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Efficient Consumer Altruism and Fair Trade Products∗
David Reinstein†and Joon Song‡
August 17, 2012
Abstract
Consumers have shown a willingness to pay a premium for products labeled as “Fair Trade”
and a preference for retailers that are seen to be more generous to their suppliers/employees.
A fair trade product is essentially a bundle of a base product and a donation to the supplier
(e.g., a coffee farmer). An altruistic rational consumer will only choose this bundle if doing so is
less expensive than buying the base product and making a direct donation. For fair trade to be
sustainable either in a competitive equilibrium or in a monopolistic environment, this bundling
must yield an efficiency. This efficiency is generated in the following context. A supplier’s
investment reduces the retailer’s cost or boosts the final product’s quality, but this investment is
not immediately observable and cannot be enforced, hence there exists a moral hazard problem.
In this environment, the altruism of the consumer can facilitate a more efficient contract: by
paying the supplier more, the retailer can both extract more consumer surplus and increase the
level of contracted investment, while preserving the supplier’s incentive compatibility constraint.
We assess our model in the context of the coffee industry.
Keywords: fair trade, consumer altruism, non-verifiable investment, contracts
∗We thank Christian Ghiglino, Abhinay Muthoo, Joe Ostroy, Motty Perry, Pierre Regibeau, Emmanuel Saez,
and seminar participants at University of Essex, MILLS Seminar in Milan (IGIER), EARIE 2008 in Toulouse, UC
Berkeley, the University of San Francisco, and the University of Carlos III in Madrid. We also thank two anonymous
referees and an associate editor for invaluable comments and suggestions.
†Department of Economics, University of Essex, drein@essex.ac.uk
‡corresponding author, Department of Economics, Sungkyunkwan University, joonsong.econ@gmail.com
1
1 Introduction
A significant subset of consumers have shown a willingness to pay a premium for products labeled
as “Fair Trade” (henceforth, FT) and a preference for retailers that are seen to be more generous
to their suppliers and employees, domestically and internationally (The Economist [2007], Maietta
[2003], De Pelsmacker, Driesen and Rayp [2005], Howard and Allen [2008], Basu and Hicks [2008]).1
The size of fair trade and “ethical products” market is large and growing: global sales exceed e3.4
billion worldwide (Fairtrade Labeling Organizations International (FLO)[2010]) for FLO labeled
products alone. The main goal of the FT movement is to improve the standards of living for farmers
and artisans by ensuring a “fair” price. The most prominent product is FLO-certified coffee. The
FLO selects and maintains a registry of cooperatives that meet certain minimum requirements. To
qualify for a FT label, importers and roasters must buy from these cooperatives at a set minimum
price at or above the world market rate, plus a “social premium”.2
Does this practice actually help the targeted group and/or improve welfare? Several economists
and policy analysts have been dismissive of this practice, arguing that altruistic consumers could
help the suppliers more effectively by making direct transfers (Zehner [2002], Booth and Whetstone
[2007], The Economist [2006]). These authors imply that consumers who purchase fair trade prod-
ucts must be uninformed or irrational. On the contrary, we show through a formal model that even
consumers who are fully informed and rational may prefer to purchase the fair trade product.3
We model a fair trade product as a bundle of a base product and a donation. For intuition,
1We are not discussing “fair trade” in the context of a government’s international trade policy. Our model applies
to products directly marketed to consumers as fair trade. It is also relevant when consumers care about employees’
surpluses, such as in the case of the anti-sweatshop movement.
2The social premium is currently (as of 2007) $0.10/lb., and must be used for specific projects to benefit members
of the cooperatives. Requirements for cooperatives and importers/roasters include labor, governance, environmental
standards, and specified contract terms which include providing short-term credit to farmers. For simplicity, our
model naturally abstracts away from many of these institutional features. Note that our analysis is generalizable
to altruistic products beyond FLO registered Fair Trade coffee. Further institutional details and description can be
found in Renard (2003) and Smith (2009).
3Some recent work, such as Smith (2009) and Nicholls and Opal (2005) has discussed and responded to prominent
criticisms of fair trade.
2
we state our model in terms of coffee, and give anecdotal evidence from this industry, but our
analysis applies to a wider set of markets and interactions. In our model, one type of consumer is
altruistic; this consumer’s utility function partly depends on the impact of her actions on others –
in particular, the effect of her purchase on the welfare of coffee farmers.4,5The rational altruistic
consumer will choose this bundle (the base product and a direct donation) only if purchasing the
bundle is cheaper than purchasing both elements separately. The bundle can be produced at a
lower cost through the following mechanism.
We model a vertically-structured industry in which a retailer (henceforth, the “roaster”) buys
inputs from a supplier (henceforth, the “farmer”), and the two parties have a repeated contractual
relationship.6In producing these inputs, the farmer can make an investment that will reduce the
cost (to the roaster) of providing the final product. Because this investment is non-verifiable, it will
typically be set below the first-best efficient level.7A roaster who pays the farmer more than the
price of the regular coffee is in essence offering a direct donation, and thus can capture the increased
altruistic component of the consumer’s utility. At the same time, this larger payment also increases
the farmer’s net benefit of complying with the contract. Thus, the contract can specify a higher
4The consumer weighs these outcomes according to an anonymous social welfare function (e.g., Rawls [1971] or
Harsanyi [1955]). This implies that utility from altruism does not depend directly on the amount sacrificed, nor
on the manner of the contribution, but on the amount the targeted group receives. This is consistent with several
models of giving, including the public goods model (Becker [1974]), the impact model (Duncan [2004]), and a specific
interpretation of the reciprocity model (Sugden [1984]) or the warm glow model (Andreoni [1990]).
5We can not rule out that other psychological motives such as “group fairness” (Rabin [1993], Moreno [2008]): if a
consumer identifies with farmers, she may be willing to pay more to a producer who is kind to these farmers. However,
such models of “psychological games” are known to predict very broadly, and are tied to a particular definition of
fairness. In contrast, our model is able to explain FT in a more standard setup, merely assuming a degree of rational
altruism.
6We are not assuming a fixed long term contract per se, but two parties who are in this industry for the indefinite
long-term and have the opportunity to repeatedly meet and agree on, or reaffirm, the contract terms (which must be
self-enforcing). This resembles the typical interaction between farmers and professional importing firms (roasters),
as described in Nicholls and Opal (2005).
7There is much evidence of a moral hazard problem in the coffee industry. Zehner [2002] notes “growers may lie
about the geographical origin of their crop or add low-quality beans or dirt and stones to the bags of coffee they
supply.”
3
self-enforcing level of the farmers’ investment and thus reduce the roaster’s costs. Through this
increased investment and through capturing the increased altruistic component of the consumer’s
utility, the bundling yields an efficiency. Thus, the bundle can be produced at a lower cost than its
elements, as claimed above. Consequently, we further show that the rational altruistic consumer’s
willingness to pay a premium for a fair trade product results in an even larger premium going to
the supplier. A variation of the mechanism above, where the investment boosts the quality of the
base product, yields the same results.
Our setup bears some similarities to Shapiro (1983) and Klein and Leffler (1981) in that these
authors also considered the agency problem in an infinitely repeated context; however, they do not
consider altruism. The efficiency benefits (and profitability) of altruism in the context of agency
costs has been modeled by Casadesus-Masanell (2004) and various models surveyed by Rotemberg
(2006), who notes that an altruistic supervisor puts less weight on “the cost of transferring resources
to a subordinate.” These papers investigate the value of committing to be altruistic (or hiring an
altruist), either for an agent or for a principal – this contrasts from our own model which takes
preferences as given.8More importantly, our paper is the first to consider the effect of an altruistic
third-party, the consumer. In fact, the explicit marketing appeal to the consumers’ altruism is the
hallmark of FT products, and the presence of this altruistic third-party is the defining characteristic
of our model.
Some scholars have argued that labeling certain products as fair trade will decrease market
efficiency by distorting market price (Lindsey [2004], Booth and Whetstone [2007], Harford [2006],
Sidwell [2008]). In contrast, our model suggests that fair trade is a successful innovation even in a
competitive environment (and with rational consumers).9This innovation increases welfare, even
when we measure the welfare excluding the altruistic component of consumers’ utilities.
Our model offers advantages over previously proposed explanations for the existence of fair trade
8Several of these papers follow Rotemberg (1994) in allowing an agent “to mold his behavior payoffs to serve best
his object self ” – in other words, an individual has some ability to commit to a level of altruism that will maximize
his material payoffs.
9The perfectly competitive environment also offers the clearest demonstration of the welfare gain from FT. How-
ever, we also show that most of the results derived in a competitive environment are still valid with a monopolistic
retailer.
4
products. None of these models can explain the retailer paying a larger premium than the consumer
while explaining FT products’ survival in a competitive environment. Hayes (2006) argues that
FT achieves this through the elimination of monopsony rents; but his model cannot explain how
fair trade roasters can take over a market controlled by a monopsony.10 The proponents of “trade
not aid” (Rugasira [2007]) do not provide an economically meaningful distinction between trade
and aid.11 When consumers are rational altruists, the argument that FT allows for profitable price
discrimination (Harford [2006]) requires counter-intuitive assumptions.12 Finally, neither a market
segmentation story (Booth and Whetstone [2007], Bechetti and Solferino [2008]) nor a marketing
strategy argument can explain why there are roasters serving FT coffee exclusively and others
serving both FT and non-FT coffee.13
Section 2 presents our model and our theoretical results. Throughout this section we incorporate
anecdotal evidence from the coffee industry to assess our assumptions and results. Section 3
concludes and offers suggestions for future research.
2 Model
Our model shows how consumer altruism can lead a firm to offer a fair trade product in a competitive
environment. (In the appendix, we also present a model with a monopolistic retailer and show that
most of the results derived here are preserved.) We assume that all retailers have access to the
10Monopsony rents can be maintained through barriers to entry, or if a local market is a natural monopsony (Bain
[1956]). FT retailers would need to enter these markets and force the incumbent to exit, in spite of the higher input
costs implied by the premium to the farmer.
11They argue that traditional public-sector aid and charity will have a demoralizing and dis-incentivizing effect,
fostering a dependent mentality. But offering a higher-than-usual price could also be considered a “handout”.
12Bundling coffee and a donation is only useful for price discrimination if altruists have a lower valuation of the
base product; this is illustrated in the Appendix A.1. However, conventional wisdom (e.g., Harford [2006] himself)
suggests that consumers of fair trade are premium consumers.
13These authors claim that FT can be used to segment the market and give firms greater market power. However,
the coffee market is not highly concentrated; there are many choices (FT and non-FT) in supermarkets and boutique
cafes. The segmentation story also fails to explain why stores like Starbucks offer both types of coffee. Another
argument is that the roasters offer fair trade coffee as a “loss-leader”; this cannot explain why some roasters solely
offer FT products.
5
same production process, and that fair trade producers do not have an inherent advantage over
charities in providing the altruistic good.
2.1 Primitives
There are four types of actors in our model: coffee farmers, coffee roasters, altruistic consumers,
and non-altruistic consumers.
A unit of coffee is produced jointly; a farmer (F) grows and prepares the beans and a roaster/retailer
(R) buys them, processes them, and sells them to a consumer whose valuation of the coffee is v. The
retail market for coffee is perfectly competitive. However, each roaster has bargaining power over
the farmers he buys from. Empirical work suggests that the retail coffee market is a fairly compet-
itive industry, while small coffee farmers have little to no market power, and are not well-organized
(Dicum and Luttinger [1999], Hayes [2006], Zehner [2002], Lindsey [2004]).14
Each farmer can either produce a unit of coffee or produce nothing. A roaster bears the cost
of processing a unit of coffee c(m). This cost is determined by the farmer’s investment m≥0. For
example, a farmer may carefully sort and clean the beans, and thus save the roaster the cost of
doing so.15 Investment mdecreases the processing cost at a decreasing rate, i.e., c0(m)<0 and
c00(m)>0.
Alternatively, we could interpret c(0) −c(m) as an improvement of quality resulting from in-
vestment m. Under this interpretation, the consumers’ utility from the coffee will be v−c(m), and
all of the subsequent results will be preserved. We model this interpretation in A.2.
A roaster pays p≥0 to a farmer for each unit of coffee. The farmer’s net profit from (p, m)
14The roaster is assumed to be a natural monopsony in the local coffee bean market, as long as his technology is as
efficient as any other firm. At the same time, the roaster is a perfectly competitive retailer. As an example, consider
the case with a single consumer having unit demand, two roasters each of whom has the potential to produce one
unit of roasted coffee beans, and three farmers each of whom has the capacity to produce one unit of coffee beans.
15Such investments are important in the coffee growing industry. Coffee production generally involves several
basic stages – growing, harvesting, de-pulping, drying, sorting, grading, and bagging – but there are variations in
technique and quality at each stage (Dicum and Luttinger [1999]). De Janvry et al (2009) note “tremendous quality
heterogeneity.” The most important investments may be those that ensure reliable production and maintenance of
the organic certification.
6
is π:= p−m. Profit πwill have the same effect on the altruistic consumer’s utility as making a
donation of πto the farmer. Thus, we often refer to the farmer’s net profit πas the consumer’s
“donation”. However, while the altruistic consumer values this “donation”, the regular consumer
does not – she is indifferent to any level of π. We refer to (π, m) as “the contract” between a farmer
and a roaster. The roaster’s bargaining power allows him to set the contract.
Once having purchased and processed the coffee, the roasters sell this product to the consumers.
The coffee is branded “coffee π”, or simply coffee(π), representing the bundle of the base coffee
product and the profit πgiven to the farmer. Roasters face market price P(π) for coffee(π). The
profit of a roaster producing and selling coffee(π) with contract (π, m) is
ΠR(π, m) = P(π)−p−c(m) where π=p−m.
Both the altruistic and the non-altruistic consumers have unit demand for coffee. The altruistic
component of utility is additively separable from the coffee consumption component. Let vrepresent
the two consumers’ identical valuation of coffee. Thus, the utilities are vfor the non-altruistic
consumer and v+a(π) for the altruistic consumer, where a(π) is the altruistic component. We
assume that vis large enough so that consumers always choose to consume coffee. We further
assume that the consumers have quasi-linear utility with respect to money, so their net utilities
given price P(π) are
UA(π) = v+a(π)−P(π) and U0(π) = v−P(π)
for the altruistic consumer and the non-altruistic consumer, respectively. The altruism value of zero
donation is normalized to be zero, and the marginal utility of donation πis positive, decreasing in
π, and less than unity:
a(0) = 0, a0(π)>0, a00(π)<0, a0(0) ≤1.(1)
Note that these four conditions imply a(π)≤π. Inequality a0(0) ≤1 means that the first
dollar donation gives less than a dollar utility to the altruistic consumer. We impose this stringent
condition to make the strongest case for the potential efficiency of fair trade. This assumption
implies that consumers will only buy fair trade coffee if the premium they pay for such coffee is less
7
than the resulting increase in the farmer’s income. Thus, our story of fair trade must explain how
and when this “magnification” can occur. In A.3, we provide intuition for inequality a0(0) ≤1, and
illustrate that relaxing this stringent assumption only strengthens the case for fair trade.
We consider the following repeated interaction:
(i) A roaster Rannounces contract (π, m), which becomes common knowledge.
(ii) A farmer Finvests ˜m.
(iii) The roaster Rpays p=π+mto F.
(iv) The roaster observes his production cost c( ˜m), but ˜mis unverifiable.
(vi) Consumers buy coffee (giving profit ˜π:= p−˜mto the farmer) at price P(π).
There is information asymmetry. Within each period, ˜mis unverifiable even after the roaster
observes c( ˜m) and infers ˜m. In the event that the farmer unilaterally strays from equilibrium
behavior and fails to invest, the roaster has already paid him and cannot sue to get his money
back. The typical small farmer or cooperative is poor and can be seen to have limited liability
(see, e.g., Duflo [2003]). Moreover, it would be costly to launch a suit over what is likely to be a
small amount of money, and the court systems in the origin country of many coffee growers are
problematic.16
On the other hand, we assume that the roaster always pays the p=π+mthat is specified in
the contract. This allows us to simplify our analysis and ignore the roaster’s incentive compatibility
constraint. To justify this assumption, we can assume that if the roaster pays ˜p6=p, this is publicly
observed, and the roaster will be sued by an NGO such as the Fair Trade Labeling Organization
(FLO) or Transfair and pays damages D. If Dis large enough (including direct damages, negative
publicity, and loss of reputation), the roaster will always pay p. This general claim is supported by
De Janvry et al (2009), who highlight the “effectiveness of the audits conducted by the 19 world
16This problem, the limited ability of the poor to make binding commitments, is widely cited in the development
literature; e.g., Ray (1998). For evidence on legal conditions, see an earlier draft of this paper.
8
labeling initiatives” and note “the mechanisms in place to monitor prices seem to be effective.”17
This interaction may be repeated once or infinitely. We refer to (π, m) = (0,0) as the termi-
nation of contract. This might be used to punish the farmer for deviation ˜m6=min the previous
period.
2.2 Maximization and competitive equilibrium
As a benchmark, we present a one-period interaction between the farmer and the roaster. The
farmer’s profit is p−˜m. For any level of p=π+m, it is always optimal to choose ˜m= 0.
Considering a(π)≤π, the roaster does not want to implement π > 0 since even the altruistic
consumer’s appreciation a(π) of the farmer’s profit πis smaller than the cost, π. Thus the only
sustainable contract is (π, m) = (0,0).
Next we consider an infinitely repeated interaction. Cooperation implementing strictly positive
πand mcan be sustained if the roaster plays a grim trigger strategy. Each party cooperates as
long as all parties previously cooperated; otherwise, the roaster will propose (π, m) = (0,0), and
the farmer sets ˜m= 0 for any (π, m). If the farmer defects from contract (π, m) by investing
˜m= 0, he receives p=π+mfor that period. However, the roaster will terminate contract (π, m)
after detecting the deviation. Thus the farmer will get zero profit from the next period onwards.18
Therefore, the incentive compatibility constraint for a farmer with discount factor δFis
(p−0) +
∞
X
t=2
δt−1
F0≤
∞
X
t=1
δFt−1π⇐⇒ π≥1−δF
δF
m(2)
The roaster chooses an optimal contract subject to (2). Note that there is a continuum of poten-
tial coffee products, each indexed by “ethical quality” (i.e., by the profit πgiven to the farmer).
Coffee(π) may or may not be produced depending on its price P(π) in equilibrium. The producer
17One might imagine that the farmer and the roaster could collude to deceive the consumer into believing that the
farmer has invested less, and thus gained more surplus than he actually has. However, if the roaster is paying the
FT price to the farmer, the FT level of investment is the highest that will be incentive compatible (as shown in our
model). As we have assumed that pis common knowledge, consumers will correctly infer the corresponding level of
investment.
18The assumption of of zero payoffs forever is a simplification: if the farmer who defects has the option to sign a
contract with another roaster, but with a sufficiently costly delay, the qualitative results are preserved.
9
chooses which coffee to produce given function P(π) and which level of the farmer’s investment m
to implement:
max
(π,m)[P(π)−(π+m)−c(m)] subject to (2).
This optimization can be decomposed into two steps: the roaster chooses mfor a given π,
and then he chooses π. First, facing the incentive compatibility constraint, the optimal feasible
investment for a given πis m(π) = argmaxm{P(π)−(π+m)−c(m) : π≥1−δF
δFm}. Second, a
roaster’s objective is to choose πthat maximizes his profit, i.e., the roasters’ choice of πmaximizes
ΠR(π) := [P(π)−(π+m(π)) −c(m(π))].
Facing price P(π), each consumer will chooses π(hence, choosing coffee(π)) to maximize her
net utility. The following are the maximization problems: one for an altruistic consumer and the
other for a non-altruistic consumer.19
πC
A= argmax
π
[v+a(π)−P(π)] and πC
0= argmax
π
[v−P(π)].
The altruistic consumer purchases coffee(πC
A), which we call “fair trade coffee”. The non-altruistic
consumer purchases coffee(πC
0), which we call “regular coffee”.
Because the roasters are perfectly competitive, profit will be driven down to zero. With only
two consumers, no more than two roasters can sell a positive quantity. Thus in equilibrium there
will be either two roasters, one serving the non-altruist and the other serving the altruist, or one
roaster serving both of the consumers. We define πR
Aand πR
0as the choices of the roaster serving
the altruist and the non-altruist, respectively, i.e.,
πR
A, πR
0∈argmax
π
ΠR(π).
A natural market clearing condition in our context is that the roasters’ choices and the consumers’
choices coincide. Our notion of equilibrium (where certain products are produced and the others
are not) can be understood as an extremely simple case of Ostroy (1984).
πA:= πC
A=πR
Aand π0:= πC
0=πR
0.
We summarize the equilibrium notion in the following definition.
19Although, it may seem unusual for the consumer to have a role in “setting” the input price, this simply represents
the consumer’s optimal choice over the “altruistic quality” of the coffee.
10
Definition 1. A vector <(πC
A, πC
0),(πR
A, πR
0),(P(π))π≥0>is an equilibrium if and only if the
following conditions hold.
Consumers :πC
A∈argmax
πA
[v+a(πA)−P(πA)] , πC
0∈argmax
π0
[v−P(π0)]
Roasters :πR
A, πR
0∈argmax
π
max
m(π)P(π)−(π+m(π)) −c(m(π)) : π≥1−δF
δF
m(π)
Market Clearance :πC
A=πR
A, πC
0=πR
0.
Note that the Walrasian auctioneer sets prices for all coffee that may or may not be produced.
These prices lead the consumers and the producers to choose the identical coffee products so that
supply and demand meet.
The price-taking behavior of farmers is not incorporated in the definition of equilibrium. Instead,
the farmer’s role in the definition is only through a constraint on the roasters’ achievable mfor a
given π. We will show that πAand π0are positive under certain parameter values: farmers who
have contracts with roasters (whether fair trade or not) receive strictly positive profit, while farmers
without contracts get zero profit. Without the incentive compatibility constraint of farmers, this
“rationing” would not have occurred: other farmers would have accepted a contract with lower
πand the same m; such contracts are not feasible given the incentive compatibility constraint.
This rationing prevents the incorporation of farmers’ optimization problems into the definition of
a Walrasian equilibrium.
Similar rationing is found in credit markets (Stiglitz and Weiss [1981]) and general equilibrium
principal-agent problems (Bennardo and Chiappori [2003]). We discuss the welfare implications of
this assumption in Section 2.3.
Let mEF satisfy 1 = −c0(mE F ): this defines the first best level of investment since the marginal
cost of the investment is equivalent to the marginal benefit, i.e., the marginal reduction of processing
cost. Additionally, let πEF := 1−δF
δFmEF , the minimum level of farmer profit that makes the efficient
investment incentive compatible.
Finally, we characterize an equilibrium (Proofs are in Appendix A.4).
11
Proposition 1. (i) The price P(π)that clears the market (i.e., πC
A=πR
A, πC
0=πR
0) is given by:
P(π) =
π
1−δF+cδF
1−δFπif π < πEF ,
(π+mEF ) + c(mEF )if π≥πEF .
(ii) πA≥0and π0≥0are determined by the following Kuhn-Tucker conditions:
δF−c0δF
1−δF
π0≤1and equality holds if π0>0,(3)
(1 −δF)a0(πA) + δF−c0δF
1−δF
πA≤1and equality holds if πA>0.(4)
As Proposition 1 illustrates, under perfect competition, the market-clearing price of a given
type of coffee will equal the roaster’s (marginal) cost producing this coffee. The roaster will choose
to increase the farmer’s profit (hence investment) as long as the unit marginal cost of the increase
is less than the marginal cost-reducing value of the resulting investment, plus – for the FT coffee –
the consumers’ valuation of the farmer’s profit.
We need the following conditions for an interior solution, i.e., π0>0 and πA>0.
Condition 1. −c0(0) >1
δF.
Condition 2. 1−δF
δFa0(0) + (−c0(0)) >1
δF.
Proposition 2. The surpluses of farmers πA:= πR
A=πC
Aand π0:= πR
0=πC
0satisfy:
(i) π0>0if and only if Condition 1 holds, and
(ii) πA>0if and only if Condition 2 holds.
As the farmer becomes impatient, the potential for long-term cooperation declines.20 In order to
have positive investment without altruism, the first-dollar marginal benefit of investment (−c0(0))
must exceed the marginal cost of inducing the investment ( 1
δF). This includes both the marginal
(unit) cost of compensating the farmer for his investment and the marginal cost of providing the
farmer an incentive (1−δF
δF, derived from (2)) not to deviate. With an altruistic consumer, the
roaster gets an additional benefit from the first unit of investment, 1−δF
δFa0(0). However, since
20It is trivial for (i). For (ii), note that the condition is equivalent to (1 −δF)a0(0) + δF(−c0(0)) >1. −c0(0) must
be larger than a0(0) to have πA>0. (If not, (1 −δF)a0(0) + δF(−c0(0)) ≤1 since a0(0) ≤1.) Thus the result follows.
12
a0(0) ≤1, consumer altruism alone will never be sufficient for positive investment; the investment
must also be sufficiently cost-reducing.
We derive the following corollary which further characterizes the equilibrium.
Corollary 1. Under Condition 2, (i) πA> π0, and (ii) P(πA)> P (π0).
Essentially, inducing higher investment is “cheaper” for FT coffee than for regular coffee, as
payments to the farmer also benefit the altruistic consumer. Thus, as the corollary notes, ceteris
paribus, farmers’ investments are always higher for fair trade coffee. Those involved in fair trade
directly make this claim of a higher level of investment (Rodney North of Equal Exchange [2007]).
In summary we have characterized the equilibrium contracts for four cases, as shown in the
following table.
Without Altruism With Altruism
Short-term interaction [1] (π, m) = (0,0) [2] (π, m) = (0,0)
Long-term interaction [3] (π, m)=(π0, m0)[4] (π, m)=(πA, mA)
We argue that the institution of fair trade moves the equilibrium contract from [3] to [4].
However, if fair trade itself makes cooperation possible, (i.e., the transition from [1] to [4]), as
some advocates claim, the benefits of fair trade are even greater. For example, the provision of
advance credit may help alleviate credit constraints, essentially lowering farmers’ discount rate, so
Condition 1 and 2 become more likely to be satisfied.
2.3 Comparative statics and welfare analysis
The comparative statics with respect to δFare straightforward: as δFincreases, the equilibrium
investment mwill increase, for either type of coffee. As the farmer grows more patient (and/or
the delay between periods decreases) the farmer’s incentive compatibility constraint is relaxed, and
this lowers the net cost (to the roaster) of inducing additional investment. A formal proof is in A.5.
Next, we consider how an increase in altruism affects the economic agents’ utilities/profits as
well as the welfare of the economy. Government and NGO policies aiming to “raise awareness”
of fair trade may succeed in increasing the altruism of consumers, or the number who consider
13
purchasing a fair trade product. As we show below, this will increase the efficiency of production
(by increasing the chosen level of investment m). This is also relevant to a recent strain of literature
(e.g., Casadesus-Masanell [2004], Fehr and Fischbacher [2002], Kaplow and Shavel [2007]) that
hearkens back to Smith (1759) and examines the impact of “moral sentiments” such as as altruism
on the behavior and efficiency of the economy. We consider a parametrized altruism function βa(π)
with β∈[0,1]. An increase in βimplies an increase in the utility an altruistic consumer derives
from the income passed to the farmer.21 We restate Condition 2 for this parametrization:
Condition 2a (1 −δF)βa0(0) + δF(−c0(0)) >1.
Note that βis included in Condition 2a, as the new altruism function is βa(π).
For certain parametric values, altruism makes a non-trivial contract possible when it was im-
possible otherwise. Suppose a(·) and c(·) fail to satisfy Condition 1, but satisfy Condition 2a.
Proposition 1 implies that π0= 0 and πA>0; hence, m0= 0 and mA>0.
More generally, altruism increases the level of investment mand the profit of the farmer π.
Proposition 3. Under Condition 2a,
dπA
dβ >0and dmA
dβ >0.
Proof. With the re-defined altruism component of utility βa(π), the first order condition for the
altruistic consumer is
(1 −δF)βa0(πA) + δF−c0δF
1−δF
πA= 1.
Total-differentiating the constraint with respect to βand πA, we derive
dπA
dβ =−a0
βa00 −δF
1−δF2c00
>0; hence, dmA
dβ =δF
1−δF
dπA
dβ >0.
21An alternative parametrization would be through an increase in the proportion of altruistic consumers. In the
previous section, we derived πA> π0and mA> m0. These four values remain the same even if we increase the
proportion of altruists. However, the average level of farmers’ profit and investment will increase as more altruists
means an increased demand for the fair trade product.
14
Thus, we show the result.
Proposition 3 implies that as altruism increases, the marginal altruistic utility from giving more
profit to the farmer increases. A greater profit for the farmer implies greater investment.
We also prove that the fair trade premium the farmer receives exceeds the premium the altruistic
consumer pays, i.e., the altruistic consumer’s willingness to pay a small additional amount results
in an even larger rent to the farmer.
Proposition 4. Under Condition 2 (and 2a), P(πA)−P(π0)< πA−π0.
Proof. The fact that the altruistic consumer has chosen πAover π0implies
v+βa(πA)−P(πA)≥v+βa(π0)−P(π0).
Thus we derive P(πA)−P(π0)≤βa(πA)−βa(π0). We also derive βa(πA)−βa(π0)< πA−π0from
βa0(·)≤1. The result follows.
Since the altruistic consumer gains less from a dollar of farmer’s profit than from a dollar of
consumption, if she chooses to pay a premium for FT coffee, the roaster must be passing on an
even larger premium to the farmer. This proposition can be tested empirically by estimating and
comparing the consumer and producer premia; we leave this for future work.22
Finally we analyze the effect of the increased altruism on the welfare of the economy. We
consider only the welfare of altruistic consumers, fair trade coffee roasters, and fair trade farmers,
22Both Maietta (2003) and Gallaraga and Markandya (2004) estimate the consumer premium with hedonic regres-
sions using retail data, but these studies use data from small and nascent markets. Zehner (2002) presents a simple
comparison of three pairs of coffee products and finds “the Fair Trade premium is an inefficient subsidy.” However,
his result depends on which coffee the FT product is compared to, and similar comparisons reverse these results, as
do the (also simple) findings of Eshuis and Hansen (2003). Nicholls and Opal (2005) offer a range of evidence on
the financial returns to FT labeling and administrative costs, and on the social returns to FT, broadly defined. Our
own preliminary estimates using data from Amazon.com suggest that consumers are paying little or no more for FT
than for non-FT coffee (although as de Janvry et al [2009] suggest, given the current high world price of coffee, the
fair-trade premium itself may currently be small or zero). This limited evidence is summarized in our Essex working
paper (2008). Overall, the evidence is neither consistent nor definitive; in the case of fair trade coffee this remains
an open question.
15
since βhas no effect on the other parties. Welfare is:
W(π, m)=[v+βa(π)] + [−(π+m)−c(m)] + [π] = v+βa(π)−m−c(m).
In contrast to the classical general equilibrium approach, we include the monetary transfer p=π+m
(hence, πas well) in our definition of welfare because the transfer affects the altruistic consumer’s
utility.
We also define welfare net of altruism:
Wπ(π, m) := W(π, m)−βa(π) = v−m−c(m).
We examine welfare net of altruism as a benchmark; the welfare gain from the scaled-up utility
function is itself trivial. Furthermore, some policy-makers may not consider the altruistic “warm
glow” as an important component of social welfare.
The effect of increased altruism on welfare can be decomposed into three parts: (a), (b), and
(c) in the equation below.
d
dβ [v+βa(πA)−mA−c(mA)] = ∂
∂β [βa(πA)]
| {z }
(a)
+βa0(πA)dπA
dβ
| {z }
(b)
+d
dβ [v−mA−c(mA)]
| {z }
(c)
We focus on the case satisfying Condition 2a, i.e., πA>0 and mA>0. Otherwise, an increase in
altruism will have no effect on welfare, since the farmers receive zero surplus both before and after
a small increase in β.
(a) measures the direct effect of the increase in β. The direct effect represents the obvious
increase in surplus as the product takes on additional altruism value. (b) measures β’s indirect
effect through the increased π. As the consumer altruism increases, the roaster adapts the product
to this change, which in turn increases welfare. (c) measures the indirect effect, as higher investment
leads to a net reduction of costs:
d
dβ [v−mA−c(mA)] = d
dβ Wπ(π, m) = −(1 + c0(mA)) dmA
dβ >0 since 1 + c0(mA)<0.
We can think of the beneficial effect of altruism as being magnified through the investment of the
farmer. Since the indirect effect (c) is positive, we see that not only will an increase in altruism
increase welfare, it will also increase welfare net of altruism. Thus we prove our main proposition:
16
Proposition 5. If Condition 2a holds, an increase in altruism increases welfare net of altruism.
Otherwise, a small change in altruism has no effect on welfare.
As roasters and consumers are largely in “Northern” countries, and coffee farmers in “Southern”
countries, some Northern policy makers may be solely interested in the welfare of consumers and
retailers. Thus, we alternatively consider Northern welfare, the welfare excluding farmers’ utility:
WD(π, m)=[v+βa(π)] + [−(π+m)−c(m)] = v+βa(π)−(π+m)−c(m).
The incentive-constrained efficient allocation (with respect to the Northern welfare) is defined as
the choice of (π, m) that maximizes the Northern welfare subject to the incentive compatibility
constraints of the farmers:
max
π,m [v+βa(π)−(π+m)−c(m)] s.t. π≥1−δF
δF
m.
The first order condition for the maximization problem is identical to the first order condition of
the altruistic consumer, equation (8). In other words, the equilibrium outcome is also the policy
maker’s most preferred outcome. Thus we have proved a welfare theorem.
Proposition 6 (Welfare Theorem).The equilibrium of Definition 1 is incentive-constrained ef-
ficient with respect to the Northern welfare. Also, a incentive-constrained efficient allocation in
terms of the Northern welfare can be obtained as an equilibrium.
Since the equilibrium with FT is incentive-constrained efficient, no better outcome for consumers
and roasters can be achieved, hence FT can not be harmful to Northern welfare.
We modeled a competitive retailer both as a standard baseline case and as a reasonable ap-
proximation for major coffee markets. However, most of our results carry over to a model with a
monopolistic roaster. Under the same condition (Condition 2), the roaster will choose to offer both
a regular and a FT coffee, charging the consumer a premium for the latter, but also paying a cor-
respondingly larger premium to the farmer, and inducing greater cost-saving investment. Scaling
up the altruism component of utility leads to a more efficient outcome for FT coffee production.
However, under certain parameters, greater altruism will decrease the efficiency of non-FT coffee
17
production, since the monopolist wants to reduce non-FT farmers’ profit to discourage altruists
from buying non-FT coffee. Thus, the welfare consequence becomes ambiguous. Further details
are in Appendix A.6.
3 Conclusion
A typical economic argument for laissez faire is that prices signal economic agents to maximize their
own welfare, and this leads to efficiency. This view criticizes the practice of fair trade by claiming
that catering to consumers’ altruism distorts prices, and thus reduces efficiency. However, we have
shown that, in the presence of an information asymmetry problem (the moral hazard problem of
farmers), what may seem to be a “distortion” of price (the higher premium for fair trade coffee)
may actually represent the use of a concerned outsider (altruistic consumers) to increase efficiency
(more efficient investment).
Our finding suggests a generalization that is applicable to contract theory. Parties involved in
a bargaining situation may find it useful to involve an outsider who is concerned with the outcome.
In turn, this could alleviate the inefficiency caused by the presence of information asymmetry.
As previously noted, our model is applicable not only to fair trade coffee but to any case in which
a good or service is produced using inputs (with a market structure and information asymmetry
resembling our model), and sold to a consumer (or business or government purchaser) who cares
about the net income of the input producer. We provide a potential justification for “bundling”
altruistic behavior and consumption decisions. Our model explains both why a rational altruist
would prefer such products and how this improves the efficiency of production.
There are also implications for government policy. Governments may choose to purchase inputs
from favored suppliers (from an altruistic or national interest perspective); our model provides
an argument for the efficiency of doing so (rather than buying the cheapest input and offering
a direct subsidy) under certain conditions. However, the simplest public policy implication is
that governments may want to advocate policies that tend to favor fair trade industries. The
European Union has pursued this, passing a handful of opinions, resolutions, and directives aimed
18
at promoting fair trade and encouraging the purchase of fair trade products by public authorities.23
Our result that “welfare net of consumer surplus increases as consumers become more altruistic”
implies that a campaign to make people aware of fair trade products could be welfare improving.
Furthermore, governments often play a role in monitoring claims made by retailers to minimize
problems of asymmetric information; in this context, government may want to regulate which
products may label themselves as “fair trade.”
Future empirical work will be able to more precisely test the relevance of our model to particular
industries and markets. Our model implies that non-verifiable investment will be below the efficient
level, even in repeated relationships, while consumer altruism can induce a more favorable long-
term contract. A detailed examination of production data will reveal whether, ceteris paribus,
suppliers getting a larger premium (e.g., fair trade farmers) invest more in quality and in reducing
downstream costs. Our model predicts that the consumer premium for fair trade should not exceed
the premium paid to farmers. This could be tested empirically by comparing the coefficient on a
fair trade dummy in a hedonic regression at the consumer level (using, e.g., recent supermarket
scanner data) to a similar coefficient in a regression at the farmer level.
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A Appendix
A.1 Price discrimination
Suppose the altruists value the unit of pure coffee at Vaand value donations Dat a(D)< D and
the non-altruists value the coffee at V > Vaand do not value donations. (Note that the altruists’
residual willingness to pay for a donation can be no more than D, otherwise they would make the
donations directly.) In such a case the retailer could price discriminate by selling the unbundled
coffee product at a “premium” price P=Vto non-altruists, and selling the bundle of coffee and
donation Dat price p+a(D) to the altruists, where p<P <p+a(D). On the other hand, suppose
altruists have a greater willingness to pay for the unit of coffee itself (Va> V ), and the firm tries to
sell the unbundled coffee at price Pand the bundled coffee at some higher price. Altruists will be
willing to pay no more than P+a(D)< P +Dfor the bundled product, as they could always choose
to purchase the cheaper coffee at price Pand make a direct donation. As (absent the efficiencies
discussed in our own work) it will cost the retailer at least D to make such a donation, the retailer
can not profit by offering the bundle.
A.2 Quality interpretation
Coffee is branded “coffee (π, q)”, where πis the transfer to the farmer, and qis the quality of the
coffee. Consumer’s valuation of coffee is v+q. The quality of the coffee, q, depends upon the
farmer’s investment m, i.e., q=q(m). We impose the same conditions on −q(m) as we impose on
c(m) in the main text. Since the characteristics of each coffee are represented by vector (π, q), the
23
price is also indexed by vector (π, q), i.e., P(π, q). The consumers’ problems are:
max
π,q [v+q−P(π, q)] and max
π,q [v+q+a(π)−P(π, q)]
for the non-altruistic consumer and the altruistic consumer, respectively.
The producer’s problem is
max
π,q nP(π, q)−(π+m) : q=q(m) and π≥1−δF
δF
mo
From the assumption of perfectly competitive roasters, we derive
P(π, q) = π+m(q)
where m(q) is an inverse function of q(m).
We consider a pair of (π, q) satisfying the binding incentive compatibility constraint, i.e., π=
1−δF
δFm(q). A pair satisfying π < 1−δF
δFm(q) is not feasible, and a pair satisfying π > 1−δF
δFm(q) is
not optimal. Hence, the price function is simplified into
¯
P(q) := P1−δF
δF
m(q), q=1−δF
δF
m(q) + m(q) = m(q)
δF
where π(q) := 1−δF
δFm(q).
In summary, even though the price system seems more complex than the one in the cost reduc-
tion story (as it is indexed by a two-dimensional vector (π, q) rather than πonly), the price system
can be reduced to be one dimensional.
Finally we show that these two interpretations are identical by demonstrating that the first order
conditions under the quality interpretation are identical to those derived from the cost reduction
model. The consumers’ maximization problems with the derived price function ¯
P(q) are:
max
q[v+q−¯
P(q)] and max
q[v+q+a1−δF
δF
m(q)−¯
P(q)].
The first order conditions are:
1−¯
P0(q)=0⇔1 = m0(q)
δF
⇔δF=1
q0(m)
and 1 + 1−δF
δF
a0(π)m0(q)−m0(q)
δF
= 0 ⇔1 + 1−δF
δF
a0(π)1
q0(m)−1
δFq0(m)= 0
Replacement of q0(m) with −c0(m) makes the above two equations identical to the first order
conditions of altruistic and non-altruistic consumer, (8) and (9).
24
A.3 Altruism Component of Consumer’s Utility
The assumption of a0(·)≤1 is stringent; it requires us to build a model in which the altruistic
consumer buys fair trade coffee, even though he would not make a direct donation to the farmer.
Although the altruistic consumer may have a marginal utility of giving that is larger than unity
(a0(·)>1), the assumption that a0(·)≤1 is without loss of generality. We show this in two ways.
A.3.1 Residual willingness to donate
We define u(z) as the value a consumer places on making a gift of zto the farmer. Assume u0>0,
u00 <0, and limz→∞ u0(z)<1: the marginal return to such gifts is positive, decreasing in the gifts,
and less than the marginal cost of donation for large gifts.
We assume a “costless” technology (e.g., a charity) for transferring donations to farmers, so
that a donor who wants to give zto the farmer can do so at cost c(z) = z.24 Thus, u0(z) = c0(z)
determines the optimal donation amount. If no such positive zexists, z= 0 (no donation) is the
optimal solution. Define a(x) = u(x+z)−u(z). Function a(x) is the “residual” willingness to pay
for the fair trade attribute (assuming separability and no income effect).
In reality, the consumer will choose the optimal bundle of the donation, fair trade coffee, and
other commodities simultaneously. However, the consumption of fair trade coffee will be only a
small fraction of the entire bundle. Thus consideration of the consumer’s residual altruism (i.e.,
assuming a0(·)≤1) is a reasonable approximation.
A.3.2 Simultaneous decision
Again, u(z) is the value a consumer places on making a gift of zto the farmer. We do not need
to assume, as in the previous section, that the decision over direct donations precedes the decision
whether to buy the fair trade product. Because the consumer can make a direct donation at unit
price (i.e., a costless technology for transferring money to farmers), the consumer is willing to pay
24 We could generalize this to a case where c(z) = (1 −t)(1 + k)z, where tis the consumers’ marginal tax rate
(if a consumer itemizes tax-deductions), and krepresents the fees associated with transferring such a donation.
Furthermore, we could imagine other charitable donations are close substitutes, perhaps valued more highly than
gifts to farmers.
25
at most xto increase the farmer’s income by x. Thus, the willingness to pay for xis
a(x) = min(u(x), x).
Thus a0(x)≤1 is derived from the above.
This yields a very strong result. Because of the agency problem, passing money through FT is
more efficient than giving directly to the farmers. This would imply that a very altruistic consumer
(e.g., for an extreme example if a0($10,000) = 1) would channel all her generosity through FT,
(buying a single very expensive bag of coffee). However, as the price the farmer receives increases,
the marginal impact on the agency problem becomes minimal. Thus, if a highly altruistic consumer
gets even slightly more utility from money going to a charitable cause (e.g., because this help those
in the most dire poverty, rather than only coffee farmers) then she will buy FT coffee and also
make a donation. Furthermore, it is unlikely that there are many consumers who care about coffee
farmers to such an great extent to make such an extremely “generous” product commercially viable.
A.4 Characterization of an equilibrium
Let mEF satisfy 1 = −c0(mE F ); this defines the first best level of investment since the marginal cost
of the investment is equivalent to the marginal benefit, i.e., the marginal reduction of processing
cost. Let πE F := 1−δF
δFmEF . For given π, if the incentive compatibility constraint (2) does not
bind, the optimal investment is m(π) = mEF . Since 1 + c0(m)<0 for an investment m<mEF ,
we conclude
m(π) = min mEF ,δF
1−δF
π
Note the incentive compatibility constraint, m≤δF
1−δFπ. For a given farmer’s profit π, if π≤πEF
then the roaster wants to increase investment muntil the incentive compatibility constraint binds.
We derive the profit function of the roaster supplying coffee(π):
ΠR(π) =
P(π)−π
1−δF−cδF
1−δFπif πis such that m(π) = δF
1−δFπ, i.e., π < πEF
P(π)−(π+mEF )−c(mEF ) if πis such that m(π) = mEF ,i.e., π≥πE F
26
Since roasters are perfectly competitive each roaster earns zero profit, i.e.,
P(π) =
π
1−δF+cδF
1−δFπif π < πEF ,
(π+mEF ) + c(mEF ) if π≥πEF .
(5)
Given the price in (5), the altruistic consumer’s problem is:
πC
A=
argmax
π
[v+a(π)−π
1−δF−cδF
1−δFπ] if π < πEF ,
argmax
π
[v+a(π)−(π+mEF )−c(mEF )] if π≥πEF .
But note that d
dπ [v+a(π)−(π+mEF )−c(mEF )] = a0(π)−1<0. In other words, π≥πEF cannot
be an optimum. I.e., coffee(π) is never produced in equilibrium for π≥πEF . Thus, it is enough to
consider only the case of π < πEF , i.e.,
πC
A= argmax
π
[v+a(π)−π
1−δF
−cδF
1−δF
π].(6)
For the non-altruistic consumer, we can derive a similar result,
πC
0= argmax
π
[v−π
1−δF
−cδF
1−δF
π].(7)
The first order conditions of (6) and (7) are:
(1 −δF)a0(πA) + δF−c0δF
1−δF
πA≤1 and equality holds if πA>0,(8)
δF−c0δF
1−δF
π0≤1 and equality holds if π0>0,(9)
For each of these to have an interior solution of π0>0 and πA>0, the Condition 1 and
Condition 2 are trivially required.
Proof of Corollary 1: Since a0(π)>0, we trivially derive the first result from the two first order
conditions. P(π) = π
1−δF+cδF
1−δFπwithin a relevant range of δF
1−δFπ < mEF . The first derivative
of the price is P0(π) = 1
1−δF+δF
1−δFc0δF
1−δFπ>0. Thus the price increases in π.
A.5 Comparative statics with respect to δ
We re-write the first order conditions (8) and (9) as:
(1 −δ)a0(1−δF
δF
mA) + δ−c0(mA)= 1 , δ −c0(m0)= 1.
27
The first equation is for FT coffee, and the second one is for non-FT coffee.
Totally differentiating them with respect to mA,m0, and δF, we get:
dδFa0(·) + c0(·)−(1 −δF)a00(·)−nA
δF
+1−δF
δ2
F
mA=dmA(1 −δF)1−δF
δF
a00(·)−δFc00 (·),
dδF−c0(·)−m0
δF
+1−δF
δ2
F
m0+dm0−δFc00(·)= 0
Thus we get:
dmA
dδF
=
a0(·) + c0(·) + (1 −δF)a00(·)hmA
δ2
Fi
(1−δ)2
F
δFa00(·)−δFc00 (·)
,dmA
dδF
=c0(·)
−δFc00(·).
Since c(m)<−1 for m < mEF and a0(·)≤1, we derive a0(·) + c0(·)<0. Thus both dmA
dδFand dm0
dδF
are positive because a00(·)<0, c0(·)<0, and c00(·)>0.
A.6 Monopolistic retailer
In this section we assume that the roaster is a monopolist. The incentive compatibility condition
for the farmer is identical, i.e., m≤δF(π+m). For a given farmer’s profit π, the monopolistic
roaster wants to maximize investment m. Thus, the incentive compatibility constraint is binding.
Note π+m=m
δFand m=δF
1−δFπunder the binding incentive compatibility constraint. Thus, the
monopolist’s objective function is:
max
P(πA),P (π0),m0,mAP(π0)−m0
δF
−c(m0)+P(πA)−mA
δF
−c(mA)
In order to price-discriminate, the monopolist needs to make sure that altruistic consumers do
not have an incentive to purchase non-fair trade coffee, and the non-altruistic consumer does not
purchase fair trade coffee., i.e.,
v+a(πA)−P(πA)≥v+a(π0)−P(π0),(10)
v−P(π0)≥v−P(πA).(11)
We also need to impose individual rationality constraints:
v+a(πA)−P(πA)≥0,(12)
v−P(π0)≥0.(13)
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In other words, the monopolist must set prices low enough so that consumers actually purchase
coffee. These constraints were not required in the previous model: all we had to assume was that
the consumers’ valuation of coffee was larger than the cost of production, and perfect competition
among roasters drove the price down to the cost of production. However, when the monopolis-
tic roaster has ability to set prices, the monopolist needs to explicitly consider these incentive
compatibility and individual rationality constraints.
Note that constraint (10) implies constraint (12) as long as πA≥π0. We will verify πA> π0
later, so that we can ignore constraint (12). In other words, the individual rationality constraint
for the altruistic consumer is not binding.
We can write the three remaining constraints as follows:
[a(πA)−a(π0)] + v≥[a(πA)−a(π0)] + P(π0)≥P(πA)≥P(π0)
where the first inequality comes from constraint (13), the second from constraint (10), and the third
from constraint (11). For given πAand πA, the monopolist wants to increase P(πA) and P(π0) as
much as she can. From the first inequality, we derive P(π0) = v. From the second inequality, we
derive P(π0) = v+ [a(πA)−a(π0)]. In other words, the roaster extracts all the consumer surplus
from the non-altruistic consumer, but leaves some consumer surplus for the altruistic consumer.
This surplus is necessary to prevent the altruists from mimicking non-altruists.
As long as πA> π0(which we will verify later), the last constraint does not bind. In other
words, the incentive compatibility constraint for the non-altruistic consumer does not bind.
Plugging these optimal prices into the monopolist’s objective function, we derive
max
m0≥0,mA≥0v−m0
δF
−c(m0)+v+ [a(πA)−a(π0)] −mA
δF
−c(mA).
Kuhn-Tucker conditions for this maximization problem are:
(1 −δF)a0(1−δF
δF
m∗
A)−δFc0(m∗
A)≤1,equality if m∗
A>0 (14)
and −(1 −δF)a0(1−δF
δF
m∗
0)−δFc0(m∗
0)≤1,equality if m∗
0>0.(15)
29
The second order conditions are:
(1 −δF)2
δF
a00(1−δF
δF
m∗
A)−δFc00(m∗
A)<0,
det
(1−δF)2
δFa00(1−δF
δFm∗
A)−δFc00(m∗
A) 0
0−(1−δF)2
δFa00(1−δF
δFm∗
0)−δFc00(m∗
0)
>0
Note (1−δF)2
δFa00(1−δF
δFm∗
A)−δFc00(m∗
A)<0 by the assumption of a00 <0 and c00 >0. Thus, we only
need the following condition for the second order conditions to hold:
−(1 −δF)2
δF
a00(1−δF
δF
m∗
0)−δFc00(m∗
0)<0.(16)
This constraint means that as the farmer’s profit and investment increase, the marginal value of
farmer profit to the altruistic consumer declines more slowly (by a certain magnitude) than the
marginal cost-saving value of the corresponding increase in investment. For global concavity of the
monopolist’s objective function, we assume the following.
Assumption 1.
−(1 −δF)2
δF
a00(1−δF
δF
m0)−δFc00(m0)<0,∀m0≥0.(17)
We discuss the case where Condition (17) is not satisfied at the end of this appendix.
We need additional conditions to have interior solutions for m∗
0>0 and m∗
A>0.
Condition 3. −(1 −δF)a0(0) −δFc0(0) >1.
We re-state Condition 2 for the sake of convenience.
Condition 2. (1 −δF)a0(0) −δFc0(0) >1.
We derive the following proposition trivially.
Proposition 7. (i) m∗
0>0(hence, π∗
0>0) if and only if Condition 3 holds.
(ii) m∗
A>0(hence, π∗
A>0) if and only if Condition 2 holds.
Proof. Proofs follow directly from Kuhn-Tucker conditions (14) and (15).
Similarly to the previous model, we derive the following to verify π∗
A> π∗
0:
30
Corollary 2. In general, we derive πA≥π0and P(πA) = v+(a(π∗
A)−a(π∗
0)) > P (π0) = v. Under
Condition 2, (i) π∗
A> π∗
0,m∗
A> m∗
0, and P(πA)> P (π0).
Proof. Proofs follow directly from Kuhn-Tucker conditions (14) and (15).
Corollary 3. In general, P(π∗
A)−P(π∗
0)≤π∗
A−π∗
0. Under Condition 2, P(π∗
A)−P(π∗
0)< π∗
A−π∗
0.
Proof. P(π∗
A)−P(π∗
0) = a(π∗
A)−a(π∗
0)< π∗
A−π∗
0by the strict concavity of a(·) and a0(·)≤1.
As in the comparative statics of Section 2.3, we can parameterize altruism through βby re-
defining altruism component as βa(·).
Since the first order condition determining m∗
A(equation (14)) is identical to that in the previous
model, we also derive the following proposition identical to Proposition 3.
Proposition 8. Under Condition 1a,
dπ∗
A
dβ >0and dm∗
A
dβ >0.
However, there is a crucial difference between the previous model and the monopolistic model:
m∗
0is also affected by altruism. The price discriminating monopolist has an incentive to reduce π0
(implying a reduction in m∗
0) to discourage altruists from buying non-FT coffee. This is shown in
equation (15), where the determination of m∗
0is influenced by altruism component a(·).
To be more specific, by total-differentiating equation (15) where a(·) was replaced with βa(·),
we derive:
dπ∗
0
dβ =a0
−βa00 −δF
1−δF2c00
and dm∗
0
dβ =δF
1−δF
dπ∗
0
dβ .
The sign of both is negative under Assumption 1. In summary, the increase in altruism decreases
efficiency for the production of regular coffee. As a result of this, the investment for regular coffee
will be reduced by the introduction of fair trade coffee, as shown below.
Proposition 9. m∗
0< m∗< m∗
Awhere m∗satisfies 1
δF=−c0(m∗).
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Proof. Proofs follow directly from Kuhn-Tucker conditions (14) and (15).
Regular coffee is produced at an inefficient level since 1
δF<−c0(m∗
0). In other words, more
efficient cost reduction (by investing more) is possible. However, this cost reduction is being deterred
because the corresponding increase in farmer profit makes the regular coffee more attractive to
altruists, tightening their incentive compatibility constraint and increasing the surplus they must
be paid; i.e., limiting price discrimination.
A.6.1 Violation of Assumption 1
Suppose that Assumption 1 is violated and that inequality (17) is reversed, i.e.,
−(1 −δF)2
δF
a00(1−δF
δF
m0)−δFc00(m0)>0,∀m0≥0.(18)
In other words, we now suppose that the marginal altruism decreases faster in investment (by
a certain magnitude) than the investment’s marginal return on the cost reduction decreases in
investment. In this case, as we have already mentioned, the second order conditions are not
satisfied. More precisely, the first order condition for (m∗
0, m∗
A) is satisfied at a saddle point. Also
note (1−δF)2
δFa00(1−δF
δFm∗
A)−δFc00(m∗
A)<0 is still true. Thus, the optimal (corner-) solution is at
(m0= 0, mA=m∗
A) or at (m0=∞, mA=m∗
A).
Mathematically speaking, (m0=∞, mA=m∗
A) is not an impossible solution under our as-
sumption that c00 >0 and a00 <0. However, this is clearly not a sensible solution in that it implies
that the roaster will pay an infinite amount of money to farmers. Under the reasonable assumption
that the (altruistic and cost-reducing) benefit of the investment would be lower than the cost of
the investment for such a large investment, this case can be ruled out.
Finally, for the optimal (m0= 0, mA=m∗
A), our results are still valid except that
∂m∗
0
∂β =∂π∗
0
∂β = 0.
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