to be homogeneous over all available land. Without loss of generality, we
focus on the right-hand side of the region, the left-hand side being perfectly symmetrical.
Distances and locations are expressed by the same variable x, measured from the city center.
Each urban dweller consumes a residential plot of fixed size 1/δ (where δ > 1 is the density
76
of the city) so that the right endpoint of the city is given by
¯xu=λu
2δ(3.1)
Farmers settles at the periphery of the urban area. They produce either conventional or
alternative goods. Assuming that each farmer uses one unit of land for cultivation, the right
endpoint of the region is :
¯x=λu
2δ+λr
2(3.2)
We also suppose the mass of land units is large enough to accommodate both urban and
farming activities at the equilibrium. This assumption does not affect our conclusions on land
allocation because alternative and conventional farming use the same quantity of land, and
the regional distribution between urban and agriculture (λu/λr) is fixed.
3.2.2 Preferences and demand
Preferences are defined over three consumption goods : an alternatively-grown agricultural
product, a conventional agricultural product, and a homogeneous aggregate good Q, chosen
as the num´eraire. The latter represents the consumption of all goods other than agricultu-
ral products. In order to abstract from income effects, we assume that the marginal utility
with respect to the num´eraire is constant. Consumers do not differentiate conventional goods
produced in the region they live from imported goods. We further assume that the utility
function is additive with respect to the consumed quantity of agricultural goods (qaand qc)
and the composite good (Q) and given by 3
U(Q;qc;qa) = Q+αc−qc
2qc+αa−qa
2qa−γqaqc(3.3)
The parameters αa,αcand γare positive and we posit γ < 1 to ensure the quasi-concavity
of the utility function. γmeasures the substitutability between the two agricultural varieties,
ranging from zero when alternative and conventional goods are independent, to values close to
one when they are perfect substitutes. αaand αcrepresent the intrinsic quality of alternatively-
grown and conventional goods, respectively. The gap between αaand αcis therefore a measure
of the quality differentiation between the two agricultural goods and reflects the consumers’
3. This specification is similar to that used by Singh and Vives [1984] with the simplification βi=βj= 1.
77
willingness to buy products identified as alternatively-grown ; the larger αa−αc, the greater
the consumers’ sensitivity towards the farming practices.
Consumers live in the urban area and work in the CBD. They bear urban costs, given
by the sum of the commuting costs and the land rent. Denoting tuand Ruas the per-mile
commuting cost and the (urban) land rent, the budget constraint of a urban dweller residing
at xis :
qcpc+qapa+Q+Ru(x)
δ+tux=wu+Q(3.4)
where pcand paare the prices of the conventional and the alternative good, and wuis the
urban wage prevailing in the city. The initial endowment in num´eraire Qis supposed to be
large enough to ensure strictly positive consumption in equilibrium. Maximizing the utility
(3.3) subject to the budget constraint (3.4) leads to the following individual demand functions :
qd
a=αa−γαc
1−γ2−pa
1−γ+γ
1−γ2(pa+pc) (3.5)
qd
c=αc−γαa
1−γ2−pc
1−γ+γ
1−γ2(pa+pc) (3.6)
3.2.3 Technologies and agricultural profits.
Alternative food production Products from alternative farming are intended for regional consump-
tion only. Farmers operating in this sector only use organic fertilizer and one unit of land to
produce. Denoting by ¯qthe natural ability of soils to grow crops in the region, the individual
production in alternative goods is given by :
qs
a= ¯qκ (3.7)
where κis a positive coefficient that can be interpreted as the agricultural labor efficiency.
The costs to transport the goods from the farm to the city are borne by the farmer and
are supposed to be linear in weight and distance. Letting tabe the transportation cost per
unit of good and distance and Ra(x), the land rent paid by a farmer involved in alternative
farming, the profits of a farmer located at xare :
πa(x)=(p∗
a−tax)¯qκ −Ra(x).(3.8)
As alternative farmers produce for the domestic market only, the equilibrium price is de-
termined at the regional scale. Denoting by λathe share of farmers involved in alternative
78
production, the total amount of goods produced is such that Qs
a= ¯qκλrλa. Using (3.5) and
the expression of Qs
a, the market clearing condition for alternatively-grown goods leads to
p∗
a= [αa−γ(αc−pc)] −1−γ2λaλr¯qκ
λu
(3.9)
The term in square brackets captures the maximum willingness to pay for alternatively-
grown goods, while the last term in RHS of (3.9) encompasses both the effect of the competition
between farmers (λaλr¯qκ) and that of regional market opportunities (through the inverse
measure of the demand sensitivity to price 1−γ2
λu).
Conventional food production In conventional farming, production requires one unit of land
and an amount zof synthetic fertilizer. The yield response to synthetic fertilizer is assumed
to be positive, increasing and concave. The individual supply in conventional goods can be
written as qs
c≡¯q κF (z) with F0(z)>0 and F00(z)<0. For the ease of calculation, we retain
a Cobb-Douglas specification as in Beckmann [1972], so that
qs
c= ¯qκ√z+ 1 ∀z≥0 (3.10)
Note that when no synthetic fertilizer is used (z= 0), yields in conventional farming equals
those of alternative farming (qs
c(0) = qs
a= ¯qκ).
Regarding the food transportation, commodities are first gathered in a regional grain
elevator located at the border of conventional fields ˆx, before being brought to the central
market by larger vehicles 4. To send its production to the elevator, the farmer has to pay tcper
unit of product and distance covered. We further assume tc< ta, meaning that conventional
farmers benefit from lower transportation costs than alternative farmers5. Let pzand Rcbe
the unit cost of synthetic fertilizer and the land rent paid by conventional farmers. The profits
of a farmer located at xare then given by :
πc(x)=(pc−tc|x−ˆx|)qs
c(x)−pzz−Rc(x) (3.11)
4. Although other locations can be envisaged, this option offers the advantage to abstract from the effects
of the location strategy within the conventional agricultural area.
5. This assumption is consistent with the reality, the higher transport costs in the organic sub-sector being
mainly due to the lack of economies of scale [CEC,2004].
79
For simplicity, we suppose that pcand pzare exogenously fixed ; the regional supply in
conventional goods is assumed to be small enough to not significantly impact the equilibrium
price pcdetermined on the global market.
Conventional farmers choose the amount of synthetic fertilizer to be applied so as to
maximize their profit πc(x), leading to :
z∗(x) =
pc−tc|x−ˆx|
2pz
¯qκ2
−1>0 if ˆx<x≤˜x
0 if ˜x < x < ¯x
(3.12)
and
qs∗
c(x) =
pc−tc|x−ˆx|
2pz
(¯qκ)2if ˆx<x≤˜x
¯qκ if ˜x < x < ¯x
(3.13)
where ˜x≡ˆx+pc
tc−2pz
¯qκtc
. As shown by (3.12), the amount of synthetic fertilizer used by
conventional farmers is decreasing with the distance from the regional grain elevator, and
increasing with the natural ability of land ¯q. Moreover, the expression of ˜xsuggests that
the spatial extent of the high input conventional farming area depends only on exogenous
parameters. This result is of particular importance as it implies that conversion to alternative
farming does not systematically lead to a decrease in synthetic fertilizer use (Fig. 3.2.2) 6.
Figure 3.2 – Farming conversion and regional use of synthetic fertilizer
A closer look at the nature of the conventional farming reveals that three cases can be
envisaged. First, all the conventional farmers use synthetic fertilizer if ¯x < ˜xthat is, if the
6. Observe that this result stems from the assumption that the transportation cost from the grain elevator
to the CBD in conventional farming is sufficiently low to be neglected.
80
transportation cost per unit of good supported by the farmer located at the limit of the
region is small enough. Using (3.2) and the expression of ˜x, we show that this condition can
be written as (1−λa)λr
2tc< pc−2pz
¯qκ or equivalently :
λa>˜
λa≡1−2
λr
¯qκpc−2pz
¯qκtc
.(3.14)
Second, if ˜x≤ˆx, or equivalently, if ¯q≤2pz
κpc, none of the conventional farmers use synthetic
fertilizer 7; in this case, the natural ability of soil is not high enough to make the use of
synthetic fertilizer economically beneficial. Finally, conventional farming includes both farmers
who use fertilizer and others who do not use fertilizer if ˆx < ˜x < ¯x(that is, if ¯q > 2pz
κpcand
λa<˜
λa).
Summing up, the share of conventional farmers using synthetic fertilizer (λc|z>0) is such :
λc|z>0=
0 if ¯q≤2pz
κpc
2
(1 −λa)λr
¯qκpc−2pz
¯qκtc
if ¯q > 2pz
κpc
and λa<˜
λa
1 if ¯q > 2pz
κpc
and λa>˜
λa
(3.15)
λc|z>0increases with the share of alternative farming (λa) provided that the natural ability of
soils is high enough. Plugging (3.12) and (3.13) into (3.11), the profits for farmers involved in
conventional production are finally given by :
πc(x) =
(pc−tc|x−ˆx|)2
4pz
(¯qκ)2−Rc|z>0(x) + pzif ˆx<x≤˜x
(pc−tc|x−ˆx|) ¯q−Rc|z=0 (x) if ˜x < x < ¯x
(3.16)
3.3 The equilibrium pattern of agricultural land use
We now determine the agricultural pattern that would emerge at the market equilibrium.
3.3.1 Equilibrium land allocation
As in Von Th¨
unen models, the regional land allocation is derived from the equilibrium
rent function. Bid rent functions are obtained by equating the location costs (transportation
and land cost) within each area (see Appendix B.1). Each plot of land being allocated to the
7. Under this threshold value of ¯q,˜
λais always higher than one, so that λa<˜
λa.
81
highest bidder, the equilibrium land rent is such that :
R∗(x) = max{Ru(x), Ra(x), Rc|z>0(x), Rc|z=0 (x)}(3.17)
Depending on the bid rent curves’ ranking, several land use configurations can occur (Fig.
3.3). In order to ease the discussion, we concentrate on the following configuration : a CBD
surrounded by a residential urban area, followed by a zone dedicated to alternative farming,
finally bordered by a conventional farming area (See. Fig. 3.3.A1, A2 and A3).
Figure 3.3 – Bid-rent functions and regional land allocation
We show in Appendix B.2 that this spatial configuration occurs if and only if the share of
alternative farmers is not too high, that is, for λa<ˆ
λawith ˆ
λa=4(2pzta−¯qκpctc)
¯qκt2
cλr>08. In this
case, the equilibrium land rent is given by :
R∗(x) =
R∗
u(x) = δtu|¯xu−x|+R∗
a(¯xu) if 0 < x ≤¯xu
R∗
a(x) = ta|ˆx−x|¯qκ +R∗
c|z>0(ˆx) if ¯xu< x ≤ˆx
R∗
c|z>0(x) = pc+tcˆx−x+˜x
2
2pz
tc|˜x−x|¯q2κ2+R∗
c|z=0 (˜x) if ˆx<x≤˜x
R∗
c|z=0 (x) = tc|¯x−x|¯qκ if ˜x < x < ¯x
(3.18)
8. Note that for values of tcsufficiently low compared with ta, this condition is always met.
82
If the above condition is not met (i.e. if λa>ˆ
λa), a spatial pattern where the land allocated
to alternative farming is enclosed in the conventional farming area occurs (Fig. 3.3.B).
Equilibrium profits in alternative and conventional farming are obtained by plugging (3.18)
into (3.8) and (3.16) :
π∗
a=p∗
a−taλu
2δ+λaλr
2−(¯qκpc−2pz)2
4¯qκpz−(1 −λa)λr
2tc¯qκ (3.19)
π∗
c=pc−tc
(1 −λa)λr
2¯qκ (3.20)
The price of alternatively-grown goods decreases with respect to the share of alternative
farmers (Eq.(3.9)). Therefore, profits in alternative farming are decreasing with λawhile
they are increasing in conventional farming. Consequently, starting from a very low share
of alternative farming (i.e. λaclose to 0), there can be an interior solution for the regional
distribution of farmers between conventional and alternative activities at the equilibrium.
Such an equilibrium occurs when no farmer can be better off by converting to the other
farming practice. Solving π∗
c=π∗
afor λa, we derive the equilibrium share of farmers involved
in alternative farming :
λ∗
a=
αa−γ(αc−pc)−taλu
2δ−pz
¯qκ +p2
c¯qκ
4pz
λr¯qκ1−γ2
λu+ta
2(3.21)
Since the profit differential between alternative and conventional farming decreases mo-
notonically with respect to the share of alternative farmers, this equilibrium is unique and
stable. Moreover, we show in Appendix C that λ∗
avaries from 0 to 1 for intermediate values
of ta.
3.3.2 Urbanization and agricultural practices
According to (3.21), the share of alternative farming describes a concave function with
respect to the urban population’ size (λu). This inverted U-shaped relation stems from the
interplay of two competing effects, namely, the market size effect ( 1−γ2
λu) and the transpor-
tation bill effect (−taλu
2δ). In a first step, the larger the urban population, the stronger the
market size effect. Farmers are thus encouraged to convert to alternative production so as
to benefit from additional outlets. However, a larger urban population is also equivalent to
83
a more extended residential area, resulting in higher transportation costs for farmers. Since
the marginal impact of the market size effect is decreasing with the urban population’ size
while that of the transportation bill is constant, there is a threshold level of urbanization ¯
λu
at which the equilibrium share of alternative farming achieves a maximum (thereafter referred
as ¯
λa) :
¯
λu=2¯qκ 1−γ2
ta"s1 + δ
(1 −γ2) ¯qκ αa−γ(αc−pc)−4p2
z+p2
c¯q2κ2
4¯qκpz−1#(3.22)
Beyond ¯
λu, transportation costs outweigh the market size effect so that farmers have incentives
to return to conventional production.
Proposition 4 Alternative farming is more likely to thrive in a region hosting a city which
population is neither too large nor too small (other things being equal).
The shape of the relationship between alternative farming and urbanization and the value
of ¯
λuare strongly influenced by the parameters defining the consumers’ preferences. First,
the quality differentiation between conventional and alternatively-grown goods affects the
equilibrium farming pattern as follows : the greater αa−αc, the larger the share of alternative
farming regardless the level of urbanization. Second, as illustrated by Figure 3.4, the maximum
alternative share ¯
λais positively (resp. negatively) related to the degree of agricultural goods’
substituability provided that the quality of the alternatively-grown good valuated by the
consumers is high (resp. low).
Figure 3.4 – Alternative farming share (λ∗
a) and urban population’ size (λu) for different level of goods’
substituability.
84
Last, agricultural goods’ substituability also determines the level of ¯
λu. When agricultural
goods are almost-perfect substitutes (γclose to one), the market effect is weak and more
likely offset by the transportation bill, so that alternative farming can only develop in very
low urbanized regions. As γdecreases, the market effect plays more significantly, allowing
alternative farming to become economically viable in regions hosting a larger city.
3.3.3 Soil quality and fertilizer use at the equilibrium
The use of synthetic fertilizer in conventional farming varies in space and depends on
the natural ability of the regional soils (¯q). As a consequence, both the individual and the
total amount of fertilizer use in conventional farming in equilibrium vary according to this
characteristic (Fig. 3.5).
For a very low natural ability of soils, the region hosts mainly synthetic-free conventional
farming. As the quality rises (while remaining below 2pz
κpc), the share of alternative farming
increases. From the threshold ¯q > 2pz
κpc, using synthetic fertilizer in conventional production
becomes economically beneficial. As a consequence, any further soils’ quality increase results
in the development of high-input conventional farming at the expense of both alternative and
synthetic-free conventional farming. Finally, for a very large value of ¯q, farmers are all engaged
in conventional production and mainly use synthetic fertilizer.
Figure 3.5 – The regional farming pattern at the equilibrium
85
3.4 Agricultural pattern and regional welfare
We now evaluate the optimality of the equilibrium farming pattern. We start by assessing
the impact of alternative farming on the indirect utility of urban households. In a second step,
we define the farming pattern that maximizes the regional social welfare and we discuss the
conditions for which fostering alternative farming leads to a welfare improvement.
3.4.1 Urban households utility and alternative farming.
Let Vube the indirect utility of a urban household living in the region given by :
Vu(λa) = wu−R∗
u(x)
δ−tux+Q+αc−pc−γ¯qκλaλr
λu21−γ2
2
| {z }
CS c
+¯qκλaλr
λu21−γ2
2
| {z }
CS a
(3.23)
CScand CSaare the consumers’ surpluses evaluated at the equilibrium prices associated
with the consumption of the conventional and the alternatively-grown goods, respectively. For
the range of values of pcthat allows the individual demand of conventional goods qd
cto be
positive, we have ∂CSa
∂λa>0, ∂CSc
∂λa<0 and ∂2C Sa
∂λ2
a
>∂2CSc
∂λ2
a
.
Replacing R∗
u(x) by its expression in (3.23) and rearranging, the indirect utility becomes :
Vu(λa) = C−¯qκ ta−tc
2δ+(αc−pc)γ1−γ2
λu!λrλa+¯q2κ21−γ4λ2
r
2λ2
u
λ2
a(3.24)
where Cis a constant that only depends on exogenous parameters. The relationship between
Vu(λa) and λabeing convex, the share of alternative farming that would maximize the indi-
rect utility of urban households is a corner solution. Stated differently, the utility of urban
households is maximized under full specialization only, be it either alternative or conventional.
Figure 3.6 depicts the relationship between the indirect utility of urban households and
the level of urbanization. The plain and the dashed lines represent respectively the cases
where the regional agriculture is exclusively alternative (λa= 1) and exclusively conventional
(λa= 0). As seen from (3.24), Vu|λa=0 decreases at a constant rate of −tu
2δwhile Vu|λa=1 describes
an inverted N-shaped curve. Furthermore, since lim
λu→0Vu|λa=1 = +∞and lim
λu→+∞(Vu|λa=0 −
Vu|λa=1 ) = ¯qκ(ta−tc)λr
2δ>0, the two curves always intersect once and only once, implying that
alternative farming improves the utility of urban households only in regions hosting a city not
too crowded (i.e. λu<˜
λu).
86
Figure 3.6 – Urban households’ utility under fully-alternative and fully-conventional farming patterns.
From the urban households standpoint, alternative farming has two opposite effects. On
the one hand, more farmers involved in alternative production implies both a lower price
and a higher individual consumption level, leading to a larger consumers’ surplus. On the
other hand, alternative farming causes a rise in urban land prices; differentiating R∗
u(¯xu) with
respect to λain (3.18), we show that the marginal opportunity cost of urban land –that is,
the extra land cost that urban households have to pay for each additional alternative farmer–
is given by ¯qκ(ta−tc)λr
2δ. Thus, alternative farming can either improve or reduce the urban
households’ utility, depending on which effect outweighs the other. Since the land costs plays
with even more weight in highly urbanized regions, the development of alternative farming
near large cities leads to a rise in urban land prices that cannot be positively compensated
by the consumers’ surplus. This explains why promoting alternative farming in the most
urban-crowded may be detrimental to urban households.
3.4.2 The welfare-maximizing solution
We finally broaden the discussion on the optimality of the market equilibrium by including
the farmers’ well-being. To this end, we define the regional social welfare function as :
SW (λa) = λuVu(λa) + λaλrπ∗
a(λa) + (1 −λa)λrπ∗
c(λa) (3.25)
with ∂2SW
∂λ2
a
<09.
9. Recalling that alternative and conventional profits are respectively decreasing and increasing with the
share of alternative farmers and knowing that π∗
a(0) > π∗
c(0), we can show that SW is a concave function of
87
Solving ∂SW
∂λa= 0 for λa, the optimal share of farmers involved in alternative farming is
given by :
λo
a=
αa−γ(αc−pc)(2 −γ2)−taλu
2δ−pz
¯qκ +p2
c¯qκ
4pz+tcλu
2δ+λr
2
λr¯qκ(1−γ2)2
λu+ta(3.26)
Comparing (3.21) to (3.26), we can derive the conditions under which the market lead to
a farming pattern close to the optimal solution. As for the equilibrium, we show in Appendix
D that the shape of the relationship between the optimal farming pattern and the size of the
urban population (λu) is concave. Therefore, plotting λ∗
aand λo
aas a function of λu, curves
can either cross once, twice or never cross.
Figure 3.7 – Equilibrium and Optimal farming pattern in function of the urban population’ size
From (3.21) and (3.26), we get the following properties :
lim
λu→+∞λo
a=−∞ and lim
λu→+∞λ∗
a=−∞ (3.27)
lim
λu→0λo
a= 0 and lim
λu→0λ∗
a= 0 (3.28)
lim
λu→+∞(λo
a−λ∗
a) = +∞(3.29)
lim
λu→0∂λo
a
∂λu−∂λ∗
a
∂λu>0 (3.30)
We derive from (3.27) that the market always leads to an optimal situation for the most-
urbanized regions, where no alternative farming can develop. Moreover, (3.28) and (3.30)
suggest that the market never allows enough alternative farming to establish itself in the
regions hosting a very small city. This situation can even be observed for intermediate and
λa.
88
large cities if the marginal opportunity cost of urban land is sufficiently low (see Fig.3.7.1).
On the contrary, if this cost is high, we have previously shown that alternative farming is
detrimental to the utility of large-cities dwellers. In this situation, the two curves intersect
and we draw from (3.27)–(3.30) that λo
ais always higher than λ∗
afor small values of λuand
lower than λ∗
afor intermediate values of λu. Hence, from the welfare standpoint, alternative
farming is not enough developed in low urbanized regions and too much developed in high
urbanized regions (see Fig.3.7.2) 10.
Proposition 5 Fostering the development of alternative farming always leads to a welfare
improvement in low-urbanized regions. This result can be extended to more urbanized regions
provided that the marginal opportunity cost of urban land remains low enough.
3.5 Does alternative farming development lead to a decrease in GHG emissions ?
Suppose the region seeks to meet its population’ food needs whilst reducing the GHG
emissions stemming from the whole supply chain. As emissions come from both production
and transportation, the region faces a trade-off between (i) fostering alternative farming so as
to lessen the emissions due to the use of synthetic fertilizer and (ii) sharing its land between
alternative and conventional production so as to curb the emissions due to the transportation
flows.
In this section, we assess the way the emissions from the regional food supply vary accor-
ding to the share of alternative farming and we determine the conditions for which, modifying
the equilibrium pattern so as to improve the social welfare contributes to a concomitant de-
crease in GHG emissions. It is worth noting that the emissions accounting we propose in this
work differs somewhat from an environmental assessment of the food supply system of the city,
as we do not include the emissions due to conventional goods grown abroad and consumed in
the region. Although analytically feasible, doing so would require additional calculations to
determine the share of goods produced and consumed locally and would, thereby, complicate
10. Note that λo
aand λ∗
acan also intersect twice before crossing the x-axis. In this case, alternative farming
is not enough developed low urbanized and high urbanized regions, and too much developed in regions hosting
an intermediate-size city.
89
the analysis. Instead, we focus on the volume of GHG emissions at the regional scale; we
account for the emissions stemming from conventional and alternative production, food trans-
portation within the region but also for the emissions due to incoming or out-coming flows
in conventional goods (i.e. inter-regional trade, be it exports or imports). Besides, in order to
avoid double-counting of emissions, we assume that the region takes into account only half of
the inter-regional trade flow. Hence, summing the flows on all the regions that belong to the
geographical unit we consider would give the aggregate level of emissions from the whole food
supply chain.
3.5.1 Synthetic fertilizer use and agricultural production
As previously mentioned and illustrated by Figure 3.2, promoting alternative farming does
not necessarily involve less fertilizer. According to the characteristics of the region, there may
be cases where converting to alternative practices does not provide any GHG benefit in the
production stage. This is readily verified by calculating the use of synthetic fertilizer and the
supply in conventional goods in the region. Using (3.12) and (3.13), we have :
Z=
(¯qκpc+ 4pz)(¯qκpc−2pz)2
6¯qκp2
ztc
if λa<˜
λa
p2
c−4p2
z
¯q2κ2+tc(1 −λa)λr
2tc(1 −λa)λr
6−pc(1 −λa)λr
4p2
z
¯q2κ2if λa>˜
λa
(3.31)
and
Qs
c= 2 Z¯x
ˆx
qs∗
c(x)dx =
(¯qκpc−2pz)2
2pztc
+ ¯qκ(1 −λa)λrif λa<˜
λa
¯q2κ2
pzpc−tc(1 −λa)λr
4(1 −λa)λr
2if λa>˜
λa
(3.32)
As suggested by (3.31), a decrease in conventional farming results in a lower use of synthetic
fertilizer only if the share of alternative farming is already sufficiently high (i.e. λ∗
a>˜
λa), or
if the conversion from conventional to alternative farming is large enough. Regarding the
regional production in conventional goods, it decreases linearly with the share of alternative
farming as long as the conversion involves conventional farmers who do not use synthetic
fertilizer. Then, from λ∗
a>˜
λa, the production falls more rapidly with increasing λa.
90
For simplicity, we limit the rest of the analysis to the most relevant and realistic case, that
is the situation where all the conventional farmers use synthetic fertilizer to produce their
goods (λa>˜
λa). Hence, assuming that GHG emissions are linear with the production, the
flow of emissions arising from food production is given by :
EP(λa) =eaQs
a+ecQs
c
=eaλaλr¯qκ +ec
¯q2κ2
pzpc−tc(1 −λa)λr
4(1 −λa)λr
2( with λa>˜
λa)
(3.33)
where ecand eaare the emission factors associated with the conventional and the alternative
practices, respectively. ecis assumed to be higher than ea. As for the production in conven-
tional goods, the emission flow stemming from agricultural production in the region decreases
concavely as the share of alternative farming increases (Fig. 3.9.2).
3.5.2 Intra-regional food transportation and trade
Intra-regional food transport Alternative goods are transported to the central market located
at x= 0 by each farmer involved in alternative production. Recalling that alternative fields
are located from ¯xuto ˆx, the sum of alternative freight flows within the region is given by :
Ta= 2¯qκ Zˆx
¯xu|x−¯xu|dx +λ∗
aλr¯xu=λaλr
2λaλr
2+λu
δ¯qκ (3.34)
Not surprisingly, intra-regional transport flows of alternative goods increase with the regional
share of alternative farming (Fig. 3.8.2).
In conventional farming, transportation is organized in two stages. In a first step, farmers
carry their goods to the regional grain elevator located at ˆx:
Tx→ˆx
c= 2 Z¯x
ˆx
qs∗
c(x)|x−ˆx|dx =3pc−tc¯qκ(1 −λa)λr
6pzׯqκ(1 −λa)2λ2
r
4(3.35)
The production from all the conventional farmers operating in the region is then collected
and bundled in order to be sent, in a second step, to the central market :
Tˆx→CB D
c=Qs
cˆx=¯q2κ2
pzpc−tc(1 −λa)λr
4(1 −λa)λr
2λu
δ+λaλr(3.36)
Because fostering the development of alternative farming has an impact on both the dis-
tance covered by farmers and the volume of agricultural goods transported from farms to
91
the CBD, its final effect on intra-regional conventional transportation is ambiguous. Focusing
on the volume effect first, raising the share of alternative farmers implies mechanically less
conventional production. Recalling that λa>˜
λa, the volume of goods transported decreases
concavely as λaincreases. Regarding the distance covered, trips decrease from conventional
farms to the grain elevator, but increase from the elevator to the CBD. In the end, since both
the volume and the distance fall in the first step of the conventional freight, Tx→ˆx
cis always
decreasing with the share of alternative farming. In contrast, Tˆx→C BD
cmay either increase or
decrease, depending on which effect outweighs the other (Fig. 3.8.1).
Inter-regional food trade. We finally account for the trade in conventional goods between
the region and its trade partner. The perfect competition on the conventional agricultural
markets implies unidirectional flows ; the region is either importer, exporter, or self-reliant
and the volume of trade flows can be expressed as :
|Qs
c−Qd
c|=Z¯x
ˆx
qs∗
c(x)dx −qd
cλu(3.37)
Letting νbe the distance between the region and its trade partner, the inter-regional flow
of conventional goods is such that
TT rade
c=
¯q2κ2[4pc−tc(1 −λa)λr](1 −λa)λr
8pz−αc−pc−γ¯qκλaλr
λuλuνif λa< λX|M
a
0 if λa=λX|M
a
αc−pc−γ¯qκλaλr
λuλu−¯q2κ2[4pc−tc(1 −λa)λr](1 −λa)λr
8pzνif λa> λX|M
a
(3.38)
where
λX|M
a= 1−2¯qκpc−4γpz
¯qκtcλr
+2pc
tcλrs1−2γpz(2pc−tcλr)
¯qκp2
c
+4γ2p2
z
¯q2κ2p2
c−2(αc−pc)pztcλu
¯q2κ2p2
c>˜
λa
(3.39)
is the alternative-conventional distribution for which the region is self-reliant in conventional
goods.
92
As illustrated by Figure 3.8.3, the impact of farming conversion on inter-regional flows
depends on the trade status of the region : if the region is exporter, promoting alternative
farming leads to decrease the trade flows since less farmers in the conventional activity is
equivalent to less regional production (Equation (3.38.1)). On the contrary, if the region is
importer, raising the share of alternative farming would widen the gap between the regional
supply and the demand, inducing a rise in inter-regional trade flows (Equation (3.38.3)).
Figure 3.8 – GHG emissions from food transportation
Emissions from food delivery We finally convert all these flows (expressed in weight×distance)
into emissions. Let eih,ebh and etbe the emission factors associated with individual haulage,
bundling haulage, and inter-regional trade flows respectively. Consistently with the reality, we
further assume that the transport modes used for consolidated shipments and inter-regional
trade are less emission-intensive than that used for individual transportation (i.e. ebh < eih
and et< eih). Using (3.34)–(3.38), the total emissions stemming from food transportation
are :
ET(λa) = eih[Ta(λa) + Tx→ˆx
c(λa)] + ebhTˆx→C BD
c(λa) + et
TT rade
c(λa)
2(3.40)
3.5.3 Emissions from the regional food supply chain
Emissions and agricultural pattern Combining (3.33) and (3.40), we finally obtain the total
emissions stemming from the regional food supply system. For the sake of readability, its
expression has been reported in Appendix E and we only discuss its graphical representation
provided in Figure 3.9.
As illustrated by the graphs, fostering alternative farming could alternately induce less or
more emissions at the regional scale. The first graph illustrates the case where emissions from
inter-regional trade are negligible. Under this condition, the emissions due to conventional
93
goods imports are more than compensated by the cut in emissions stemming from the lower
use of synthetic fertilizer, so that the development of alternative farming always leads to a
decrease in GHG emissions (Fig. 3.9.1). By contrast, if trade in conventional goods accounts
for a significant part in emissions, the region is wise to limit inter-regional flows and even tend
toward self-reliance. As a consequence, promoting alternative farming would induce lower
emissions as long as the region is exporter in conventional goods (Fig. 3.9.2). In this situation,
fostering the development of alternative farming so as to improve the regional welfare induces
a concomitant cut in GHG emissions only provided that λ∗
a< λo
a< λX|M
a.
Figure 3.9 – Total GHG emissions from the regional food supply
Emissions and urbanization As regards to the impact of urbanization, we can show that emis-
sions are always increasing with the size of the urban population when the region is importer,
and can either increase or decrease otherwise. The effect of λuon emissions is twofold, playing
both on intra-regional flows through the extent of the urban area, and on inter-regional trade
through a demand effect. Hence, comparing the emissions of two exporting regions hosting
a city of different size, the impact of alternative farming development is not clear; on the
hand, it would increase the emissions due to intra-regional flows to a greater extent in the
most-urbanized region. On the other hand, the emissions stemming from inter-regional trade
would also decrease more significantly in this region. The total effect is thus always conditional
upon the relative importance of these two variations.
94
3.6 Assessing the impact of an energy price rising.
We finally use our model to evaluate the effects of a rise in energy prices on the regional
farming pattern at the equilibrium. To do so, we assume that such an increase can affect both
the fertilizer price (pz) and the transportation costs (tcand ta). Moreover, we suppose that
technology is given, so that farmers can neither avoid nor lessen the impact of the increase in
energy prices by changing their production behavior.
3.6.1 The impact of a fertilizer price rising
Suppose that the energy price rising leads to increase the fertilizer price (pz). Using the
results from Section 1 and 2, a basic comparative static analysis allows to draw the implications
on the equilibrium farming pattern.
Assuming first that ¯q > 2pz
pcκ, we know from (3.15) that farmers distribute themselves
between alternative production, intensive conventional production, and synthetic-free conven-
tional production. Starting from this farming pattern, any rise of pzleads to an increase of
λ∗
a– as π∗
aincreases while π∗
cstays constant (Eqs. (3.19) and (3.20)) – and consequently, to
an increase of the equilibrium value of ˆx. In the same time, as pzrises, the equilibrium value
of ˜xdiminishes, so that the spatial extent of lands where the use of synthetic fertilizer is
economically viable (˜x−ˆx) becomes smaller. Furthermore, as producing goods becomes more
expensive, conventional farmers tend to lessen their use of synthetic fertilizer whatever their
location (Eq. (3.12)). In the end, the regional use of fertilizer in conventional farming decreases
because of the reduction of both the individual use z∗(x) and the share of conventional farmers
using fertilizer λc|z>0.
The share of alternative farming keeps rising with pzand achieves a maximum value when
¯q=2pz
pcκ. From this specific value, any further rise in pzleads to a decrease in λ∗
a; alternative
farmers convert to synthetic-free conventional production.
Proposition 6 A rise in the synthetic fertilizer price would favor the conversion to alternative
farming while transforming conventional farming from high-input to reduced-input practices.
95
Figure 3.10 – The impact of a fertilizer price rising on the equilibrium farming pattern.
3.6.2 The impact of an agricultural transport cost rising
Suppose now that the energy price rising results in higher costs of agricultural transpor-
tation for both conventional and alternative farmers (i.e. taand tc). According to (3.21), the
equilibrium share of alternative farming is decreasing with the transportation cost ta. Hence,
any measure involving a rise in tainduces a decrease in λ∗
a. This results stems from the fact
that, even though the rise in transportation costs affects both conventional and alternative
farmers, profits in conventional activity decrease less sharply than those in alternative farming.
Regarding the conventional activity, we easily show from (3.12) that farmers use less syn-
thetic fertilizer as tcincreases ; since transporting goods becomes more expensive, conventional
farmers have incentives to maintain their production qs
c(x) at a low level whatever their loca-
tion x. In the same time, the share of farmers using fertilizer λc|z>0decreases as a result of the
transportation cost increase. Hence, a transportation costs rising has the effect of reducing
both the share of alternative agriculture and that of conventional agriculture using fertilizers.
For a very sharp cost increase, agriculture in the region becomes predominantly synthetic-free
conventional farming (λc|z=0 →1).
3.7 Conclusion
Feeding the population in a sustainable way has emerged as a growing concern for public
authorities in most of developed countries. Although the trade-off is quite trivial, solutions
96
to implement are not nearly that obvious. First, because current food supply chains have
reached a high level of sophistication. Hence, when considering the environmental impact of
food travels, the question of ”how far ?” is as important as that of ”how ?”. Second, because of
the tight economic linkages between countries, implying that addressing a sustainability issue
occurring at a regional scale requires to adopt a much broader approach than a local-focused
one. Finally, because one viable solution for some regions may not be generalizable to all,
making it necessary to take into account economic and demographic characteristics such as
the level of urbanization or the regional soils’ quality.
In this chapter, we have developed a model that allows accounting for the land alloca-
tion between conventional and alternative farming systems. Focusing on the market outcome,
we find that, even though urbanization may promote the development of alternative goods
production through a market size effect, it is more likely to foster a growth in conventio-
nal agriculture ; given our spatial specification, the share of farmers involved in alternative
agriculture tends to decline significantly, due to urban pressure and a fiercer competition
on land market, making its development more likely in regions hosting an intermediate-size
city. Regarding the optimality of the farming pattern at the equilibrium, we highlight that
fostering the development of alternative farming always leads to a welfare improvement in
low-urbanized regions. Moreover, we show that this result can be extended to more urbanized
regions provided that the marginal opportunity cost of urban land remains low enough.
Finally, when looking at the environmental aspects, we find that fostering alternative
farming does not necessary lead to a cut in GHG emissions. In particular, we stress that
promoting alternative farming when inter-regional trade in conventional goods accounts for a
large part in emissions may increase the emissions through spillover effects ; if the region is
already importer in conventional goods, raising the share of alternative farming will strengthen
the food dependency of the region and result in a rise in emissions due to trade.
97
3.8 R´ef´erences
Beckmann, M. J. (1972). Von th¨
unen revisited : a neoclassical land use model. The Swedish
Journal of Economics, pages 1–7. 79
Bellows, A. and Hamm, M. (2001). Local Autonomy and Sustainable Development : Testing
Import Substitution In Localizing Food Systems. Agriculture and Human Values, 18 :271–
284. 75
Born, B. and Purcell, M. (2006). Avoiding the Local Trap : Scale and Food Systems In
Planning Research. Journal of Planning Education and Research, 26 :195–207. 75
CEC (2004). European Action Plan for Organic Food and Farming. Technical report,
European Commision. http://ec.europa.eu/agriculture/organic/files/eu-policy/
action-plan/working_doc_en.pdf.79
Deutsch, L., Dyball, R., and Steffen, W. (2013). Feeding Cities : Food Security and Ecosystem
Support in an Urbanizing World. In Elmqvist, T., Fragkias, M., Goodness, J., G¨
uneralp, B.,
Marcotullio, P. J., McDonald, R. I., Parnell, S., Schewenius, M., Sendstad, M., Seto, K. C.,
and Wilkinson, C., editors, Urbanization, Biodiversity and Ecosystem Services : Challenges
and Opportunities, pages 505–537. Springer Netherlands. 74
Edwards-Jones, G., Mila i Canals, L., Hounsome, N., Truniger, M., K. G., Hounsome, B.,
Cross, P., York, E., Hospido, A., Plassman, K., Harris, I., Edwards, R., Day, G., Tomos,
A., Cowell, S., and Jones, D. (2008). Testing the Assertion that Local Food Is Best :
The Challenges of an Evidence-Based Approach. Trends in Food Science and Technology,
19 :265–274. 75
Halweil, B. (2002). Home grown : The case for local food in a global market, volume 163.
Worldwatch Institute. 74
Hinrichs, C. (2003). The practice and politics of food system localization. Journal of Rural
Studies, 19(1) :33 – 45. 75
98
Kloppenburg, Jack, J., Hendrickson, J., and Stevenson, G. (1996). Coming in to the foodshed.
Agriculture and Human Values, 13(3) :33–42. 74
Niggli, U., Fliessbach, A., Hepperly, P., and Scialabba, N. (2009). Low Greenhouse Gas Agri-
culture : Mitigation and Adaptation Potential of Sustainable Farming Systems. Technical
report, FAO. ftp://ftp.fao.org/docrep/fao/010/ai781e/ai781e00.pdf.74
Peters, C. J., Bills, N. L., Wilkins, J. L., and Fick, G. W. (2009). Foodshed Analysis and Its
Relevance to Sustainability. Renewable Agriculture and Food Systems, 24(01) :1. 74
Pimentel, D., Hepperly, P., Hanson, J., Douds, D., and Seidel, R. (2005). Environmental, Ener-
getic, and Economic Comparisons of Organic and Conventional Farming Systems. BioS-
cience, 55(7) :573 – 582. 74
Pirog, R., Van Pelt, T., Enshayan, K., and Cook, E. (2001). Food, fuel, and freeways : An iowa
perspective on how far food travels, fuel usage, and greenhouse gas emissions. Technical
report, Leopold Center for Sustainable Agriculture. 75
Singh, N. and Vives, X. (1984). Price and quantity competition in a differentiated duopoly.
The RAND Journal of Economics, pages 546–554. 77
Appendix A : Fertilizer use in conventional farming
Figure 3.11 – Variation of synthetic fertilizer use in space
99
Appendix B.1 : Equilibrium land rent
Bid rents are derived by equating the location costs (transportation and land cost) within
each area. For conventional farmers, the equilibrium land rent must solve ∂πc(x)
∂x= 0 or,
equivalently
∂Rc|z>0(x)
∂x +¯q2κ2tc(pc −tc|x−ˆx|)
2pz
= 0 if x < ˜x
∂Rc|z=0 (x)
∂x + ¯qκtc= 0 if x≥˜x
As a consequence, the bid rents of conventional farmers are such that
Rc|z>0(x) = ¯rc|z>0−¯q2κ2tc(pc −tc|x−ˆx|)
2pz
xif x < ˜x
Rc|z=0 (x) = ¯rc|z=0 −¯qκtcxif x≥˜x
where ¯rc|z>0and ¯rc|z=0 are constants. Similarly, the equilibrium land rent for alternative far-
mers must satisfy ∂πa(x)
∂x= 0 or, equivalently, ∂Ra(x)
∂x+ ¯qκta= 0, which solution is Ra(x) =
¯ra−¯qbarqκtax, where ¯rais a constant. Assuming that Ra(x)> Rc|z>0(x) for x∈[0; ˆx[ the
(right-hand side) conventional farmers locate in the land strip ]ˆx, ¯x] where ˆxis the boundary
between alternative and conventional fields, and ¯x=λu/(2δ) is the region limit, whereas al-
ternative farmers locate in ]¯xu,ˆx]. Because the opportunity cost of land is equal to zero, the
land rent at the region limit is zero, i.e. R∗
c(¯x) = 0. This implies that ¯rc|z=0 = ¯qκtc¯x.
Land rents of conventional farmers using synthetic fertilizer and those who do not use
fertilizer must be equal at ˜x(i.e., Rc|z>0(˜x) = Rc|z=0 ( ˜x)), so that ¯rc|z>0= ¯qκtc(¯x−˜x) +
¯q2κ2tc˜x[pc−tc(˜x
2−ˆx)]
2pz. In the same way, land rents between conventional farmers and alternative
farmers must be equal at ˆx(i.e., Ra(ˆx) = Rcz (ˆx)), so that ¯ra= ¯qκtaˆx+ ¯qκtc(¯x−˜x) +
¯q2κ2tc[2pc−tc(˜x−ˆx)]( ˜x−ˆx)
4pz.
As for urban households, they choose their location so as to maximize their utility under
the budget constraint. Because of the fixed lot size assumption, the value of the consumption of
the non-spatial goods qcpc+qapa+Qat the residential equilibrium is the same regardless of the
urban worker’s location. Denoting by tuthe commuting cost, the equilibrium urban land rent
must solve ∂Vu(x)
∂x= 0 or, equivalently, ∂Ru(x)
∂x+δtu= 0, which solution is Ru(x) = ¯ru−δtux,
where ¯ruis a constant. At the equilibrium, urban and agricultural land rents must be equal
at the city limit ¯xu, leading to ¯ru=δtu¯xu+Ra(¯xu). As a result, the equilibrium land rent in
100
the region is given by :
R∗(x) =
R∗
u(x) =δtu|¯xu−x|+ta(ˆx−¯xu)¯qκ +¯q2κ2(pc−tcˆx)2
4pz
+pz−(pc−tc¯x) ¯qκ if 0 < x ≤¯xu
R∗
a(x) =ta(ˆx−x)¯qκ +¯q2κ2(pc−tcˆx)2
4pz
+pz−(pc−tc¯x) ¯qκ if ¯xu< x ≤ˆx
R∗
c|z>0(x) = ¯q2κ2(pc−tcx)2
4pz
+pz−(pc−tc¯x) ¯qκ if ˆx<x≤˜x
R∗
c|z=0 (x) =tc|¯x−x|¯qκ if ˜x < x < ¯x
Appendix B.2 : Intra-regional spatial patterns
Let xu|a,xu|cand xa|cbe the abscissa of the intersection point between R∗
u(x) and R∗
a(x),
R∗
u(x) and R∗
c|z>0(x), and R∗
a(x) and R∗
c|z>0(x), respectively. Since R∗
c|z>0(x) is a convex func-
tion of x, alternative and conventional bid rents can intersect once or twice. Hence, two spatial
configurations can occur :
i) Alternative farming develops near the urban fringe which occurs if R∗
c|z>0(0) < R∗
a(0) (im-
plying that R∗
a(x) and R∗
c|z>0(x) intersect once) or, if the first intersection between R∗
a(x) and
R∗
c|z>0(x) occurs before the intersection between R∗
u(x) and R∗
a(x) (i.e. x1
a|c< xu|a< x2
a|c).
ii) The land allocated to alternative farming is enclosed in the conventional farming area which
occurs if R∗
c|z>0(0) > R∗
a(0) and xu|a< x1
a|c< x2
a|c.
From these conditions, we draw that alternative farming takes place at the city boundary
provided that x1
a|c< xu|a< x2
a|cwhich leads λa<4(2pzta−pc¯qκtc)
¯qκt2
cλr.
Appendix C : The agricultural distribution at the equilibrium
Profits in alternative and conventional farming are given by :
π∗
a=p∗
a−taλu
2δ+λaλr
2−(¯qκpc−2pz)2
4¯qκpz−(1 −λa)λr
2tc¯qκ
π∗
c=p∗
c−tc
(1 −λa)λr
2¯qκ
with ∂π∗
a
∂λa<0 and ∂π∗
c
∂λa>0. At the equilibrium, the farmers distribution (λ∗
a) is such that
profits in conventional and alternative farming are the same. Solving π∗
a=π∗
cleads to :
λ∗
a=
αa−γ(αc−pc)−taλu
2δ−pz
¯qκ +p2
c¯qκ
4pz
λr¯qκ1−γ2
λu+ta
2(3.41)
101
Figure 3.12 – Net incomes differential and equilibrium
From (3.41), we derive the conditions on parameter tafor λ∗
ato be positive and lower than
1 :
λ∗
a>0 if ta< ta≡
αa−(αc−pc)γ−pz
¯qκ +p2
c¯qκ
4pz
λu
2δ
λ∗
a<1 if ta> ta≡
αa−(αc−pc)γ−pz
¯qκ +p2
c¯qκ
4pz+¯qκ(1−γ2)λr
λu
λr
2+λu
2δ
(3.42)
Appendix D : The optimal farming pattern
Solving ∂SW
∂λa= 0 for λa, the optimal share of farmers involved in alternative farming is
given by :
λo
a=
αa−γ(αc−pc)(2 −γ2)−taλu
2δ−pz
¯qκ +p2
c¯qκ
4pz+tcλu
2δ+λr
2
λr¯qκ(1−γ2)2
λu+ta(3.43)
Let denote by Noand Dothe numerator and the denominator of λo
a. Since Do>0, we
posit No>0, as the pertinent range for the study of λo
ais [0; 1]. Recalling ta> tc, we get
from (3.43)∂No
∂λu<0, ∂Do
∂λu>0, ∂2No
∂λ2
u
= 0 and ∂2Do
∂λ2
u
<0 so that
∂2λo
a
∂λ2
u
=∂2Do
∂λ2
u×No+ 2 ×∂Do
∂λu×∂No
∂λu
+∂2No
∂λ2
u×Do<0 (3.44)
As for the equilibrium, the optimal share of alternative farming is concavely related to the
urban population’ size.
102
Appendix E : The GHG emissions from the regional food supply chain
Combining (3.33) and (3.40), the total GHG emissions are given by :
E(λa) =ea(¯qκλaλr) + ec¯q2κ2
pzpc−tc(1 −λa)λr
4(1 −λa)λr
2+
eih ¯qκ λ2
aλ2
r
4+ ¯qκ pc
2pz−tc(1 −λa)λr
6pz(1 −λa)2λ2
r
4+λu
2δ¯qκλaλr+
ebh ¯q2κ2
pzpc−tc(1 −λa)λr
4(1 −λa)λr
2λaλr
2+λu
2δ+
et
2
¯q2κ2
pzpc−tc(1 −λa)λr
4(1 −λa)λr
2−(αc−pc)λu+γ¯qκλaλrν
(3.45)
with λa>˜
λa.
TaTx→ˆx
cTˆx→CB D
cTT rade
λa↑ ↓ ↑ if λa< λˆx→C BD
a↓if λa< λX|M
a
↓if λa> λˆx→C BD
a↑if λa> λX|M
a
λ2
a+ + - -
λu+ 0 + +
λaλu+ 0 - 0
Tableau 3.1 – Variations of transportation flows with respect to alternative farming share (λa) and urbaniza-
tion (λu).
where
λˆx→CB D
a=2
3+4
3λr
spc
tc−δλr+λu
4δ2
+pc(δλr+λu)
4tcδ−pc
tc
and
λX|M
a= 1 −2 ¯qκpc−4γpz
¯qκtcλr
+2pc
tcλrs1−2γpz(2pc−tcλr)
¯qκp2
c
+4γ2p2
z
¯q2κ2p2
c−2(αc−pc)pztcλu
¯q2κ2p2
c
Appendix F : Endogenizing the regional grain elevator location
For simplicity, we have assumed that the grain elevator was located at the boundary
between alternative and conventional areas ˆx. In this appendix, we release this assumption
and we briefly discuss the implications on the equilibrium pattern.
103
λa
Ta
Tx→ˆx
c
Tˆx→CB D
c
TT rade
ET
λˆx→CB D
aλX|M
a
+ + +
− − −
+− −
− − +
− − +
Tableau 3.2 – Variations of transportation flows with respect to alternative farming share (λa) for low-
urbanized regions
λa
Ta
Tx→ˆx
c
Tˆx→CB D
c
TT rade
ET
λX|M
aλˆx→CB D
a
+ + +
− − −
+ + −
−+ +
−+ +
Tableau 3.3 – Variations of transportation flows with respect to alternative farming share (λa) for high-
urbanized regions
Suppose that the transportation in the conventional farming is organized by a monopo-
listic logistics firm. This firm charges farmers for transporting goods from their farm to the
grain elevator, and incurs a cost of ηtcby unit of product and distance to ship the collected
production from the elevator to the CBD. Hence, denoting by xcthe location of the grain
elevator, the profit of this firm is given by :
πL=tcZ¯x
ˆx|x−xc|dx −ηtcxcZ¯x
ˆx
qs∗
c(x)|x−ˆx|dx (3.46)
The firm chooses the location of the elevator so as to maximize its profit (3.46). Substituting
ˆxand ¯xby their respective expression and solving ∂πL
∂xc= 0 for xcyields :
xc= ˆx− pc+2pz
¯q2κ2η
2tc
+(3λa−1)λr+2λu
δ
8!<ˆx(3.47)
From (3.47), we show that endogenizing the location of the elevator leads to decrease the
profits of conventional farmers, as the distance they have to cover to bring their production
104
to the elevator is larger than |x−ˆx|.
Regarding the equilibrium farming pattern, this new location may have two major conse-
quences. First, since profits in the conventional farming are lower for every location xin the
region, we might expect a higher equilibrium share of alternative farming whatever the set
of parameters’ values. Second, as the cost of transportation in conventional farming now de-
pends on the share of alternative farming λa, the profit differential between alternative and
conventional farming is no longer linear. Indeed, carrying on the calculations for this new
elevator’ location, we can show that profits in conventional farming are now decreasing with
the share of alternative farming while those of alternative farmers are concavely related with
λa. Consequently, the profit differential is concave and there can be either one, two or no
equilibrium. Moreover, in the “two equilibria” case, only the second one is stable.
105
Chapitre 4
Direct Selling Farming Under
Varying Spatial Externalities
In this chapter, we develop a spatial economic model which takes into account the ex-
ternality of urban pollution on agricultural yields. We study how the proximity to cities
affects the decision of farmers to enter the direct selling market and therefore food diver-
sity, as well as the quality of the agricultural goods supplied to consumers. We highlight
that direct selling farming is more likely to provide a wide range of varieties when located
in a region hosting an intermediate-size city, the exposure to varying spatial externali-
ties implying that, in highly urban crowded regions, only the most productive farmers
can stay on direct selling market. Additionally, we find that the greater the variations of
urban pollution over space, the smaller the opportunities for farmers to engage in direct
selling, and the larger the quality differentiation between varieties. We finally show that
the market equilibrium always leads to a number of direct selling farmers which is too
low to fully satisfy urban households, but too much high from the farmers standpoint.
Keywords : Urban pollution, Peri-urban Farming, Land allocation
JEL Classification : F12 ; Q10 ; Q54 ; Q56 ; R12
107
4.1 Introduction
In the present context of rapid worldwide urbanization, feeding the cities in the ”Global
North” is drawing a substantial public awareness [Morgan,2014]. Evidence of this trend is
found in the growing policy support for sustainable food supply chains, combining geographical
proximity, reduced-reliance on synthetic inputs, and food quality and traceability. In the
US as in several European countries, national programs for sustainable development now
often address urban food supply, with a strong emphasis on building local alternatives (see
notably USDA [2014] for the US, Kneafsey et al. [2013] for the EU, or DGAL [2011] for
France). Initiatives of cities such as New York, Montreal, London, or Paris are among the
many examples illustrating that urban agriculture is gradually gaining ground.
However, when considering the impact of pollution stemming from urban activities on
agricultural yields, benefits local food production can be seriously questioned. As now shown
by recent research, urban pollution adversely affect agriculture in many complex ways, causing
reduced yield and quality in crops exposed to pollutants. Avnery et al. [2011] notably estimate
that reductions of global yields due to ozone exposition could reach 2% for maize, 3.9 to
15% for wheat, and 8.5 to 14% for soybean. Still focusing on ozone pollution, Holland et al.
[2006] show that the directly-induced economic consequences are far from being negligible,
establishing the losses for Europe in 2000 to 6.7 billion Euros.
In addition, undesirable environmental impacts can be expected. From a transportation-
related emissions standpoint first, yields losses are likely to create local significant imbalances
between supply and demand and may, as a result, lead some regions to source food from remote
locations. Second, if farmers located near the largest cities decide to use more synthetic inputs
in order to compensate yields’ losses, additional negative impacts on environment and goods
quality have to be considered.
In this chapter, we investigate whether direct selling farming can develop in the neighboring
of highly-crowded cities. Even though the literature on periurban agriculture is quite exten-
sive, covering diverse topics such as the impacts of sub-urbanization on agriculture [Berry,
1978], neighboring conflicts [Wu et al.,2011], or land value impacts of urbanization (Anderson
and West [2006] ; Plantinga and Miller [2001]), there is to our knowledge no theoretical for-
108
malization of the issue we propose to handle. Besides, in the existing literature, neighborhood
effects have mainly been analyzed from the environmental amenities standpoint, most of the
works focusing on the impacts of agriculture on cities but rarely the reverse.
The objective of this chapter is twofold. First, we attempt to establish the required condi-
tions under which direct selling farming can develop in the periphery of large-size cities. Se-
cond, we try to determine whether the market leads to less or more variety than the optimal
outcome.
Formally, we explore these questions by developing a spatial economic model where farmers
can choose between two types of agricultural goods : conventional goods and direct direct
selling goods. The conventional products are assumed to be homogeneous. They are grown
under perfect competition, the price of these goods being exogenously fixed and given by
the equilibrium on the global market. The direct selling goods are both horizontally and
vertically differentiated. Farmers engaged in this sector operate on a local market and face
lower competition. They have the opportunity to set their price in an optimizing way. In order
to account for these features, we suppose monopolistic competition for direct selling farming.
The framework used in this chapter also displays heterogeneity between farmers ; the
latter face spatial externalities that depend on the size of the city and that induce different
productivity levels according to their location within the region. As for the spatial aspect, the
model follows the pioneering contribution of Alonso [1964]. We consider a monocentric city
model in which urban pollution acts as a distance-dependent externality.
As in standard non-spatial model displaying monopolistic competition, we can show that
the profit of farmers involved in direct selling rises as the size of the population increases.
However, when accounting for the spatial externalities related to the city size, the relationship
and therefore, the incentives for farmers to engage in direct selling farming, become more
complex. Notably, we show that the exposure to varying spatial externalities induces that,
in highly urban crowded regions, only the most productive farmers can stay on direct selling
market. Additionally, we highlight that the greater the variations of urban pollution over
space, the smaller the opportunities for farmers to engage in direct selling, and the larger
the quality differentiation between varieties. As regards to the market outcome, we find that
109
direct selling farming is more likely to provide a wide range of varieties when located in a
region hosting an intermediate-size city. Lastly, from a welfare standpoint, we derive that the
market always provides too few varieties, this result being all the more compelling for highly
urban crowded regions.
The chapter proceeds as follows. Section 4.2 presents the model. In Section 4.3, we deter-
mine the short-run equilibrium and we deliver some findings on the way spatial externalities
affect both the direct selling and the land markets. Section 4.4 presents the long-run equili-
brium and provides some insights on the relationship between goods variety, goods quality,
and the city size. We finally discuss the conditions ensuring that fostering direct selling deve-
lopment near cities leads to a welfare improvement from the urban consumers standpoint in
Section 4.5.
4.2 The framework
Consider an economy formed by a total population exogenously split into urban and rural
households, and two sectors : a perfectly competitive sector providing a homogeneous ag-
gregate good, and an agricultural sector where farmers can choose between direct selling and
conventional market. Agricultural goods are produced using labor, land, and fertilizer. Conven-
tional farmers produce a homogeneous good under perfect competition while farmers engaged
in direct selling operate under monopolistic competition and provide a quality-differentiated
good through a short supply chain.
4.2.1 The spatial structure
The economy is formally described by a one-dimensional space made of an urban area
including a CBD and urban households’ lots, and a rural area where farmers live and produce
agricultural goods. Natural amenities are homogeneously supplied within the region. Distances
and locations are denoted by xand measured from the CBD located in the center of the region.
Without loss of generality, we focus on the right-hand side of the region, the left-hand side
being perfectly symmetrical.
The urban area is entirely used for residential purposes. Urban inhabitants are assumed
to be uniformly distributed across the city. They inelastically consume a residential plot of
110
fixed size 1
δ,δcapturing the urban density (with δ > 1). Letting λube the size of the urban
population, we get the right endpoint of the city given by
¯xu=λu
2δ(4.1)
Farmers live and produce in rural areas located at the periphery of the city. Then, assuming
that each farmer uses one unit of land to produce, the right endpoint of the region is given
by :
¯x= ¯xu+λs
r+λc
r
2.(4.2)
where λs
rand λc
rstand for the number of direct selling farmers and conventional farmers,
respectively.
4.2.2 Preferences and demand
In order to capture both the consumer’s taste for variety as in the Spence-Dixit-Stiglitz
framework, and the consumers’ relative valuation of goods’ quality, we use the utility specifi-
cation of Kugler and Verhoogen [2012]. Consumers share the same Cobb-Douglas preferences
for two types of goods ; a homogeneous aggregate good M(chosen as the num´eraire) and
agricultural differentiated products indexed by v1:
U(Q, M ) = QαM1−α(4.3)
with
Q=Zλs
r
1
θ(v)βq(v)σ−1
σdvσ
σ−1
(4.4)
and where q(v) and θ(v) stand respectively for the quantity and the quality of the variety
v, and σrepresents the elasticity of substitution between two varieties. Utility is increasing
with respect to the range of varieties λs
rand the quality. Besides, we assume 0 < β < 1 which
implies that the marginal utility of improving the quality of agricultural good is decreasing.
1. For simplicity, we assume that farmers consume a fraction of their own production and supply the
remaining.
111
Goods quality The goods supplied by direct selling farmers differ in quality θ(v). This quality,
perceived by the consumers, is assumed to be directly linked to the quantity of inputs used in
the production and can be described as follows :
θ(v) = ¯
θ
z(v)(4.5)
where ¯
θis the maximum quality level and z(v) the amount of input used to produce the
variety v.
Demand Consumers live in the urban area and work in the CBD. They bear urban costs,
given by the sum of the commuting costs and the land rent. Letting tuand Rbe the per-mile
commuting cost and the land rent respectively, these costs are such that
UC(x) = tux+R(x)
δ(4.6)
Then, denoting by Pthe price index for the range of agricultural goods supplied in the
region and wuthe urban wage, the budget constraint for any urban dweller is given by :
P Q +M=wu−UC(x) (4.7)
The individual demand for the composite good and the aggregate demand for the agri-
cultural goods are derived from the maximization of the utility (4.3) subject to the budget
constraint (4.7) :
Md=1−α
α¯wu(x) (4.8)
Qd=¯wu(x)
P(4.9)
where ¯wu(x)≡α(wu−UC(x)) is the share of the urban net income available for direct selling
goods consumption. Finally, denoting by p(v) the price of the variety vof agricultural goods
and maximizing CES sub-utilities subject to the budget constraint ¯wu=Rλs
r
1p(v)q(v)dv leads
to the following demand function for the variety v:
qd(v) = θ(v)σβ p(v)−σPσ−1λu¯wu(4.10)
with
P=Zλs
r
1
θ(v)σβ p(v)1−σdv1
1−σ
(4.11)
112
4.2.3 The direct selling sector
Spatial externalities and production Farmers produce a unique variety vusing labor, one unit
of land and an amount z(v) of input. They have to carry their production to the central
market located in the CBD, incurring costs that are increasing with the distance. These costs
–referred to as opportunity cost of transportation t(x)in the following– can be seen as units
of working-time required for shipping goods to the market and that cannot be allocated to the
production. The net labor supply of any farmer is then obtained by subtracting transportation
time from his total time available 2. Transportation therefore affects the individual production
level through a reduction of the time spent in growing agricultural goods : the farthest from
the city center, the lower the time available to grow crops, and the fewer the production. It
creates an incentive for farmers to locate close to the urban fringe and captures thus, the
opportunity cost of remoteness from the city center.
Fields located in the land strip ]¯xu,¯x] are exposed to urban pollution, causing losses in
yields that are proportional to the level of pollution encountered in each location. The source
of this pollution is located in the CBD. The pollution intensity h(x, λu) is supposed to be
increasing with the level of urban activities (hλu>0) but decreasing with respect to the
distance from the CBD (h(0, λu)>0 and hx<0). Moreover, we suppose that the level of
pollution encountered in the region in the absence of urban population is zero (h(x, 0) = 0),
and that the urban population size does not interact with the spatial diffusion of the pollution
(hx,λu= 0).
The technology The production function accounts for the effects of both the transportation
and the pollution on the total output. Denoting by ¯qthe natural ability of soils to grow crops
in the region, we define the individual production for the agricultural variety vas :
qs(v, x, λu) = ¯qz(v)×E(t(x), h(x, λu)) (4.12)
2. Note that this specification where producers allocate their working time between goods production and
another related activity is used by Lucas and Moll [2014]. In their model, firms allocate a fraction of time to
production while the remaining part is used for innovative activities.
113
where 0 < E(t(x), h(x, λu)) <1 stands for the agricultural productivity coefficient at x,
which value is influenced by the total space-related effect of location on the production level.
Formally, it encompasses the pollution externality cost and the opportunity cost of trans-
portation, that operate in opposite directions as the distance from the city center increases.
E(t(x), h(x, λu)) is decreasing with its two arguments t(x) and h(x, λu). Moreover, we posit
E(0,0) = 1 meaning that, without spatial externalities, the agricultural production is given
by the combination of soil quality and input use. In order to keep the discussion as broad as
possible, we dot not specify the shape of E(t(x), h(x, λu)). We only assume that the function
is additively separable, which implies that there is no correlation between the yields losses
stemming from the pollution and transportation time (Et,h = 0).
The marginal productivity of the input is increasing with respect to the quality of the land
and the agricultural productivity coefficient. Rewriting (4.12) so as to isolate zand setting
¯q= 1 without loss of generality, yields the quantity of inputs used by the farmer located at x
and producing the variety v:
z(v, x, λu) = qs(v)
E(t(x), h(x, λu)) with z > 0 (4.13)
We easily verify from (4.13) that supplying a large quantity of any variety valways re-
quires more inputs. Likewise, the use of the input is all the more intensive that the pollution
externality and the opportunity cost of remoteness are high. This offsetting effect lies in the
specification of the production function which allows farmers to compensate some of the yields
losses due to the space-related factors by using more input.
Productivity, distance and city size. Differentiating E(t(x), h(x, λu)) with respect to the dis-
tance from the city center xyields :
Ex≡∂E(t(x), h(x, λu))
∂x =∂E(t(x), h(x, λu))
∂t(x)
∂t(x)
∂x +∂E(t(x), h(x, λu))
∂h(x, λu)
∂h(x, λu)
∂x
=Ett0(x) + Ehhx
(4.14)
Eq.(4.14) displays the comparative effect of transportation and pollution. Locating near
the city allows to keep a high productivity since the opportunity cost of transportation is
lower but can, in the same time, diminish it because of the pollution externality. Hence, from
114
a location to the direct neighboring one, productivity will decrease if the opportunity cost
of remoteness (transportation effect Ett0(x)) outweighs the losses in crop yields due to urban
pollution (pollution effect Ehhx), and increase otherwise.
The relationship between the spatial variation of productivity and the urban population
size is given by :
Ex,λu≡∂2E(t(x), h(x, λu))
∂x∂λu
=Eh,h ×hx×hλu(4.15)
where Eh,h is the second order impact of pollution on yields losses. It can be either positive
or negative, depending on both the nature of the pollution and the type of crops considered.
The sign of (4.15) is given by the opposite sign of Eh,h : as the urban population size
grows, the impact of externalities on productivity – and therefore, the spatial heterogeneity in
agricultural production – tends to smooth over space if Eis convex in hand to intensify for
Econcave.
For simplicity of notations, we further denote E(t(x), h(x, λu)) by E(x, λu).
The market structure Direct selling farmers operates under monopolistic competition. They
supply close substitutes and are free to enter and exit the market. They neglect their mutual
strategic interdependence and act as if they were monopolists. Since each variety is produced
by a single farmer, the number of differentiated goods is given by the number of farmers
involved in direct selling and any variety vcan therefore be identified by the location xwhere
it is grown.
The profit of a farmer producing a direct selling variety at xis given by the receipts from
his sales minus a total cost which consists of a fixed cost associated with the purchase of one
unit of land, and a constant marginal cost of inputs. Hence, letting pzand R(x) be the unit
cost of the input and the unit rent of land at x, we have :
π(x, λu) = p(x, λu)×q(x, λu)
| {z }
receipts
−[R(x) + pzz(x, λu)]
| {z }
total cost
(4.16)
where q(x, λu) is the Marshallian demand for the variety produced at x, obtained by plugging
(4.13) into (4.5) and by substituting the resulting expression of θ(x, λu) into (4.10) :
q(x, λu) = ¯
θE(x, λu)σβ
1+σβ p(x, λu)−σ
1+σβ (λu¯wu)1
1+σβ Pσ−1
1+σβ (4.17)
115
Each farmer sets his price so as to maximize his profit, considering that his decision has
no impact on the other prices 3. Taking the price index Pas a constant and differentiating
π(x, λu) with respect to p(x, λu), leads to the equilibrium price of the variety produced at x:
p(x, λu) = σ
σ−1−σβ pz
E(x, λu)(4.18)
where σ > 1
1−βmust hold for p(x, λu) to be positive.
The first element of (4.18) is the monopolistic mark-up. It includes the parameter βand
increases with it, reflecting the fact that consumers value the quality of the agricultural goods.
The term in parentheses represents the marginal cost of production for the variety grown at
x. It increases with the unit cost of the input pz, but also with the urban pollution externatity
cost and the opportunity cost of transportation, highlighting the fact that farmers partially
pass on the charge of their own location costs to consumers through the productivity coefficient
E(x, λu).
p(x, λu) and E(x, λu) share similar properties regarding their variation in space. Denoting
by xaand xbtwo neighboring locations such that ¯xu< xa< xb<¯xs, we can consequently
show that p(xa, λu)< p(xb, λu) if and only if E(x, λu) is decreasing from xato xb. Hence,
provided that the opportunity cost of remoteness from the city center outweighs the yields
losses due to the pollution externality, the price of the variety grown at xawill be lower than
that produced at xb.
Using Eqs (4.5) and (4.13)-(4.18) in (4.11), we obtain the price index of agricultural goods :
P=λu¯wu
¯
θσβ
σ−1σpz
σ−1−σβ σ−1−σβ
σ−12×Z¯xs
¯xu
E(x, λu)dx−1
(4.19)
where ≡σ−1
1+σβ is the elasticity of the demand with respect to the direct selling price index.
Observe that, in the case where spatial externalities would not be considered (i.e. E(x, λu)=1
for all x) and where consumers would not value the quality of the agricultural goods (β= 0),
we recover the standard Dixit–Stiglitz framework where P=σ
σ−1pzλs
r
1
1−σ.
3. The number of competitors is assumed to be large enough so that the effect of p(x, λu) on Pcan be
disregarded.
116
Market share and competition Multiplying (4.17) by (4.18), we can derive the receipts of the
direct selling farmer located at x:
rs(x, λu) = λu¯wu
2R¯x
¯xuE(x, λu)dx ×E(x, λu)(4.20)
where the first element is common to all the farmers involved in direct selling, while the second
term is the relative location-dependent part of the receipts at x. We can then calculate the
market share defined as :
s(x, λu)≡rs(x, λu)
2R¯xs
¯xurs(x, λu)dx =E(x, λu)
2R¯xs
¯xuE(x, λu)dx (4.21)
with 0 ≤s(x, λu)≤1. It is readily shown that, without spatial externalities, direct selling
farmers have a same market share given by s=1
λs
r. The market share varies with the distance
from the city center, reflecting the fact that farmers are affected by spatial externalities at
different extents :
sx(x, λu)≡∂s(x, λu)
∂x =Ex
E(x, λu)×s(x, λu) (4.22)
The spatial variation of the market share follows that of E(x, λu) ; it is therefore decrea-
sing with the distance from the CBD if the effect of the opportunity cost of transportation
dominates that of the urban pollution externality, and increasing otherwise.
Since the nature of the competition on direct selling market depends on both the number
of farmers involved on the market (supply-side) and the urban population size (demand-side),
it is interesting to examine how the market share varies with λs
rand λu. For simplicity of
notation, the market share of the farmers located at both edges of the direct selling area
s(¯xu, λu) and s(¯xs, λu) will be denoted thereafter as ¯suand ¯s, respectively.
Differentiating the (4.21) with respect to λs
r, we obtain the variation of the market shares
value in each location with respect to the number of direct selling farmers :
sλr(x, λu) = −s(x, λu)¯s(4.23)
We get from (4.23) that the market share is always decreasing with the number of com-
petitors. Additionally, we can show that the larger the weight of the farmer located at x, the
greater his loss in market share. This implies notably that the market concentration defined
as ¯su−¯ssis always decreasing with λs
r.
117
Note that this unequivocal relationship between the market concentration and the number
of varieties holds because of the monopolistic competition ; the farmers set their price without
taking into account the weight of their decision on the sector. Consequently, by neglecting
the supply-side market size, their supply does not correctly responds to competition. With
the entry of a new competitor, they adjust their production far less than optimally needed,
leading the farmers with the highest market share to encounter a more significant decrease
of their operating income than the other farmers. Notably, the farmer located at the urban
fringe always faces a decrease in his market share larger than that located at the right-hand
side boundary. Finally, as a result of this lower operating profit, the bid of the farmer located
at the urban fringe on the land market decreases and causes the fall of the opportunity cost
of urban land.
As regards to the urban population size, differentiating s(x, λu) with respect to λuyields :
sλu(x, λu) = s(x, λu)×"|Ehhλu| R¯xs
¯xuE(x, λu)−1dx
R¯xs
¯xuE(x, λu)dx −1
E(x, λu)!+¯su
2δ#(4.24)
The first term in the square brackets captures the overall pollution intensity effect. Recal-
ling that 0 < E(x, λu)<1 for all x, we can show that R¯xs
¯xuE(x, λu)−1dx > R¯xs
¯xuE(x, λu)dx
whatever Eand , which implies that this effect at xis positive if and only if E(x, λu)>
R¯xs
¯xuE(x,λu)dx
R¯xs
¯xuE(x,λu)−1dx or equivalently, provided that the losses in aggregate receipts in direct selling
due to a rise in pollution intensity outweigh the individual losses in x.
The second term accounts for the decrease in competition between direct selling farmers,
stemming from the fact that, in a region hosting a larger city, some plots of land located at the
urban fringe are under urban use while they would be dedicated to agricultural production in
lowly-crowded regions. It is always positive but negatively correlated to the urban density.
We can state from (4.24) that the market share of a farmer located at xis positively linked
to the urban population size provided that the productivity coefficient in xis sufficiently high :
E(x, λu)>R¯xs
¯xuE(x, λu)dx
R¯xs
¯xuE(x, λu)−1dx +E(¯xu,λu)
2δ|Ehhλu|
(4.25)
Condition (4.25) is more likely to occur in regions hosting a low-density city (δlow) or,
as regards to the features of the externality, when pollution causes low yields losses (Ehlow
) and/or is weakly correlated to the urban population size (hλulow). Moreover, it is readily
118
verified that if the market share of the farmer located at ¯xsis increasing with the urban
population size, then the market share of every farmer involved in direct selling increases.
4.3 The short-run equilibrium.
We now turn to the short-run equilibrium. We determine first the spatial allocation of land
between urban households and farmers (land market equilibrium) and then, the quantity and
the quality of each variety of goods supplied in the region (direct selling market).
4.3.1 The land market
In the manner of Von Thunen, we suppose that each plot of land is allocated to the highest
bidder. The short-run equilibrium land rent is thus given by the upper envelop of bid rents,
that is :
Rsr(x) = max{Φu(x), Φs
r(x), Φs
c(x)}(4.26)
Φu(x), Φs
r(x), and Φs
c(x) being the bid land rent of urban households, direct selling farmers,
and conventional farmers, respectively. For simplicity, we further assume that the conventional
bid land rent equals to the opportunity cost of land ¯
R.
The urban bid rent Plugging (4.8) and (4.9) into (4.3) and rearranging gives the indirect
utility of urban households :
Vu(x) = α
Pα(1 −α)1−α(wu−UC) (4.27)
At the residential equilibrium, the urban bid rent Φu(x) must solve V0
u(x) = 0 or equiva-
lently, tu+Φ0
u(x)
δ= 0, which solution is given by :
Φu(x) = ¯ru−δtux(4.28)
¯rubeing a constant. Using (4.28) in (4.6), we obtain the urban net income available for direct
selling goods consumption :
¯wu(x)≡¯wu=αwu−¯ru
δ(4.29)
Observe that, because of the fixed lot size assumption, the total value of non-spatial goods
consumption at the residential equilibrium does not depend on locations ; the equilibrium value
119
of urban costs – and therefore, the share of the urban net income available for agricultural goods
consumption ¯wu– is the same across urban households.
The direct selling bid rent The farmers location choice is driven by two considerations. On the
one hand, producing goods near the urban boundary allows reducing the opportunity cost of
transportation. On the other hand, as urban activities generate pollution, locating away from
the city center allows farmers to be less affected by this externality and, therefore, to reduce
yields losses.
Plugging the price index (4.19) into the agricultural supply for variety v(4.17) and sub-
stituting q(x) by the resulting expression in (4.16) yields the agricultural profit for a farmer
located at x:
π(x, λu) = [ψλu¯wu×s(x, λu)] −Rr(x) (4.30)
where ψ≡1+σβ
σis the monopolistic power index, common to all farmers regardless of their
location, and capturing the constant non-spatial share of the growth in profit stemming from
increasing market opportunities. It varies from 0 to 1 and plays as the Home Market Effect ; as
the size of the urban population rises, the incentive to enter the direct selling market increases.
The operating income, given by the term in brackets, depends on the two factors that allow to
qualify the degree of competition on the direct selling market : the monopolistic power index
that gives an overview of the power of producers relative to consumers, and the market share
that accounts for the power of each producer relative to his competitors.
Differentiating π(x, λu) with respect to xand equating to zero, we get that the direct
selling bid rent must satisfy Φs
r0(x) = ψλu¯wu×sx(x, λu), which solution is given by :
Φs
r(x) = ¯rr+ψλu¯wus(x, λu) (4.31)
¯rrbeing a constant.
Land use equilibrium Let suppose that conventional farming takes place on plots of land
located farthest from the CBD than direct selling farming. Denoting by ¯xsthe right-hand
boundary of the direct selling area and knowing that the bid rents of conventional and direct
120
selling farmers must equalize at ¯xs, we find ¯rr=¯
R−ψλu¯wu¯ss, so that we now have :
Φs
r(x) = ¯
R+ψλu¯wu[s(x, λu)−¯ss] (4.32)
Assuming that direct selling farming takes place at the periphery of the residential area,
we know that urban bid rent and direct selling bid rent must equal at the urban fringe ¯xu.
Hence, replacing ¯wuby its value in (4.32) and equating Φu(¯xu) to Φs
r(¯xu) yields :
¯ru=¯
R+δtu¯xu+αψλu(¯su−¯ss)wu
αψλu
δ×(¯su−¯ss)+1 (4.33)
and the constant of the direct selling bid rent becomes :
¯rr=¯
R−(δwu−δtu¯xu−¯
R)ׯss
δ
αψλu+ (¯su−¯ss)(4.34)
From (4.34), we can note that the entry of a new farmer on direct selling market leads
to a decrease in the intercept of the bid land rent function but tends, in the same time, to
flatten the function since its slope is also decreasing with respect to λs
r. As a result, we can
show that a rise in direct selling farmers can either lead to an increase or a decrease of the
bid, depending on the location within the region.
The explanation of this result is to be found in the variation of the direct selling profit
with respect to the number of varieties; as previously mentioned, a new entrant always leads
to a decrease in the market share of all the competitors already engaged in direct selling.
Their operating profit is consequently lower, as a result of a loss in terms of location rent.
However, in the same time, the new competitor enters the market with a smaller share, leading
to lower the benchmark value to which the profit of all the farmers should equalize at the land
market equilibrium π(¯xs, λu). In the end, each farmer can either make a larger or a lower bid,
depending on his own loss in operating profit relative to the overall decrease in direct selling
profits.
Plugging ¯ruinto the urban and the direct selling bid land rents leads to :
Φu(x) = δwu−tux−δwu−δtuxu−¯
R
δ+αψλu(¯su−¯ss)(4.35)
for the urban households and to
121
Φs
r(x) = δwu−tu
λu
2−¯
R×s(x, λu)−¯s
¯su−¯s+δ
αψλu
+¯
R(4.36)
for the direct selling farmers.
The direct selling bid rent follows the spatial variations of E(x, λu) ; it is thus decrea-
sing with the distance from the CBD if the effect of the opportunity cost of transportation
dominates that of the urban pollution externality, and increasing otherwise.
Still from (4.36), we can show that the bid land rent is positively linked to the market
size effect αψλu
δ, but negatively related to the market share gap ¯su−¯ss. The latter (thereafter
referred to as the land rent bill index ) reflects the power of direct selling farmers relative to
urban households and conventional farmers on the land market ; the lower ¯su−¯ss, the flatter
the direct selling bid land rent, and the smaller the part of the direct selling profit captured
by the land rent.
Combining (4.35) and (4.36), the short-run equilibrium land rent is finally given by :
Rsr(x) =
δtu(¯xu−x) + Rr(¯xu) if 0 < x ≤¯xu
δwu−tu
λu
2−¯
R×s(x, λu)−¯ss
¯su−¯ss+δ
αψλu
+¯
Rif ¯xu< x ≤¯xs
¯
Rif x > ¯xs
(4.37)
Depending on the bid rent curves’ ranking, several land use configurations can occur. For
our study, we concentrate on the configuration where the zone dedicated to direct selling
farming is located at the periphery of the city and right-bordered by the conventional farming
area. The occurrence of this intra-regional land use pattern requires that two conditions be
satisfied. First, the derivative of s(x, λu) with respect to xat the right-hand direct selling
boundary ¯xsmust be negative to allow the direct selling bid land rent to be lower than the
opportunity cost of land ¯
Rfor any distance xgreater than ¯xs. Second, as direct selling farming
takes place immediately at the urban fringe, we have ¯su>¯ss. If this condition is not met,
spatial patterns where urban and direct selling farming areas are separated by a zone dedicated
to conventional farming can occur. Besides, since s(x, λu) is positive over the full range [¯xu; ¯xs]
and larger than ¯ss,Rr(x) is also ensured to be positive in all locations. According to the shape
of the agricultural productivity coefficient E(x, λu), the direct selling bid rent can be either
122
first increasing or always decreasing over space, implying that the regional land allocation can
alternatively be depicted by the two following graphs.
Figure 4.1 – The regional land allocation
Proposition 7 At the short-run equilibrium, a spatial pattern where direct selling farming is
located at the periphery of the city occurs provided that the agricultural productivity coefficient
is greater at the urban fringe than at the right-hand boundary of the direct selling area, and
tends to a very low value for the farthest plots of land from the CBD.
From the spatial externality standpoint, this notably implies that, far from the city center,
the opportunity cost of transportation always dominates the pollution cost.
4.3.2 Direct selling goods market
Plugging the equilibrium land rent (4.37) into (4.29) and using the resulting expression in
(4.19) yields the short-run equilibrium value of the price index for direct selling goods :
Psr =λu¯wsr
u
¯
θσβ
σ−1σpz
σ−1−σβ σ−1−σβ
σ−12×Z¯xs
x=¯xu
E(x, λu)dx−1+σβ
σ−1
(4.38)
with
¯wsr
u=
αwu−tuλu
2δ−¯
R
δ
αψλu
δ×(¯su−¯ss)+1 (4.39)
and where the properties of E(x, λu) ensure that the price index is always positive.
As shown from (4.38), the impact of the number of direct selling farmers on the price index
is twofold. It has a positive income effect through ¯wsr
u; the larger the number of varieties, the
123
lower the market concentration, the higher the urban net income, and the greater the price
index. It also has a negative effect due to the fiercer competition between farmers.
The total impact of λs
ron Psr is given by the combination of these two effects. We can easily
show from (4.38) that the competition effect always offsets the net income effect, implying
that the price index is always decreasing with the number of direct selling farmers :
∂P sr
∂λs
r×1
Psr =−¯ss
σ−1 1 + 1
αψλu
δ×(¯su−¯ss)+1!(4.40)
Competition, location and goods quality Using (4.38), we obtain the quantity and the quality
of the variety produced at xat the short-run equilibrium, respectively given by :
qsr(x, λu) = 1
pz
σ−1−σβ
1 + σβ
δwu−tuλu
2−¯
R
¯su−¯ss+δ
αψλu×s(x, λu)E(x, λu) (4.41)
and
θsr(x, λu) = ¯
θpz
1 + σβ
σ−1−σβ
¯su−¯ss+δ
αψλu
δwu−tuλu
2−¯
R×s(x, λu)−1(4.42)
qsr(x, λu) and θsr (x, λu) vary in opposite direction with respect to the distance from the
city center ; letting xaand xbbe two neighboring locations such that ¯xu< xa< xb<
¯xs, we can state that qsr (xa, λu)> qsr (xb, λu) and θsr(xa, λu)< θsr (xb, λu) provided that
s(xa, λu)−s(xb, λu)>0. More generally, we derive the following proposition :
Proposition 8 At the short-run equilibrium, the supply of any direct selling variety decreases
with the distance from the city center provided that the marginal impact of transportation is
larger than that of the urban pollution externality. In this situation, the farther from the CBD,
the lower the supply of a variety, but the higher its quality.
The implication of Proposition (8) in terms of goods quality may be counter-intuitive; since
we have shown from (4.13) that the use of inputs zis decreasing with respect to E(x, λu), we
may have expected that the quality would be lower for the varieties grown at low-productivity
locations (E(x, λu) low). Instead, we find that the quality of high-productivity varieties is
always lower than that produced at remote locations from the city center and displaying low-
productivity levels. The explanation of this result lies in the relationship between productivity,
market share, and goods supply. By definition, the highest market share farmers have to supply
124
a larger quantity of goods, giving them an incentive to use more input so as to meet the demand
(see Eq.(4.13)), and making the quality of their variety lower.
As regard to the features of the competition on direct selling market, we show that the
quality of any variety is improving with the land rent bill index, but decreasing as the mo-
nopolistic power index rises. Additionally, by differentiating (4.41) and (4.42) with respect to
λs
r, we can show that increasing the number of direct selling goods always leads to decrease
the supply of each variety while improving its quality. Urban households have thus access to
a wider range of better quality goods, but in lower quantity.
4.3.3 Direct selling profit and spatial externalities.
We finally assess the impact of spatial externalities on the direct selling market profitability.
From (4.30), we can rewrite the direct selling profit at the short-run equilibrium as :
πsr(λs
r, λu) = (δwu−tuλu
2−¯
R)ׯss
¯su−¯ss+δ
αψλu−¯
R(4.43)
Then, differentiating πsr(λs
r, λu) with respect to λs
r, we can show that the short-run equili-
brium profit decreases as the number of farmers involved in direct selling increases. Given
our framework, the latest entrant on the direct selling market always supplies a variety less
expensive and in a lower quantity than his competitors. His operating income is consequently
lower than that of the other farmers (see Eq.(4.30)). However, since profits must equalize over
space at the short-run equilibrium, spatial externalities are captured by the equilibrium land
rent which, once fed back into the profit, leads to smooth the direct selling net incomes and
results in lower profits for every farmer.
From (4.43), we can capture the net effect of the spatial externalities. First, supposing
that farmers produce in a non-spatial framework (i.e. E(x, λu) = 1 for all x), and denoting
by hat the non-spatial value of any variable, we get :
ˆπsr(λr, λu) = δwu−tuλu
2−¯
R
ˆ
λs
r×δ
αψλu−¯
R(4.44)
As highlighted by (4.44), when farmers are neither affected by urban pollution nor trans-
portation, the operating income is given by the total market size in value –that is, the total
urban net income available for direct selling goods consumption, weighted by the monopolistic
125
power index – divided by the number of direct selling farmers. Then, comparing (4.43) to
(4.44), we can calculate the relative rate of change of the operating income due to spatial
externalities :
ˆπsr −πsr
ˆπsr = 1 −ˆ
λs
rׯss
(¯su−¯ss)×αψλu
δ+ 1 (4.45)
This rate can be either positive or negative, depending on the value of the spatial-adjusted
coefficient given by the last term of (4.45). More precisely, if the value of the market share
in the non-spatial configuration is higher than the spatial-adjusted coefficient, then spatial
externalities always lead to decrease profitability in direct selling market.
4.4 The long run equilibrium.
Farmers enter the direct selling market as long as the profit they can earn is higher than
the (exogenous) equilibrium profit prevailing in conventional farming πc. In the long run, the
number of direct selling farmers adjusts to ensure that they all earn a profit equal to πc.
4.4.1 The equilibrium number of direct selling varieties.
As the agricultural profit is decreasing with the number of farmers involved in direct
selling, the long-run equilibrium is ensured to be a unique stable interior solution. Posing
πc≡¯π−¯
Rand equating it to πsr, we get that the number of direct selling varieties at the
equilibrium λs
r∗must verify :
αψλu=δ
φ¯ss−¯su
(4.46)
where φ≡δwu−tuλu
2−¯
R+¯π
¯πcan be likened to a standard-of-living index.
The LHS of (4.46) stands for the market size effect. It is increasing with the urban popu-
lation size and the monopolistic power index. The RHS captures the supply-side competition
effect (or monopolistic competition effect) and is increasing with the number of direct selling
farmers. Eq.(4.46) can alternatively be written as ¯ss=¯su+δ
αψλu
φ, meaning that farmers keep
entering the market until the market share of the latest entrant reaches a floor value. Graphi-
cally, λs
r∗is given by the abscissa of the intersection point between the market size effect and
the supply-side competition effect.
126
Observe finally that without spatial externalities, the equilibrium would be simply given
by ˆ
λs∗
r=αψλu
δ×(φ−1), which corresponds to the market size effect adjusted by the standard-
of-living index.
Figure 4.2 – The long-run equilibrium
4.4.2 Direct selling varieties and the city size.
The relation between the urban population size and the number of direct selling varieties
is not trivial as it jointly affects the supply and the demand sides. On the one hand, a highly
crowded city creates an incentive for farmers to enter the direct selling market since they
would benefit from a large demand. On the other hand, the city size influences the level of
the spatial externalities, playing on both the pollution intensity and the opportunity cost of
transportation, and inducing changes in the relative productivity gap between farmers. These
externalities, captured by the land rent, modify the level of competition on the land market,
implying income changes for both urban and rural households.
Direct Selling Market Land Market
remoteness cost (Ett0(x)) pollution cost (Ehhλu)
Market size effect Standard-of-living index Land rent bill index
(αψλu↑with λu) (φ↓with λu) (¯su−¯ss↓or ↑with λu)
λs
r↑λs
r↓λs
r↓if (¯su−¯ss)↑
λs
r↑if (¯su−¯ss)↓
Tableau 4.1 – Factors influencing the number of direct selling varieties
127
Table 4.1 summarizes the elements to be considered when studying the relationship bet-
ween the urban population size and the number of direct selling varieties. It notably highlights
that urbanization may favor diversity in direct selling farming provided that the home market
effect offsets the disincentives occurring on the land market.
This result can be analytically derived by studying the variations of the direct selling profit
with respect to the urban population size at the equilibrium. Recalling that πsr (λu, λs
r∗) does
not vary in the long-run and using the total differential, we can draw the relationship between
the urban population size and the number of direct selling varieties, given by :
∂λs
r∗
∂λu
=∂πsr (λu, λs
r∗)
∂λu×
∂πsr (λu, λs
r∗)
∂λs
r
−1
(4.47)
λs
r∗will be then positively (resp. negatively) correlated to λuprovided that πsr(λu, λs
r∗) is
increasing (resp. decreasing) with λu. Differentiating (4.43) with respect to λuand rearranging,
we get :
∂πsr (λu, λs
r∗)
∂λu
=¯π
(φ−1)¯ss×φ¯ss−¯su
λu−tuׯss
2¯π+φsλu(¯x, λu)−sλu(¯xu, λu)(4.48)
where the terms in brackets stand respectively for the market size effect, the standard-of-living
effect, and the land rent bill effect.
Figure 4.3 – Direct selling varieties and urbanization (without spatial externalities)
Urban population size and direct selling farming without externalities Consider first that spatial
externalities do not affect the agricultural productivity, so that there is no heterogeneity
128
between farmers. In this case, s(x, λu) = 1
λs
rfor all xand (4.48) describes a concave relationship
which expression is given by ¯π
λu−tu
2(φ−1) . It only displays two standard competing effects in
urban economics : (i) a market size effect that plays positively, leading farmers to enter the
direct selling market so as to benefit from the additional outlets, but loses strength as the
urban population grows, and (ii) a net income effect which restricts the urban households
spending at an increasing rate. The interplay of these two effects gives rise to a bell-shaped
relationship between the urban population size and the direct selling varieties ; the latter rises
as long as the market size effect outweighs the net income effect and reaches a threshold value
ˆ
λs∗
rbeyond which, any further urban population growth would lead to a decline in goods
variety. As a result, we derive that direct selling farming provides wider ranges of varieties in
regions hosting an intermediate size city.
How do spatial externalities change the bell-shaped outcome ? Accounting for the spatial ex-
ternalities induces two major changes. Regarding the market size effect first, it is readily
shown from (4.48) that spatial externalities lessen its impact from a coefficient φ¯ss−¯su
(φ−1)¯ss<1.
The incentive to enter direct selling market in presence of externalities is consequently lower,
implying less varieties for a same city size, all things being equal.
Second, spatial externalities introduce a new effect stemming from the fact that, because
of the heterogeneity in productivity over space, increasing the urban population size applies
with different weight among locations, and captured by :
φsλu(¯xs, λu)−sλu(¯xu, λu)=(φ¯ss−¯su)× |Ehhλu|R¯xs
¯xuE(x, λu)−1dx
R¯xs
¯xuE(x, λu)dx +¯su
δ!
−|Ehhλu| × φ¯
E−1
s−¯
E−1
u
R¯xs
¯xuE(x, λu)dx
(4.49)
The first line refers to the overall variation of the aggregate receipts in direct selling due to
the rise in both pollution intensity and city size. It is always positive. The second line represents
the comparative individual pollution effect between the two boundaries of the direct selling
area. It can be either positive or negative depending on the sign of φ¯
E−1
s−¯
E−1
u.
In order to better understand the trade-off at play, it may be convenient at this stage to
structure the discussion according to the effect of urban pollution on agricultural yields.
129
(i) Suppose first that the pollution intensity is weakly influenced by the urban population size
(Ehhλu→0). In this case, only the competition effect matters so that (4.49) becomes :
φsλu(¯xs, λu)−sλu(¯xu, λu) = (φ¯ss−¯su)ׯsu
δ(4.50)
which is always positive. Returning to (4.48), we can calculate the change in the magnitude of
the market size effect. The non-spatial market size effect ¯π
λuis now multiplied by a coefficient
φ¯ss−¯su
(φ−1)¯ss1 + ¯suλu
δthat can be either smaller or larger than 1.
Since the above coefficient depends on the urban population size, further calculations can
lead to the following statement : provided that φ¯ss−¯su
(φ−1)¯ss1 + ¯suλu
δis increasing with λu, ac-
counting for the spatial heterogeneity tends to decrease diversity in direct selling for farming
located near the smallest cities, but to increase diversity near the largest cities. In this situa-
tion, the market size effect increases as the urban population size grows, strengthening the
incentive to convert to direct selling in highly-crowded regions. It is however worth noting
that these changes only applies on the magnitude of the market size effect, so that the general
bell shape of the relationship between urbanization and direct selling varieties is preserved4.
Still in this respect, we can note that the higher the urban density, the weaker the additive
effect from spatial externalities, and the closer from the benchmark equilibrium number of
varieties ˆ
λs∗
r5.
(ii) The pollution intensity is strongly influenced by the urban population size. When accounting
for the pollution effect, two elements have to be added in the discussion that are namely, the
aggregate level effect of pollution, and the comparative individual level effect. The aggregate
level effect is positive, meaning that it always concurs in direct selling development. As for
the comparative individual level effect, its impact lies on the sign of φ¯
E−1−¯
E−1
u.
From (4.49), we can show that the overall effect of pollution intensity on direct selling
farming is positive provided that :
R¯xs
¯xuE(x, λu)−1dx
R¯xs
¯xuE(x, λu)dx >φ¯
E−1−¯
E−1
u
φ¯
E−¯
E
u
(4.51)
4. More precisely, it is readily shown that accounting for the spatial externalities does neither cancel nor
modify the nature of the net income effect.
5. φ¯ss−¯su
(φ−1)¯ssis increasing with δ.
130
If this condition is not verified, the overall effect is negative, meaning that pollution always
restrict direct selling development. Finally, combining the different steps of the above analysis,
we can derive the following proposition :
Proposition 9 Direct selling farming is likely to provide a wider range of varieties in regions
hosting an intermediate-size city, whatever the shape of the spatial externalities.
Figure 4.4 – Direct selling varieties and urbanization (with low pollution effect)
Besides, we can add that urbanization may favor agricultural goods diversity provided
that the market concentration in direct selling is low enough. This is notably the case for
regions where the spatial variations of the urban externalities are low, so that farmers tend
to be equally affected by pollution and remoteness ( ¯
Eu→¯
E). By contrast, when urban
externalities greatly differ over space, the heterogeneity between farmers due to the location-
specific impact on productivity is wide. The aggregate profit is then significantly absorbed by
the land rent – as a result of individual profit smoothing –, lowering the incentive to enter
direct selling and leading, in turns, to limit the number of varieties. In this case, the larger
the size of the urban population, the lower the direct selling profit and therefore, the lower
the range of varieties.
Lastly, observe that, provided that the additive effects of spatial externalities are highly
significant, taking them into account may, in some specific cases, either induce a strong joint
development between the urban population size and direct selling farming (i.e. λs
ralways
131
increases with λu), or fully prevent its development near cities (λs
r→0 even for the least-
crowded cities.). In this respect, urban density plays a significant role as it allows to modify
the weight of the distance effect relative to the level effect.
4.5 Direct selling farming and regional welfare.
We finally evaluate the welfare implications of direct selling farming. To do so, we assess
the indirect utility of urban households at the long-run equilibrium and we examine whether
increasing the number of varieties leads to a utility improvement. In a second step, we enlarge
the analysis to include the considerations of farmers.
4.5.1 Urban households utility
Direct selling farming interacts with urban households utility at two levels : it has a direct
impact on consumption through the available range of varieties, the quality and the price
level, and a net income spillover effect through the land market.
Diversity, quantity and quality Using (4.46), we can calculate the long-run equilibrium value
of the quantity and the quality of the variety produced at x:
q(x, λu)∗=¯π
pz
σ−1−σβ
1 + σβ ×E(x, λu)+1
E(¯x∗
s, λu)(4.52)
θ(x, λu)∗=¯
θpz
¯π
1 + σβ
σ−1−σβ ×E(¯x∗
s, λu)
E(x, λu)(4.53)
First, remark that in order to better highlight the role of spatial externalities, (4.52)
and (4.53) can be rewritten as q(x, λu)∗= ˆq∗×E(x,λu)+1
E(¯x∗
s,λu)and θ(x, λu)∗=ˆ
θ∗×E(¯x∗
s,λu)
E(x,λu),
respectively. Hence, comparatively to a non-spatial framework, the quantity of good supplied
in presence of urban externalities is higher for the varieties grown on locations experiencing a
productivity coefficient larger than E(¯x∗
s, λu)
+1 , and lower otherwise. Regarding the quality
however, we get that externalities always lead to a quality loss for each variety except that
produced at ¯xs. For a given variety x, this loss will be even greater that the location benefits
from a large productivity coefficient compared to the right-hand side boundary of the direct
selling area.
132
Second, we can assess the impact of an increase in goods variety. Differentiating q(x, λu)sr
and θ(x, λu)sr with respect to λs
rand evaluating them at the equilibrium value yields :
∂qsr
∂λs
r|λs
r=λs∗
r
=−φ¯ss−¯su
φ−1q(x, λu)∗<0 (4.54)
∂θsr
∂λs
r|λs
r=λs∗
r
=φ¯ss−¯su
φ−1θ(x, λu)∗>0 (4.55)
The combination of (4.54) and (4.55) illustrates the trade-off between quantity and quality.
Urban households will be willing to accept lower levels of consumption in each variety provided
that they gain in both diversity and quality.
Urban net income Increasing the number of varieties affects the urban net income both
through the total expenditures in direct selling goods and the opportunity cost of land. The
consumers expenditures in direct selling goods can be obtained by multiplying (4.18) by (4.52)
and integrating over xwhich, after rearrangement, yields :
Isr =(φ−1)¯π
¯su−¯ss+δ
αψλu×1
ψ(4.56)
Expenditures are rising with the number of direct selling varieties, meaning that, although
the quantity supplied of each good decreases with the number of direct selling varieties, the
extra cost spent on the new variety always offsets the savings on the previous range available.
Regarding the opportunity cost of land, we derive from (4.37) :
Rsr( ¯xu)−¯
R=(φ−1)¯π
¯su−¯ss+δ
αψλu×(¯su−¯ss) (4.57)
Equilibrium vs urban households optimum Plugging (4.38) and (4.39) into (4.27), the indirect
utility at the short-run equilibrium becomes :
Vsr
u=Ω2Z¯xs
¯xu
E(x, λu)dxα
×αψλu
δ(¯su−¯s)+1ασβ
σ−1−1
(4.58)
where Ω≡¯
θ
λuασβ
σ−1σ−1−σβ
σpzασ−1−σβ
σ−11−α
α1−αα(φ−1)¯π
δ1−ασβ
σ−1is a constant.
First, we can easily show that without externalities, the market outcome always leads to a
smaller set of varieties than the optimum ; posing E(x, λu) = 1 for all x, we get Vsr
u=Ω×(λs
r)α
for all x, which is increasing with λs
r. In this case, increasing the number of varieties leads
133
to a rise in the aggregate agricultural productivity, inducing a stronger competition between
farmers and leading, as a result, to lower prices. Moreover, as in this case the productivity is
the same for all the farmers, the direct selling bid rent is flat and new entries in the sector do
not affect the urban households net income.
Assuming then that cities creates externalities but that they do not vary in space (i.e.
E(x, λu) = e(λu), with 0 < e(λu)<1), we have Vsr
u=Ω×[λs
re(λu)]α
which is still increasing
with the number of direct selling varieties but at a lower rate. Any rise in varieties is thus
beneficial to consumers but entails changes in the market share distribution ; the productivity
gap increases which implies lower net income because of spillover effects on land market.
Lastly, when accounting for the spatial varying externalities, we can show that the result
whereby the equilibrium always leads to a smaller range of available varieties than the opti-
mum holds. Indeed, differentiating Vsr
uwith respect to λs
rand evaluating it at the long-run
equilibrium gives :
∂V sr
u
∂λs
r
=Vsr
u¯ss×2α
+
ασβ −σ+ 1
σ−1
¯su−¯ss
(φ−1)¯su(4.59)
which is always positive. Then, knowing that the indirect utility describes a concave parabola
in λs
r, we directly derive from (4.59) that direct selling provides less varieties at the equilibrium
than optimally wished ; given our framework, a rise in goods diversity will always increase the
satisfaction of urban households, as they will get more varieties of higher quality.
Observe anew that the non ambiguous relationship between the urban households utility
and the number of varieties holds because of the monopolistic pricing on direct selling market
which, combined with the bidding process on land market, implies that strengthening the
competition on direct selling market always leads to a lower cost of land at the urban fringe
and therefore, to a positive urban net income effect 6.
6. Another way to figure out this result is to remark from Eq.(4.27) that Vuis decreasing with the price
index but increasing with the urban net income. Decomposing the total effect of the number of direct selling
farmers on Vu, we get ∂Vu
∂λs
r
=∂Vu
∂P
∂P
∂λs
r
+∂Vu
∂¯wu
∂¯wu
∂λs
r
which is always positive because of the properties of the CES
that gives ∂P
∂λs
r
<0.
134
4.5.2 Regional welfare
We finally add the farmers considerations to the analysis. From the previous subsection, we
derive that the urban households utility is increasing with the number of varieties. However,
since direct selling profits are decreasing with the number of competitors, there is a conflict
between urban and rural wishes, meaning that the welfare-maximizing number of varieties is
necessarily lower than the optimal outcome for urban households.
Let the farmers utility be defined as the sum of the rural households profits :
Vsr
r(λs
r, λu) = λs
rπsr(λs
r, λu)+(λr−λs
r)¯π(4.60)
Vsr
r(λs
r, λu) describes a concave parabola in λs
rpassing through (0,¯π) and (λs
r∗,¯π). At
λs
r= 0, all the farmers earn a same profit ¯π. The entry on direct selling market allows some
farmers to benefit from the monopolistic competition and, consequently, to get a higher profit
πsr >¯π. The utility of farmers is therefore first increasing with the number of competitors,
until reaching a threshold from which the gains from imperfect competition vanish. From this
value, any new entry would entail a decrease in direct selling profit.
Figure 4.5 – Direct selling farming and welfare components.
Therefore, as illustrated by the Fig.(4.5), the market equilibrium always leads to a number
of direct selling varieties too much high compared to that which would maximize the farmers
utility.
135
The welfare function can finally be defined as the sum of the urban and the farmers indirect
utilities :
Wsr(λs
r, λu) = λuVsr
u(λs
r, λu) + λrVsr
r(λs
r, λu) (4.61)
Because of the non linearity of (4.61), searching for an analytic solution of the welfare-
maximizing problem is intricate. Some general findings can however be drawn ; using the two
previous subsections, we can easily show that the optimal number of direct selling farmers
is necessarily lower than that allowing to maximize the urban households welfare, but larger
than the farmers’ optimum. Yet, as indirect utilities are weighed by the population type, this
result can be refined if jointly appreciated with the relative size of the urban population. More
precisely, it is readily verified from (4.61) that the optimal outcome would be all the more
close to the urban household optimum that the region hosts a highly crowded city.
4.6 Conclusion
In this chapter, we have investigated the conditions for which direct selling farming could
emerge under free-market. We have derived that, at the short-run equilibrium, the supply of
any direct selling variety would decrease with the distance from the city center provided that
the marginal impact of transportation is larger than that of the urban pollution externality.
In this situation, we have shown that the farther from the CBD, the lower the supply of a
variety, but the higher its quality since quantity and quality vary in opposite direction with
respect to the distance from the city center.
As regards to the relationship between the urban population size and direct selling farming,
we have succeeded in proving that regions hosting an intermediate-size city are more likely
to provide a wider range of varieties. Besides, even if accounting for the spatial heterogeneity
between farmers does not cancel this result, it nonetheless modifies the value of the variety
range achieved at each level of urbanization. In this respect, we have found that, even when
urban pollution affects agricultural yields, cities may benefit from a large set of varieties
provided that the productivity coefficient varies weakly over space.
Finally, we have shown that the market equilibrium always leads to a number of direct
selling farmers which is too low to fully satisfy urban households, but too much high from the
136
farmers standpoint. In this respect, it is worth noting that this general finding on welfare lays
some ground for further research on the public policy aspects. Notably, we can logically think
that implementing a subsidy to reward farmers who engage in direct selling may be welfare
improving as long as the cost of this measure does not exceed the gains in urban households
utility.
137
4.7 R´ef´erences
Alonso, W. (1964). Location and Land Use : Toward a General Theory of Land Rent. Harvard
University Press. 109
Anderson, S. T. and West, S. E. (2006). Open space, residential property values, and spatial
context. Regional Science and Urban Economics, 36(6) :773–789. 108
Avnery, S., Mauzerall, D. L., Liu, J., and Horowitz, L. W. (2011). Global crop yield reductions
due to surface ozone exposure : 1. year 2000 crop production losses and economic damage.
Atmospheric Environment, 45(13) :2284 – 2296. 108
Berry, D. (1978). Effects of urbanization on agricultural activities. Growth and Change,
9(3) :2–8. 108
DGAL (2011). Le Programme national pour l’alimentation. Technical report, Ministere de
l’agriculture, de l’agroalimentaire et de la foret. 108
Holland, M., Kinghorn, S., Emberson, L., Cinderby, S., Ashmore, M., Mills, G., and Harmens,
H. (2006). Development of a framework for probabilistic assessment of the economic losses
caused by ozone damage to crops in europe. 108
Kneafsey, M., Venn, L., Schmutz, U., Balazs, B., Trenchard, L., Eyden-Wood, T., Bos, E.,
Sutton, G., and Blackett, M. (2013). Short Food Supply Chains and Local Food Systems in
the EU. A State of Play of their Socio-Economic Characteristics. Technical report, European
Commission. 108
Kugler, M. and Verhoogen, E. (2012). Prices, plant size, and product quality. The Review of
Economic Studies, 79(1) :307–339. 111
Lucas, R. E. and Moll, B. (2014). Knowledge growth and the allocation of time. Journal of
Political Economy, 122(1). 113
Melitz, M. J. (2003). The impact of trade on intra-industry reallocations and aggregate
industry productivity. Econometrica, 71(6) :1695–1725.
138
Morgan, K. (2014). Nourishing the city : The rise of the urban food question in the global
north. Urban Studies.108
Plantinga, A. J. and Miller, D. J. (2001). Agricultural land values and the value of rights to
future land development. Land Economics, 77(1) :56–67. 108
USDA (2014). Strategic Plan for 2014-2018. Technical report, USDA. 108
Wu, J., Fisher, M., and Pascual, U. (2011). Urbanization and the viability of local agricultural
economies. Land Economics, 87(1) :109–125. 108
139
A : The shape of the space-related productivity E(t(x), h(x, λu))
The second derivative of E(t(x), h(x, λu)) with respect to the distance from the city center
xis given by :
Ex,x(x, λu)=[Et,tt0(x) + Eh,hhx(x, λu)] ×[t0(x) + hx(x, λu)]
+Et,h ×[t0(x) + hx(x, λu)]2+Ett00 (x) + Ehhx,x(x, λu)
(4.62)
Then, assuming for simplicity that the marginal effects of transportation and pollution on
productivity are constant (i.e. Et,t = 0 and Eh,h = 0), and that there is no cross-interactions
between transportation and pollution (i.e. Et,h = 0) yields :
Ex,x(x, λu) = Ett00 (x) + Ehhx,x (x, λu) (4.63)
Then, recalling that Et<0 and Eh<0, the second derivative of Eis negative provided
that :
(i) t(x) and h(x, λu) are convex or
(ii) t(x) (resp. h(x, λu)) is convex and h(x, λu) (resp. t(x)) is slightly concave.
140
Tellement pr´evisible... :-*
Conclusion
L’agriculture fait plus que jamais l’objet de fortes attentes de la soci´et´e en termes d’ali-
mentation et de qualit´e des produits. Dans un contexte d’urbanisation croissante de notre
´economie, il se dessine aujourd’hui les contours d’une nouvelle probl´ematique autour de la
durabilit´e du syst`eme d’approvisionnement alimentaire des villes; s’il s’agit toujours de four-
nir une production agricole suffisante pour r´epondre `a une demande nette croissante, il est
d´esormais de nouvelles contraintes `a int´egrer. Ces derni`eres peuvent se regrouper en trois
grandes cat´egories, portant sur les pr´ef´erences des consommateurs, les impacts environnemen-
taux, ainsi que sur les tensions en mati`ere d’allocation des ressources humaines et fonci`eres
entre usages urbain et rural.
L’´emergence de syst`emes d’approvisionnement alimentaire alternatifs d´edi´es `a l’approvi-
sionnement de certains grands pˆoles urbains, constitue une premi`ere tentative de r´eponse `a la
probl´ematique. Bien que de natures multiples, ces initiatives sont toutes le symbole d’efforts
consentis `a la re-spatialisation et la re-socialisation conjointes des chaines d’approvisionne-
ment alimentaire. Cependant, en l’absence de recul suffisant sur ces exp´eriences, la capacit´e
de ces solutions `a apporter une r´eponse viable et correctement adapt´ee aux enjeux soulev´es
par la nouvelle probl´ematique alimentaire reste incertaine.
A travers cette th`ese, nous avons tent´e de fournir un ´eclairage th´eorique `a cette probl´e-
matique de durabilit´e alimentaire en milieu urbain. En abordant tout d’abord la question
de localisation `a une ´echelle multir´egionale, nous avons pu montrer que la promotion d’un
syst`eme o`u l’ensemble des villes d´ependraient d’un approvisionnement exclusivement local ne
saurait ˆetre intrins`equemet optimale ; en pr´esence d’un ensemble g´eographique caract´eris´e
par une forte h´et´erog´en´eit´e dans la taille des villes notamment, contraindre l’int´egralit´e des
143
villes `a l’autosuffisance alimentaire contribuerait `a d´egrader le bilan ´ecologique, les ´emissions
additionnelles induites par l’allongement des distances intra r´egionales ´etant moins que com-
pens´ees par les ´economies d’´emissions r´ealis´ees sur le commerce inter-r´egional. Dans un tel
cas de figure cependant, nos r´esultats n’excluent pas la possibilit´e pour certaines r´egions de
d´ependre d’un approvisionnement exclusivement local ; le sch´ema optimal correspondrait alors
`a une configuration o`u les villes de tailles interm´ediaires seraient autosuffisantes en denr´ees
alimentaires tandis que les r´egions `a faible population urbaine exporteraient leurs exc´edents
agricoles vers les villes de grande `a tr`es grande taille.
En se focalisant dans un second temps sur la nature de l’agriculture, nous avons pu mettre
en ´evidence qu’en l’absence d’intervention publique, une agriculture de type alternative pro-
posant une gamme vari´ee de produits est plus susceptible de se d´evelopper durablement dans
la p´eriph´erie des villes de taille interm´ediaire. Par ailleurs, bien que n’aboutissant pas de ma-
ni`ere syst´ematique `a un meilleur bilan environnemental, nous avons montr´e cependant que
promouvoir l’implantation d’une agriculture alternative `a proximit´e des villes peut conduire `a
une am´elioration du bien-ˆetre, `a condition que le coˆut d’opportunit´e marginal des terrains ur-
bains reste suffisamment faible. Enfin, en prenant en compte les effets n´egatifs de la pollution
urbaine sur les rendements agricoles, nous sommes parvenu `a d´emontrer qu’en pr´esence de
fortes disparit´es spatiales dans l’impact de l’externalit´e, une agriculture de proximit´e dispose
de peu d’opportunit´e pour se d´evelopper et proposera, le cas ´ech´eant, des biens particuli`ere-
ment h´et´erog`enes en terme de qualit´e.
De mani`ere g´en´erale, les travaux de cette th`ese font apparaˆıtre l’´el´ement majeur suivant :
du fait de la forte et inextricable interconnexion entre milieux urbain et rural, l’´evaluation en-
vironnementale, sociale et ´economique d’un syst`eme alimentaire ne peut se faire qu’en connais-
sance des caract´eristiques d´emographiques (taille de la population) et physique (indicateur de
densit´e, pollution) de la ville concern´ee. Bien que pouvant apparaitre comme trivial, ce r´esul-
tat constitue tout de mˆeme une invitation `a engager des recherches ad´equates en amont afin
de bien saisir et pr´evoir les potentiels effets pervers associ´es `a la promotion d’une solution
alternative.
En proposant un traitement th´eorique de la question, nous esp´erons que cette th`ese contri-
144
bue `a faire avancer le d´ebat de fa¸con constructive. Si nous gardons `a l’esprit que ces travaux
n’offrent qu’une vue parcellaire de la probl´ematique et peuvent, par cons´equent, n’aboutir qu’`a
des recommandations “sous condition”, nous pensons toutefois qu’ils constituent un point de
d´epart int´eressant pour jeter les bases d’une r´eflexion th´eorique rigoureuse sur la question de
l’approvisionnement alimentaire dans les ´economies `a dominance urbaine. Ce travail ouvre
ainsi la voie `a de futures extensions, invitant `a poursuivre les efforts de mod´elisation dans le
but d’affiner les m´ecanismes qui sous-tendent aux dynamiques spatiales de relocalisation des
agents. Notons `a ce sujet que deux voies m´eritent notamment d’ˆetre davantage explor´ees :
– la question de l’endog´en´eisation de l’ensemble des dynamiques de migrations, le rai-
sonnement `a localisation de la population urbaine non fix´ee permettant notamment de
basculer dans une logique de long terme (horizon temporel d’autant plus l´egitime pour
aborder les questions de durabilit´e).
– l’introduction d’une dynamique temporelle afin d’appr´ehender la nouvelle probl´ematique
alimentaire comme un processus d’adaptation et de convergence vers un ´etat station-
naire. Primordiale pour la construction de politiques publiques, ce passage d’une analyse
statique `a une analyse dynamique permettrait de gagner en r´ealisme en introduisant des
ph´enom`enes de rigidit´e et d’irr´eversibilit´e.
145
R´esum´e
Au cours des soixante derni`eres ann´ees, la population mondiale a connu un sursaut spec-
taculaire, passant de 2,5 milliards d’habitants `a la fin de la Seconde Guerre mondiale `a 7
milliards en 2011. Cette croissance d´emographique se distingue des pr´ec´edents ´episodes tant
par son importance que par l’apparition conjointe d’une tendance nouvelle et soutenue `a la
concentration des populations au sein des villes. Appel´ee `a se renforcer partout dans le monde,
cette tendance au grossissement des villes lance un v´eritable d´efi `a la communaut´e interna-
tionale en mati`ere de durabilit´e de notre syst`eme ´economique en g´en´eral et alimentaire en
particulier.
Cette th`ese propose un traitement th´eorique de la question de la durabilit´e des syst`emes
d’approvisionnement alimentaires en milieu urbain. A la fronti`ere entre ´economie publique
et ´economie g´eographique, elle poursuit comme objectif principal de permettre la conduite
d’une analyse formalis´ee des arbitrages environnementaux et sociaux dans un cadre spatial
explicite. En outre, l’id´ee selon laquelle aucune r´eponse ne saurait ˆetre satisfaisante sans qu’une
attention sp´ecifique soit port´ee aux interactions spatiales, ´economiques et ´ecologiques entre
espaces urbains et agriculture constitue l’un des positionnements cl´es d´efendus dans ce travail.
De mani`ere g´en´erale, les travaux de cette th`ese font apparaˆıtre l’´el´ement majeur suivant :
du fait de la forte et inextricable interconnexion entre milieux urbain et rural, l’´evaluation en-
vironnementale, sociale et ´economique d’un syst`eme alimentaire ne peut se faire qu’en connais-
sance des caract´eristiques d´emographiques et physiques de la ville concern´ee.
I
Abstract
Over the past sixty years, the world population has experienced a dramatic surge from 2.5
billion people by the end of WW2, to 7 billion in 2011. This population growth differs from
previous episodes not only in importance, but also because of the joint emergence of a new
and ongoing trend of rising urbanization. Expected to strengthen worldwide, this trend is a
real challenge for the international community in terms of sustainability, especially for food
supply.
This thesis provides a theoretical treatment of food supply chain sustainability in a context
of rapid and unrelenting urbanization. Halfway between economic geography and environmen-
tal economics, its primary goal is to allow for a theoretical formalization of ecological and
social trade-offs in a spatially explicit framework. Besides, we argue that this issue cannot
satisfactorily resolved without paying specific attention to urban-rural interactions.
Our work discloses the following major element : because of the tight and inextricable
interconnection between urban and rural areas, the ecological assessment of any food supply
chain can only be achieved by taking into account both the demographic and physical features
of cities.
III
