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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)

28

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∗).

31

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.

32