Fair Trade-Is it Really Fair

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					                            Fair Trade - Is it Really Fair?
                             Tomáš Koneµ ný, Jan Mysliveµ ek1
                                       c                c

                                               CERGE-EI2

                                                April 2008




                                                  Abstract
The introduction of Fair Trade certi…cation scheme has the capacity to increase the incomes of both par-
ticipating and non-participating farmers. The minimum contracting price as part of Fair Trade standards,
                                                        s
however, precludes the full realization of the program’ potential bene…ts. Despite being consistent with
the objective of maximizing farmers’ participation in the scheme and under more stringent conditions
with the maximization of participating farmers’revenues, the minimum price might reduce their payo¤s
relative to the free-contracting alternative and paradoxically increase pro…ts of the middlemen whose local
monopsony power it originally aimed to retrench. Furthermore, the total surplus generated by Fair Trade
cooperatives as the primary form of farmer organization declines, which translates into reduced investment
resources available for community investment. From the policy perspective, measures to reduce excess-
supply such as relaxed-price setting over a stipulated time period or gradual replacement of participating
cooperatives by new applicants could provide a superior alternative.




   Keywords: Certi…cation, regulation, price setting, co¤ee, Fair Trade, monopsony

   JEL classi…cation: D18, D21, D43, D45, D71, J51, Q17, Q56
   1 We would like to thank Leven Celik, Libor Dušek, Peter Katuš ák, Andreas Ortmann, Avner Shaked, Krešimir
                                                                  c
                                                                  µ
µ c
Zigiµ for their comments All remaining errors are ours.
   2 CERGE-EI is a joint workplace of the Center for Economic Research and Graduate Education, Charles Uni-

versity, and the Economics Institute of Academy of Sciences of the Czech Republic.
                                                         e nu
Address: CERGE-EI, PO Box 882, Politických vµ zµ ° 7, 11121 Prague, Czech Republic.                      E-mail:
tomas.konecny@cerge-ei.cz, jan.myslivecek@cerge-ei.cz. CERGE-EI is a joint workplace of the Center for Economic
Research and Graduate Education, Charles University, and the Economic Institute of the Academy of Sciences of
the Czech Republic.



                                                       0
1     Introduction

As Fair Trade products gradually move from specialized ethno shops to supermarket shelves, the

actual impact and potential of Fair Trade has become an increasingly discussed topic. Acad-

emics, journalists, policymakers as well as NGOs and other stakeholders involved in Fair Trade

                                                                    s
scheme present their worries and expectations regarding the movement’ actual capacity to im-

prove livelihoods of the poor. Besides the common assertion that Fair Trade helps marginalized

producers through guaranteed minimum price and other provisions like access to pre-…nance or

market information(FLO, 2007), most vocal concerns of Fair Trade opponents relate to the excess

Fair Trade supply, impact on non-participating producers, and the uncertain nature of Fair Trade

demand (The Economist (2006), Washington Post (2005), Weber (2007) etc.).1 These opinions

certainly deserve a more detailed analysis as the potential reach of Fair Trade extends to millions

of households living in poverty.

    This paper aims to address some of the most frequently expressed concerns relating to Fair

Trade, namely the excess of Fair Trade supply due to guaranteed minimum price, impact on non-

participating producers, and the limited scope of Fair Trade demand. In particular, it aims to

answer the following questions: Does the higher Fair Trade price disadvantage those producers

which do not engage in Fair Trade compared with those which do? How do costs and bene…ts of

Fair Trade depend on the situation on global markets? Is it optimal for the farmers to face excess

supply on the Fair Trade market?

    We develop a simple framework incorporating the empirical regularities of the largest and most

successful Fair Trade market - co¤ee. Our framework allows to evaluate the overall distribution of

producers’costs and bene…ts in response to the regulated Fair Trade price, demand characteristics,

and a particular transmission mechanism at work. The following section provides a brief expose to
   1 There are, of course, additional arguments against Fair trade such as e.g., the ine¢ ciencies in the processing

                                     s
and distribution due to Fair Trade’ bypassing of specialized intermediaries exploiting economies of scale. Fair
Trade has also been criticised as yet another instrument for price discrimination across customers. For the sake of
clarity, our paper does not address these issues and instead focuses exclusively on the excess supply argument and
the corresponding impact on farmers.




                                                         1
the structural changes on the global co¤ee market in the 90s and the success of Fair Trade labelled

co¤ee. Section 3 reviews the organization of Fair Trade labelling scheme and major arguments

favoring the Fair Trade idea. Section 4 develops a model that addresses some of the bene…ts and

concerns relating to Fair Trade in a simple framework …rst without monopsonistic middlemen and

then with the middlemen that control access to world markets. For the ease of exposition, Section

4 also contains numerical results obtained from explicit supply and demand structures. The …nal

section concludes.




2     Fair Trade and global co¤ee market

The Fair Trade idea is usually associated with co¤ee, the most successful Fair Trade commodity

with the largest share in total sales and the longest history among traded Fair Trade commodities.2

The growth of Fair Trade can be neatly illustrated by the story of this aromatic commodity. The

yearly average increase in total sales volumes of Fair Trade co¤ee over the period 2001-2006

amounted to 27%, with growth rates increasing on a yearly basis and reaching as much as 53% in

2006 (FLO, 2007). The extraordinary growth can be attributed mostly to the expanding markets

in the United States, where only in 2006 the sales volumes more than doubled. Nonetheless,

in Europe with its 79,000 salespoints, the market shares of Fair Trade co¤ee have been likewise

increasing substantially. In the United Kingdom, the market share of ground Fair Trade co¤ee

boosted from 1.5% in 1999 to 20% in 2004 (FINE, 2005).3 While in other European countries

the growth rates and market shares have been more modest, they still exceed the annual growth

of world co¤ee demand (0.4%) by the order of magnitude. Hence, despite still negligible share

in the overall world co¤ee consumption (0.8% out of total 6.7 million tons in 2006 FLO (2007)

and ICO (2007)),4 the continuing expansion of specialty markets and rising consumer awareness
   2 In North America, co¤ee accounted for 34% of all Fair Trade sales in 2003 ?. According to the European

Commission (1999), the estimated share of Fair Trade food products totaled 60% of the overall Fair Trade retail
turnover within the EU. Co¤ee made approximately 50% of the above-mentioned share.
   3 Note that the …gures refer to ground co¤ee, for instant co¤ee the shares are much lower (FLO, 2007).
   4 According to the FLO (2007), the worldwide certi…ed sales of all Fair Trade products amounted to roughly

2.3bln USD. The overall sum will be slightly higher given that the …gure thus does not include non-certi…ed Fair


                                                       2
of Fair Trade concept5 call for closer evaluation of the respective pros and cons. We begin with

developments on world co¤ee markets over last few decades.



2.1     Co¤ee crisis in the 90s

Until 1989, the global co¤ee market had been regulated through the International Co¤ee Agree-

ment (ICA), a set of agreements which stipulated production quotas and governed quality stan-

dards for a major part of produced co¤ee. The ICA disintegration and the following sharp rise in

co¤ee supply coincided with stagnating demand and market concentration of major roasting and

trading companies. On the supply side, the quota abolition led to the output expansion of existing

producers (e.g., Brazil), as well as the entry of new signi…cant players (Vietnam) specializing in the

production of lower quality Robusta co¤ee. Demand side, on the other hand, witnessed improved

processing technologies that removed bitter taste of cheaper co¤ee beans such as Robusta and

’natural’Arabica. These advances shifted roasters’demand away from traditional co¤ee exporters

from Central America specializing in a more expensive mild Arabica (Lindsey, 2003).6 The co¤ee

glut has been further exacerbated by long adjustment lags typical for co¤ee production.7

    Except for short periods of recovery in mid-90s due to Brazilian frost, co¤ee prices reached

historical lows and led to substantial hardship in a¤ected rural economies.8 In October 2001, the

price of higher quality Arabica co¤ee9 quoted at the New York Board of Trade reached its lowest

level in 30 years at 45 cents/lb. For the sake of comparison, Bacon (2005) puts the estimated

average monetary production costs of small farm producers to vary between 49 and 79 cents/lb.

Nonetheless, since 2001 the price of Arabica co¤ee has gradually risen so that in October 2007 it
Trade articles.
    5 Moore (2004) cites survey evidence on expanding shares of consumers describing themselves as ’           ,
                                                                                                       ethical’ or
’strongly ethical’.
    6 According to Wasserman (2002), cited in Lindsey (2003), the estimated percentage of mild Arabica in the

roasters’leading co¤ee blends dropped from 50% in 1989 to 35% in 2001.
    7 It takes several years before beans can be …rst harvested.
    8 Bacon (2005) mentions substantial rural-urban migration in Matagalpa, Nicaragua and erosed farmlands

following the substitution from co¤ee to cattle pasture in Coto Brus, Costa Rica. Similar observations from other
regions can be found in e.g. Raynolds (2002) or Ronchi (2002).
    9 Arabica and Robusta are two main co¤ee species produced. While Arabica is grown mostly in Latin America

and Eastern Africa, major producers of Robusta co¤ee locate in Brazil, Uganda, India and South-East Asian
countries (ICO, 2007).


                                                        3
has surpassed the Fair Trade minimum price 121 cents/lb.



2.2    Shifts in market power

In general, co¤ee beans leaving the farm gate have to pass several intermediate stages before

they reach …nal consumer. Harvested beans are usually purchased to private intermediary and

then proceed for further processing and distribution through processing plant, local exporters

and/or international traders, roasting companies and retailers. Co¤ee crisis in the 90s coincided

with the extended upstream integration of the commodity chain. While sluggish co¤ee demand

and general market liberalization facilitated corporate consolidation in the lower parts of the

commodity chain, empty space left after the disintegration of the ICA has been swiftly resumed

by the roasters and trading companies (Ponte, (2002) cited in Bacon (2005)). In fact, the co¤ee

roasting market happens to be the most heavily concentrated part of the commodity chain. The

two largest groups, Nestlé and Philip Morris, control 49% of the world market for roasted and

instant co¤ees. Three following roasters - Sara Lee, Procter and Gamble and Tchibo - make up

additional 20%. Less but still highly concentraded are international traders. The two largest

international co¤ee traders as of 1998, Neusmann and Volcafé, controlled 29% of the market, and

the top six companies the overall 50% (Milford, 2004).

   Progressive concentration of the intermediate and downstream parts of the value chain also

translated in the share of producer countries’ in the …nal price. Talbot (1997) cited in Bacon

(2005) reports producer countries’ share of the …nal retail price decreased from close to 55% in

the past to about 22%. More recent estimates suggest that farmers get about 6% of the value at

which co¤ee pack is sold in store (Milford, 2004).



2.3    Growth of specialty markets

Stagnating demand and falling prices in the market for normal ’bulk’ co¤ee on the other hand

contrast with the successful record of specialty co¤ee market niche. For example, the U.S. gourmet


                                                4
co¤ee market in 2001 represented 40% of the total market value and 17% by volume with the annual

growth rates well above 5% (Giovanucci, 2001). The continuing success of specialty brands has

re‡                                                                        story’ behind each
   ected increasing consumer demand for high quality, taste and attractive ’

cup of co¤ee. Fair Trade and organic labels were able to keep up with these market di¤erentiation

trends and although they represent still a relatively minor share in specialty co¤ee sector (3-5%

in the U.S. specialty co¤ee retail market (Giovanucci, 2001)), their position becomes stronger

year-by-year. Apart from increasing market shares in gourmet sector, growing importance of

Fair Trade in co¤ee market becomes likewise apparent from both its increasing recognition by

customers and widening presence in common distribution channels. The former can be illustrated

by survey evidence according to which 74% of the French population understood the notion of Fair

Trade and 50% of the adult population in the UK recognized the Fair Trade label (FINE, 2005).

Fair Trade products have also become increasingly available in ’mainstream’ retail outlets and

public o¢ ces. In Europe only, the number of supermarkets with Fair Trade sortiment increased

from 43,100 in 1999 to 56,700 in 2004 (FINE, 2005), i.e., by 32%. The origins, organization and

working of Fair Trade networks facilitating the above-mentioned market progress is described in

more detail in the following section.




3      The origins, organization and bene…ts of Fair Trade

The origins of the Fair Trade movement can be traced more than 40 years ago when …rst Alternative

Trade Organizations (ATO) established trade networks connecting marginalized producers in the

South with socially aware customers in developed markets. These entities were run mostly by

religious organizations and various solidarity groups with the aim to provide a viable alternative

                                                                 s
to what they perceived as inequitable world market relations. ATO’ initial e¤orts, however, did

not succeed in transforming the Fair Trade idea into a major alternative to the existing system.

                                        s
In order to gain a new impetus, the ATO’ initial focus on handicrafts gradually shifted towards



                                                5
agricultural commodities and in 1988, the …rst certi…cation scheme introduced by a Dutch ATO

Solidaridad started a qualitatively new era of Fair Trading. Through the guarantee that labelled

products meet basic environmental and labor standards, the novel Max Havelaar label simpli…ed

interface between participating producers and customers in developed markets and by so doing

set the basis for the future successful entry of Fair Trade into mainstream distribution channels.

            s
Max Havelaar’ success had been followed by further similar projects. Finally, in 1997 several

independent labelling initiatives formed Fair-trade Labelling Organization International (FLO).10

    The FLO is itself an umbrella organization of 20 labelling initiatives in 21 countries and

3 producer networks. The organization currently works with 569 Fair Trade-certi…ed producer

organisations representing over 1,4 million farmers and workers in 57 countries in Africa, Asia

and Latin America (FLO, 2007). Similar to other Fair Trade initiatives, the FLO supports Fair

Trade through the linking of producers with traders in order to match supply and demand, liaison

with producer organizations to strengthen their production and export capacities, and lobbying at

international forums on trade and development. Nonetheless, the main task of the FLO is standard

setting, certi…cation and monitoring of the Fair Trade Certi…cation Trademark recipients.



3.1     Fair Trade and labelling

Of course, co¤ee is not the only Fair Trade article and not all Fair Trade products are certi…ed.

According to the FLO data, the retail value of all Fair Trade products sold in 14 European

countries in 2005 totaled 657m e at minimum, out of which 597m e (i.e., approximately 90%)

came from the sales of certi…ed products.11 The labelling scheme covers almost exclusively food
   1 0 FLO is one of four members of the umbrella organization FINE, which also includes International Fair Trade

Association, Network of European Worldshops and European Fair Trade Association. The ultimate goal of each
participating organization is to facilitate Fair Trade, yet only FLO serves as a certi…cation and standard-setting
body. In North America, the most important organization is Fair Trade Federation (FTA). FTA is an association
of Canadian and American fair trade wholesalers, importers and retailers providing matching services and di¤using
information about Fair Trade.
   1 1 As p. 32, FLO (2007) notes, the overall …gure does not include non-labelled food products sold in Worldshops

(i.e., smaller, locally based shops specialized in Fair Trade), nor does it include Fair Trade products o¤ered through
less common supply channels like mail orders or gift shops. Accounting for these …gures most likely would not
reverse the overall dominance of Fair Trade certi…ed sales.




                                                          6
products. Besides co¤ee as a leading and most successful commodity, the Fair Trade certi…cation

portfolio covers a number of other major crops including bananas, cocoa or rice. The certi…cation

standards vary by commodity and production process (small-scale farming vs. production by hired

labor) and distinguish between producers and traders.

   In case of co¤ee, traders have to trade directly with Fair Trade producers and


   1. pay at least a guaranteed minimum price (121 cents/lb for Arabica co¤ee) or above to cover

      the costs of sustainable production. In case the co¤ee price quoted at the New York Board

      of Trade exceeds the Fair Trade Minimum Price, the Fair Trade price equals the New York

      price,


   2. pay the Fair Trade premium 10 cents that should be used by producers for community

      development or investments by individual producers,


   3. o¤er pre-…nancing up to 60% of the contract value,


   4. sign contracts that promote long-term sustainable planning.


   Fair Trade co¤ee producers, on the other hand, have to


   1. be small-scale farmers associated in a democratic organization,


   2. have the necessary export capacity,


   3. pursue environmentally friendly production techniques (FLO, 2007).


   The most apparent Fair Trade bene…t to the participating farmers seems to be the guaranteed

Fair Trade Minimum Price. Shocks and long adjustment lags of inelastic supply and demand in the

global co¤ee market directly translate into price ‡                         ict
                                                   uctuations, which can in‡ signi…cant hardship

on micro- and small-scale producers accounting for a signi…cant part of the overall co¤ee production

structure.12 These farms face limited opportunities to cope with adverse market developments
 1 2 In Central America, approximately 85% or 250,000 farms are micro- and small-scale (CEPAL (2002) cited in

Bacon (2005)).


                                                     7
especially in periods of prolonged low prices. The valuable case study by Bacon (2005) mentioned

both intensive and extensive measures taken by many non-participating farms during the past

decade of co¤ee crisis. The measures that were essentially intensive in nature included crop

diversi…cation,13 increased labor input often coupled with the withdrawal of children from the

education system, sharing resources through kinship networks, or increased reliance on barter.

The micro-producers with minimal farmland had to search for labor on larger plantations in order

to provide a living for their families. A qualitatively di¤erent, ’extensive’form of farm household

adaptation was migration.

    The stability of Fair Trade prices and the contribution of long-term relationships during the

times of co¤ee crisis has been emphasized also by Raynolds (2002) and Moore (2004).14 However,

the stability of price results necessarily in excess supply that forces FT farmers to sell part of

their production via traditional channels. Depending on the relative price of their production on

FT and regular market, it is possible that the excess supply does not bene…t the farmers. In the

following section, we develop a model that allows us to study these e¤ects.



3.2     Fair trade - stability of price and other bene…ts

The anecdotal evidence points to the importance of a higher Fair Trade price and the corresponding

feeling of security of participating farmers. Raynolds (p.417, 2002) cites a Fair Trade farmer from

a Mexican region Oaxaca:


       "We have seen the prices paid to co¤ee growers in the region collapse. Everyone is

       leaving. We are able to keep producing because of the more favourable Fair Trade

       price. We are able to provide food and clothes for our families, even medicine. The
  1 3 Majority of farms maintains a strong subsistence ethic with co¤ee production serving as a primary source of

cash income. Bacon (2005) surveys among Nicaraguan households observed that 61% of the interviewed farmers
grew half or more of the food they ate, including corn, beans, bananas and other fruits. Surveyed farmers sold
between 80-90% of their co¤ee harvest. The earned income reserved for o¤-farm purchases of food had been mostly
spent on basic items such as salt, sugar, oil, and meat.
  1 4 Moreover, the feeling of security is further reinforced by the ability of pre-…nancing at Northern interest rates

(Raynolds, 2002).




                                                          8
      children still attend school. We are not rich, but we are moving forward."


   According to the estimates of the co¤ee growers in the Oaxaca region, the Fair Trade farmers

received close to three times higher income from the sales through the Fair Trade as opposed to

conventional channels. Ronchi (2002) reports that over 1989-1995, the farmers from a Costa Rican

Fair Trade cooperative SARAPIQUI received prices that were, on average, 39% higher than the

those of the private middleman (’         ),
                                 bene…cio’ a local competitor to Fair Trade. Ronchi (pp 10-11,

2002) claims that


      "many of the farmers interviewed explicitly appreciate their continued participation

      in co¤ee whilst witnessing the disappearance of neighboring communities and the em-

      igration of family members and acquaintances."


   It is not only higher Fair Trade price that bene…ts the participating farmers. The interviewed

farmers often mention the bene…ts of stability rather than the actual level of price. As a small-scale

co¤ee producer in Costa Rica puts it:


      "The prices before? They were worse - very bad! The price now is more sustainable -

      more …xed. A family can get ahead."(ibid.)


   Even more important dimension of Fair Trade, however, seems to be the access to developed

markets as well as the expert assistance from Fair Trade organizations aimed to improve farmers’

position on the market. Fair Trade cooperatives often perceive the scheme as an opportunity

to learn about current demand trends and quality expectations by customers. Relationships

between the cooperatives and ATOs usually exceed the notion of a common market transaction

and can include joint investments or the development of marketing strategies for developed market.

Raynolds (p. 419, 2002b) claims that


      "in many cases the technical expertise and market information provided through Fair

      Trade may be more important for producer associations than the …nancial and com-

                                                  9
      modity arrangements... This information is critical for those selling their co¤ee via

      conventional channels or seeking organic speci…cation."


    Ronchi (p.14, 2002) adds the experience of the Costa Rican Fair Trade cooperative Coocafé:


      "The export department entirely credits the successful production of …nal products to

      the assistance received from ATOs. The experience has had a positive impact that

      is only inadequately described in …nancial terms. Producing for the …nal market had

      given them an important understanding of the full co¤ee marketing chain and hence

      allowed them to learn a great deal about a number of markets."


                                             s
    The elimination of middlemen and Coocafé’ direct Fair Trade experience involved a great deal

of learning as well as transmission of skills and in the end led to a markedly improved bargaining

position vis-a-vis other market agents and o¢ cial authorities. A similar experience has been made

by a Mexican cooperative ISMAM (Raynolds, 2002) and many other producers (FLO, 2007).




4     Model


While the farmers’narratives consistently report on higher or at least stable incomes and improved

living conditions due to the guaranteed Fair Trade price, the question still remains open as to how

the very existence of Fair Trade, the minimum price and other dimensions of the scheme impact

upon the non-participating producers. The existence of Fair Trade has been sometimes contended

as a mechanism creating excess supply of co¤ee, which ultimately hurts the non-participating

farmers through a lower equilibrium price on the global market (The Economist, 2006). In the

following section we argue that regardless of the degree of competition on local co¤ee markets,

the introduction of Fair Trade market per se leads to the improvement or at worst preservation

of all farmers’incomes unless the total demand for both types of co¤ee decreases. In this respect,

what many critics seem to address is not the actual existence of Fair Trade but the impact of

                                                10
guaranteed rather than market-determined Fair Trade price. This is also the major focus of our

study.

   In this section we develop a model that allows for several transmission channels that might

impinge upon both participating and non-participating farmers. The model hopes to address the

following questions: What is the impact of the introduction of Fair Trade markets on farmers’

incomes? Does the guaranteed Fair Trade price disadvantage those producers which do not engage

in Fair Trade compared with those which do? How do costs and bene…ts of the scheme depend on

               s
the Fair trade’ position in global markets?

   For the case of simplicity, the starting minimalistic setup presents a world describing two

coexisting, perfectly competitive markets (one for conventional, the other for Fair Trade co¤ee)

supplied from regions by farmers. We compare the outcomes to the case with a single market

for normal co¤ee and then examine the impact of Fair Trade price set above its market-clearing

level. In the second part, this framework will then be extended to allow for the presence of the

middlemen who purchase normal co¤ee from regional farmers and then deliver their shipping to

global market. Note that the world without middlemen is a useful benchmark, but it is not an

existing structure of the co¤ee market. Our analysis thus allows us to compare the impact of the

                                                                                    t.
Fair Trade mechanism in markets which do have powerful middlemen with those that don’ It

also allows us to predict what would happen if the role of middlemen were somehow eliminated.

Should the FT continue to operate if middlemen were absent?



4.1      Fair Trade in world without the middlemen

Assume there are n regions producing co¤ee and two types of economic agents: farmers producing

co¤ee, and consumers. Assume each farmer produces 1 unit of co¤ee and has a choice of either

consuming it (this outside payo¤ is normalized to zero), sell it on world market with normal co¤ee

and get p, or to the Fair Trade market (henceforth FT) at a price pF . All farmers can enter the

FT market, yet the cost of doing so for each farmer is f . Finally, in each region there is a measure


                                                 11
one of farmers with heterogeneous production costs c and FT compliance costs f . The production

costs c follow a general distribution function with c.d.f. G (c) de…ned over support h0; 1i.

    Before proceeding further, we will provide a bit more detailed justi…cation for the above-

mentioned assumptions. The introduction of n regions re‡ects the fact that co¤ee growing areas are

typically spatially divided among private middlemen taking a monopsonist position with respect

to local farmers. Arbitrage among regions is in practice limited given the fair lack of information,

poor infrastructure and natural barriers in mountaneous areas where many small-scale co¤ee

producers live (see e.g. Ronchi (2002)).15 We also do not allow for the production adjustment at

the intensive margin and instead assume a …xed output per farmer. As Weber (2007) observes,

FLO does not induce higher Fair Trade supply of presently participating farmers and instead re-

channels the existing production from conventional markets through the certi…cation of additional

applicants. Even if this was not the case, however, the situation of farmers often does not permit

a signi…cant expansion of output due to either the absence of key productive assets such as land

or capital, or the replacement of the former co¤ee growing areas by urban development (Ronchi,

2002),?. This fact has also been acknowledged by the European Fair Trade Association which

stated that "given the parcels of land they (the farmers) possess and the lack of working capital

and resources, it (the expansion of output) is almost out of the question" (EFTA (1998) cited in

Ronchi (2002)).

    Finally, the assumption of the heterogeneous productivity of farmers draws from numerous

empirical observations. New entrants into the Fair Trade scheme need to meet a number of

requirements relating to quality standards, organization, delivery conditions or contracting. In

this context, Raynolds (2002b) mentions the case of a Mexican cooperative that succeed in Fair

Trade largely through its years of experience in conventional markets. Similarly, Weber (2007)

reports the di¢ culties of younger, less experienced producer organizations with entering the Fair

Trade markets while Raynolds (2002) emphasizes the necessary strong leadership and capacity to
  1 5 For the ease of exposition we normalize n regions to 1. Note that this does not impact the results. Interested
                                                    1
reader may simply multiply demand functions by n and proceed with the analysis.


                                                        12
innovate.


4.1.1    Market-clearing in perfectly competitive markets


In our model, a farmer has three options. She can consume her production (outside option of zero

value), sell to the market with normal co¤ee, or pay for the FT standards at a cost f and sell on

the FT market. The participation constraints are



                                        consume:      p < c & pF      c<f

                             sell to middleman:       p     c & pF    p<f

                                          sell FT: pF       c   f & pF      p   f



These constraints de…ne potential combinations of c and f (as well as the corresponding cut-o¤

points) that are consistent with particular participation choices of the farmers. For simplicity, we

will assume f = kc, where k         1 is a parameter. Figure 1 illustrates the participation constraints

and the respective supplies for normal and FT co¤ee generated by the line f = kc with k = 1 and

c distributed uniformly over h0; 1i.16



  1 6 Our speci…c assumption of the linear relationship between production costs c and compliance costs f greatly

simpli…es the subsequent analysis. We might further allow for the part of compliance costs to be independent of
productivity so that f = a + kc. This would translate into a threshold price pF > p, below which the FT markets
would not be viable. Nonetheless, our story would not change much once pF > pF . Adopting this more general
structure would lead to the same qualitative results, yet at the cost of a much higher computational complexity.




                                                       13
   We will assume that world demand for FT co¤ee DF p; pF depends on prices of both types

of co¤ee and satis…es the following restrictions:17


                  F             F                 F
                 Dp p; pF > 0; DpF p; pF < 0 and Dp p; pF                     F
                                                                           < DpF p; pF



A symmetric pattern is required to hold for normal co¤ee demand DN p; pF . We are interested

in an equilibrium with both markets being active.
  1 7 Since FT market is relatively small, we also provide an extension in which we assume that the price of FT

co¤ee does not impact demand for regular co¤ee. Such change does not have a signi…cant impact on the results,
but slightly simpli…es the analysis.




                                                      14
   The equilibrium on both markets has to satisfy


                                          pF       p
                                      G                  = DF p; pF
                                               k
                                               pF        p
                                  G (p)   G                  = DN p; pF
                                                    k


Assumption 1 We assume the existence of market-clearing equilibrium.


   We discuss conditions that guarantee existence of such equilibrium in the Appendix.

   The following lemma shows that the presence of Fair Trade in our model bene…ts all farmers

under quite general conditions.


Lemma 2 Incomes of all farmers (weakly) increase if and only if the total realized demand does

not fall after the introduction of the Fair Trade market.


Proof. If the newly introduced Fair Trade market remains relatively small and does not in‡uence

world co¤ee price p, it can exist only if the participating farmers are relatively better o¤ than selling

through the conventional channels. The normal farmers’payo¤s are furthermore unchanged due

to a constant price p. If the Fair Trade is relatively large and impacts upon prices in conventional

markets, the impact on farmers depends on the reaction of total demand.

   If the overal demand in a new Fair Trade equilibrium increases, the non-participating farmers

have to be better o¤ since the actual increase becomes only possible if the previously inactive

farmers enter the production and this can only happen once the purchase price of normal co¤ee

p rises. Furthermore, the participating farmers are unambiguously better o¤ using the same

argument as in the case of small Fair Trade market.

   If the total demand declines following the introduction of Fair Trade, the fall in the consump-

tion of conventional co¤ee has been less than compensated by the purchases of Fair Trade co¤ee.

As a result, normal farmers become worse o¤ while the impact on participating farmers is unam-

biguously positive, since otherwise they would not have entered the Fair Trade market in the …rst

                                                        15
place.

   In other words, unless total realized demand does not fall after the introduction of the Fair

Trade market, the very introduction of the scheme by the Fair Trade Organization (FTO) absent

any price-setting constraints helps the participating farmers and at least does not hurt the incomes

and participation of normal co¤ee producers. The justi…cation of the minimum binding price pF

          s
as the FTO’ optimal policy measure and its impact on farmers’payo¤s and participation choices

will be discussed in more detail in the following sections.


4.1.2    The excess supply


This section focuses on the equilibrium where the FTO enforces price pF above its market-clearing

level and thus induces excess supply on the FT market. As a result, the participating farmers sell

only part of their production through the FT channel, the rest being directed back to markets

with normal co¤ee.

   This is a fairly justi…ed assumption. According to Bacon (2005), close to 70% of Fair Trade

cooperatives’ production goes to conventional co¤ee markets and attributes this …gure to low

demand and high quality requirements. The Costa Rican cooperatives examined by Ronchi (2002)

sold mere 49% of their co¤ee production as Fair Trade. In 2002, the FLO had to temporarily reject

pending applicants due to the discrepancy between supply and demand. In the same year the FLO

estimated that the supply of Fair Trade co¤ee was seven times the total Fair Trade volume actually

exported (Weber, 2007). While there are other possible explainaitions why FT farmers might sell

their co¤ee through conventional markets (e.g, liquidity problems during the harvest season Bacon

(2005)), in light of the above-mentioned evidence it seems that excess supply plays an important

role. In our model, the assumption of FT sales ‡owing partially through conventional channels

relies fully on the excess supply argument.




                                                 16
   Farmers’choices become slightly modi…ed.



                            consume      :     p < c & pF + (1                  )p     c<f

               sell as regular co¤ee     :     p       c&    pF       p <f

                              sell FT    :         pF + (1    )p        c        f &       pF   p < f;



where     represents farmers’ beliefs on the proportion of harvest they can actually sell via Fair

Trade channels.18 In the rational beliefs equilibrium, these beliefs will have to coincide with the

realized proportion of the total FT output sold to FT customers.

   If the price pF becomes market-determined, farmers supply either to normal or FT co¤ee

market. In the excess supply setup, however, we need to distinguish between the local participation

choices and the realized supplies to global markets.




                                                                                 !
                                                   F              pF        p
                                        [FT] : S       =G
                                                                    k
                                                                                           !
                                                                                pF     p
                                         [N] : S N = G(p)         G
                                                                                  k

                            [Realized FT] : S W F = S F

                              [Realized N] : S W N = S N + (1                   ) SF



where N stands for "normal/regular co¤ee market" and FT for "Fair Trade market". While

   pF    p =k of the total population of farmers choose to participate in the FT scheme, they are

not able to sell exclusively to FT markets. Not being able to …nd enough buyers, their remaining

harvest (1      ) S F has to be sold through the conventional channels.
  1 8 In general, beliefs may depend on some characteristic of the farmer (e.g., knowledge of FT market, size or

experience). For simplicity, we abstract from these considerations.




                                                        17
   In the rational beliefs equilibrium markets for normal and FT co¤ee have to clear.



                                         SF       ; p; pF = DF p; pF

                       SN    ; p; pF + (1            )S F    ; p; pF = DN p; pF ;

                                              =     pF ; p = p pF



Assumption 3 We assume the existence of the excess-supply equilibrium.


   Assuming that the equilibrium exists, we are interested how it compares with the market-

clearing equilibrium at which there is no excess supply on the FT market ( = 1).


Lemma 4 If there are no middlemen, an increase in price pF above its market-clearing level

increases the excess supply (1         ) and reduces the price of regular co¤ ee p


                                               d        dp
                                                 F
                                                   < 0; F < 0
                                              dp       dp


   All proofs are provided in the Appendix, unless noted otherwise.


Lemma 5 By increasing the price pF above its market-clearing level, the farmers’ participation

in the Fair Trade scheme increases if and only if


                                   N   SW N                       F
                                 "D
                                  pF        < "pF           and "D
                                                                 pF   < "pF
                                       SW F


The payo¤ s of farmers participating in Fair Trade decrease unambiguously relative to the market-

clearing case.


   The intuition behind both lemmas is quite straightforward. Holding other things constant,

if the Fair Trade Organization sets the contracting price pF above its market-clearing level, the

demand for Fair Trade has to fall. Despite the concomitant rise of the demand for conventional


                                                       18
co¤ee (given our assumption on the demands’interdependence), the excess supply of co¤ee remains

preserved and translates into the corresponding pressure to reduce the price p. Furthermore, if the

demand elasticities are low vis-a-vis excess-supply elasticity "pF , the decrease in price p becomes

so pronounced that it makes Fair Trade scheme more attractive and thus increases participation.

This result has a simple corollary


Corollary 6 Following the rise of the Fair Trade price, the participation in the Fair Trade scheme

can increase despite the fall of the participating farmers’ payo¤ s.


    Increasing the price pF above its market-clearing level hurts all farmers regardless of their

status, unless participation in the Fair Trade scheme raises. In such a situation the farmers that

switched from the production of the conventional co¤ee towards Fair Trade represent the only

group that could potentially gain. In addition, some of the least productive farmers are driven

out of the market given that the price of normal co¤ee p is now relatively lower.

    The FT farmers are nonetheless still better o¤ as compared to the setup with the non-existent

Fair Trade market. To see this, note that if the Fair Trade price pF were gradually raised up

to the level prohibiting the existence of the Fair Trade market, all farmers would supply to the

normal market, thus imitating the equilibrium with the normal market. Further results discuss

impact of Fair Trade on aggregate pro…t of farmers.19


Proposition 7 The aggregated pro…t of all farmers is decreasing in pF above market equilibrium.


    The fact that total pro…t of all farmers is decreasing in pF does not tell us whether it is because

pro…ts of both FT and regular farmers decrease, or because one group bene…ts while the other

does not. The following result partially answers this question. It formalizes the intuition that
  1 9 The literature on Fair Trade lists a number of bene…ts of Fair Trade that the present framework addresses

only indirectly or not at all (for a brief outline and references see the Appendix). One of the frequently mentioned
improvements concerns the pooling of resources for the production of positive externalities. Ronchi (2002) reports
the e¤orts of the Costa Rican cooperative COOPELDOS aimed at the maintenance of local roads, other cooperatives
provide a number of services such as extended credit or reforestation support also to the non-members. Strong
rural linkages operating through large expenditure shares of local non-tradeables (e.g., perishable and/or locally
processed foods and services) have been emphasized in an integrating study by ?. These results explore the impact
of the excess-supply price pF both on the aggregated pro…ts of all farmers and on Fair Trade participants only,
where the aggregated pro…ts proxy resources available for community investment.


                                                        19
FT farmers cannot bene…t in aggregate if their participation decreases as a result of an increase

in price pF : Note that Lemma 13 strengthens this result by showing that even an increase in

participation may not be su¢ cient to guarantee an increase in their pro…ts.


Proposition 8 If participation of FT farmers decreases as a result of an increase in pF , then the

overall FT farmers’ pro…t decreases.


      The observation is intuitive. If an increase in pF discourages some farmers, it has to be because

their pro…ts decreased. However, such condition is not su¢ cient, as one can see from Lemma 13 in

Appendix. Our numerical example shows that even if participation is increasing, total pro…t may

be decreasing. This is possible because the value of outside option (i.e., price of regular co¤ee) is
                            dp                                                    dR    dC
decreasing. Indeed, if     dpF
                                 > 0 and large enough, then it is possible that   dpF   dpF
                                                                                              > 0 even if

 d       (pF    p)
dpF         k        < 0, as one can see from equation (11) in the Appendix. .


The FTO’ objective function The preceding discussion closely relates to the issue as to what
        s

the actual objective function of the Fair Trade Organization (FTO) is, once it sets the minimum

price pF above its market-clearing level. In Lemma 2 we claim that unless total realized demand

falls after the introduction of the Fair Trade market, the FTO absent any price-setting constraints

helps the participating farmers and does not hurt the incomes and participation of normal co¤ee

producers. In the excess-supply setup without the middleman, the FTO does not improve neither

the incomes nor participation of all farmers (i.e., regardless of their status). Similarly, setting

price above equilibrium is not consistent with maximization of the per capita revenues for the

participating farmers as these decline unambiguously in the excess-supply equilibrium. Thus, the

only objective consistent with the present setup seems to be the maximization of participation

within the Fair Trade scheme. Given such objective, the FTO might opt for a minimum price pF

above its market-clearing level, so that the revenues of individual participants are not maximized,

yet the bene…ts become shared among a relatively larger number of farmers. The ful…llment of

the objective is however not costless - it is the normal farmers that either keep harvesting normal

                                                     20
co¤ee or those that had to opt out that bear the costs of such a policy.20



4.2       Fair Trade in world with the middlemen


Previous sections have dealt with two interconnected markets absent any intermediaries. The

middlemen, however, play a signi…cant role in the overall distribution chain and their allegedly

exploitative position in fact stood at the very roots of the whole Fair Trade movement (see previous

sections). For these reasons we extend the model to allow for the presence of intermediaries that

purchase co¤ee from local farmers.

   Assume that such a middleman is small with respect to global markets, yet she holds some

monopsony power vis-a-vis the farmers. Farmers’choices are identical to those from the previous

market-clearing case, yet now instead of global market price p they receive a price pM o¤ered by

the middleman. Assume that they face probability                       1 of being able to sell their production

on the FT market. The case         = 1 corresponds to no excess supply, while if            < 1 there is excess

supply.

   Each middleman maximizes her pro…t so that



                                         max (p      pM ) S N + (1              ) SF
                                          pM
                                                                                  !
                                                                  pF       pM
                                s.t. S N = G(pM )        G
                                                                       k
                                                                  !
                                                    pF       pM
                                     SF = G
                                                         k


which for a given      leads to the …rst order condition de…ning an implicit solution for pM .
  2 0 One of the objections to the above-mentioned analysis might be that the world market share of Fair Trade

co¤ee is very small (<1%). In the Appendix we provide an analogous analysis for the case when Fair Trade is
relatively small that it does not in‡uence world price of normal co¤ee. That is, we assume there is a very small
number of consumers treating normal and Fair Trade co¤ee as imperfect substitutes, so that the impact of their
choices on the aggregate demand for co¤ee is negligible. In the same fashion, we assume that there is only a
small fraction of regions producing Fair Trade, so that their supplies do not signi…cantly in‡uence world supply
of conventional co¤ee. The world price of normal co¤ee p can then be treated as given. The exercise covers cases
both with and without the middleman, see the Appendix for details.




                                                      21
                                                                                                               !!
              M               N                 F               M             M
                                                                                   2         pF       pM
            [p ] :       [S       + (1     ) S ] + (p           p ) g(p ) +            g                            =0   (1)
                                                                                  k               k

or alternatively,

                                                                         !!                                         !
                     M             M
                                            2          pF        pM               M                   pF       pM
            (p    p ) g(p ) +                   g                             = G(p )       G                            (2)
                                           k                k                                              k


    One can immediately observe that the middleman’ optimal price pM is a function of the
                                                   s

success rate of Fair Trade farmers                  , the price of the Fair Trade co¤ee pF , and the price p the

middleman on the world market with conventional co¤ee. The following lemma summarizes the

relationship between purchase price pM and the above-mentioned variables.


Lemma 9 The middleman’ optimal price pM is an increasing function of all its arguments, i.e.,
                      s
@pM           M
                                   @pM
 @    > 0; @p F > 0; and
           @p                       @p   > 0.


Proof. The middleman has an incentive to o¤er as low a purchase price pM as possible, subject

to farmers’ supply constraint. More formally, the left-hand side of (2) represents lost revenues

due to a marginal decline in the o¤ered purchase price pM and the corresponding drop in farmers’

normal supply, while the right-hand side captures the resulting cost savings on the remaining

deliveries. The middleman sets the optimal price pM so as to equate the two expressions. If either

 , pF , or p increase, the marginal revenue loss for a given pM increases unambiguously, while

the marginal cost savings fall or remain unchanged. Since the marginal gains in revenues from

additional normal co¤ee purchases exceed the corresponding marginal costs if pM is relaxed, it is

optimal21 for the middleman to raise the purchase price to pM 0 in order to compensate for the

improved outside options of the farmers (upward shifts in                              and/or pF ) or to exploit favorable

conditions on world markets (higher p).

                                         s
    One can also note that the middleman’ optimal price setting brings about a disconnect between
  2 1 The second order condition implies that the slope of the marginal cost-savings function is steeper than the

slope of the marginal revenue loss function. As a result, the equality can be restored only at the higher price pM .


                                                                    22
the price p determined on world markets and the price pM o¤ered to the farmers, which basically

means that any market developments re‡ected in price p translate only indirectly into farmers’

revenues.22 In order to proceed with our analysis, we now integrate the middleman into the

framework developed in Section 4.1.


4.2.1      Market clearing equilibrium with the middlemen



First, we analyze the behavior of the middlemen who face supply from those farmers who do not

sell on the FT market.23


                                                                                  pF       pM
                                     max (p         pM ) G(pM )             G
                                      pM                                               k


First order condition is then


                                            1       pF        pM                                pF       pM
                   p      pM     g(pM ) +     g                             G(pM )         G                  =0           (3)
                                            k             k                                          k


      If the price pF is not constrained, the market equilibrium conditions require that market for

normal and FT co¤ee are in equilibrium


                                                              pF       pM
                                       [FT]:          G                         = DF (p; pF )
                                                                   k

                                        [N]:          G(pM ) = DN (p; pF );



where pM is the price o¤ered by middlemen, as derived in the previous section. We assume the

existence of this equilibrium and compare it to the equilibrium with middlemen but without active

FT market.
 22                       @pM
       Typically, it is    @p
                                < 1; but the proof depends on the behavior of the derivative of density function g 0 :
                                                               @pM
Thus, there might exists an equilibrium in which even           @p
                                                                        > 1: For uniform distribution, one can easily show that
@pM
 @p
       = 1:
          2
  23   Note that one can also just plug in        = 1 into the results derived in the previous section.



                                                                   23
Lemma 10 All farmers are better-o¤          if and only if the price pM o¤ ered by the middlemen

increases once the FT market opens. This happens if the overall demand for co¤ ee does not fall

substantially, i.e., if the world price of the normal co¤ ee p is relatively insensitive to the price of

FT co¤ ee pF ; or if it actually increases as a result of new FT market.


   The statement of the preceding lemma conforms to our results from Lemma 2 that dealt with

the world without the middlemen. In fact, the present results are slightly stronger than those from

Lemma 2. The reason is that contrary to the case without the middleman, the non-participating

farmers now fare strictly better even if the price of normal co¤ee remains unchanged. This happens

as a consequence of a strategic behavior of the middleman, who …nds it pro…table to adjust her

price pM slightly so as to mute the out‡ of farmers towards Fair Trade. A direct consequence
                                        ow

                 s
of the middleman’ behavior is also that the non-participating farmers can be better o¤ even in

the case the normal co¤ee price p falls, given that the price decline is no too sharp.


4.2.2     Excess supply and markets with the middlemen



We now move the equilibrium where the FTO enforces price pF above its market-clearing when

the middleman is present. This exercise builds upon the section with excess supply without the

presence of the middleman. Again, the participating farmers sell only part of their production

through the FT channel, the rest being directed back to the middleman operating on normal co¤ee

market.

   Farmers’choices now change to




                         consume:    pM < c &       pF + (1       )pM    c<f

               sell to middleman:    pM     c&      pF    pM < f

                          sell FT:      pF + (1     )pM       c   f &    pF    pM      f


                                                  24
where pM is the middleman’ optimal price taking into account part of the FT production that
                         s

could not match on FT markets. Again, we restrict our attention to the case c = kf: Similar

to the previous case when the middleman is not present, one has to distinguish between farmers’

local participation choices and the realized supplies.

   We have

                                                                           !
                                             F               pF       pM
                                 [FT] : S        =G                                          (4)
                                                                  k
                                                                                         !
                                             N        M                    pF       pM
                                   [N] : S       = G(p )      G
                                                                                k

                       [Realized FT] : S W F = S F

                         [Realized N] : S W N = S N + (1              ) SF



   In the excess-supply equilibrium we need to have



                              SW F = SF           ; pM ; pF = DF p; pF

                 SW N = SN       ; pM ; pF + (1       )S F        ; pM ; pF = DN p; pF ;

                             =     pF ; p = p pF ; p M = pM                ; p; pF


                                 @pM
Proposition 11 Assume that        @    > 0 is small enough. Then, we show that


                                        dp             d
                                             < 0; and     >0
                                       dpF            dpF
                                        dp             d
                                             > 0; and     >0
                                       dpF            dpF




                                                    25
are not possible. Thus, there are only two possible cases


                                           dp            d
                                             F
                                               < 0; and     <0
                                          dp            dpF
                                           dp           d
                                              > 0; and     <0
                                          dpF          dpF


   Note that in both interesting cases, an increase in pF increases the excess supply, which is

quite intuitive.


Proposition 12 In the excess-supply equilibrium, the non-participating farmers are unambigu-
                                                                                                  dpM
ously worse o¤ relative to the situation with the market-clearing Fair Trade scheme, i.e.,        dpF
                                                                                                        < 0.

             dp                                                                dpM
Proof. If   dpF
                  > 0, the overall demand falls unambiguously and hence        dpF
                                                                                     < 0 in order to have a
                          dp                                    dpM
viable equilibrium. If   dpF
                               < 0, it still has to hold that   dpF
                                                                      < 0, otherwise the monopsonist does

not behave optimally. Given that price pF rises and holding price p constant, the demand for Fair

Trade falls, so a part of production previously sold Fair Trade needs to be sold on normal markets,

which generates the pressure on price p to decrease (note that even though the demand for normal

co¤ee increased as a consequence of the rise in price pF , the released Fair Trade production more

than o¤sets this increase). Regardless of the farmers’ participation choices, given pM and p the

middleman now faces a higher supply from farmers and can adjust optimally. Increasing pM given

p would decrease her pro…ts even if one ignores the unexpected windfall coming from FT. Taking

into account the windfall would make her decision even more unpro…table. So the middleman will

adjust by decreasing the price pM . The e¤ect of the adjustment would depend on the supply and

demand parameters, but in general the middleman can mute the excess supply to the extent that

the price p might ultimately increase as stated in the previous lemma.




Corollary 13 The revenue of all farmers is decreasing in pF above its equilibrium value.




                                                     26
Proof. The proof is identical to the proof of Proposition 8, if one substitutes pM in place of p:

The di¤erence between these cases comes from the di¤erence between prices p and pM : In case of

market with middlemen, price p is not directly relevant for decision making of a farmer, because

he cannot trade at this price.

   Finally, it is easy to replicate results about pro…t of FT farmers in the world with middlemen


Lemma 14 If participation of FT farmers decreases if pF increases, then the aggregate FT farm-

ers’ pro…t decreases.


Proof. Again, use pM instead of p to obtain the proof.

   The preceding lemmas show that it is very unlikely that the aggregate pro…ts of any group

of farmers would increase as a consequence of the excess supply Fair Trade regime. The only

theoretical possibility remains the increase in the aggregate pro…t of the farmers participating in

Fair Trade. However, even for this case our numerical results produce falling aggregate pro…ts.

   Similar to the setup without the middlemen, the excess-supply equilibrium generates losses

for the non-participating farmers. Analogous outcomes can be expected also with respect to the

impact of the excess-supply regime on payo¤s and participation of Fair Trade farmers. For the

ease of exposition, the results will be illustrated on an example with explicit functional forms

rather than general demand and supply structure.



4.3    Example with explicit demands


In this section, we illustrate our general results from previous discussion on a speci…c example with

quasilinear demand preferences and uniform productivity distribution. We specify demand func-

tions using a model of consumers that consider normal and FT co¤ee to be imperfect substitutes.

    s
Let’ assume a quasilinear utility function



                                       ~
                                       U = U (xN ; xF T ) + Q

                                                 27
                                                    1                2                             2
                  U (xN ; xF ) =    xN + xF                 xN           + 2 xN xF + xF
                                                    2

                                          2 h0; 1i;     ;        > 0;



   where xN and xF are consumptions of normal and FT, Q is the numeraire good. Note that

while Richardson and Stähler (2007) treat FT and normal products as perfect substitutes, we take

an alternative approach and model FT good as an imperfect substitute for normal co¤ee. In our

framework, the degree of substitutability      is assumed to depend negatively the so called "warm

glow e¤ect" discussed by Andreoni (1990), which in the present context re‡ects the additional

utility due to the consumption of co¤ee grown under "fair" standards. Note that higher                 implies

"lower warm glow e¤ect", i.e., regular and FT co¤ee are easier to substitute.

   Consumers maximize their utility given the budget constraint



                                        pxN + pF xF + Q                  M



   The maximization problem leads to the demand function for normal and FT co¤ee respectively


                                                                                   1
                              xN    =           +            2
                                                                 pF                        2
                                                                                               p
                                          1+        1                         1
                                                                               1
                             xF T   =           +            2
                                                                 p                     2
                                                                                           pF
                                          1+        1                     1




4.3.1   Numerical results


In the following we plot three groups of graphs with our numerical results, each block capturing a

speci…c model dimension. For all graphs, the x-axis represents the excess of the Fair Trade price

pF above its market equilibrium value. The results have been derived for three di¤erent values of

the substitution parameter , namely 0 (dots), 0; 5 (circles) and 0:99 (x).


                                                  28
                                  Equilibrium pi                     Equilibrium p
                      1                                1.05
                                                          1
                    0.5                                0.95
                                                        0.9
                                                       0.85
                          0       0.1 0.2 0.3                 0     0.1 0.2 0.3
                               Excess of FT price                 Excess of FT price
                              Price p , total supply
                                     m
                    0.8


                    0.6


                          0     0.1 0.2 0.3
                              Excess of FT price


                                         Figure 1: Equilibrium prices


   The …rst group depicts the behavior of equilibrium prices and probability of a successful Fair

Trade match. The graphs show that this probability decreases with the excess pF T , but this e¤ect

is smaller if   is lower. Consistent with Lemma 7, the graphs also show that equilibrium price on

the world market of normal co¤ee p can be both increasing and decreasing, depending again on

the degree of substitutability. If both types of co¤ee are easier to substitute (lower ), then an

increase in price pF "hits" mostly the Fair Trade market.



   The second group shows how pro…ts depend on the excess of pF above its market equilibrium

value. Farmers pro…ts are decreasing in degree of substitutability between normal and Fair Trade

co¤ee. One can also see that increasing the price pF above its equilibrium level bene…ts the

middlemen, especially if the degree of substitutability is high.

   Finally, we plot graphs that describe farmers choices and realized supplies as functions of the

excess-supply price pF :

   The intuition and a more detailed discussion of the above-mentioned results are the core focus

of the following sections.

                                                       29
        FT farmers profit                      normal profit
                                    0.16
0.2                                 0.14
                                    0.12
0.1                                  0.1
                                    0.08
                                    0.06
      0         0.2                        0        0.2
       Excess of FT price                   Excess of FT price
           total profit                      Middlemen: profit
                                    0.25



                            gamma
0.4
                                     0.2
0.3
                                    0.15
0.2
0.1                                  0.1
      0        0.2                         0        0.2
       Excess of FT price                      Excess of FT


               Figure 2: Equilibrium pro…ts




         normal supply                      Realized FT trades
0.5
                                     0.3
0.4                                  0.2
                                     0.1
0.3
      0        0.2                         0         0.2
       Excess of FT price                   Excess of FT price
           FT supply                         Middlemen: output
0.4                                  0.5
                            gamma




0.3                                 0.48
0.2                                 0.46
0.1                                 0.44
                                    0.42
      0        0.2                         0        0.2
       Excess of FT price                   Excess of FT price


             Figure 3: Equilibrium quantities




                            30
4.4     Objectives of the FT and farmers’participation

Our example with explicit functional forms provides an illustration of the potential incentives

of the FTO to raise the price pF above its market-clearing level. The argumentation is very

similar to the Section 4.1 discussing the objective function of the FTO in the excess supply setup

without the middleman. One can observe that neither the revenues of farmers regardless of their

status nor the participation of normal farmers fare better than in the market-clearing Fair Trade

equilibrium. The only exception is the increased participation in the Fair Trade scheme occurring

due to the pronounced fall in pM . This decline forces some normal co¤ee farmers to join the Fair

Trade scheme so as to avoid losses from conventional sales.

   The explicit example is thus consistent with our general results that increasing the price pF

above its market-clearing level hurts all farmers (relatively to the Fair Trade market clearing)

regardless of their status, except for the case when the participation in the Fair Trade scheme

raises. Then for a given parametrization, the farmers that switched from conventional co¤ee

towards Fair Trade represent the only group of producer bene…ciaries.


4.4.1    The equilibrium values of p; pM and the middlemen’ pro…ts
                                                           s


The excess-supply measure         and the monopsonists price pM decline monotonically with increases

in pF . The response of the conventional co¤ee price p is, however, ambiguous, depending on the

speci…c values of .24 In particular, for low values of            the price p declines in the excess-supply

                     s
equilibrium, larger ’ support values of p in excess of its market-clearing counterpart.

   Note that the latter constellation would not be possible in the world without the middleman,

since there is no mechanism that would work against the downward pressure on prices of con-

ventional co¤ee. When the middleman is present, however, she has a motivation to reduce the

purchase price pM so as to maximize pro…ts (see previous subsection). This motivation is higher
  2 4 The parameter     captures the degree of substitutability between normal and Fair Trade co¤ee. The higher is
 , the closer substitutes the two arts of co¤ee are.




                                                       31
                                                                                                         1
the higher is , because the released Fair Trade supply increases with                   (the term    1       2   dpF is

increasing in ) and so a given downward adjustment of pM generates higher additional cost sav-

ings.25 26 The higher marginal pro…tability and net excess supply decreasing in               27
                                                                                                   thus make the

increasing price p relatively more likely. In such a situation, one might observe declining living

standards of normal farmers and the marginal, least e¤ective farmers leaving the market despite

the increase in the world price of normal co¤ee p.28




5       Conclusion


The recent success story of Fair Trade has provoked a lively debate on the scope and intensity of

          s
the scheme’ actual bene…ts and shortcomings. We develop a simple framework and …nd that the

introduction of a new Fair Trade market per se has the capacity to improve the living conditions of

                        s                                               s
all farmers. The scheme’ potential is not fully met, however, as the FTO’ supplementary policy

of a minimum contracting price brings about costs in terms of the lower-than-possible payo¤s of

the majority of farmers, higher-than necessary exit of the non-participating farmers from the co¤ee

production, and less resources for community investment. The above equilibrium FT price can be

justi…ed merely as a policy of increasing farmers’participation within the Fair Trade scheme.

       The major bene…ciary of the minimum price policy are paradoxically the middlemen whose

allegedly exploitative position stood at the very roots of the whole Fair Trade movement. In our
  25                                   s
      In our discussion of the model’ adjustment mechanism, we assume that the middleman is not able to
distinguish between normal and Fair Trade farmers so that she o¤ers the same price pM to both groups. In
other words, the middleman is not able to discriminate between the two types of producers. The middleman’        s
ability to ration depending on the producer type would lead to the optimal response pM being set to zero for
unsold Fair Trade production, which would in turn lower the Fair Trade farmers’expected payo¤s as well as their
participation in the scheme. The remaining participating farmers would then de facto play an in…nite lottery with
the probability of winning pF       c f and the probability 1          of making a loss (c + f ). While we did not
…nd any empirical evidence on the middlemen’ discrimination based on farmers’ status, the main reason for our
non-rationing assumption is that the lottery setup represents a rather special sub-case of the present model with
no signi…cant changes in results.
  2 6 Of course, by decreasing pM , the middleman forgoes some farmers on the produce/stay inactive margin, yet

                                                                     s
this amount depends on only indirectly through the middleman’ reaction on released Fair Trade output.
  2 7 The net excess supply is the part of the released Fair Trade supply not absorbed by the increased demand for
                                                  1
conventional co¤ee. The term corresponds to 1+ dpF and depends negatively on .
  28                                            dpM        1
       Formally, such a situation occurs when   dpF
                                                      >   1+
                                                               .




                                                               32
numerical example we show that the middlemen use their monopsony position to appropriate part

of farmers’ payo¤s that would have been realized under the market-clearing setup. The excess

supply thus allows the middlemen to exploit the farmers more than she could in case of market

clearing on FT market. The pro…tability of the excess-supply regime for the middlemen also raises

with the substitutability (as measured by ) between the normal and Fair Trade co¤ee. For a high

degree of substitutability, one might even observe an increase in the world price of normal co¤ee

p and a simultaneous decline in the living standards of normal farmers.

   Our paper does not focus on certain aspects of Fair Trade, including the impact on migration

and local environment, self-governance, credibility or nation-wide reallocation of resources. By

no means do we claim that these concerns are of lower or no importance. Nonetheless, given the

absence of an integrated modelling approach, we focus on a speci…c area of interest and analyze it

within a well de…ned framework. This area relates to the distributional impact of the Fair Trade

scheme.

             s
   The model’ results should serve as a comment on potential risks and limitations of the other-

wise successful Fair Trade scheme. It seems quite reasonable that the very existence of Fair Trade

alleviates the informational asymmetry between ’socially-conscious’Western consumers, distribu-

tors and farmers located in developing countries. Given that consumers value ’fair’production, the

absence of credible information and non-negligible …xed costs hinders the functioning of Fair Trade

market and some sort of market intervention thus might be justi…ed. Nonetheless, the scheme’s

optimal design remains an open question and we hope to provide at least a partial answer.

   From the policy perspective, we agree that the guaranteed minimal pF can take a number of

other important roles such as the insurance against volatile co¤ee prices or improved outside option

for the farmers participating in sharecropping agreements. Our results should rather be understood

as a selective contribution to the debate on the bene…ts of alternative policy instruments. For

example, stability of Fair Trade prices can be achieved through other instruments than a …xed

minimum price. The related problem of the excess-supply on Fair Trade markets can be addressed


                                                33
e.g. through the introduction of a pre-determined schedule and gradual replacement of established

Fair Trade producers by their less experienced counterparts.




6       Appendix

6.1     Existence, comparative statics and proofs for the model without


        the middlemen

6.1.1    Existence of equilibria without the middlemen


[Missing but easy]


6.1.2    Comparative statics in the world without the middlemen


Proof of Lemma 4. To show that


                                        d       dp
                                           < 0; F < 0
                                       dpF     dp


    take total derivatives of the market equilibrium conditions and rearrange them to obtain


                                    d                        dp
                       SF + SF         +      F
                                             Sp         F
                                                       Dp          F
                                                                = DpF    F
                                                                        SpF
                                   dpF                      dpF


                                 d                       dp
                         SW N          W
                                    + Sp N     N
                                              Dp               N
                                                            = DpF   SpF N
                                                                     W
                                dpF                     dpF




                                                  34
                                                                                   !
                                              F                      pF        p
                                          S       =G
                                                                       k
                                                                                         !
                                      N                                     pF       p
                                  S       = G(p)               G
                                                                              k
                                                                                              !
                                     WF                   F                    pF        p
                                 S         = S                = G
                                                                                 k
                                                                                              !
                                     WN                                        pF        p
                                 S         = G(p)                  G
                                                                                 k


where


                                                                pF         p
                                                   t=
                                                                  k
                                         pF        p
                           S F = g(t)                     F
                                                       ; Sp =                F
                                                                     g(t) ; SpF = g(t)
                                              k                          k             k
                                                                   pF p
                                 SW N =                       g(t)             SF
                                                                      k
                                           W
                                          Sp N = g(p) + (g(t))
                                                                                    k
                                                   W
                                                  SpF N =              g(t)
                                                                               k


Substituting for supply relationships and expressed in a convenient matrix form we obtain:

         2                                                                     32             3   2                    3
                          F                            2                                                           2
         6 S +F
                    g(t) p k p             g(t)       k    )+    F
                                                                Dp             76
                                                                                         d
                                                                                        dpF   7 6      F
                                                                                                      DpF   g(t)   k   7
         6                                                                     76             7=6                      7
         4        F
                                                                               54             5 4                  2
                                                                                                                       5
            g(t) p k   p
                            SF   g(p) + (g(t)) k                      N
                                                                     Dp                  dp
                                                                                        dpF
                                                                                                       N
                                                                                                      DpF + g(t)   k


Note that the signs of the individual cells are unambiguous

                                     2                 32               3      2         3
                                                                 d
                                     6 +               76       dpF     7 6              7
                                     6                 76               7=6              7
                                     4                 54               5 4              5
                                                                 dp
                                                  +             dpF
                                                                                     +




                                                                35
Rearranging comparative statics one gets

                                                                        2                           2
                                                                                                             F
                                 d
                                             F
                                            DpF            g(t)                          g(t)       k   ) + Dp             dp
                                                                       k
                                       =                     F                  +                             F                                                (5)
                                dpF        SF    +     g(t) p k p                        SF   +         g(t) p k p        dpF
                                                                            2
                                                 N                                                                              N
                                 d              DpF + g(t)                  k             g(p) + (g(t)) k                     Dp dp
                                       =                               pF                                             pF
                                                                                                                                                               (6)
                                dpF          S F + g(t)                         p
                                                                                               S F + g(t)                     p   dpF
                                                                            k                                             k


                                                                                                                                                               d
Equations (5) and (6) give us comparative statics in the FT market with the equilibrium                                                                       dpF

         dp
and     dpF
              . Of course, in the overall equilibrium both equations have to be satis…ed simultaneously,

                                                  d                     dp
which allows us to compute both                  dpF
                                                           and         dpF
                                                                                :

       Given our demand assumptions, a closer look at the system tells us that

                        2                                 2                                             2
                                                                                                                 F
        F
       DpF      g(t)                    N
                                       DpF + g(t)                                            g(t)   k       ) + Dp                  g(p) + (g(t)) k        N
                                                                                                                                                          Dp
                       k                               k
                   pF       p
                                <                    pF       p
                                                                  and 0 <                                      pF     p
                                                                                                                          <                        pF     p
                                                                                                                                                               ;
   S F + g(t)          k              S F + g(t)       k                                 S F + g(t)               k                   S F + g(t)      k



                                                                                  F       N
because we assume that the direct price e¤ect is stronger than the indirect one jDpF j > DpF ;

  N      F                                                                                                   d                 dp
jDp j > Dp : This implies that the solution has to satisfy                                                  dpF
                                                                                                                  < 0,        dpF
                                                                                                                                    < 0. This is easy to see

- while both relationships are not linear, the intercept of (5) is unambiguously lower than the

intercept of (6), while the slope of (5) is positive yet not as steep as that of (6). This implies that

both curves (given that they exist and continuous, which we assume) can cross only in the 3rd

quadrant,29 or in other words
                                                               d       dp
                                                                  < 0; F < 0
                                                              dpF     dp



  29                                        dp
       Alternatively, one can express      dpF
                                                 from (5) and (6) to see that the sign has to be negative:

                                                                  D FF          2
                                                                                    =k       D N + 2 =k
                                                                                                F
                                                                   p                           p
                                            dp                         2S F
                                                                                         +         2S F
                                               =                                                                    <0
                                           dpF                 N
                                                              Dp       (1+ 2 )=k                   2 =k+D F
                                                                                                          p
                                                                       2S F
                                                                                         +           2S F
                                                           d
Once this is established, one can infer that              dpF
                                                                  < 0 from (5).




                                                                                    36
6.1.3     The impact of Fair Trade on farmers’ payo¤s and participation without the

          middlemen


Proof of Lemma 5. 1) In the excess-supply equilibrium, the farmers’participation in the Fair

Trade scheme increases if and only if


                                         N   SW N                              F
                                     "D
                                      pF          < "pF            and "D
                                                                        pF          < "pF .
                                             SW F


   We will …rst start with the calculation of a change in farmers’additional Fair Trade revenues

as a consequence of exclusively a fall in the probability . Note that the transition to a new equi-

                                                                                                                      d
librium on both normal and Fair Trade market restricts the possible adjustment of                           pF   p   dpF
                                                                                                                           ,

which in turn narrows the potential range of new equilibrium payo¤s pF + (1                                ) p. Using the

                                                         d               dp
information on the signs of the derivatives             dpF
                                                               and      dpF
                                                                              , we then derive the necessary conditions

for the increase in participation that is consistent with our comparative-statics results. Finally,

we transform the results into a more intuitive elasticity form.


                                              d
        Step 1a: Analyzing pF            p   dpF
                                                   on the Fair Trade market.


   The farmers’pro…t equals pF + (1                     ) p. We have

                                                           2                                          3
                    d          pF + (1        )p        16
                                                         6 + pF                    d                dp 7
                                                    =                           p     + (1       ) F7                 (7)
                   dpF              k                   k4                        dpF              dp 5
                                                            |                  {z    } |        {z    }
                                                                               <0               <0



   Consider an increase of pF above its equilibrium value. In the new equilibrium, the realized

FT supply S F has to match the FT demand DF , hence it has to hold that


              d    SF      ; p; pF           dDF
                                       =
                         dpF                 dpF
                                                                    !
                  d SF     ; p; pF      1            pF        p                         d            dp
                                       = g                                pF        p       +   1
                         dpF            k              k                                dpF          dpF



                                                               37
     Plug this into
                                               d       SF         ; p; pF               dDF
                                                                                   =
                                                              dpF                       dpF

and obtain

                                           (pF         p)
                                 kG
                      d                            k             d                         k                 dDF                         dp
             pF    p     =                                          +                                                           1
                     dpF             g     (pF p)               dpF   g                 (pF p)               dpF                        dpF
                                             k                                            k



Step 2a: Getting the values of consistent with the new Fair Trade market equilibrium and the

                                  d                  dp
signs of the total derivatives   dpF
                                         and        dpF
                                                          .

     Substitute the above-mentioned expression into the total derivative of Fair Trade farmers’

payo¤s and get


                                                                             (pF   p)
                           F                                      G            k                          F
                                                                                                         DpF
                   d      p + (1           )p                                                   d
                                                       =                                            +                                   +
                  dpF         k                                     g        (pF p)            dpF         F
                                                                                                       g (p k               p)
                                                                               k
                                                              0                                     1
                                                                              F
                                                                             Dp                   1 A dp
                                                       +@                                      +
                                                                    g        (pF p)               k dpF
                                                                               k



     In order to obtain the sign of the Fair Trade payo¤ derivative, one needs to evaluate

                                                                        2                               !                                     3
                                                                               G
                                                                                        (pF        )
                                                                                                   p
                                                                                               k                             F
                                                              6                                              d
                                                                                                                  +
                                                                                                                            DpF
                                                                                                                                             + 7
                                                              6                         (pF        p)       dpF             (pF         p)     7
                   d       F
                          p + (1          )p                  6                    g                                    g                      7
                                                       = sign 6                                                                                7
                                                                                               k                                    k
          sign                                                6                        0                                    1                  7
                  dpF         k                               6                                          F                                     7
                                                              4                        @               Dp
                                                                                                                   + k A dpF
                                                                                                                     1    dp                   5
                                                                                                       (pF   p)
                                                                                               g         k




     Hence given our comparative-statics results, we can argue that the Fair Trade payo¤ increases

i¤
                                  F                       (pF     p)          d
                                 DpF           G              k              dpF                                   F
                                                                                                                  DpF
                         dp                                                              d
                            >                                                      or       <
                        dpF           F
                                     Dp + k g                  (pF p)                   dpF   G                   (pF p)
                                                                 k                                                  k

                                          d
     Step 1b: Analyzing pF       p       dpF
                                                   on the normal co¤ee market.




                                                                        38
         Use the same procedure for the normal co¤ee market and obtain


                                                                          (pF       p)
                                            d G (p)          G                k                    dDN
                                                                                               =
                                                            dpF                                    dpF




                               N dp     N
              d             k Dp dpF + DpF                           kg(p)                dp                        dp               kS F         ; p; pF    d
     F
 p         p     =                                     +                                                     1
             dpF                 g    (pF    p)
                                                            g         (pF      p)        dpF                       dpF                g       (pF p)        dpF
                                        k                                 k                                                                     k



         Step 2b: Getting the values of consistent with the new normal co¤ee market equilibrium as

                                                            d                  dp
well as the signs of the total derivatives                 dpF
                                                                     and      dpF
                                                                                    .

         Plug the relationship from the normal co¤ee equation into the total derivative of the payo¤

function and obtain

                                                             0                                                                        1
                                                                               N                         F             F
                 d          F
                        p + (1              )p                                DpF                   S             ; p; p         d A
                                                   =         @                                 +                                      +
                dpF         k                                         g        (pF p)
                                                                                                      g           (pF p)        dpF
                                                                                 k                                  k
                                                             0                                                                      1
                                                                                                                  N
                                                                              g(p)                               Dp               1 A dp
                                                           +@                                                                   +
                                                                      g        (pF p)
                                                                                                      g           (pF p)          k dpF
                                                                                 k                                  k



Similar to the case of Fair Trade market, we have

                                                                          2                                                                         3
                                                                                           N              F                F     d
                       d         pF + (1          )p              6                       DpF      +S              ; p; p       dpF
                                                                                                                                          +         7
               sign                                        = sign 6
                                                                  4
                                                                                                                                                    7
                                                                                                                                                    5
                      dpF             k                                                         N   1                  (p   F
                                                                                                                                p)           dp
                                                                                  g(p)         Dp + k g                     k               dpF



         and




                                                                           N                       (pF       p)      d
               F                                                          DpF + G                    k              dpF                                            N
                                                                                                                                                                  DpF
 d             p + (1       )p               dp                                                                                                    d
                                     > 0 ()     >"                                                                !#                  ()              <
dpF                k                        dpF                                   1            pF            p                                    dpF   G         (pF p)
                                                                                                                             N                                      k
                                                                     g(p) +         g                                       Dp
                                                                                  k               k
                                                                 |                             {z                               }
                                                                                               >0



                                                                       39
     Step 3: Take the two conditions together so that


                                                     N                                                 F
                                    d               DpF                       d                       DpF
                                       <                              and        <
                                   dpF   G          (pF p)                   dpF   G                   (pF p)
                                                      k                                                  k


                                                                                             !
                                                             G(p)       G
                                                                                  (pF   p)
                                                                                    k
                                               pF
     Multiply both inequalities by                  and                           (pF   p)
                                                                                                  = 1 and you get the elasticities in
                                                             G(p)       G           k

the lemma.

     2) In the excess-supply equilibrium without the middlemen, the Fair Trade farmers’ payo¤s

decrease unambiguously.

                                                                                                                                                d
     To show that the participating farmers’ payo¤s decrease unambiguously, note that                                                          dpF
                                                                                                                                                     <
      F
     DpF                      dp                                                                  d
      (pF     p)
                   implies   dpF
                                   < 0, so for more negative values of                           dpF
                                                                                                                               s
                                                                                                           the change in farmer’ revenues
G         k
                                                                                              F
                                                                             d               DpF
from FT becomes less and less favorable, i.e., for                          dpF
                                                                                   =             (pF      p)
                                                                                                                   represents the best possible
                                                                                        G             k
                                                                                                                          F
                                                                                                   d                     DpF                   dp
scenario consistent with transition to a new equilibrium. Now                                     dpF
                                                                                                               =         (pF   p)
                                                                                                                                    implies   dpF
                                                                                                                                                    =0
                                                                                                                   G       k

and we have

                                          2                                                               3            2                       3
     d         pF + (1        )p        16
                                         6 + pF                  d                          dp 7 1 6                                     d 7
                                    =                         p     + (1                 ) F 7 = 6 + pF                               p     7 (8)
    dpF             k                   k4                      dpF                        dp 5 k 4                                     dpF 5
                                            |                {z    } |                  {z    }      |                               {z    }
                                                             <0                         <0                                           <0


                                                             F
                                          d                 DpF
     But we also know that for           dpF
                                               =            (pF   p)
                                                    G         k




                                                              F
                                         d                  kDpF                             k                     dDF
                             pF    p        =                                +                                                 ;
                                        dpF             g     (pF      p)
                                                                                    g        (pF          p)       dpF
                                                                  k                               k




                                                                       40
   so that

                                                        2                                                       3
                d          pF + (1        )p          16
                                                       6 + pF                     d                        dp 7
                                                  =                            p     + (1               ) F7=              (9)
               dpF              k                     k4                         dpF                      dp 5
                                                          |                   {z    } |                {z    }
                                                                              <0                      <0
                                                        F
                             1             F          dD                           1              F    dp
                                          DpF +              =                                   Dp         = 0;          (10)
                   g     (pF p)                       dpF                g        (pF p)              dpF
                           k                                                        k



   which is the best possible impact on the Fair Trade farmers’payo¤s that is consistent with the

excess-supply equilibrium.

Proof of Corollary 6. Following the rise of the Fair Trade price, the participation in the Fair

Trade scheme can increase despite the fall of the participating farmers’payo¤s.

   The total derivative of the Fair Trade participation equals


                       (pF       p)                               !"                                  !#
              dG         k                            pF     p                d            pF     p
                                      = g                                                                   =
                     dpF                                k                    dpF             k
                                          |            {z            }
                                                      >0
                                                                         !"                                           #
                                           1           pF        p            d        pF + (1        )p         dp
                                      =      g
                                           k             k                                dpF                   dpF


where
                                                                 dG(x)
                                                  g (x) =
                                                                  d(x)

Hence the sign of the total derivative depends on the sign of the part in square brackets. Even if

the Fair Trade payo¤s decline after the move from                        = 1, i.e.,


                                              d   pF + (1                )p
                                                                                  < 0;
                                                     dpF


                                                        dp
the bracketed term can be positive since               dpF
                                                             > 0.




                                                             41
6.2    Aggregate farmers’pro…ts

Proof of Proposition 7. Unless world price of co¤ee p increases signi…cantly when price of FT

co¤ee increases, the aggregated pro…t of all farmers is decreasing in pF above market equilibrium.

   Revenues of the farmers in the excess-supply regime without middlemen



                       R = S W N p + S W F pF = (S N + S F )p + S F (pF                     p);
                                                            !
                                                    pF p
                                      SF = G
                                                      k
                                                                 !
                                    N                   pF p
                                  S = G(p) G
                                                          k
                                                              !
                                                     pF p
                           R = G(pM )p + G                      (pF p)
                                                       k


   The costs are slightly more complicated


                                    Z     t                          Z        p
                               C=             (k + 1)cg(c)dc +                    cg(c)dc
                                      0                                   t
                                        Z     pM                 Z       t
                                 C=                cg(c)dc + k            cg(c)dc;
                                          0                          0
                                                        pF       p
                                                t=
                                                          k


These costs change with the change in pF in the following way


                 dC              dp                dp             pF p d
                         = pg(p)    + ktg(t) (1        ) + ktg(t)         ;
                 dpF            dpF         k     dp F              k dpF
                                 dp            d pF p                 dp
                         = pg(p) F + ktg(t)               +      1
                                dp            dpF    k       k       dpF




                                                        42
the change in revenues is


    dR     dp                 d                                                     dt                dp
       F
         = F (G(p) + pg(p)) + F G(t)(pF                 p) + (pF          p)g(t)       + G(t) 1                ;
    dp    dp                 dp                                                    dpF               dpF
                                    dt   d                                  dp
                                       = F pF         p =k +          1
                                   dpF  dp                        k        dpF


Note that

                                                                      !!
              dR      dC    dp                              pF    p             d
                          = F            G(p)     G                        +       G(t)(pF    p)
              dpF     dpF  dp                                 k                dpF


                    (pF   p)                                                                        dp          d
Since       1 and     k         p in an equilibrium, the outcome depends on the sign of            dpF
                                                                                                         and   dpF
                                                                                                                     :

                                    d                                                         dp
We have already shown that         dpF
                                         < 0 in any relevant equilibrium. Thus, unless       dpF
                                                                                                   > 0 and large

enough, pro…t of all farmers is decreasing in pF above market equilibrium.

Proof of Proposition 8. If participation of FT farmers decreases as a result of an increase in

pF , then the overall FT farmers’pro…t decreases.

   Revenue and costs of FT farmers



                               R    = G(t)( pF + (1      )p) = G(t)(kt + p)
                                      Z t
                               C    =     (k + 1)cg(c)dc
                                           0



We can compute the derivatives


                          dR                          dt          dt  dp
                                   = g(t)(kt + p)        + G(t) k F + F
                          dpF                        dpF         dp  dp
                          dC                          dt
                                   =     (k + 1)tg(t) F ;
                          dpF                        dp
                           dt             d                       dp
                                   =           pF p =k +       1
                          dpF            dp F              k     dpF




                                                       43
The di¤erence is


            dR     dC                       dt           dt  dp                               dt
                         = g(t)(kt + p)         + G(t) k F + F                (k + 1)tg(t)            (11)
            dpF    dpF                     dp F         dp  dp                               dpF
                               dt             pF       p                      dp
                         =        g(t) p                    + kG(t) + G(t)                            (12)
                              dpF                  k                         dpF


Note that
                                             pF        p
                                 g(t) p                    + kG(t)   >0
                                                  k

and thus
                               dt       dp       dR                  dC
                                 F
                                   < 0; F < 0 =)                         <0
                              dp       dp        dpF                 dpF




6.3     Existence, comparative statics and proofs for the model with the


        middlemen

6.3.1    Existence of equilibria with the middlemen


In order to proceed with the analysis, we will assume that there exists equilibrium in which both

markets are active, and which generates market-clearing prices p and pF , ie. equilibrium in which

  = 1. This section informally discusses under which conditions the equilibrium will exist. We

do not claim that these conditions are necessary, as the existence of the equilibrium is not of

our primary interest. In particular, we discuss price ranges for which one may hope to …nd an

equilibrium.

   The market-clearing condition are



            FT market :      DF p; pF = G( pF              pM =k) = S F pF ; pM p; pF

        Normal market    :   DN p; pF = S N pF ; pM p; pF             = G(pM )     G( pF     pM =k)


                                                   44
   Obviously, we may have equilibrium only if



                                   0   SF       1; 0   SN       1; S F + S N       1



We will be interested in those equilibria in which both markets are active. In case of uniform

distribution G(x) = x; g(x) = 1, we can discuss range of prices for which there might be an

equilibrium.

                                       0 < SF ; 0 < SN ; SF + SN           1


The last constraint can be expressed in the form


                                                p    pF
                                                  +                   1
                                                2 2 (k + 1)


The other two constraints are



                               (2k + 1)pF        p(1 + k) > 0; p + kp      pF > 0



Possible combination of prices p; pF is the triangle on the following picture

                           5
                       p
                           4

                           3

                           2

                           1

                           0
                               0            1          2          3            4         5
                                                                                       p_f

    Feasible combinations of p; pF for equilibria. Black line k = 1; green dashed line k = 0:5



                                                           45
   We can see that if k decreases, which means that it is relatively cheaper for all farmers to

produce FT co¤ee, the set of prices which might correspond to an equilibrium shrinks. This is an

intuitive result - for very low k; it is cheap to obtain a FT certi…cate and thus prices on regular

market (p) must be close to the FT prices (pF ) in the market equilibrium. Note that this result

holds in the excess supply equilibrium with appropriate modi…cations of the picture (pF has to

be replaced with pF on the supply side). Expected value from participation in FT and regular

market must be similar if participation costs in FT market are low.


6.3.2    The impact of Fair Trade on farmers’payo¤s and participation with the mid-

         dlemen


Proof of Lemma 10.          All farmers are better-o¤ if and only if the price pM o¤ered by the

middlemen increases once the FT market opens. This happens if the overall demand for co¤ee

does not fall substantially, i.e., if the world price of the normal co¤ee p is relatively insensitive to

the price of FT co¤ee pF ; or if it actually increases as a result of new FT market. It is easy to

observe that compared to the situation without Fair Trade, all farmers bene…t only if the price of

co¤ee set by middleman pM increases and such increases indeed attract new farmers. If the price

pM decreases, some FT farmers might be better o¤ than before, but there is a group of farmers

who stop selling co¤ee altogether. These farmers lose, since in the absence of FT they used to

make small yet positive pro…ts. In general, the middleman’ price pM might move both ways,
                                                          s

because the movement of the price p is ambiguous and might dominate the other e¤ects working

through the Fair Trade price pF or the success rate                  . Nonetheless, it is easy to show that for

…xed p, price pM 0 in the world with active FT market is larger than pM when FT market does not

exist. To see this, compare the …rst order conditions of the middleman



   [no FT] :        p    pM g(pM )     G(pM ) = 0

                                             1     pF 0       pM 0                        pF 0       pM 0
        [FT] :      p0   pM 0   g(pM 0 ) +     g                           G(pM 0 )   G                     = 0;
                                             k            k                                      k


                                                      46
It is obvious that once we plug the values of pM and p from the …rst line, the last element on the
                              pF       pM                                                     1        pF       pM
second line, G(pM )       G        k        is smaller than G(pM ). Also, trivially           kg            k         > 0: Thus,

if we plug in pM from the …rst FOC into the second one and evaluate the sign, we see that


                                                                1     pF       pM         pF           pM
              p     pM g(pM )      G(pM ) + p          pM         g                 +G                           >0         (13)
                                                                k          k                       k


or alternatively,


                                            1     pF       pM                            pF        pM
                    p   pM    g(pM ) +        g                       > G(pM )      G
                                            k          k                                       k


Since the marginal gains in revenues from additional normal co¤ee purchases exceed the corre-

sponding marginal costs for pM from the world without Fair Trade, it is optimal for the middleman

to raise the purchase price to pM 0 :30 Thus the inequality implies that pM 0 > pM .

      This argument requires that …rst order condition of the FT market middleman is monotonic

(unique local maximum) and that p is …xed. If the world price p is not very sensitive to the

introduction of FT co¤ee (e.g., FT market is small), then the argument holds by continuity (the

expression (13) remains positive for small changes in p). It is obvious to see that if p actually

increases, then the argument holds as well, so the only case when it might not hold is when p

decreases signi…cantly as a result of FT market opening. However, this can only happen once the

overall world demand declines sharply after the introduction of Fair Trade, which is consistent

with our results from Lemma 2 that dealt with the world without the middlemen. In fact, the

results for the market-clearing case with the middleman are slightly stronger than those in Lemma

2. In the world with the middleman, the non-participating farmers are better o¤ even if the price

of the normal co¤ee does not change. This happens as a consequence of a strategic behavior of

the middleman, who …nds it pro…table to adjust her price slightly pM in order to mute the out‡ow

of farmers towards Fair Trade. Hence the non-participating farmers can fare better despite the
 30   The proof follows a similar logic as in Lemma XX.



                                                            47
possible fall of the normal co¤ee price p, given that the decline is not too sharp.


6.3.3    Comparative statics in the world with the middlemen


Proof of Proposition 11. Again, similarly to the excess supply analysis without the middleman

we di¤erentiate the whole system (4):


         d              d                @pM   @pM d    @pM dp                                            dp
  SF        +     SF          F
                           + SpM             +        +                                    F
                                                                                        + SpF        F
                                                                                                  = Dp          F
                                                                                                             + DpF
        dpF            dpF               @pF    @ dpF    @p dpF                                          dpF
                        d                @pM   @pM d    @pM dp                                            dp
                SW N          W
                           + SpMN            +        +                                    W
                                                                                        + SpF N      N
                                                                                                  = Dp          N
                                                                                                             + DpF ;
                       dpF               @pF    @ dpF    @p dpF                                          dpF


where S W N is a partial derivative of S W N with respect to ; for example.

   Rearranging, one gets


                  @pM F         d                          @pM F                    dp                          F @p
                                                                                                                     M
 SF + SF +           SpM           +              F
                                                 Sp +         S M          F
                                                                          Dp                    F
                                                                                             = DpF     F
                                                                                                      SpF      SpM (14)
                   @           dpF                          @p p                   dpF                             @pF
                       @pM     d                                         @pM        dp                        @pM W N
                 W
        S W N + SpMN                 W
                                  + Sp N                   N
                                                          Dp + SpMN
                                                                W                               N
                                                                                             = DpF    W
                                                                                                     SpF N       S(15)
                                                                                                                   M
                        @     dpF                                         @p       dpF                        @pF p


We can plug in for S F ; S N ; S F ; S W F ; S W N and their derivatives:

                                                                              !
                                                 F             pF       pM
                                             S       =G
                                                                    k
                                                                                   !
                                         N                          pF        pM
                                     S        = G(p)       G
                                                                         k
                                                                                        !
                                         WF           F                  pF       pM
                                     S        = S         = G
                                                                              k
                                                                                         !
                                     WN               M                  pF        pM
                                 S           = G(p )           G
                                                                              k




                                                            48
                          @pM F                                       pF              pM              @pM
                  SF +       SpM                  = g(t)
                           @                                                      k                  k @
                                M                                         2
                   F  @p                                                @pM
                  Sp +    S FM                    =      g(t)               ;
                       @p p                                           k @p
                             M                                                        2
                F      F @p                                                                   @pM
              SpF + SpM F                         =      g(t)                             g(t)     ;
                          @p                             k     k                               @pF
                          @pM                              @pM                                     pF               pM       @pM
                      W
             S W N + SpMN                         = g(pM )                                   g(t)                                        SF
                           @                                @                                                   k           k @
                                @pM                                                                  @pM
              W      W
             Sp N + SpMN                          =      g(pM ) + g(t)
                                 @p                                                          k        @p
                       @pM W N                                                                       @pM
              W
             SpF N   +    S M                     =      g(pM ) + g(t)                                              g(t)
                       @pF p                                                                 k       @pF                   k
                                                                  F               M
                                                              p               p
                                            t     =
                                                                      k


We can rewrite the equations (14) into matrix form

  2                                                                                                                                      32         3
              F                 pF          pM         @pM                                                      2 @pM           F              d
  6          S + g(t)                   k             k @                                                g(t)   k @p           Dp        76   dpF   7
  6                                                                                                                                      76         7=
  4           M
                                                                                                                                         54         5
                                pF          pM         @pM                                                                 @pM
      g(pM ) @p
              @          g(t)           k             k @                     SF            g(pM ) + g(t) k                 @p
                                                                                                                                     N
                                                                                                                                    Dp         dp
                                                                                                                                              dpF
                                    2                                                                                     3
                                                                                                 2
                                                                   F
                                    6                             DpF                 g(t)      k                         7
                                    6                                                                                     7
                                    4                                                                                     5
                                             N                                                      @pM
                                            DpF        g(pM ) + g(t) k                              @pF
                                                                                                          + g(t) k


                                                                                                                    @pM
Note that the signs of the individual cells depend on the size of                                                    @


                                                  2                   32                     3       2          3
                                                                                   d
                                                  6 +                 76          dpF        7 6                7
                                                  6                   76                     7=6                7
                                                  4                   54                     5 4                5
                                                                                   dp
                                                              +                   dpF
                                                                                                          +




                                                                                      pF        pM          @pM
                                                      S F + g(t)                                                               > 0
                                                                                            k              k @
                                                                                                     2
                                                                                                       @pM           F
                                                                                           g(t)                     Dp         < 0
                                                                                                     k @p
                                     @pM                          pF              pM                  @pM
                         g(pM )                        g(t)                                                          SF        < 0
                                      @                                       k                     k @
                                                                                                         @pM
                                                          g(pM ) + g(t)                                              N
                                                                                                                    Dp         > 0
                                                                                                 k        @p



                                                                                  49
                                   @pM                           @pM
From Lemma 10, we know that         @    > 0, so we need          @       small for this result to hold.

    For notational simplicity, we will write

                                   2                 32         3     2      3
                                                           d
                                   6 A         B 76       dpF   7 6 E 7
                                   6             76             7=6   7
                                   4             54             5 4   5
                                                           dp
                                     C         D          dpF
                                                                    F


To show that
                                           dp         d
                                              < 0 and F > 0
                                          dpF        dp

                                                d                    dp
is not possible, we need to show that if       dpF
                                                     > 0; then      dpF
                                                                          > 0: To do this, we write


                                           d     dp
                                         A    +B F                  = E
                                          dpF   dp
                                           d     dp
                                         C F +D F                   = F
                                          dp    dp


                                                                            d
We know that A > 0 > C; D > 0 > B; F > 0 > E: So if                        dpF
                                                                                 > 0; A > 0; but E < 0; it must
           dp                                                                             dp
be that B dpF < 0 in equilibrium, which means, because B < 0; that                       dpF
                                                                                               > 0. Same argument

                                                       d
holds for the second equation: F > 0; …rst element (C dpF < 0) is negative, so the second element
                                                                                  dp
on the second line must be positive. Since D > 0, it implies                     dpF
                                                                                       > 0: So the previous results

                          d               dp
about impossibility of   dpF
                               > 0;and   dpF
                                                > 0 seems to be preserved.Thus, we have the following


combinations that are of theoretical interest


                                          dp              d
                                                 < 0; and    <0
                                         dpF             dpF
                                          dp              d
                                                 > 0; and F < 0
                                         dpF             dp


We can see that it is not possible to have


                                          dp           d
                                            F
                                              > 0, and F > 0
                                         dp           dp


                                                          50
                                                                                          dp               dpM
in equilibrium. The reason is that we already know from Lemma 10 that if                 dpF
                                                                                               > 0; then   dpF
                                                                                                                 < 0:

Thus, such equilibrium is not possible, because it would require that FT farmers leave FT market

and sell more through middlemen. This is not possible because the expected value of FT trade

increases (both       and pF increase), while the price o¤ered by middlemen (pM ) decreases.Thus,

these outcomes are impossible:


                                            dp             d
                                                  > 0; and    >0
                                           dpF            dpF
                                            dp             d
                                                  < 0; and F > 0
                                           dpF            dp


So one can see that an increase in FT price pF leads to an increased excess supply, but the impact

on the world price is ambiguous p:31



6.4     Small FT market - …xed p

We extend our analysis to situation when the FT market is too small to impact world price p of

co¤ee. For example, we may assume that there is large number of regions, but in only very few

of them are farmers participating in Fair Trade. Middlemen, if present, adjust to the FT market

only if there are FT farmers in their region.


Lemma 15 If there are no middlemen, Fair Trade market where price is set to clear the market

always helps the farmers.


Proof. Since price p does not change, the number of active farmers G(p) does not change. Those
                                                             F
farmers who decide to sell on the FT market (G( p             k
                                                                  p
                                                                      ) of them) are all better-o¤, because they

could have stayed in the non-FT market

    In the world where FT market clears, but there are middlemen, the situation is slightly more

complicated. Middlemen react to FT market and thus alter the revenue of non-FT farmers.
  3 1 Note that the e¤ect on the world price, even if theoretically predicted, is likely to be extremely small given

the relative sizes of both markets. Thus, the results is more of a theoretical interest than a testable prediction.



                                                        51
However, we have shown before that all active farmers are strictly better o¤ if the price pM

increases and that this happens when p is not very sensitive to pF : We can thus apply the same

argument as in Lemma 9 here, because price p is assumed to be …xed. For …xed p, the argument

is very intuitive - middlemen increases price to attract more farmers to o¤set the loss from those

who left for FT market. This increase in price helps all non-FT farmers, but FT farmers are still

better of then non-FT ones.


Lemma 16 When FT market clears, it helps all farmers even if there are middlemen.

Proof. See Lemma 9 and note that p is …xed.


   In case of FT market with price pF above market equilibrium (and thus                     < 1), but no

middlemen, we will analyze the impact of a small increase in pF . Farmers bene…t if the expected

revenue, pF , increases. This happens when


                                     @( pF )        @
                                               =        pF +         >0
                                      @pF           @pF
                                        @
                                               >
                                        @pF              pF


We can use market equilibrium conditions to proof the following result.

Lemma 17 Farmers bene…t from a marginal increase in pF if and only if


                                  F
                                 DpF (p; pF )       2
                                                        g(t)=k
                                                                 >         ;
                                         G(t) + tg(t)                 pF


            pF p
where t =     k


Proof. We use comparative statics to show that



                       DF (p; pF )      G(t)    =   0
                                                                           2
                                        @
                                                      F
                                                     DpF (p; pF )          k   g(t)
                                                =                                     < 0;
                                        @pF                   G(t) + tg(t)

                                                    52
         F
because DpF < 0: From previous discussion, we know that if farmers bene…t from FT market if

 @
@pF
       is large enough:
                                                                         2
                                    @
                                            F
                                           DpF (p; pF )  k g(t)
                                       F
                                         =                      >
                                    @p         G(t) + tg(t)                               pF




      Final case, excess supply on the FT market and middlemen on the normal co¤ee, is slightly

                                                        t
more complicated. Because of the middlemen, farmers don’ get …xed price p for their normal

co¤ee but price pM that in general depends on the price pF : Equilibrium condition on the FT

market is



                                          DF (p; pF )            =      G (t0 ) ;

                                                                        pF       pM
                                                           t0    =
                                                                             k



Lemma 18 If middlemen never increase their price pM more than price on the FT market in-
           @pM
creased,   @pF
                 < 1; and they do not increase their price too much when the probability of success

on the FT market increases
                                          @pM   t0                    G(t0 )
                                              <k 2                             +1 ;
                                           @                         t0 g(t0 )

then probability of successful trade on FT market decreases when FT price increases.


Proof. We can again use comparative statics argument to show


                                             F           0        2                 @pM
                                    @      DpF     k g(t )(1                        @pF
                                                                                          )
                                        =
                                    @pF   G(t0 ) + g(t0 ) t
                                                           0                      @pM
                                                                                 k @



                  @pM           M
                                         t0     G(t0 )
Assuming that     @pF
                          < 1; @p
                                @   <k    2    t0 g(t0 )   + 1 , and by observing that


                                    t0         @pM                           @pM   t0           G(t0 )
                  G(t0 ) + g(t0 )                               > 0 ()           <k 2                    +1
                                              k @                             @                t0 g(t0 )



                                                                 53
                         @
We can conclude that    @pF
                              < 0:

   Note that this lemma also allows the possibility that probability of success on FT market
                                                      @pM
( ) is locally increasing in pF : This happens when   @pF
                                                            is very large and such condition is rather

intuitive. If middlemen increase relatively to an increase in pF , it is possible that more FT farmers

switches back to regular co¤ee production. However, this e¤ect has to be stronger than a decrease

in demand by FT co¤ee consumers. It is clear that such case is very unlikely.



6.5    Bibliography


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                                              56