Feeding the Cities and Greenhouse Gas Emissions: A New Economic Geography Approach

Abstract

Buying local food' is sometimes advocated as a means of reducing the 'carbon footprint' of food products. This statement overlooks the trade-off between inter-and intra-regional food transportation. Concentrating food production around large cities might reduce emissions due to interregional food trade, but might increase emissions due to transportation within food production areas. We investigate this issue by using an m-region, new economic geography model. 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 ('pure local-food'). We show also that market forces do not lead to trade flows that minimize emissions. Finally, 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.

Full text

Feeding the Cities and Greenhouse Gas Emissions:
A New Economic Geography Approach
Abstract
’Buying local food’ is sometimes advocated as a means of reducing the ’carbon
footprint’ of food products. This statement overlooks the trade-off between inter- and
intra-regional food transportation. Concentrating food production around large cities
might reduce emissions due to interregional food trade, but might increase emissions
due to transportation within food production areas. We investigate this issue by us-
ing an m-region, new economic geography model. 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 (’pure local-food’). We show also that market forces do not lead to
trade flows that minimize emissions. Finally, 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: Agricultural location; Transport; Greenhouse gas emissions; Food
miles; Local food.
JEL Classification: F12; Q10; Q54; Q56; R12
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 sus-
tainability of food supply chains (Wu et al., 2011). Agglomeration economies and fierce
competition over land imply that only firms with high value-added per unit of land can
operate profitably in the most urbanized regions (Fujita and Thisse, 2002). Thus, 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). Larger volumes of food products
transported over longer distances will lead to greater energy use and increased greenhouse
gas (GHG) emissions from the food transportation sector.
In this context, the environmental impact of food transportation has emerged as a
growing concern for public authorities. Promoting ‘local-food’ and reducing ‘food-miles’
(Paxton, 1994) have become recurring themes in Climate Change Action Plans (OECD,
2008; EPA, 2010; Kampman et al., 2010). The rationale is that food production should be
located closer to consumption centers so as to reduce reliance on food imports from distant
regions, and to mitigate GHG emissions due to food transportation. The objective of the
present analysis is to examine the validity of these recommendations from a social welfare
perspective.
In this paper, we argue that, even without differences in technology and natural endow-
ment across regions, ’buying local’ does not necessarily minimize transport-related GHG
emissions. An essential feature of the impact of food systems on the environment is the
trade-off between intra- and inter-regional trade, a trade-off which, to a large extent, has
been overlooked so far. On the one hand, intra-regional trade represents a significant
share of food transportation. Table 1 shows that the average shipment distance of agri-
cultural and food products is relatively short.1Intra-regional transport, primarily handled
by trucks, has an important influence on GHG emissions. On the other hand, the average
distance traveled by commodities within a region may increase with the area devoted to
1U.S. data suggest that freight flows predominantly occur within the same State or with immediately
neighboring States (FHWA, 2011): for nine states out of ten, within-state haulage accounts for at least
50% of total flows, and local flows (i.e., when including the commodity freight flows with the surrounding
states) represent at least 78%.
1

agriculture, and therefore with the level of production. If the relocation of agricultural
production to the most populated regions reduces inter-regional trade but is accompanied
by increased intra-regional flows, the net environmental impact remains unclear. To an-
alyze this trade-off, an in-depth analysis is needed that includes each stage of the supply
chain, is conducted at the level of the entire urban system rather than just the city level,
and accounts for the land-market effects of urbanization on the location of agricultural
production within and between regions. To the best of our knowledge, no such analysis is
available in the literature.
Ton-miles All Truck Rail Water
Commodity [109] [Miles]
U.S.A.
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
France
Agricultural products 17.2 76 86 232 169
Food products 19.3 94 111 294 175
Sources: Adapted from BTS and U.S. Census Bureau (2010) for U.S. Data and
DAEI/SES (2008) for French data
Table 1: Total ton-mileage and average shipment distance of agricultural commodities and
food products by mode of transport in 2007 in the U.S. and in France.
We develop a new economic geography model that accounts for the damage caused
by emissions from the food-transportation sector (both within and between regions), as
2

well as the welfare implications for urban and rural households. The spatial allocation
of food production across regions depends on land rents, which in turn are affected by
transport costs and the (exogenous) distribution of the urban population. 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 analytically 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 endogenously determined.
Our results show that analyses 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. First, intra-regional flows are minimized when
food production is clustered mainly in the least-urbanized regions. This implies that re-
ducing interregional trade in food products by relocating agricultural production closer to
large cities may increase intra-regional trade. Hence, configurations in which all regions are
self-sufficient –referred to as ‘pure local-food’– do not necessarily minimize emissions due
to food transportation. 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. 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). We also discuss 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.
Second, the analysis highlights that the economic consequences of the spatial allocation
of food production extend beyond solely environmental impacts. The proposed model
accounts for two effects on the utility of rural households. On the one hand, farmers
located in a more urbanized region benefit from access to a wider range of services. On the
other hand, larger urban areas generate higher land rents. The former effect favors location
of farmers in the most urbanized regions, whereas the second tends to spatially separate
3

urban and rural activities. The spatial-equilibrium allocation of rural population for a
given distribution of the urban population depends on the relative magnitude of these two
effects. We 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.
Third, the welfare-maximizing spatial allocation of food production results from a com-
bination of the various agglomeration and dispersion effects regarding both the environment
and the utility of urban and rural households. The conditions under which the welfare-
maximizing and pure local-food configurations coincide depend on the relative magnitude
of these effects. If these conditions are not met, imposing that all regions be self-sufficient
leads to a spatial misallocation of food production. Interestingly in this case, we find that
the optimal allocation of food production does not exclude the possibility that some regions
should rely solely on local food. However, this possibility is however 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.
In order to disentangle the various effects on welfare, we proceed in three main steps.
After presenting the model (Section 1), we analyze the emissions-minimizing spatial dis-
tribution of food production and highlight the trade-off between intra- and inter-regional
trade related emissions (Section 2). In Section 3, we focus on the market forces driving
farmers’ location choices and analyze the resulting spatial equilibrium. In Section 4, we
examine the effects on welfare by combining the impacts on urban and rural households’
surpluses, and on the environment. Section 5 discusses the robustness of the results to
some alternative assumptions. Section 6 concludes.
1 A model
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 dif-
ferentiated good using only (urban) labor. The agricultural market is integrated across
4

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 nor-
malized to 1, and split into λuand λrurban and rural inhabitants, respectively. This
economy comprises mregions, indexed by j={1, .., m}. Each region hosts an urban and
rural population of λuj and λrj , respectively (Pjλuj +Pjλrj =λu+λr= 1). The spa-
tial 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 popu-
lation across regions.
1.1 Spatial structure
The largest city is assumed to be located in the ‘core’ region, indexed by j= 1. The m−1
remaining regions–hereafter referred to as ‘peripheral’–are located on a circle centered
around region 1 (radius ν). Without loss of generality, peripheral regions are ordered by
decreasing urban population, so that λu1≥λu2≥ · · · ≥ λum. 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 1.5), 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.
2See the survey in Duranton and Puga (2004) for the reasons for the existence of a CBD
5

The right endpoint of region jis thus:
¯xj=λuj
2+λrj
2µ.(1)
1.2 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 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 5, we consider the case where the number
of elevators depends on the mass of farmers). The right-hand side elevator in region jis
located at:
xc
j=λuj
2+λrj
4µ.(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 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.
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 5). 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,
transport costs are given by:
Caj (x) = tax−xc
j+taxc
j+f(3)
6

¯xj
0
CBD
¯xuj xc
j
ElevatorElevator
Urban area
Pop. : λuj
Pop. : λr j
2Pop. : λr j
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
j= 1
ν
j= 3
j= 2
j= 4
j= 5
Figure 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.
1.3 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, this farmer’s profit for this farmer is given by
πaj (x) = pa−Rj(x)
µ−Caj (x) (4)
1.4 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
7

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
2qa+αZ¯vj
0
qs(v)dv−β−γ
2Z¯vj
0
[qs(v)]2dv−γ
2¯vjZ¯vj
0
qs(v)dv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 by a > 0 and b > 0) of the second term in Eq. (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. γmeasures 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 (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) (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(7)
8

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 (5) subject to budget constraints (6) and (7) leads to the inverse
demand function for the agricultural good:
pa(qa) = max {a−bqa,0}(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(9)
where Psj =R¯vj
0psj (v)dv is the price index of services for the range supplied in region j.
1.5 Equilibrium
Given our assumptions related to the supply-side of the farming sector, agricultural output
in region jis equal to λrj . Combined with Eq. (8), the market clearing price for the
agricultural good then is:
p∗
a=a−bX
j
λrj =a−bλr(10)
Our assumptions related to the agricultural market (integrated inter-regional market,
perfect competition, homogeneity of the agricultural commodity) imply that the price
received by all farmers is unique (p∗
a) regardless of the region of production. Therefore,
total agricultural 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−λr j . Replacing qawith its equilibrium value and using
simple algebraic manipulations, imports in region jbecome λuj λr−λr j 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 qsunits of service requires 1/φ > 0 units of labor so that φis equivalent
3Note that these assumptions imply that product differentiation based on the region of origin or the
effect of local market size are ignored in this framework.
9

to the labor productivity in services. The profits of a services firm operating in region j
are given by
πsj (v) = qsj (v)psj (v)−wj/φ (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. (9)) and taking the price
index Psj as given. Hence, Psj and wjare treated as parameters (see, for instance,
Ottaviano et al., 2002). Since all firms are identical, profit maximization leads to an equi-
librium price that is common to all varieties and all regions:
p∗
s=α(β−γ)
β+ (β−γ)>0.(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 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 ).(13)
Eq. (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
exclusively 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 (6) and (7) and equilibrium quan-
tities and prices into (5):
Vuj (x) = p∗
aqa(p∗
a) + Zvs
0
p∗
sj (v)qsj (p∗
sj )dv+q0+w∗
j−Rj(x)−tux. (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).(15)
10

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 (14) and (15)) is the same
regardless of the household’s location.
For urban workers, the equilibrium land rent must solve ∂Vuj (x)/∂x = 0 or, equiv-
alently, ∂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 ∂Vrj (x)/∂x = 0. As
a consequence, the bid rents of rural workers are such that Rj(x) = ¯rrj −µtax−xc
j. As-
suming 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 ¯rrj =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) = 


tuλuj
2−xif x≤xuj (urban households)
µtaλrj
4µ−x−xc
jif xuj < x ≤xj(rural households) (16)
1.6 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
Figure 1, left). 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 (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
11

regions (see right side of Figure 1):
Tb(λr,λu) =
m
X
j=2
ν|λrj λu−λuj λr|(18)
Comparing Eqs. (17) and (18) highlights the trade-off between intra- and inter-regional
trade flows. For a given rural population λr, total intra-regional ton-mileage is minimized
when λrj =λr
m+2µ
3λu
m−λuj , while inter-regional trade 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 regions.4Total emissions (E) are thus:
E(λr,λu) = Tw(λr,λu) + ebTb(λr,λu) (19)
2 Emissions-minimizing spatial distribution of food produc-
tion
‘Pure local-food’ systems are sometimes advocated as a way to minimize the impact of food
transportation on emissions. To what extent does such a statement hold? More generally,
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
envisaged:
•(i) a ‘pure local-food’ system where all regions are self-sufficient in food (λuλrj =
λrλuj for all j).
4As 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.
12

•(ii) a global food system where all regions export or import agricultural products
(λuλrj 6=λrλuj for all j).
•(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(20)
Because of the absolute values in Eq. (18), solving (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 Appendix A for details):
ˆ
λrj =










λr
λuλ+2µ
3λ−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
(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)!(22)
λ≡1
mM+mX X
k∈M
λuk +X
k∈X
λuk +4λ2
uµνeb
3λr+ 2λuµ(2mX+ 1)!(23)
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 Appendix A) is given by:
ˆ
λr1=




λr
λuλ+λ
2+2µ
3λ+λ
2−λu1if region 1 imports, i.e. if λu1>λ+λ
2
λr
λuλu1if region 1 is self-sufficient, i.e. if λu1≤λ+λ
2
(24)
13

Note that, in Eqs. (21)-(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 (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
distribution of urban population across regions, Eqs. (21)-(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(25)
Since λ−λis positive, the inequalities defining the existence of self-sufficient regions
in Eq. (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 on Eq. (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
5Note 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 )
14

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
Proof: See Appendix B.
Whenever the condition given by Proposition (1) 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.
The intuition behind Proposition (1) is as follows. If the difference in urban population
between any two self-sufficient regions is large enough, it is possible to reduce total emis-
sions by shifting some food production from the more to the less urbanized region. This
increases interregional trade flows (the region with the smaller urban population becomes
an exporter) but decreases within-region ton-mileage (because distances are shorter in the
region with the smaller urban population). The right-hand side of the inequality in the
proposition reflects the ratio of the corresponding marginal effects on emissions due to
inter- relative to intra-regional flows. 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. Consider now a marginal shift in rural population d` from region 1
to region msuch the total rural population λris 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. (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.
Proposition (1) conveys two important messages. First, contrary to the usual recom-
mendation 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
15

highlights the importance of taking into account the relative intensity and magnitude of
intra- vs. inter-regional transportation related emissions. Second, the proposition under-
scores 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. 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. 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 values6chosen for this example are
such that the condition given in Proposition 1 is 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, 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).
In this example, imposing that all regions be self-sufficient would significantly increase
emissions (by 67%, see Table D.1 in Appendix D) compared to the emissions-minimizing
configuration.
6Although the parameter values were chosen mostly for illustrative purposes, they capture some essen-
tial 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. In solving the
problem numerically, importing/exporting regions are determined iteratively by incrementing mMand mX
and updating the values of λand λaccordingly until the conditions given in Eq. (21) are met.
16

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: 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 trian-
gles. Parameter values: m= 50, λu≈0.53, λr≈0.47, λu1≈0.0796, λuj =λu1/(j0.79) for
all j,µ≈0.025, eb≈0.08, ν= 4.
17

3 Spatial-equilibrium distribution of food production
We next examine the economic drivers of farmers’ locations7among regions, and analyze
the spatial-equilibrium allocation of food production for a given distribution of the urban
population. Such an equilibrium occurs if no farmer is better off by moving to another
region (see for instance Fujita and Thisse, 2002). Using the number of varieties defined by
the labor market-clearing condition (¯vj=φλuj ), the indirect utility of a rural household
established in region j(Eq. (15)) becomes:
Vrj (λrj , λuj ) = ¯q0+b
2λ2
r+α2β
2(2β−γ)2φλuj + (a−bλr)−f−taλuj
2+λrj
2µ(26)
The second and third terms in Eq. (26) 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.
Based on a well-established tradition in migration modeling if more than two regions
are involved (see Tabuchi et al., 2005), 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(27)
An interior equilibrium8is stable if and only if the slope of the indirect utility differential
is strictly negative in the neighborhood of the equilibrium (i.e. ∂∆Vr j /∂λrj <0 at λ∗
rj ).
Combining Eqs. (26) and (27), the indirect utility differential becomes:
∆Vrj (λr,λu) = λuj −λu
mφδ −ta
2λuj −λu
m+λrj
µ−λr
µm(28)
where δ≡α2β
2(2β−γ)2. Since ∆Vrj is decreasing with respect to λr j , the interior equilibrium
is stable. Solving ∆Vrj (λ∗
r,λu) = 0 leads to:
λ∗
rj (λuj ) = λr
m+µλuj −λu
m2φδ
ta
−1for all j(29)
7Arguably, at the individual level and in the short run, farmers are tied to their land. The question
addressed here is that of the spatial allocation of food production in the longer run.
8An 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.
18

The spatial equilibrium defined by Eq. (29) results from the interactions between various
agglomeration and dispersion forces. The term in square brackets in Eq. (29) 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. (29). 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 2 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 jand/or (ii) ta=2φδλuµ
λr+λuµ
If neither condition holds, then the spatial-equilibrium rural population in any region jis
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 Appendix B.
The proposition indicates that, in general, the spatial-equilibrium allocation of food
production leads to inter-regional trade. It coincides with a pure local-food configuration
only under very specific conditions. Moreover, whether food production tends to locate in
19

the most or in the least urbanized regions depends on the comparison between inter-sectoral
agglomeration 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
production 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 3
for two values of ta(left side: ta<2φδλuµ
λr+λuµand right side: 2φδλuµ
λr+λuµ< ta<2φδ).
4 Welfare-maximizing spatial distribution of food produc-
tion
The previous two sections highlighted various possible effects of the spatial distribution of
food production on emissions and on the utility of rural households. All these effects must
be accounted for in a social welfare analysis which, in addition, should also integrate the
effects of the spatial distribution of food production on the utility of urban households.
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) (30)
where d > 0 measures the marginal environmental damage (expressed in units of num´eraire
and taken constant for simplicity) due to the emissions from the food transportation sector.
Plugging the values of ¯vjand wjat the equilibrium of the urban labor market into
Eq. (14), we obtain:
Vuj (λrj , λuj ) = ¯q0+b
2λ2
r+φδλuj +2φδ(β−γ)
β(λuj +λrj )−tu
λuj
2(31)
20

The fourth term in Eq. (31) 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.
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(32)
Since W(λr;λu) integrates the environmental damage due to emissions, resolution of
(32) closely follows that of (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. (21)–(24), and detailed in Appendix C. 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
(33)
As in Eq. (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 Appendix C). Since
λoand λodepend 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,
it is possible to further characterize the welfare-maximizing distribution of food production
by examining the difference:
λo−λo=8λ2
uµνebd
(3d+ 4ta)λr+ 2λuµd+ta−2δφ 3β−2γ
β(34)
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.
valuation of the range of services, and market-size effect on urban wages). The difference
is unambiguously increasing with respect to the emission factor (eb) and distance (ν) as-
sociated with intra-regional trade. Note that if marginal damage is low (if d→0), then
21

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, λo−λois not necessarily positive. In particular, if the inter-sectoral agglom-
eration 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 3 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 Appendix C.
The proposition underscores that the welfare-maximizing spatial allocation of food
production 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 allocation. 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 population, 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 populations in the latter regions should be neither too large, nor too
small (such that λo≤λuj ≤λoor λo≤λuj ≤λo, depending on the sign of λo−λo).
22

The spatial equilibrium examined in Section 3 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) urban wages.
The discrepancy between the two situations is depicted in Figure 3 for the same distribution
of the urban population and the same values for µ,eb, and νas in Figure 2, and two values of
the within-region transportation cost ta. If tais high (right side of Figure 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
regions should be self-sufficient (i.e. such that λo< λuj < λo). The number of self-sufficient
regions in the welfare-maximizing configuration rises to eleven for the smaller value of ta
(left side of Figure 3). In both examples, the emission level in the welfare-maximizing
configuration 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 D.1 in Appendix D).
5 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 as-
sumption 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 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
23

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●
●
●
●
●
●
●
●
●
●
●
●
λoλo
Urban population (λuj)
Rural population (λrj)
0 0.05
0
0.025
0.05
0.075
●
●
●
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●●
●●●
●●
●●●●
λoλo
Urban population (λuj)
Rural population (λrj)
0 0.05
0
0.025
0.05
0.075
ta= 0.04 ta= 1
Figure 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≈0.025, eb≈0.08, ν= 4, φ= 1, δ= 1, and
d= 0.5.
24

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 Appendix E. 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. (58) in Appendix E). 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 λr j 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
agricultural 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 farmers operating in regions with the best-quality land will enjoy a
higher income, the incentives to produce in these regions will increase.
25

6 Concluding remarks
Should local food be promoted on the basis that it contributes to the reduction of the
distance 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 might be expected. It depends on the extent to which emissions savings permitted by
less inter-regional trade are offset by potentially larger intra-regional transportation flows.
Thus, food trade does not necessarily conflict with the objective of mitigating emissions
from the food transportation sector. Beyond these purely environmental considerations,
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 paper,
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
strongly 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 equilibrium, 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 difference 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, 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 system-
atically ruled out. Indeed, our results indicate that the welfare-maximizing allocation of
26

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.
27

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30

A Emissions-minimizing distribution of food production
To deal with the absolute values in (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 (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
(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] (36)
The first-order conditions lead to:
3
4µλ2
u
(X1−M1+λu1λr) + λu1
2λu
−ρ1=ρ21 =−ρ31 (37)
3
4µλ2
u
(Xj−Mj+λuj λr) + λuj
2λu
−ρ1=ρ2j−νeb=ν eb−ρ3jfor j6= 1 (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 (37) and (38), eliminating ρ3jand ρ1, and reverting back the change of variables, the
F.O.C. become:
ˆ
λr1=λr
m+2µ
3λu
m−λu1+4µλu
3m"(m+ 1 −2mM)νeb−X
k∈S
ρ2k#(39)
ˆ
λrj =λr
m+2µ
3λu
m−λuj +4µλu
3m"mρ2j+ (1 −2mM)νeb−X
k∈S
ρ2k#for j6= 1 (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(41)
31

Re-injecting in Eqs. (39) and (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(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}
(43)
ˆ
λrj =3λr+ 2λuµ
3λu(mM+mX) λu−X
k∈S
λuk −4λ2
uµνeb(2mM−1)
3λr+ 2λuµ!−2µ
3λuj if j∈X(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 (21) and (24).
Proof of Proposition 1 Notice 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.
QED.
B Spatial-equilibrium distribution of food production
Proof of Proposition 2 A pure local-food configuration is characterized by λrj =
(λr/λu)λuj for all j. Using Eq. (29), it is easy to see that, for such a configuration to
emerge in equilibrium, we need that λuj −(λu/m) = 0 for all jand/or 2φδ
ta−1µ=λr
λu.
The analysis of the sign of the slope of λ∗
rj with respect to λuj in Eq. (29) completes the
proof. QED.
32

C Welfare-maximizing distribution of food production
The resolution of program (32) closely follows that of (35) (see Appendix A). 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
λuφδ(3β−2γ)
βλuj −λuj +Xj−Mj+λuj λr
µλuta
2−dE (45)
For interior solutions, the first-order conditions for the core region lead to:
φδ(3β−2γ)
β−ta
2µλuλu1−3d+ 4ta
4µλ2
u
(X1−M1+λu1λr) + ρ1=−ρ21 =ρ31 (46)
Eq. (46) implies that ρ21 =ρ31 = 0. As for peripheral regions (j6= 1), the F.O.C. lead to:
φδ(3β−2γ)
β−ta
2µλuλuj −3d+ 4ta
4µλ2
u
(Xj−Mj+λuj λr) + ρ1=dνeb−ρ2j=ρ3j−dν eb
(47)
Eq. (47) implies that ρ2j+ρ3j= 2dνeb. The complementarity slackness conditions impose
that ρ2j= 0 if Xj>0 and ρ2j= 2dνebif Mj>0. Substituting into (46) and (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)
βλu
m−λu1+λu
m (m+ 1 −2mM)dνeb−X
k∈S
ρ2k!#
(48)
and for peripheral regions (j6= 1):
λo
rj =λr
m+4µ
3d+ 4ta"d+ta
2µλu
−φδ(3β−2γ)
βλu
m−λuj +λu
m mρ2j+ (1 −2mM)dνeb−X
k∈S
ρ2k!#
(49)
As in Appendix A, PSρ2kis eliminated by summing Eq. (49) over j∈S:
X
k∈S
ρ2k=m
m−mS3d+ 4ta
4µλ2
u
λr+d+ta
2λu
−φδ(3β−2γ)
β X
k∈S
λuk −mS
mλu!+mS(2mM−1)
m−mS
dνeb
(50)
The values in Eq. (33) are obtained by re-injecting the value of PSρ2kinto Eq. (49),
and using that ρ2j= 0 for j∈Xand ρ2j= 2dνebfor j∈M\{1}. The threshold values λo
33

and λoin Eq. (33) are then derived from the conditions λo
rj <λr
λuλuj and λo
rj >λr
λuλuj for
j∈Mand j∈X, respectively:
λo≡1
mM+mX
X
k∈M
λuk +X
k∈X
λuk −4λ2
uµνebd(2mM−1)
(3d+ 4ta)λr+ 2λuµd+ta−2δφ 3β−2γ
β
(51)
λo≡1
mM+mX
X
k∈M
λuk +X
k∈X
λuk +4λ2
uµνebd(2mX+ 1)
(3d+ 4ta)λr+ 2λuµd+ta−2δφ 3β−2γ
β
(52)
If λo> λo, then as in Appendix A, 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∈X
if λuj < λo. If λo< λo, the signs of the above inequalities change.
As for region 1, re-injecting the value of PSρ2kinto Eq. (48), using Eqs. (51) and (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
βiλo+λo
2−λu1if λuj >λo+λo
2
λr
λuλuj if λuj ≤λo+λo
2
(53)
If λo< λo, region 1 can only be an exporter or self-sufficient and the signs of the inequalities
in Eq. (53) change.
Proof of Proposition 3 If 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.
34

D Simulation results
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)
Table D.1: 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≈0.025, eb≈0.08, ν= 4, φ= 1,
δ= 1, and d= 0.5.
35

E Discussion and Extensions with Kjelevators and bundling
capacity τ
E.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 area9and 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
.(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 (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.10
The individual cost associated with the distribution of farmers’ output is now given by:
Caj (x, k) = f+tax−xk
j+taxk
jτ(56)
9Note 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.
10In practice, low values of τare adapted to the case of commodities such as cereals, while values of τ
close to 1 are more adapted to the case of fresh fruits and vegetables.
36

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 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) = ...Vrj (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 costs 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) = µtaλrj
4µKj
−x−xk
j+τλrj
2µKj
(Kj−k)(57)
Finally, using (55), (56) and (57), the net income received by a farmer becomes:
πj(x)=(a−bλr)−f−taτλrj
2µ+λuj
2−(1 −τ)ta
2µκ ≡π∗
j.(58)
E.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
jbe
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=λrj (2 + τ)
4Kj
and ¯xj−bxK,K−1
jµ=λrj (2 −τ)
4Kj
.
As for the other K−2 elevators, we have
bxk,k+1
j−bxk,k−1
jµ=λrj
2Kj
with k∈ {2, ..., K −1}.
37

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
µx−xk
jdx+ 2
K
X
k=1
xk
jbxk,k+1
j−bxk,k−1
jµτ
E.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
jx−xk
jdx=λrj
4µKj2
+Kj−1
2(λrj (1 + τ)
4µKj2
+λrj (1 −τ)
4µKj2)
=λrj
4µKj2
+ (Kj−1) λrj
4µKj2
(1 + τ2)
=λrj
4µKj2Kj+ (Kj−1)τ2
and
Kj
X
1
xk
jbxk,k+1
j−bxk,k−1
j=λuj
2
λrj
2µ+λrj
4µKj2
(2 + τ) + K−2
2
λrj
2µKj
λrj
2µKj
+(Kj−2)(Kj−1)
2
λrj
2µKj
λrj
2µKj
+λrj
4µKj
+ 2(K−1) λrj
4µKjλrj (2 −τ)
4µKj
=λuj
2
λrj
2µ+λrj
4µKj2
(2 + τ) + 2(Kj−2)Kλrj
4µKj2
+ (2Kj−1)(2 −τ)λrj
4µKj2
=λuj
2
λrj
2µ+λrj
4µKj2
[2K2
j−2τ(Kj−1)]
Hence, the sum of agricultural flows within region jis:
Twj =λ2
rj
4µ"τ2+Kj(1 −τ2)+2τ K2
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
38