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IDP Working Papers
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ABSTRACT
In this paper, we study how proximity to cities affects the decisions of farmers to enter the
direct-sales market in the presence of spatial heterogeneity in agricultural yields. We
develop a theoretical model which takes account of the externality of urban pollution and
market access costs on direct-selling profits. We find that regions hosting an intermediate-
size city are more likely to supply a wider range of direct-selling varieties. Additionally,
we highlight that spatial heterogeneity in productivity creates distortions in the
competition among farmers, and can have concomitant undesired effects on both the
quality and range of available varieties.
Keywords: Direct-selling farming, spatial heterogeneity, urban pollution, city size.
JEL Classification: D43; Q13; Q53; R32
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I thank Carl Gaigné, Fabien Moizeau, Lionel Ragot, Stéphane Riou, Stéphane De Cara and
Pierre-André Jouvet for their valuable comments and suggestions.
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Working Papers
Anne J. FOURNIER
Univ. Polytechnique Hauts-de-France, EA1384 - IDP, F-59313 Valenciennes, France.
Contact information: anne.fournier@uphf.fr
Direct-Selling Farming and Urban Externalities :
What Impact on Product Quality and Market Size ?
Economics WP Series
March 2018
1 Introduction
The last two decades in many developed countries have seen a revival of Short Food Supply Chains
(SFSCs) and local food systems–i.e. systems where production, processing, trade and consumption
occur within a particular, narrowly defined geographical area, and with a limited number of interme-
diaries. As Martinez [2010] points out in the context of the US market, SFSCs account for a growing
share of total agricultural sales, an indication that distribution networks are changing continuously to
better meet the needs of customers.
To some extent, the recent global trend towards SFSCs can be explained by the wish of consumers
to re-establish long lasting trusting relationships with farmers. In a✏uent cities in particular, con-
sumers expectations have grown regarding the quality, origin and safety of the food they purchase
[Deutsch et al.,2013]. Food supply crises such as BSE and the Belgian dioxin incident have caused
widespread anxiety among citizens [Miles and Frewer,2001]. In addition to concerns over safer food,
the growing environmental awareness of consumers has led them to question modern agricultural
practices and use of pesticides, with their residues in food perceived as associated to long-term and
unknown e↵ects on health [Williams and Hammitt,2001].1SFSCs benefit not only consumers but also
producers. Kneafsey et al. [2013] report that in recent years they have become an increasingly used
diversification strategy of farmers to react to continuous price squeezes and capture new segments of
demand for local and fresh food. SFSCs usually enable producers to obtain a fairer share of profit by
eliminating the need for intermediaries, and also provide opportunities to diversify activities [Alonso,
2011]. Moreover, empirical studies conducted in the last ten years support the idea that for a majority
of consumers, products sold directly are perceived to be of higher quality than those sold in regular
grocery stores (see e.g. Dodds et al. [2014]). Hence, farmers operating in the direct-selling market
have substantial leeway to bargain and add a price premium [Pearson et al.,2011], contributing in
turn to improving the economic viability of rural communities [Renting et al.,2003].
Since the most-urbanized cities host wealthier populations (on average) with higher willingness to
pay for alternative marketing channels, the opportunities for direct-selling farming in the surrounding
rural areas can be expected to be greater. This intuition seems to be supported partially by current
1For further information on demand-side aspects, readers should consult Trobe [2001] which examines the reasons
why customers increasingly are attracted by direct-selling marketing.
1
contributions on farming developments in areas under urban influence which tend to emphasize that
SFSCs are more likely to meet significant and fast-increasing new kinds of demand. For instance,
Low and Vogel [2011] show that “farmers marketing food locally are most prominent in [...] areas
close to densely populated urban markets” and “climate and topography favoring the production of
fruits and vegetables, as well as good transportation and market access are found to be associated with
higher levels of direct-to-consumer sales”.
However, the existing research pays relatively little attention to potential negative factors that
might counter the attractiveness of peri-urban areas, and put the brake on direct-selling development.
First, the transition towards city-wide food networks inevitably raises questions about land use and
access costs. Competition for land is fierce in the periphery of highly-urbanized spaces which increases
its cost, and implies that low-added value activities such as agriculture may not thrive [Berry,1978].
Second, alongside tensions over land, there are environmental issues that need to be considered,
and specifically, the detrimental e↵ects of urban pollution on crops. Extensive research shows that
urban pollution has multiple and complex adverse e↵ects on agricultural activity, and that pollution
causes reduced crop yields and reduced crop quality (see e.g. Adams et al. [1986]; Kuik et al. [2000]).
Avnery et al. [2011] estimate that reductions in global yields due to exposure to ozone could be in the
range 3.9%-15% for wheat, and 8.5%-14% for soybean.2Holland et al. [2006] show that the directly-
induced economic consequences of urban pollution are far from negligible, and show that in Europe,
losses in 2000 amounted to 6.7 billion euros. In this context, the benefits of proximity to an urban
space are questionable.
The literature analyzes issues related to peri-urban agriculture from the point of view of amenities;
most studies focus on the impacts of agriculture and farmland on cities but rarely study the reverse
situation (see e.g. Cavailh`es et al. [2004]; Bento et al. [2006]; Coisnon et al. [2014]). To the best of
our knowledge, only a few theoretical contributions address urban-rural linkages focusing primarily
on the farming sector. These few works include contributions from Lopez et al. [1988] and Wu et al.
[2011]. The former develops a framework to estimate the e↵ects of sub-urbanization on agricultural
production choices, prices, and profits, and finds that although vegetable production may benefit from
urbanization, other agricultural sub-sectors such as grain crops and livestock are adversely a↵ected. In
2Note that in developing countries such as India and Pakistan where ambient pollution reaches very high levels, ozone
related yield losses in sensitive crops can be over 40% in rural areas in the periphery of large cities [Marshall et al.,1997].
2
our view, the paper by Wu et al. [2011] o↵ers a very comprehensive theoretical study. It investigates
the e↵ects of urbanization on the viability of farm-supporting sectors, and proposes a model in which
opportunities arise from the benefits of being part of a large farming community. They emphasize that
the e↵ects of urbanization on the agriculture infrastructure, input costs, and profit can be positive or
negative.
The purpose of the present paper is to develop a theoretical framework to allow investigation of
whether direct-selling farming can develop in the periphery of highly-crowded cities if the negative
e↵ects (externalities) associated to urban proximity are taken into account. We explore this by de-
veloping a spatial economic model in which (i) farmers can choose between producing homogeneous
conventional goods or direct-selling goods, and (ii) urban externalities on agricultural yields (namely,
urban pollution and market access costs) are introduced. In contrast to Wu et al. [2011] whose anal-
ysis is based on how urbanization a↵ects the viability of farm-supporting sectors (i.e. input suppliers
and output processors), and consequently, on the profitability of agriculture, we consider directly the
linkages between size of the urban population and direct-selling farming through land and agricultural
goods markets.
To do so, we borrow from spatial economic and monopolistic competition theories. We consider
direct-selling farming as a sector supplying local urban households with horizontally- and vertically-
di↵erentiated goods sold under a monopolistic competition market structure. Within this framework,
the number of farmers engaged in direct-selling (and consequently, the set of varieties) can be deter-
mined endogenously as a function of the size of the urban population. Regarding spatial aspects, our
model builds on the pioneering contributions of Von Th¨unen [1827] and Alonso [1964]. However, we
relax the simplifying assumption that space is homogeneous in all respects except for distance to the
city center, and instead, consider that the features of the city a↵ect the characteristics of each loca-
tion. Thus, the economy is modeled as a monocentric city where market access and urban pollution
are spatial externalities. These externalities which depend on the size of the city and the spread of
the pollution over space, induce spatially-varying levels of productivity within the region, and lead
to heterogeneity among farmers.3Hence, although farmers are supposed ex ante to be homogeneous
3Note that in this respect, this paper is related to the literature on international trade with monopolistic competition
and heterogeneous firms which shows that productivity heterogeneity is important for explaining the structure of markets
and trade flows [see e.g. Melitz [2003]; Helpman et al. [2003]; Yeaple [2005]].
3
producers with the same ability to grow crops, they may become heterogeneous ex-post due of their
spatial location within the region. For simplicity, we adopt a partial equilibrium approach in which
conventional farming and the urban sectors are not described explicitly. However, it should be noted
that the inclusion of a land market allows us to retain important urban-rural linkages.
As in a standard non-spatial model with monopolistic competition, we find that the profit of
farmers involved in direct-selling increases with population size. However, when accounting for the
spatial externalities related to city size, the relationship becomes more complex. For instance, we
show that in highly urban-crowded regions, only the most productive farmers remain in the market
because of the fiercer competition over land acquisition. As a result, regions hosting an intermediate-
sized city are more likely to show a wider range of variety. Additionally, we would stress that spatial
heterogeneity in productivity levels a↵ects our benchmark results. We highlight that by creating
distortions in the competition among farmers, heterogeneity can have concomitant undesired e↵ects
on both the quality and range of available varieties. We provide some preliminary findings showing
that higher urban pollution can hinder as well as foster the production of a direct-selling farmer relative
to competitors, with explicit consequences for the quality of the goods supplied. Thus, we emphasize
a quality-quantity-variety trade-o↵which depends completely on spatial variations in agricultural
productivity. This supports our previous statement that when introducing the impact of externalities
on a surrounding space, it is necessary to account for potential heterogeneity in order to properly
capture the implications of urban proximity on direct-selling developments.
The paper is organized as follows. Section 2presents the model. Section 3describes the mar-
ket equilibrium, keeping the range of direct-selling varieties fixed, and studies how the relationships
between quantity, quality and variety are a↵ected by externalities depending on whether they are
spatially-varying (heterogeneous case) or not (homogeneous case). Section 4discusses the free-entry
equilibrium, and provides some insights into the relationship between market entry and city size.
Section 5summarizes our findings and identifies some possible extensions to this research.
4
2 The framework
Consider an economy which includes a population split exogenously into urban and rural households,
and two sectors: a perfectly competitive sector which provides a homogeneous aggregate good, and
an agricultural sector where farmers can choose between direct-selling or conventional marketing.
Conventional farmers produce a homogeneous good under perfect competition, while farmers en-
gaged in direct-selling operate under monopolistic competition and provide a quality-di↵erentiated
good through a short-supply chain.
2.1 The spatial structure
The economy is described formally as a one-dimensional space encompassing both urban and rural
areas. The region has a central business district (CBD). Distances and locations are denoted xand
measured as the distance from this CBD. Without loss of generality, we focus on the right-hand side
of the region since the left-hand side is perfectly symmetrical.
The urban area is used entirely for residential purposes. Urban households are assumed to be
distributed uniformly across the city, and consume a plot of fixed size 1
(thus, captures the urban
density, i.e. the number of urban households per unit of land). Let ube the size of the urban
population, then the right endpoint of the city is:
¯xu=u
2.(1)
Farmers live and produce in areas located in the city periphery. Assuming that each farmer uses
one unit of land to produce, the right endpoint of the region is given by:
¯x=¯xu+s+c
2(2)
where sand care the numbers of direct-selling farmers and conventional farmers respectively.
Finally, ¯xsdenotes the boundary between direct-selling and conventional farming, and Xsis the
range of locations hosting direct-selling production. It should be noted that depending on the regional
land allocation, the direct-selling farming takes place either near the city on plots such that x2[¯xu;¯xs]
(described as ”near-city farming”), or on plots far from the city such that x2[¯xs;¯x] (described as
”rural farming”). Figure 1depicts these two configurations.
5
Figure 1: The spatial structure and urban pollution.
Urban pollution Rural areas are exposed to urban pollution which causes yield losses that are pro-
portional to the level of pollution in each location. The source of this pollution is located in the CBD,
and its intensity h(x, u) is supposed to be increasing with the level of urban activities (hu>0) but
decreasing with respect to the distance from the city center (h(0,
u)>0 and hx<0).
2.2 The direct-selling farming
Farmers engaged in direct-selling produce a unique variety vusing labor, one unit of land, and an
amount zof productivity-enhancing inputs (i.e. synthetic chemicals such as pesticides and fertilizers).
We assume that each variety is produced by a single farmer, implying that any variety vcan be
identified equivalently by the location xwhere it is grown.
Supply-chain and market access costs. To sell their production, direct-selling farmers must transport
it to the central market located in the city center. This incurs market access costs t(x) which are
increasing with distance, and are expressed as units of working-time required for transporting goods
6
to the market.4Therefore, market access costs a↵ect production levels by the reduction in the time
spent growing agricultural goods: the farther from the city center, the less time is available to grow
crops, and the smaller will be the production. This creates an incentive for farmers to locate close to
the urban fringe, and captures the opportunity cost of remoteness from the city center.
Production and externalities. The production function accounts for the e↵ects of both market access
costs and urban pollution on total output. Using ¯qto denote the natural ability of soils to grow crops
in the region, and qv(z, x, u) to denote the quantity of the variety vproduced at x, we assume:
qv(z,x, u)= ¯qz ⇥e(t(x),h(x, u)) (3)
where 0 <e(t(x),h(x, u)) 1 is the agricultural productivity coefficient at xfor a city size of u–or
similarly, e(t(x),h(x, u))11 corresponds to the yield-loss rate. The function eis decreasing with
t(x) and h(x, u), and its value is influenced by the total space-related e↵ect of location on production
levels. Formally, it encompasses the impacts of pollution and market access costs which operate in
opposite directions as the distance from the CBD increases. It is easily verified that di↵erentiating
e(t(x),h(x, u)) with respect to x, yields ex⌘@e
@t
dt
dx +@e
@h
@h
@x=|ett0(x)|+|ehhx|. Hence, from any
location to the directly neighboring one that is farther from the city center, productivity is decreasing
if the impact of market access costs (|ett0(x)|) outweighs the reduced yield losses due to urban pollution
(|ehhx|), and increasing otherwise.
In order to keep the discussion as broad as possible, we do not specify the shape of e(t(x),h(x, u)).
However, for the sake of tractability, we assume that the function is additively separable. This implies
that there is no correlation between yield losses due to the pollution and to market access costs
(et,h = 0). We posit also that e(0,0) = 1 meaning that in the absence of spatial externalities,
agricultural production is given by combining soil quality and inputs use. Finally, observe that if
the externalities are invariant in space (i.e. e(t(x),h(x, u)) = ˆe(t, h(u)) 8x), direct-selling farmers
operate in a spatially-homogeneous competitive environment: they experience the same productivity
levels ˆe(t, h(u)) and supply the same quantities ˆqof the same quality ˆ
✓.
4This specification where producers allocate their time between 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.
7
Rewriting (3) so as to isolate z, and for simplicity setting ¯q= 1, yields the quantity of synthetic
chemicals used by the farmer located at x:
z(qv,x,
u)= qv
e(t(x),h(x, u)) (4)
We can easily verify from (4) that supplying a large quantity of any variety qvalways requires
more inputs z. Likewise, inputs use zis more intensive when the productivity coefficient at x,
e(t(x),h(x, u)) is low.
The operating profit The profit of a direct-selling farmer, ⇡s,v, is given by the receipts from his sales
minus a total cost which consists of a fixed cost associated to the purchase of one unit of land at x,
and a constant marginal cost of inputs. Letting pvbe the price of the variety v,pzthe unit cost of
the productivity-enhancing inputs, and R(x) the unit rent for the land at x,wehave:
⇡s,v(pv,q
v,x,
u)=pv⇥qv[R(x)+pzz(qv,x,
u)] (5)
2.3 Preferences and demand
Consumers have a taste for variety–in the understanding in Dixit and Stiglitz [1977]– and are sensitive
to the quality of the direct-selling products.5To capture both the taste for variety and the consumers’
valuation of quality, we use the utility specification from Hallak [2006]. Consumers share the same
Cobb-Douglas preferences for two types of goods; a homogeneous composite good M–chosen as the
num´eraire and including the conventional agricultural good– and a quantity index presenting the s
di↵erentiated varieties of direct-selling goods Qs:
U(Qs,M)=8
>
<
>
:
U(M) for s=0
Q↵
sM1↵for s>0
(6)
with
Qs=✓Zs
0
(✓v)(qv)1
dv◆
1
(7)
and where ✓vstands for the (perceived) quality of the variety v,>1 is the elasticity of substitution
between any two varieties, and represents the preference for quality (with 0 <<1 ). Utility is
increasing with respect to the number of varieties sand the quality .
5Interested readers should refer to Abdel-Rahman [1988], Fujita [1988]orOgawa [1998] for examples of models
introducing Chamberlinian monopolistic competition and taste-for-variety `a la Dixit and Stiglitz [1977]inanAlonso
[1964] type model featuring a continuous location-space.
8
Demand Consumers live in the urban area and work in the CBD. They earn the same income wuand
bear urban costs, given by the sum of commuting and housing costs. Denoting the unit commuting
cost as tu, and recalling that R(x) is the land rent at x, we can define the urban net income as:
⇣u(x)⌘wu✓tux+R(x)
◆(8)
In Appendix A we show that at the residential equilibrium, the urban net income ⇣u(x) is invariant
in space so that, ⇣u(x)=⇣u8x. Expenditure on the composite good and the aggregate of direct-selling
goods are derived from the maximization of the utility (6) subject to the (binding) budget constraint
PQ
s+M=⇣u:
M=(1↵)⇣uand Qs=↵⇣u
P(9)
where Pis the price index for the range of direct-selling varieties supplied in the region.
We establish from (9) that expenditure on aggregates of direct-selling goods are ↵⇣u;thus,the
(binding) budget constraint for direct-selling goods consumption is given by ↵⇣u=Zs
0
pvqvdv. Max-
imizing the sub-utility (7) subject to this constraint leads to the following demand function for any
variety v:
qv=(✓v)(pv)P1↵⇣uu(10)
with the (quality-adjusted) price index for direct-selling goods
P=✓Zs
0
(✓v)(pv)1dv◆
1
1
(11)
Goods quality Direct-selling goods di↵er in quality ✓v. This quality, as perceived by consumers, is
assumed to be linked to the quantity of synthetic chemicals used in production as follows:
✓v=¯
✓
z(qv,x,
u)(12)
where ¯
✓is the maximum quality level.
Observe that here, quality refers to consumers’ perceptions rather than to real organoleptic prop-
erties. In other words, we suppose that consumers are aware of the quantity of synthetic chemicals
used for each variety, and are reluctant to purchase goods grown with large amounts of these inputs.6
6Evidence on the link between food quality, safety, and the willingness-to-pay for synthetic-free products is provided
in Grunert [2005]andMarette et al. [2012].
9
Plugging (4)into(12), using the resulting expression of ✓vin (10), and solving for qvyields:
qv(pv,x,
u)=✓⇥¯
✓e(t(x),h(x, u))⇤
1p
1
v(↵⇣uu)1
1P◆⌘
(13)
where ⌘⌘1
1+ is the elasticity of demand with respect to the direct-selling price index, i.e. the
impact of a marginal increase in Pon the demand for any variety v.
2.4 The market structure
Direct-selling farmers operate in a local market under monopolistic competition; in contrast to con-
ventional farming, they can set their own prices because they sell di↵erentiated products and also do
not interact with an intermediary. They supply close substitutes and are free to enter or exit the
market.
Pricing Each direct-selling farmer sets his price so as to maximize his profit and taking the price
index Pas a constant. Plugging (13)into(5) and equating the first derivative of ⇡s,v(pv,x,
u)with
respect to pvto zero yields the equilibrium price of the variety vproduced at x:7
pm(x, u)=
(1 )1✓pz
e(t(x),h(x, u)) ◆(14)
where mlabels the equilibrium variables, and >1
1must hold for pm(x, u) to be positive. Note
that to lighten the expressions, we drop the index v, each variety being identified by the (unique)
location x2Xswhere it is grown.
The first element of (14) is the monopolistic mark-up. It is always greater than 1 and increases with
the quality elasticity of demand , reflecting the fact that farmers are well aware that consumers are
concerned over product quality. 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 pzbut also with the yield-loss
rate, meaning that farmers partially pass on the charge of urban pollution and market access costs to
consumers.
Market share and competition Using Eqs (4) and (11)–(14) to calculate the price index P, and re-
injecting its value in (13) gives the demand for any direct-selling variety qas a function of x,uand
s. Multiplying this expression of q(x, u,
s)bypm(x, u), we obtain the receipts of the direct-selling
7Note that, ⇡s,v (pv,x,
u)isconcaveinpvfor p< pz
e(t(x),h(x,u))
+(1+)
(1+), a condition verified at the equilibrium price.
10
farmer located at x:
r(x, u,
s)⌘q(x, u,
s)⇥pm(x, u)= ↵⇣uu
S(u,
s)e(t(x),h(x, u))⌘(15)
where S(u,
s)⌘2ZXs
e(t(x),h(x, u))⌘dx captures the supply-side market potential of direct-selling
food production: The higher S(u,
s), the greater the possibility for direct-selling farming to produce
large quantities of any variety (intensive margin), or alternatively, a large range of varieties (extensive
margin). We show also in Appendix B that S(u,
s) is decreasing with u; for any large city, urban
pollution and market access costs are high, inducing lower levels of the productivity coefficient at
each location x, and thereby, a lower market potential. Hence, in our model, urbanization increases
the cost of production in the neighboring farmland. This is in line with the empirical evidence that
agriculture tends to disappear near large cities.
Finally, we derive from (15) the market share sof the direct-selling farmer located at x:
s(x, u,
s)⌘r(x, u,
s)
2ZXs
r(x, u,
s)dx
=e(t(x),h(x, u))⌘
S(u,
s)(0 <s(x, u,
s)1) (16)
As (15) shows, the numerator e(t(x),h(x, u))⌘corresponds to the location-dependent part of the
receipts. Hence, the larger the productivity coefficient at x, the higher the market share of the farmer
producing at this location. In Appendix B, we establish the following properties:
1. The spatial variation of the market share follows that of e(t(x),h(x, u)) and when productivity
is homogeneous over space (e(t(x),h(x, u)) = ˆe(t, h(u)) 8x), direct-selling farmers have the
same market share given by ˆs=1
s[see Fig.(3) in Appendix B].
2. Market share is always decreasing with the number of competitors s, and the larger the share
of the farmer located at x, the greater his market share loss [see Fig.(4) in Appendix B].
3. Market share is increasing with the urban pollution h(x, u) for the most productive farmers
but decreasing for farmers with low levels of productivity.
Observe that the last property holds only if externalities vary over space. Indeed, under space-
invariant externalities, urban pollution a↵ects every location to the same extent, and consequently,
has no impact on market shares. More importantly, this underlines that introducing externalities
in our model produces di↵erent consequences, depending on whether these externalities are varying
or not over space. In particular, it is clear that spatial heterogeneity distorts the competition among
farmers, and thus, is more likely to modify the conditions to enter the direct-selling market.
11
3 Direct-selling market equilibrium and goods quality.
3.1 Spatial location and land market equilibrium
To determine the spatial allocation of land between urban households and farmers, we follow Von Th¨unen
[1827] and assume that each plot of land is allocated to the highest bidder. Then the equilibrium land
rent is given by the upper envelope of bid rents, i.e.:
Rm(x) = max{'u(x),'
s(x),'
c(x)}(17)
'u(x), 's(x), and 'c(x) being the respective bid land rents of urban households, direct-selling farmers,
and conventional farmers.
Depending on the ranking of the bid rent curves, various land use configurations emerge. In this
study, we concentrate on the case where the zone dedicated to direct-selling farming is located at the
periphery of the city and right-bordered by the conventional farming area (i.e., Xs=[¯xu;¯xs]). Also,
for simplicity we assume that the conventional bid land rent equals the opportunity cost of land ¯
R.
For ease of reading, the details of the resolution are reported in Appendix A. This shows that the
equilibrium land rent is given by:
Rm(x, u,
s)=
8
>
>
>
>
>
>
<
>
>
>
>
>
>
:
(wu⇣m
u(u,
s)tux)if 0<x¯xu(urban area)
↵ u⇣m
u(u,
s)e(t(x),h(x, u))⌘¯e⌘
S(u,
s)+¯
Rif ¯xu<x¯xs(d-s farming area)
¯
Rif x>¯xs(conventional farming area)
(18)
where ⌘1+
is the Lerner index (0 < <1), ⇣m
u(u,
s) is the urban net income at the land
market equilibrium:
⇣m
u(u,
s)⌘wutuu
2¯
R
↵ u
¯e⌘
u¯e⌘
s
S(u,s)+1 (19)
and ¯euand ¯esare respectively the productivity coefficient at each edge of the direct-selling area (i.e.
e(t(¯xu),h(¯xu,
u) and e(t(¯x),h(¯x, u)).8The positive ⇣m
uimplies that u<2⇣wu¯
R
tu⌘, a condition
assumed to hold in the following. The denominator in (19) captures the e↵ects of spatial heterogeneity.
It corresponds to a measure of the intensity of competition in the land market at the urban fringe;
the more direct-selling farmers are able to outbid, the larger the denominator and the smaller the net
income. Interestingly, we observe that if the productivity is homogeneous over space, competition over
8In our model, represents the bargaining power of direct-selling producers relative to consumers.
12
the acquisition of land at the urban fringe is lowest. Indeed, in this case, the denominator is equal to
1–so that we recover the standard expression for the equilibrium net income in bid-rent models, given
by (wutuu
2¯
R
)– and the cost of land falls to ¯
Rfor every rural location, i.e. for all the locations
x>¯xu.
3.2 Competition, location and goods quality
Using Eqs (15) and (18)–(19)in(5) and rearranging them, yields the direct-selling market equilibrium
profit:
⇡m
s(u,
s)= wutuu
2¯
R
¯e⌘
u¯e⌘
s+S(u,s)
↵ u
⇥¯e⌘
s¯
R(20)
We show in Appendix C that ⇡m
sis decreasing with the number of direct-selling farmers s.
Similarly, we can calculate the quality and the quantity of the variety produced at x, evaluated at
the direct-selling market equilibrium:
✓m(x, u,
s)=
¯
✓pz(1+)
(1)1¯e⌘
u¯e⌘
s+S(u,s)
↵ u
e(t(x),h(x,u))⌘
wutuu
2¯
Rand qm(x, u,
s)= wutuu
2¯
R
pz(1+)
(1)1¯e⌘
u¯e⌘
s+S(u,s)
↵ u
e(t(x),h(x,u))⌘+1 (21)
The terms in square brackets embed all the e↵ects stemming from the introduction of spatial
externalities. qm(x, u,
s) and ✓m(x, u,
s) vary in opposite directions with respect to the level of
productivity e(t(x),h(x, u)); letting xaand xbbe two locations such that {xa,x
b}2[¯xu;¯xs], we can
state that production (resp. the quality) at xais greater (resp. lower) than the production (resp. the
quality) at xbprovided that the agricultural productivity coefficient at xais higher than at xb(i.e.
qm(xa,
u,
s)>q
m(xb,
u,
s) and ✓m(xa,
u,
s)<✓
m(xb,
u,
s) provided that e(t(xa),h(xa,
u)) >
e(t(xb),h(xb,
u))).
The implication for good quality may be counter-intuitive. Indeed, since the use of chemicals
inputs zis decreasing with respect to e(t(x),h(x, u)), we might expect that the quality would be
lower for varieties grown in locations with low levels of productivity. The explanation lies in the
relationship between productivity, demand, and market share. By definition, a farmer with a high
market share has to supply a large quantity of goods which is an incentive to use more inputs in order
to satisfy demand but at the same time, results in loss of quality.
Among the features of the competition in the direct-selling market, we find that the quality of any
variety is improving with the productivity gap (¯eu¯es). Eq.(19) shows that an increase in (¯eu¯es)
13
induces a loss in urban net income due to a fiercer competition in the land market. Consequently,
demand for direct-selling goods is lower which in turn, contributes to an increase in quality.
Lastly, quality can be improved also by increased market potential S(s,
u). This can stem either
from a larger number of direct-selling varieties s, leading to a more competitive market and fragmen-
tation of consumer demand, or from enhancement of the productivity coefficient levels e(t(x),h(x, u)),
resulting in decreased fertilizer use.
Quality, variety and heterogeneity in productivity Table 1presents a summary of our results for the
impact of externalities on net income, quality, and quantity. Specifically, it underlines that more than
the presence or not of externalities, what matters is their variation over space. This table shows that
the space-invariant case has more in common with the scenario without externalities than with the
spatially-varying case.
No externality With externalities
space-invariant (homogeneous case) spatially-varying (heterogeneous case)
e(t(x),h(x, u)) = 1 8x e(t(x),h(x, u)) = ˆe(t, h(u)) 8x e(t(x),h(x, u))
Urban net income (⇣m
u)wutuu
2¯
R
wutuu
2¯
R
wutuu
2¯
R
↵ u
¯e⌘
u¯e⌘
s
S(u,s)+1
Goods quality (✓m)
¯
✓pz(1+)
(1)1s
↵ u⇣wutuu
2¯
R
⌘
¯
✓pz(1+)
(1)1s
↵ u⇣wutuu
2¯
R
⌘
¯
✓pz(1+)
(1)1
2
4
¯e⌘
u¯e⌘
s+S(u,s)
↵ u
e(t(x),h(x,u))⌘3
5
wutuu
2¯
R
Goods quantity (qm)↵ u⇣wutuu
2¯
R
⌘
pz(1+)
(1)1s
↵ u⇣wutuu
2¯
R
⌘
pz(1+)
(1)1s
ˆe(t, h(u)) wutuu
2¯
R
pz(1+)
(1)1
2
4
¯e⌘
u¯e⌘
s+S(u,s)
↵ u
e(t(x),h(x,u))⌘+1
3
5
Tabl e 1 : Urban net income, quality and quantity under a) no externality, b) space-invariant externalities, and c) spatially-
varying externalities.
Table 1sheds light on the quantity-quality-variety trade-o↵. For instance, if externalities do not
vary in space, it is clear that quality is increasing with the range of direct-selling goods. Also, observe
that an increase in the urban pollution has di↵erent consequences depending whether or not the
externalities are space-invariant. Under homogeneous productivity, farmers have the same market
share, implying a flat bid rent for direct-selling farming. Since the externalities do not a↵ect the
land market outcome, urban net income, and therefore, quality are not a↵ected by the level of urban
14
pollution. However, as the costs of production increase due to yield losses, farmers reduce their supply
which entails a price increase.
This result does not hold if externalities are spatially-varying. In this case, the heterogeneity in
productivity introduces distortions in the competition among direct-selling farmers. Depending on
their location, they are a↵ected unequally by yield losses, and do not provide the same quantities
of goods. Hence, although the productivity coefficients decline for all locations which restricts the
technical possibility to grow crops, farmers enjoying better yields can manage this more easily. The
quantity supplied by the least-productive farmers decreases, as does their market share in favor of the
most productive farmers. Ultimately, the market consists of a few significant producers that supply
large quantities of low-quality goods, and small producers that o↵er better-quality goods but in (very)
small quantities –or equivalently, at a (very) high price.
More generally, we derive the following proposition:
Proposition 3.1 Increasing the level of the urban pollution a↵ects the quality and the quantity of
direct-selling goods in di↵erent ways depending whether or not externalities are varying over space.
This proposition raises an essential question regarding the adequate range of direct-selling varieties.
So far, the number of farmers engaged in direct-selling has been assumed to be fixed. However, under
increasing competitive pressure, farmers may be forced to exit the market due to lack of sufficient
operating profit, resulting in a smaller range of varieties. We investigate this in the next section by
relaxing the assumption of an exogenous number of varieties.
4Thefree-entryequilibrium.
Here, we allow for free entry and exit. In our framework, the market converges to equilibrium through
the following mechanism: the entry of a new competitor in the direct-selling market drives profits
down and induces a decrease in the direct-selling bid rent which tends to smooth over space (depicted
in Figure(2)). Farmers continue to enter the direct-selling market as long as the profit they can earn
remains higher than the (exogenous) equilibrium profit prevailing for conventional farming ⇡c.
15
Figure 2: Direct-selling farmers entrance, land allocation and profits. In this example, the entry of an additional farmer
in the direct-selling sector is illustrated by the displacement of the direct-selling fringe ¯x.Thisentailsadecreaseinthe
direct-selling profit ⇡m
s,andconsequently,adecreaseinthelandbidrentofdirect-sellingfarmers's(x).
4.1 The equilibrium number of direct-selling varieties.
Since the profit of direct-selling farmer ⇡m
sis decreasing with the number of farmers sinvolved in the
market, the free-entry equilibrium is ensured to be a unique stable interior solution. Let us assume zero
profit for conventional agriculture. Then, solving ⇡m
s(u,
s)=⇡c= 0, the number of direct-selling
varieties at the free-entry equilibrium ⇤
sis verified:9
↵ u
=S(u,
s)
✓wutuu
2
¯
R◆¯e⌘
s¯e⌘
u
(22)
The LHS of (22) denotes the demand-side market e↵ect. It is increasing with the size of the
urban population uand the Lerner index , and acts as a home market e↵ect (HME); as the
size of the urban population rises, the incentive to enter the direct-selling market increases. The
RHS captures the supply-side competition e↵ect, and is increasing with the number of direct-selling
farmers. The term (wutuu
2) represents the highest potential bid of the urban households in the
land market at the urban fringe. It corresponds to the price of land that would completely absorb
their net income. Reported on the opportunity cost of land ¯
R, the ratio measures the power of
urban households in the land market at the urban fringe. It corresponds to the price of land that
would absorb their net income completely. Reported on the opportunity cost of land ¯
R, the ratio
9Note that (22) can be written alternatively as ¯ss=✓¯
R⇥¯su+
↵ u
wutuu
2◆, meaning that farmers continue to enter the
market until the market share of the latest entrant reaches a floor value.
16
measures the power of urban households in the land market, relative to the farmers. The larger
(wutuu
2
¯
R), the wealthier the households and the greater the opportunities for farmers to enter the
direct-selling market. Finally, observe that the existence of this equilibrium only holds if the di↵erences
in productivity among the farmers located at the direct-selling boundaries ¯xuand ¯xsis not too large,
i.e. 1 >¯es
¯eu>✓¯
R
wutuu
2◆1
⌘
>0.
Using the equilibrium condition (22), we can calculate the quantity and quality of direct-selling
goods at the free-entry equilibrium. These values are provided below.
Table 2is interesting in that it highlights that compared to the homogeneous case, the urban net
income and the quality of direct-selling goods are always lower under heterogeneous productivity, while
the quantities of some varieties may be larger.
No externality With externalities
space-invariant (homogeneous case) spatially-varying (heterogeneous case)
e(t(x),h(x, u)) = 1 8x e(t(x),h(x, u)) = ˆe(t, h(u)) 8x e(t(x),h(x, u))
Urban net income (⇣⇤
u)wutuu
2¯
R
wutuu
2¯
R
wutuu
2¯
R
(¯eu
¯es)⌘
Goods quality (✓⇤)
¯
✓pz(1+)
(1)1
¯
R
¯
✓pz(1+)
(1)1
¯
R
¯
✓pz(1+)
(1)1
¯
Rh¯es
e(t(x),h(x,u)) i⌘
Goods quantity (q⇤)((1)1) ¯
R
pz(1+)
((1)1) ¯
R
pz(1+)ˆe(t, h(u)) ((1)1) ¯
R
pz(1+)he(t(x),h(x,u))⌘+1
¯e⌘
si
Tabl e 2 : Urban net income, quality and quantity at the free-entry equilibrium.
4.2 Direct-selling varieties and the city size.
The relationship between the size of the urban population and the range of direct-selling varieties
is not trivial since it a↵ects both the supply and demand sides of the market. On the one hand, a
highly-populated city provides an incentive for farmers to enter the direct-selling market since they
will benefit from a high level of demand. On the other hand, city size influences the level of the spatial
externalities a↵ecting both pollution intensity and market access costs, and inducing variations in
the productivity coefficient over space. Moreover, including the land market introduces additional
spillover e↵ects related to the impact of the externalities on the level of competition for land. In what
follows, we analytically study this relationship. For clarity, we proceed in two steps.
City size and direct-selling farming with space-invariant externalities ˆe(t, h(u)).Consider first that ex-
ternalities do not vary in space. In this case, the relationship between the range of direct-selling
17
varieties at the free-entry equilibrium and the size of the urban population is given by the Cartesian
equation ↵ u¯
Rˆ
⇤
s
wutu
2u¯
R
= 0 leading to:
ˆ
⇤
s(u)=↵ u
¯
R✓wutu
2u¯
R
◆(23)
Eq.(23) describes a concave curve which emerges from the interplay between two standard compet-
ing e↵ects in urban economics: (i) a market size e↵ect which has a positive and linear e↵ect, leading
farmers to enter the direct-selling market in order to benefit from the additional consumers, and (ii) a
(negative) net income e↵ect –based on fiercer competition among urban households in the land market,
and thereby, increasing housing cost– which restricts expenditure in the direct-selling market at an
increasing rate. The range of direct-selling varieties rises as long as the market size e↵ect outweighs the
net income e↵ect. After that, it reaches a threshold value beyond which any further urban population
growth leads to decreased variety.
Proposition 4.1 In presence of space-invariant externalities, direct-selling farming is more likely to
provide a wider range of varieties in regions hosting an intermediate-sized city.
This proposition conveys an idea that is in line with Aguglia et al. [2008]; testing whether direct-
selling farming is more widely di↵used in peri-urban areas, they found both positive and negative
coefficients, suggesting that the adoption of direct-selling is the result of trade-o↵s between the ad-
vantages and drawbacks stemming from proximity to an urban center.
City size and direct-selling farming with spatially-varying externalities. Since the function e(t(x),h(x, u))
is not specified explicitly, solving the implicit Cartesian equation when externalities vary over space
becomes more complicated. However, recalling that ⇡s(u,
⇤
s) does not vary at the free-entry equi-
librium (⇡s(u,
⇤
s)=⇡c= 0), and using the total di↵erential, we can sketch the relationship between
urban population size and the number of direct-selling varieties, given by @⇤
s
@u=@⇡s
@u⇥
@⇡s
@s
1:
@⇤
s
@u
=¯ss¯su
⇣¯ss+⌘|ex(¯xs)|
2¯es⌘¯su"@ˆ
⇤
s
@u
+su(¯xs)su(¯xu)
(¯ss¯su)¯ss#(24)
with the simplifying notations ¯su⌘s(¯xu,
u,
⇤
s), ¯ss⌘s(¯xs,
u,
⇤
s), su(¯xu)⌘@s
@u(¯xu,
u,
⇤
s),
su(¯xs)⌘@s
@u(¯xs,
u,
⇤
s), and ⌘wutuu
2
¯
R.10 Note that to allow easier comparison with the space-
10The details of the calculations are provided in Appendix C.
18
invariant case, Eq.(24) has been rearranged to make the expression @ˆ
⇤
s
@uapparent. Doing so, makes it
easy to verify that introducing spatial heterogeneity in productivity induces two major changes.
Considering first the land market, the bid rent now di↵ers from one direct-selling farmer to another,
reaching a higher price than the opportunity cost of the land ¯
Rfor all locations benefiting from a
higher productivity coefficient than the border ¯xs. To confirm this, we can calculate the free-entry
equilibrium land rent using (18) and (22):
R⇤(x)=
8
>
>
>
>
>
>
<
>
>
>
>
>
>
:
tu(¯xux)+ ¯
R✓¯eu
¯es◆⌘
if 0<x¯xu(urban area)
¯
R✓e(t(x),h(x, u))
¯es◆⌘
if ¯xu<x¯x⇤
s(direct-selling farming area)
¯
Rif x>¯x⇤
s(conventional farming area)
(25)
Farmers in high-productivity locations generate a larger operating profit and can outbid other
farmers which increases competition in the land market and leads to an increase in the land cost. As
a result, urban households have a lower net income available to purchase food, producing a weaker
demand-side market potential, a lower incentive to enter the direct-selling market, and a smaller range
of varieties. This spillover e↵ect is captured by ¯ss¯su
⇣¯ss+⌘|ex(¯xs)|
2¯es⌘¯su
<1 and implies that for the same
city size, direct-selling farming will always provide a smaller range of varieties in a region with spatial
heterogeneity.11
Second, spatial heterogeneity introduces distortions in competition between the producers engaged
in the direct-selling market (su(¯xs)su(¯xu)
(¯ss¯su)¯ss). Because of the spatial variations in productivity, the
market is not distributed equally among the farmers. Therefore, as already mentioned, an increase in
the size of the city a↵ects the farmers di↵erently according to their market share (su(xa)6=su(xb)if
s(xa)6=s(xb)). Using the expressions of su(¯xs) and su(¯xu) reported in Appendix D and rearranging,
we show that:
su(¯xs)su(¯xu)
(¯ss¯su)¯ss
=⌘
2
¯e⌘1
sex(¯xs)¯e⌘1
uex(¯xu)
(¯e⌘
s¯e⌘
u)¯ss
+(¯eu
¯es)⌘1
+⌘|ehhu|
¯ss ⇠¯e⌘1
s¯e⌘1
u
¯e⌘
s¯e⌘
u!(26)
where ⇠⌘R¯xs
¯xue(t(x),h(x,u))⌘1dx
R¯xs
¯xue(t(x),h(x,u))⌘dx >1isthesectoral shortfall rate due to the externalities.12
11Observe in this respect that in the very specific case where externalities would be such that ¯eu=¯esand
e(t(x),h(x, u)) ¯es8x2]¯xu,¯xs[, the land rent would have the shape of a concave parabola that verifies '⇤(¯xu)='⇤(¯x)
and this e↵ect does not apply.
12See Appendix E for additional explanations on expected profit-loss rate, e↵ective profit-loss rate and sectoral shortfall
19
The first term in (26) embeds the comparative e↵ect of a change in productivity due to the marginal
extra distance from the city center which itself depends on the (negative) impact of the market access
cost relative to the (positive) impact of moving away from the pollution source. The second term
represents the marginal displacement of the direct-selling farming area within the regional space. The
third and last part of (26) captures the overall pollution intensity e↵ect. It compares the sectoral
shortfall rate ⇠to the di↵erential yield-losses at the boundaries ( ¯e⌘1¯e⌘1
u
¯e⌘¯e⌘
u)>1, and can be positive
or negative.
Ultimately, it seems that depending on the relative weight of each e↵ect, the range of varieties
can either decrease or increase. It should be noted that in order to obtain further insights we would
require additional assumptions about the shape and variations in the productivity coefficient over
space. However, observe that simple preliminary calculations reveal that the case where heterogeneity
would favor development of direct-selling occurs under very specific and restrictive conditions. These
include a wealthy urban population (high) and a nearly smooth spatial variation in externalities at ¯xs
but sharp at ¯xu(ex(¯xs)!0 and ex(¯xu)⌧0) –so that ¯ss¯su
⇣¯ss+⌘|ex(¯xs)|
2¯es⌘¯su
!1and su(¯xs)su(¯xu)
(¯ss¯su)¯ss>0.
Finally, we can derive the following proposition:
Proposition 4.2 For the same size of urban population, direct-selling farming is more likely to pro-
vide a smaller range of varieties in a region displaying spatial heterogeneity in productivity, all things
being equal.
5 Concluding remarks
The paper set out to develop a theoretical framework with a high level of generalization but still
analytically tractable, allowing investigation of whether direct-selling farming can develop close to
highly-crowded cities when the negative e↵ects (externalities) associated to urban proximity are taken
into account. Regarding the relationship between urban population size and direct-selling farming, we
showed that proximity to large cities can foster direct-selling farming development provided that the
market size e↵ect dominates the net income e↵ect. A corollary of this result is that regions hosting
an intermediate-sized city are likely to supply more varieties.
Additionally, we studied how heterogeneity in productivity levels a↵ects our benchmark results. We
highlighted that spatial heterogeneity in productivity creates distortions in the competition among
rate.
20
farmers; whilst the market is split equally between farmers in the homogeneous case, the spatial
variations in productivity allow farmers located on the most productive plots of land to enjoy external
rents, based on a higher market share. By modifying the conditions for market entry and survival,
spatial heterogeneity has concomitant undesired e↵ects on both the quality and range of varieties,
and could lead to a situation where just few producers share the market, supplying large quantities of
low-quality goods. This underlines that accounting for heterogeneity is necessary to properly capture
the implications of urban proximity on direct-selling development.
Depending on the main motivation, some aspects such as perception of quality (impact of urban
pollution on goods quality, soil contamination...), the type of pollution, and or the production technol-
ogy (labor employment, farm size, mixed cropping) could be examined in more depth. The analysis
could be extended also by increasing the scope to cover other environmental and welfare issues related
to urban-rural linkages. For instance, I the context of public policy, a brief overview of our findings
would seem to suggest that in general, policies are required (i) to allow direct-selling farming to develop
and thrive near very populous cities –provided that the market outcome is proven to be sub-optimal
from a welfare standpoint, and (ii) to control for the potential distortions to the competition to both
enhance the quality and diminish the price of the available range of varieties.13 It must be borne in
mind also that although we focused exclusively on the impact of cities on agriculture, the pollution
issue is a two-way relationship. Thus, handling welfare aspects would necessarily require this feature
to be accounted for.
13Note in this respect that, in ‘Future of the CAP after 2013’, the European Parliament [2010] makes it clear
that increased competitiveness at di↵erent levels including local markets, should be a fundamental objective of the
CAP post-2013.
21
References
Abdel-Rahman, H. (1988). Product Di↵erentiation, Monopolistic Competition and City Size. Re-
gional Science and Urban Economics, 18(1):69 – 86.
Adams, R. M., Hamilton, S. A., and McCarl, B. A. (1986). The Benefits of Pollution Control: The
Case of Ozone and U.S. Agriculture. American Journal of Agricultural Economics, 68(4):886–893.
Aguglia, L., De Santis, F., Salvioni, C., et al. (2008). Direct Selling: a Marketing Strategy to
Shorten Distances between Production and Consumption. In presentation at the 113th EAAE
Seminar, Greece.
Alonso, A. D. (2011). Farmers’ Involvement in Value-added Produce: the Case of Alabama Growers.
British Food Journal, 113(2):187–204.
Alonso, W. (1964). Location and Land Use : Toward a General Theory of Land Rent. Harvard
University Press.
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.
Bento, A. M., Franco, S. F., and Kaffine, D. (2006). The efficiency and distributional impacts of
alternative anti-sprawl policies. Journal of Urban Economics, 59(1):121–141.
Berry, D. (1978). E↵ects of Urbanization on Agricultural Activities. Growth and Change, 9(3):2–8.
Cavailh`es, J., Peeters, D., S´ekeris, E., and Thisse, J.-F. (2004). The periurban city: why to live
between the suburbs and the countryside. Regional Science and Urban Economics, 34(6):681–703.
Coisnon, T., Oueslati, W., and Salanie, J. (2014). Urban sprawl occurrence under spatially varying
agricultural amenities. Regional Science and Urban Economics, 44(0):38–49.
Deutsch, L., Dyball, R., and Ste↵en, W. (2013). Feeding Cities: Food Security and Ecosystem Sup-
port in an Urbanizing World. In Urbanization, Biodiversity and Ecosystem Services: Challenges
and Opportunities, pages 505–537. Springer Netherlands.
22
Dixit, A. K. and Stiglitz, J. E. (1977). Monopolistic Competition and Optimum Product Diversity.
American Economic Review, 67:297–308.
Dodds, R., Holmes, M., Arunsopha, V., Chin, N., Le, T., Maung, S., and Shum, M. (2014).
Consumer Choice and Farmers’ Markets. Journal of Agricultural and Environmental Ethics,
27(3):397–416.
European Parliament (2010). Resolution on the Future of the Common Agricultural Policy after
2013,. Technical report. http://www.europarl.europa.eu/sides/getDoc.do?pubRef=-//EP/
/NONSGML+TA+P7-TA-2010-0286+0+DOC+PDF+V0//EN.
Fujita, M. (1988). A Monopolistic Competition Model of Spatial Agglomeration: Di↵erentiated
Product Approach. Regional Science and Urban Economics, 18(1):87 – 124.
Grunert, K. G. (2005). Food Quality and Safety: Consumer Perception and Demand. European
Review of Agricultural Economics, 32(3):369–391.
Hallak, J. C. (2006). Product Quality and the Direction of Trade. Journal of International Eco-
nomics, 68(1):238–265.
Helpman, E., Melitz, M. J., and Yeaple, S. R. (2003). Export versus FDI. NBER.
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.
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.
Kuik, O., Helming, J., Dorland, C., and Spaninks, F. (2000). The Economic Benefits to Agriculture
of a Reduction of Low-level Ozone Pollution in The Netherlands. European Review of Agricultural
Economics, 27(1):75–90.
Lopez, R. A., Adelaja, A. O., and Andrews, M. S. (1988). The E↵ects of Suburbanization on
Agriculture. American Journal of Agricultural Economics, 70(2):346–358.
23
Low, S. A. and Vogel, S. J. (2011). Direct and Intermediated Marketing of Local Foods in the
United States. USDA-ERS Economic Research Report, (128).
Lucas, R. E. and Moll, B. (2014). Knowledge Growth and the Allocation of Time. Journal of
Political Economy, 122(1).
Marette, S., Messean, A., and Millet, G. (2012). Consumers Wwillingness to Pay for Eco-friendly
Apples under Di↵erent Labels: Evidences from a Lab Experiment. Food Policy, 37(2):151–161.
Marshall, F., Ashmore, M., and Hinchcli↵e, F. (1997). A Hidden Threat to Food Production: Air
Pollution and Agriculture in the Developing World. Sustainable Agriculture and Rural Livelihoods
Programme, International Institute for Environment and Development.
Martinez, S. (2010). Local Food Systems: Concepts, Impacts, and Issues. Technical report, U.S.
Department of Agriculture.
Melitz, M. J. (2003). The Impact of Trade on Intra-industry Reallocations and Aggregate Industry
Productivity. Econometrica, 71(6):1695–1725.
Miles, S. and Frewer, L. J. (2001). Investigating Specific Concerns about Di↵erent Food Hazards.
Food Quality and Preference, 12(1):47–61.
Ogawa, H. (1998). Preference for Product Variety and City Size. Urban Studies, 35(1):45–51.
Pearson, D., Henryks, J., Trott, A., Jones, P., Parker, G., Dumaresq, D., and Dyball, R. (2011).
Local Food: Understanding Consumer Motivations in Innovative Retail Formats. British Food
Journal, 113(7):886–899.
Renting, H., Marsden, T. K., and Banks, J. (2003). Understanding Alternative Food Networks: Ex-
ploring the Role of Short Food Supply Chains in Rural Development. Environment and Planning
A, 35(3):393–412.
Trobe, H. L. (2001). Farmers’ Markets: Consuming Local Rural Produce. International Journal of
Consumer Studies, 25(3):181–192.
Von Th¨unen, J. H. (1827). Der isolierte Staat in Beziehung auf Landwirtschaft und Na-
tional¨okonomie. Perthes Verlag.
24
Williams, P. R. and Hammitt, J. K. (2001). Perceived Risks of Conventional and Organic Produce:
Pesticides, Pathogens, and Natural Toxins. Risk Analysis, 21(2):319–330.
Wu, J., Fisher, M., and Pascual, U. (2011). Urbanization and the Viability of Local Agricultural
Economies. Land Economics, 87(1):109–125.
Yeaple, S. R. (2005). A Simple Model of Firm Heterogeneity, International Trade, and Wages.
Journal of International Economics, 65(1):1–20.
25
Appendix A: The land market equilibrium and land use
The equilibrium land rent is given by the upper envelop of bid rents, that is:
R(x) = max{'u(x),'
s(x),'
c(x)}(27)
'u(x), 's(x), and 'c(x) being the bid land rent of urban households, direct-selling farmers, and
conventional farmers, respectively. For simplicity, we assume also that the conventional bid land rent
equals the opportunity cost of the land ¯
R.
The urban bid rent Plugging (9)into(6) and rearranging gives the indirect utility of urban households:
Vu(x)=⇣↵
P⌘↵(1 ↵)1↵✓wutuxR(x)
◆(28)
At the residential equilibrium, the urban bid rent 'u(x) must solve V0
u(x) = 0 or equivalently,
'0
u(x)=tuwhich solution is given by 'u(x)= ¯
Rutux,¯
Rubeing a constant. Replacing R(x)by
the value of 'u(x)inEq.(8), the urban net income becomes:
⇣u(x)⌘wu¯
Ru
=⇣u(29)
which is the same across urban households, whatever their location.
The direct-selling bid rent Plugging the price index (11)into(13) and substituting q(x, u,
s)bythe
resulting expression in (5) gives the agricultural profit for a farmer located at x:
⇡s(x, u,
s)=[↵ u⇣u⇥s(x, u,
s)] R(x) (30)
where ⌘1+
is the Lerner index (0 < <1).
Farmers’ location choices are driven by two considerations. On the one hand, producing goods
near the urban boundary allows a reduction in the market access cost. On the other hand, locating
farther from the city center means the farmer is less a↵ected by urban pollution, and su↵ers lower
yield losses.
At the land market equilibrium, the direct-selling bid rent 's(x) must solve @⇡s(x, u,
s)/@x=0
or equivalently, 's0(x)=↵ u⇣u⇥sxwhich solution is given by:
's(x, u,
s)= ¯
Rs+↵ u⇣us(x, u,
s) (31)
¯
Rsbeing a constant. Note from (31) that, because of the negative relationship between the market
shares and the number of competitors, the bids from direct-selling farmers are also decreasing with
s.
26
Land use equilibrium Depending on the ranking of the bid rent curves, several land use configurations
can occur. For our study, we concentrate on the case where the zone dedicated to direct-selling
farming is located at the periphery of the city, and right-bordered by the conventional farming area
(Xs=[¯xu;¯xs]). Mathematically, the direct-selling land bid rent must verify 's(x)>¯
R8x2[¯xu;¯xs[
and 's(x)<¯
R8x>¯xswhich notably implies that:
1. 's(x) is decreasing at ¯xs, meaning that, far from the city center, the market access cost always
dominates the pollution cost (i.e. |et⇥t0(¯xs)|>|eh⇥hx(¯xs)|).
2. The direct-selling land bid rent at the urban fringe must be at least equal to the opportunity
cost of land ('s(¯xu)¯
R), entailing in turn e(t(¯xu),h(¯xu,
u)) e(t(¯x),h(¯x, u)). This condition
ensures that configurations where the direct-selling area is enclosed in the conventional farming
area cannot occur.
In the following, these two conditions are supposed to be verified. Then, knowing that the bid rents
of conventional and direct-selling farmers must equalize at ¯xs,wefind ¯
Rs=¯
R↵ u⇣us(¯xs,
u,
s),
so that we now have:
's(x)= ¯
R+↵ u⇣u[s(x, u,
s)s(¯xs,
u,
s)] (32)
Analogously, we know that the urban bid rent and the direct-selling bid rent must equalize at the
urban fringe ¯xu. Hence, replacing ⇣uby its value in (32) and equating 'u(¯xu)to's(¯xu)yields:
¯
Ru=¯
R+tuu
2+↵ u¯e⌘
u¯e⌘
s
Swu
↵ u
¯e⌘
u¯e⌘
s
S+1 and ¯
Rs=¯
R(wutuu
2¯
R)¯e⌘
s
S
↵ u+¯e⌘
u¯e⌘
s
(33)
From (33), we note that the entry of a new farmer in the direct-selling market leads to an increase
in the intercept of the bid land rent function ¯rbut at the same time tends flatten the function since
its slope is decreasing with respect to s
r. As a result, we can show that a rise in the number of direct-
selling farmers can lead to either an increase or a decrease in the bid, depending on location in the
region. The explanation of this result lies in the variation in the direct-selling profit with respect to
the number of varieties; as already mentioned, a new entrant always leads to a decrease in the market
share of all the competitors already engaged in direct-selling. Consequently, their operating profit is
lower as a result of a loss in terms of location rent. However, at the same time, the new competitor
enters the market with a smaller share which lowers the benchmark value to which the profit of all
farmers should equalize at the land market equilibrium ⇡s(¯xs,
u). Eventually, each farmer can make
27
a higher or a lower bid depending on his own operating profit loss relative to the overall decrease in
direct-selling profits.
Then, plugging ¯
Ruinto the urban and the direct-selling bid land rents leads to:
'u(x)=(wu⇣m
u(u,
s)tux) and 's(x)=↵ u⇣m
u(u,
s)e(t(x),h(x, u))⌘¯e⌘
S(u,
s)+¯
R(34)
where ⇣m
u(u,
s) is the urban net income at the land market equilibrium:
⇣m
u(u,
s)⌘wutuu
2¯
R
↵ u
¯e⌘
u¯e⌘
s
S(u,s)+1 (35)
The direct-selling bid rent follows the spatial variations of e(t(x),h(x, u)); thus, it is decreasing
with the distance from the CBD if the e↵ect of the market access cost dominates the e↵ect of the
urban pollution externality, and is increasing otherwise. Combining (27) and (34), the equilibrium
land rent is finally given by:
Rm(x, u,
s)=
8
>
>
>
>
>
>
<
>
>
>
>
>
>
:
(wu⇣m
u(u,
s)tux)if 0<x¯xu(urban area)
↵ u⇣m
u(u,
s)e(t(x),h(x, u))⌘¯e⌘
S(u,
s)+¯
Rif ¯xu<x¯xs(d-s farming area)
¯
Rif x>¯xs(conventional farming area)
(36)
Appendix B: Market share
The market share of the direct-selling farmer located at xis given by:
s(x, u,
s)=e(t(x),h(x, u))⌘
S(u,
s)(0 s(x, u,
s)1) (37)
where S(u,
s)⌘2ZXs
e(t(x),h(x, u))⌘dx captures the supply-side market potential of direct-selling
food production. Di↵erentiating S(u,
s)withrespecttouyields:
Su(u,
s)=2⇥⌘|ehhu|Z¯xs
¯xu
e(t(x),h(x, u))⌘1dx +¯e⌘
u¯e⌘
s
2<0 (38)
Market share and supply-side competition. The variation in the market shares in each location with
respect to the number of direct-selling farmers sis given by:
ss(x, u,
s)=e(t(x),h(x, u))⌘⇥e(t(¯x),h(¯x, u))⌘
S(u,
s)2=s(x, u,
s)¯s<0 (39)
highlighting that the market share is always decreasing with the number of competitors.
28
Market share and urban pollution. Di↵erentiating e(h(x, u),t(x)) and S(u,
s)withrespecttoh
yields:
@e
@h=|eh|and Sh(u,
s)=2⌘|eh|Z¯xs
¯xu
e(t(x),h(x, u))⌘1dx < 0 (40)
As shown by (40), an increase in urban pollution always leads to a reduced value of the productivity
coefficient at x–and consequently, the receipts but also reduced supply-side market potential S. Hence,
assessing the overall impact of the urban pollution on the market share at xboils down to a comparison
between the e↵ect on this location and the e↵ect on the whole sector.
Indeed, di↵erentiating the market share at xwith respect to the pollution level hand rearranging,
we have:
sh(x, u,
s)=⌘|eh|"R¯xs
¯xue(t(x),h(x, u))⌘1dx
R¯xs
¯xue(t(x),h(x, u))⌘dx e(t(x),h(x, u))1#s(x, u,
s) (41)
with R¯xs
¯xush(x, u)dx = 0.
The term in brackets captures the overall pollution intensity e↵ect. More precisely, it compares
the sectoral shortfall rate R¯xs
¯xue(t(x),h(x,u))⌘1dx
R¯xs
¯xue(t(x),h(x,u))⌘dx with the yield-loss rate at location x.Wederivethe
market share of a farmer located at xas positively linked to the urban pollution provided that the
yield-loss rate at location xis sufficiently low, i.e.:
1
e(t(x),h(x, u)) <R¯xs
¯xue(t(x),h(x, u))⌘1dx
R¯xs
¯xue(t(x),h(x, u))⌘dx (42)
Finally, observe that when productivity is homogeneous over space, the term in brackets falls to
zero, meaning that the urban pollution has no impact on the market share (sh= 0).
29
Figure 3: Variat i o ns in agr i c ultural producti v i ty eand market share sover space.
30
Figure 4: Market share and supply-side competition.
31
Appendix C: Direct-selling profit and competition.
Using the market share s, the direct-selling market equilibrium profit can be rewritten as:
⇡m
s(u,
s)=wutuu
2¯
R
¯su¯ss+
↵ u
⇥¯ss¯
R(43)
Calculating the derivative of (43)withrespecttosgives:
@⇡m
s
@s
=[¯s2
s(wutuu
2¯
R)(¯su¯ss+
↵ u)] [¯ss(wutuu
2¯
R)(¯s2
s¯su¯ss)]
(¯su¯ss+
↵ u)2
=
↵ u
(¯su¯ss+
↵ u)2<0
(44)
Appendix D: Free-entry equilibrium and the size of the urban population.
City size and direct-selling farming with space-invariant externalities ˆe(t, h(u)).When externalities do
not vary in space, the number of direct-selling varieties at the long-run equilibrium is given by:
ˆ
⇤
s(u)=↵ u
¯
R✓wutu
2u¯
R◆(45)
and its derivative with respect to uis:
@ˆ
⇤
s
@u
=↵
¯
Rwutuu¯
R(46)
City size and direct-selling farming with spatially-varying externalities. Recalling that ⇡s(u,
⇤
s) does not
vary at the free-entry equilibrium (⇡s(u,
⇤
s)=⇡c= 0), and using the total di↵erential, we can draw
the relationship between the size of the urban population and the number of direct-selling varieties,
given by @⇤
s
@u=@⇡s
@u⇥
@⇡s
@s
1. Di↵erentiating (20)withrespecttosand u, and evaluating at the
free-entry equilibrium yields:
@⇡s
@s
(u,
⇤
s)=¯
R2
¯wu✓¯ss+⌘|ex(¯xs)|
2¯es◆¯su<0 and (47)
@⇡s
@u
(u,
⇤
s)= ¯
R2
¯wu✓¯ss¯su
u¯ss
tu
2¯
R+su(¯xs,
u,
⇤
s)su(¯xu,
u,
⇤
s)
¯ss◆(48)
where ex(¯xs)⌘@e
@tt0(¯xs)+ @e
@h
@h
@x(¯xs) is the spatial variation of the productivity coefficient at ¯xsand
with the simplifying notations ⌘wutuu
2
¯
R,¯su⌘s(¯xu,
u,
⇤
s), and ¯ss⌘s(¯xs,
u,
⇤
s). Then, using
@⇤
s
@u=@⇡s
@u⇥
@⇡s
@s
1, it is readily verified that the relationship between the urban population size and
the number of direct-selling varieties when externalities are varying over space is:
@⇤
s
@u
=1
⇣¯ss+⌘|ex(¯xs)|
2¯es⌘¯su✓¯ss¯su
u¯ss
tu
2¯
R+su(¯xs,
u,
⇤
s)su(¯xu,
u,
⇤
s)
¯ss◆(49)
32
Eq. (49) can be rearranged so as to make @ˆ
⇤
s
@uapparent:
@⇤
s
@u
=¯ss¯su
⇣¯ss+⌘|ex(¯xs)|
2¯es⌘¯su"@ˆ
⇤
s
@u
+su(¯xs,
u,
⇤
s)su(¯xu,
u,
⇤
s)
(¯ss¯su)¯ss#(50)
Calculating the derivatives of the market share at the direct-selling boundaries ¯xuand ¯xswith
respect to the city size gives:
@s
@u
(¯xu,
u,
⇤
s)⌘su(¯xu)=¯su⌘ex(¯xu)
2¯eu
+¯su¯s
+⌘|ehhu|✓⇠1
¯eu◆ (51)
and
@s
@u
(¯xs,
u,
⇤
s)⌘su(¯xs)=¯ss⌘ex(¯xs)
2¯es
+¯su¯s
+⌘|ehhu|✓⇠1
¯es◆ (52)
with the simplifying notation ⇠⌘R¯xs
¯xue(t(x),h(x,u))⌘1dx
R¯xs
¯xue(t(x),h(x,u))⌘dx . Then, using (51) and (52), we find:
su(¯xs)su(¯xu)
(¯ss¯su)¯ss
=⌘
2
¯e⌘1
sex(¯xs)¯e⌘1
uex(¯xu)
(¯e⌘
s¯e⌘
u)¯ss
+(¯eu
¯es)⌘1
+⌘|ehhu|
¯ss ⇠¯e⌘1
s¯e⌘1
u
¯e⌘
s¯e⌘
u!(53)
Appendix E: The sectoral shortfall rate.
As already mentioned, e(t(x),h(x, u))1represents the yield-loss factor–i.e. the di↵erential between
the e↵ective yields and the theoretical yields that would be obtained without externalities. Therefore,
e(t(x),h(x, u))1can also be interpreted as the expected profit-loss factor which di↵ers from the
e↵ective profit-loss factor given by e(t(x),h(x, u))⌘(See Eq.15). The ratio of these two elements
gives e(t(x),h(x, u))⌘1which can be interpreted as a shortfall factor due to the externalities, i.e.
the total deviation from the theoretical profit stemming from the fact that farmers take the e↵ective
yields into account when choosing the quantity of synthetic inputs and setting their prices. Stated
di↵erently, e(t(x),h(x, u))⌘1can be seen as an adaptation (hidden) cost expressed as a ratio between
the expected and the e↵ective profit-loss. When it is summed over the whole direct-selling market, we
obtain the aggregate shortfall factor for the direct-selling sector R¯xs
¯xue(t(x),h(x, u))⌘1dx. Finally,
reported on the aggregate profit-loss rate R¯xs
¯xue(t(x),h(x, u))⌘dx, we get:
R¯xs
¯xue(t(x),h(x, u))⌘1dx
R¯xs
¯xue(t(x),h(x, u))⌘dx >1 (54)
which captures the weight of the shortfall factors in the e↵ective profit-loss factors at the sector level,
referred to as the sectoral shortfall rate.
33
