A positive analysis of Fairtrade certification

Journal of Development Economics 116 (2015) 169–185

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Journal of Development Economics journal homepage: www.elsevier.com/locate/devec

A positive analysis of Fairtrade certification Andrea Podhorsky Department of Economics, York University, Toronto M3J 1P3, Canada

a r t i c l e

i n f o

Article history: Received 15 August 2013 Received in revised form 11 March 2015 Accepted 13 March 2015 Available online 6 April 2015 Keywords: Certification Fairtrade Oligopsonistic intermediaries Supply chain

a b s t r a c t The Fairtrade program transfers income to farmers by establishing a price floor and an alternate distribution channel that bypasses intermediaries between the raw commodity and world markets. I develop a model of the international commodity supply chain, with monopolistically competitive final goods producers and consumers who value the ethical quality of goods. A small number of oligopsonistic intermediaries purchase the raw commodity from farmers in a given country and then sell to final goods producers in the world market. I consider the effects of a Fairtrade program that is too small to have an effect on the world price of the commodity. I show that the Fairtrade program decreases the intermediaries' market power and consequently, even farmers that are not selected into the program receive a higher wage than in the absence of the program. I establish the Pareto optimal Fairtrade price and assess the overall efficiency of the program. The program is a more efficient way to transfer income to farmers than a direct transfer equal to the premium commanded by certified products if the Fairtrade price is not set too high above the efficient wage for farmers. If the number of intermediaries were large, however, then the direct transfer would be more efficient than the program for all binding Fairtrade prices. © 2015 Elsevier B.V. All rights reserved.

1. Introduction This paper studies how market power in international commodity supply chains impedes the efficient and equitable functioning of markets, and evaluates the Fairtrade (FT) program as a potential solution. The FT certification program transfers income to farmers by establishing a guaranteed price for farmers and an alternate distribution channel that bypasses intermediaries in the international commodity supply chain. It informs consumers about the price paid to farmers since it certifies and labels the products of final goods producers that voluntarily participate in the program. The current FT price floor is chosen to cover farmers' production and living expenses, and is not necessarily optimal. I conduct a positive analysis of FT by analyzing the certification program as a voluntary mechanism that enables consumers to transfer income to farmers. Given consumer preferences for the “ethical quality” of products, the optimal FT price is an objective measure, determined by the certification standard (the price paid to farmers) that optimizes the returns to agents that are affected by the program. I develop a theoretical model of the international commodity supply chain to determine the Pareto optimal FT price and address several open questions about the program. For instance, does the higher price paid to farmers necessarily lead to over-supply and create additional distortions in the world market? Does the program disadvantage farmers that are not chosen to participate? Would a direct donation, rather than paying a higher price

E-mail address: [email protected].

http://dx.doi.org/10.1016/j.jdeveco.2015.03.008 0304-3878/© 2015 Elsevier B.V. All rights reserved.

for certified products, be a more efficient way to transfer income to farmers? FT is a salient and growing phenomenon. Although certified products currently comprise a small proportion of the world market,1 the absolute quantity of FT sales is large. In 2013, consumers spent 5.5 billion euros on FT products worldwide, a 15% growth rate over the previous year, and the FT system worked with 1.4 million farmers and workers across 74 developing countries (FLO Annual Report 2013/14). From 2005 to 2008, the average annual growth in sales exceeded 20% for 16 out of 19 international markets, and remained in the range of 15% to 30% for 12 of these markets from 2010 to 2011, after the global recession (Elliott, 2012). Since sales are large relative to the number of participating producers, the program can significantly affect farming communities where the program is operative.2,3 The range of certified commodities has rapidly expanded to now include flowers; bananas; sugar; coffee; cocoa; fruit juice; wine; fresh fruit; tea; cotton; rice; honey; herbs, herbal teas and spices; dried and processed fruits;

1 In 2013, world production of coffee was about 9.8 million metric tons, where 1 MT = 15 bags of green coffee. See http://www.ico.org/prices/po.htm. World FT coffee sales were 83,709 metric tons (FLO Annual Report 2013/14), which is a market share of about .9%. Note that in 2011, the market share was about 1.2%. The large drop is due to Fair Trade USA's withdrawal from Fairtrade International (FLO) at the end of 2011. 2 Between 2001 and 2011, the number of producer organizations certified as eligible to sell FT commodities grew 5-fold while the sales of certified bananas and coffee grew 10fold and 7-fold, respectively, and other products collectively grew 5-fold during just 5 years since their introduction (Elliott, 2012). 3 In 2013, the FT premium paid to farmers and workers worldwide was an estimated 86 million euros (FLO Annual Report 2013/14).

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vegetables; and quinoa (in order of sales volume for 2013) (FLO Annual Report 2013/14).4 In essence, the FT program is a development project with the specific objective to improve producer living conditions and to ameliorate poverty in the South (Paul, 2005). The program's mission is to connect disadvantaged producers and consumers, promote fairer trading conditions and empower producers to combat poverty, strengthen their position and take more control over their lives.5 Consumers buy FT certified goods with the expectation that their purchases have this effect, and resources directed toward FT could be contributed toward other development projects. There is much debate surrounding the effectiveness of the FT certification system (Booth and Whetstone, 2007; Griffiths, 2012; Stecklow and White, 2004; Weber, 2007) and, as it continues to grow, there is a need to address fundamental issues about its design and effect on the market. To provide a framework that enables an analysis of the FT program's effects on all relevant agents: farmers, intermediaries, final goods producers, and consumers, in Section 2 of the paper I model the international commodity supply chain for coffee, which is representative of most FT commodities.6 As shown in Fig. 1, a large number of atomistic farmers sell their output to oligopsonistic intermediary traders, which supply the commodity to the world market.7 While the world coffee market is best characterized as competitive (Karp and Perloff, 1993), the price paid to coffee farmers is determined by their interaction with intermediary traders that have considerable market power as buyers of the raw commodity.8 Consequently, each intermediary offers a wage to farmers that is below its marginal revenue from selling the commodity in the world market. Most green coffee beans are purchased by manufacturers (final goods producers) and the prices observed on futures markets approximate their marginal costs (Leibtag et al., 2007).9 The market for roasted coffee is best described as a differentiated products market (Nakamura and Zerom, 2010). Coffee manufacturers roast and grind the green beans and sell the packaged product to consumers via supermarkets and grocery wholesalers. Due to product differentiation among coffee brands, final goods producers possess market power as sellers to consumers and set their prices at a markup over their marginal costs. The FT program transfers income to farmers by establishing a minimum guaranteed price for farmers, and an alternate distribution channel that bypasses intermediaries in the international commodity supply chain. In a given raw commodity market, farmers that participate10 receive a number of FT contracts and sell their output to an intermediary that has been licensed by the program. Final goods producers that choose to participate in the program must purchase the commodity from a FT intermediary. The number of FT contracts is determined by the demand for the certified commodity by final goods producers, which is derived from consumer demand, and hence the FT market clears. I analyze a representative raw commodity market in Section 3, and use the model to demonstrate that unlike a conventional price floor, the FT program does not need to introduce any market distortions since the certified commodity is a differentiated product with distinct

4 Coffee and bananas are the most important FT commodities in terms of value (Raynolds et al., 2007). 5 See http://www.fairtrade.net/our-vision.html. 6 Supply chains for tea, cocoa, sugar, cotton, bananas, and various legumes and grains also exhibit buyer concentration, while commodity production is typically characterized by large numbers of producers (Asfaha, 2008; De Schutter, 2010). 7 Talbot (2004) and De Jong (1997) examine why it is exceedingly difficult for farmers to integrate forward in the coffee supply chain. 8 Ponte (2001) identifies the market shares of the 8 largest players in the coffee market in 1998: Neumann 16%, Volcafe 13%, Cargill 6%, Esteve 6%, Aron 5%, Man 4%, Dreyfus 3%, Mitsubishi 3%, others 44%. 9 Industry estimates suggest that green coffee accounts for more than half of the marginal costs of coffee production. Other marginal costs include packaging, labor, transportation, and warehousing (Yip and Williams, 1985). 10 In practice, farmers are required to form a cooperative that is monitored by the FT program.

supply and demand curves. If the number of FT contracts satisfies the demand for the FT commodity by final goods producers, the program does not result in overproduction. Proposition 1 demonstrates that the program weakens the intermediaries' market power since each intermediary optimally increases the wage it offers to farmers, and hence even farmers that are not selected to participate are better off under the program. This result provides a theoretical foundation for empirical evidence that, in the Yungas region of Bolivia, farmers of conventional coffee received a price that is 133% to 233% higher if FT cooperatives were present (Imhoff and Lee, 2007). Also, the introduction of the FT program for bananas in Peru has had an important positive effect on the price paid to farmers of conventional bananas (Ruben et al., 2009). Piyapromdee et al. (2014) employs a theoretical framework and establishes that the existence of FT intermediaries increases the wage offered by conventional intermediaries. The authors calibrate the model to reveal that the effect is likely to be small. In the authors' Cournot framework, however, rather than paying producers a price established by the FT program, FT intermediaries “care” about the welfare of farmers and each FT intermediary chooses how much to purchase by maximizing a function of its own profit and the welfare of the farmers that grow the FT commodity. Proposition 2 confirms that the program has a procompetitive effect on a given raw commodity market since, under the program, the elasticity of supply is increasing in the size of the program. Consequently, as the number of FT contracts increases, the program succeeds in extracting more profit from oligopsonistic intermediaries. Also, the wage offered to farmers by the intermediaries is increasing in the size of the program and approaches the efficient wage (intermediaries' marginal revenue from selling the commodity in the world market). This result is related to Deardorff and Rajaraman (2005), which studies markets for commodities that confront buyer concentration. The authors use a theoretical model to show that an export tax can extract some of the intermediaries' profit but also worsens the distortion that is due to their market power. Unlike an export tax, the FT program works to increase aggregate (FT and conventional) output and improves the efficiency of the raw commodity market. Although the FT program relies on the participation of consumers, it improves market outcomes without introducing additional distortions since it directly weakens the intermediaries' market power. I analyze the final goods market in Section 4. Propositions 3 and 4 establish that the Pareto optimal FT price maximizes the share of income spent on certified goods by consumers. The model offers a clear policy prescription since the share of income spent on certified goods is easily observed in the final goods market. In Section 5, I assess the efficiency of the FT program as a means to transfer income to farmers by comparing the FT program with a direct transfer to farmers. Under the program, farmers realize benefits that result from the improved efficiency of the raw commodity market. Empirical studies that implicitly assume there is perfect competition among intermediaries do not take these benefits into account. For instance, Valkila et al. (2010) compares the proportion of the retail price that remains in the producing country for FT and conventional coffee supply chains. Since the authors assume producers earn the world price of coffee, they overestimate the fraction of the retail price that remains in the producing country for the conventional supply chain. Proposition 5 demonstrates that the FT program is a more efficient way to transfer income to farmers than a direct transfer equal to the premium that consumers would have paid for certified goods under the program if and only if the FT price is not set too high above the efficient wage. This is because, for sufficiently high FT prices, the markup extracted by final goods producers and the excess transportation and processing costs for the certified commodity outweigh the program's benefits that arise from improving the efficiency of the raw commodity market. I provide an example using estimates of the model's parameters taken from other studies. It reveals that the FT program is not the ideal

A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

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Fig. 1. Conventional and FT commodity supply chains.

mechanism to transfer income to farmers during crises. If the world price of the commodity is extremely low, a FT price that covers farmers' production and living expenses far exceeds the efficient wage. Throughout the paper I consider the hypothetical case where entry barriers for intermediary traders fall to zero and the number of intermediaries becomes arbitrarily large. If final goods producers do not extract a markup, then there is perfect competition along the entire supply chain since there is perfect competition among intermediaries. In this case, I show that the FT program is equivalent to a direct transfer to farmers. This result is reminiscent of Besley and Ghatak (2007), which shows that under perfect competition, corporate social responsibility will produce public goods at exactly the same level as predicted by the standard voluntary contribution equilibrium for public goods. Using a framework that encompasses imperfect competition, this paper demonstrates that, for a given FT price, the superiority of the FT program over a direct transfer depends upon the balance of market power along the commodity supply chain. Early scholarship on FT contends that market failure is intrinsic to the free trade system, and the underlying vision of FT's pioneers was a conviction that the global market is fundamentally broken (Jaffee, 2011; Raynolds, 2000). The first book on FT argues that farmers benefit disproportionately little from free trade because of the dominant position in the world market of a small number of transnational companies, whose power derives from the scale of their resources, the integration of their operations, their access to finance, and their freedom to switch from one supplier to another (Barratt-Brown, 1993). Since its early days, the FT movement has abandoned its goal of market reform and now functions as an adjunct to the market. FT certification is a market-based policy instrument for achieving market access and poverty reduction (Fridell, 2007; Jaffee, 2011; Renard, 1999). In addition to establishing a guaranteed price for farmers (inclusive of a social premium that is spent on community development projects), the FT program enables pre-financing for producers who require it, facilitates long-term trading partnerships, and ensures that the conditions of production and trade are socially and economically fair, and environmentally responsible.11 A large number of studies demonstrate that FT is associated with significant monetary and non-monetary benefits for small producers. Nelson and Pound (2009) conduct a literature meta-review that summarizes considerable evidence that FT producers enjoy higher returns and stable incomes, improved access to credit, improvements to facilities and equipment, and access to export markets. Non-monetary benefits include minimized and safe use of agrochemicals, proper and safe management of waste, maintenance of soil fertility and water resources, and measures of producer empowerment such as improved producer self-confidence, increased influence over policy makers at the national level and stronger organizations. We must be careful about inferring causality, however, since most of the studies undertaken to measure the benefits of FT do not control for characteristics that can determine FT certification and can also cause farmers to attain these benefits. 11

See http://www.fairtrade.net/aims-of-fairtrade-standards.html.

Blackman and Rivera (2010) classify empirical studies of certification program impacts on the basis of whether they use methods that test for the causal impact of certification. Of the 9 studies related to FT that attempt to correct for potential selection bias, 3 provide evidence that certification has socioeconomic benefits and only 1 provides evidence that certification has environmental benefits. For the case of FT certified bananas, Fort and Ruben (2008) finds that FT farmers have higher net incomes and profits. While Zuniga-Arias and Saenz-Segura (2008) finds that incomes, expenditures, and profits are not significantly different for FT and non-FT households, FT households have higher levels of wealth and invest more in education and training. For the case of FT certified coffee, Arnould et al. (2009) and Bolwig et al. (2009) find that certification has significant socioeconomic benefits, and Blackman and Naranjo (2010) finds that certification has a significant environmental impact. More recently, Weber (2011) controls for self-selection using a treatment effects model and estimates that FT-organic growers in the states of Oaxaca and Chiapas in Mexico received an average premium of 12.8 cents per pound. Dragusanu and Nunn (2013) utilizes a panel containing data for 262 coffee mills in Costa Rica from 1999 to 2010. By following producers over time, this approach controls for time-invariant confounders. The authors find that FT certified farmers receive 4 cents more per pound for exports than conventional farmers and that certification leads to an increase in average income for all households residing in a given Costa Rican district, where the increase is concentrated among skilled coffee growers. Proposition 1 in this paper supports the existence of a causal relationship between the FT program and increased farmer income in these studies since, in the model, all farmers are ex-ante identical and it is inconsequential which producers participate in the FT program. The paper concludes in Section 6; the proofs of most propositions are relegated to Appendix A.

2. Overview of the model The detailed structure of the model is depicted in Fig. 2. There are n raw commodity markets (that can be identified with countries) indexed by j. In a given raw commodity market j, a large group of atomistic farmers sell their output to a small number Nj of oligopsonistic intermediary traders. Total purchases xj determine the price per unit of output rj (the farmers' wage). Each intermediary sells its purchases of the raw commodity in the world (or export) market. For simplicity, the number of intermediaries Nj is exogenously determined and the world market is sufficiently large to ensure that each intermediary is a competitive seller. There are M final goods producers (firms or roasters) that purchase the commodity from the intermediaries. The number of final goods producers M is determined according to free entry in the final goods market and is sufficiently large to ensure that each firm is a competitive buyer of the commodity. The price of the commodity pc and the aggregate quantity exchanged x are determined competitively in the world market according to world supply of the commodity by intermediaries and world demand for the commodity by final goods producers.

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Fig. 2. Overview of model.

The final goods market is monopolistically competitive. Final goods producers package and brand the commodity, and each sells a differentiated product to consumers. The price consumers pay for conventional final goods p(pc) is determined according to a markup over firms' marginal costs, and hence depends upon the price of the conventional commodity pc. Consumers purchase a quantity of each product according to its price and their valuation of its ethical quality relative to other goods. In aggregate, they consume CUL units of uncertified goods. The FT program establishes a guaranteed price for farmers rf that is comprised of a minimum price (a price floor) and a premium for investment in social, environmental or economic development projects.12,13 Since the price of final goods is determined according to a markup over firms' marginal costs, the price consumers pay for certified goods p(rf) depends upon the FT price rf. All farmers have an incentive to join the FT program since the total FT price rf exceeds the world price of the conventional commodity pc by at least the social premium,14 and intermediaries offer them a wage rf that is less than pc. Only a select number of farmers, however, are able to participate. In practice, as part of the application process to become FT certified, producers must demonstrate a certified buyer's willingness to purchase their coffee, which roughly ensures market clearing.15 As such, I assume that the total number of FT contracts xf is determined according to consumers' aggregate demand for certified goods CL. The program then allocates to a given raw commodity market j a share of the total FT contracts xfj. For ease of exposition, I assume that there is a single FT intermediary between a given raw commodity market and firms in the final goods market that acts competitively by setting the final goods producers' price equal to its marginal cost to purchase and deliver one unit of the commodity. FT intermediaries and certified firms, which are monitored by the FT program,16 perform the tasks of intermediary traders, such as locating farmers and importing the raw commodity, however they do not exploit any resulting market power. I assume that the program is too small to have a significant effect on the world price of the conventional commodity. In this case, the share of income spent by consumers on certified goods has a negligible impact on world demand for the conventional commodity. Also, the number of FT contracts granted to farmers has a negligible impact on world supply of the conventional commodity. Hence the world price of the

12 Currently, the Fairtrade minimum price for washed Arabica is 1.40 USD per pound and the Fairtrade premium is .20 USD per pound, which sums to a total Fairtrade price of 1.60 USD per pound. 13 Producers within the farmers' organization or workers on a plantation democratically decide how to invest the social premium. 14 If the FT minimum price exceeds the world price of the conventional commodity pc, then the FT price rf is the sum of the minimum price and the social premium. If the FT minimum price is less than pc, then rf is the sum of pc and the social premium. 15 See Weber (2006) and Dragusanu et al. (2013). 16 Importers and roasters must undergo, and comply with, regular desk audits and onsite audits. See http://fairtradeusa.org/certification/producers/coffee.

conventional commodity is virtually unaffected by movements in the FT price, and is well-approximated by a constant.17 Although the number of FT contracts comprises a small proportion of world output, the absolute quantity of FT contracts is large. If FT contracts are concentrated within a relatively small number of raw commodity markets, the program can have significant effects on farmers and intermediaries within these markets. In Section 5, we'll see that the marginal benefits of the program that are due to improving the efficiency of the raw commodity market are decreasing in the program's size. Consequently, we should not be loathe to spread out the total number of FT contracts equally among numerous raw commodity markets since aggregate benefits are then greatest. If there is a fixed component to farmers' cooperative and certification costs, however, then there is an upper bound on the number of raw commodity markets that should participate since the program's size must be large enough to enable benefits to cover fixed costs. All farmers are ex-ante identical and I measure the benefits that accrue to farmers in a given raw commodity market at an aggregate level that includes selected farmers organized into a FT cooperative (or producer organization) and farmers that do not participate in the program. Since aggregate producer surplus is used to analyze the effects of the program throughout the paper, which farmers are selected to participate in the program is inconsequential. The social premium is a component of aggregate producer surplus, since it boosts farmers' welfare even though it does not enter their household budgets. Evaluating the program at an aggregate level abstracts from the issue of how the monetary benefits of FT are distributed among cooperative members, which is idiosyncratic and can depend on whether the producer organization is a small farm or a large plantation with numerous hired workers. In actuality, the precise amount of direct additional income a farmer receives through the program is difficult to calculate, primarily because payments vary according to the cooperatives' handling of debt servicing, cooperative expenses, and the distribution of social premiums (Murray et al., 2006). This paper evaluates the FT program based on the total gains to farmers with the perspective that if aggregate producer surplus increases under the program, then it is possible to distribute the gains in a Pareto-improving manner. While the analysis focuses on the primary aspect of FT, the FT price r f , we should also consider the nonmonetary benefits that result from the other aspects of FT discussed in Section 1. Although these are difficult to quantify, they work to tip the balance in favor of the program. 3. The raw commodity market In the raw commodity market, farmers sell the conventional raw commodity to intermediary traders. I assume that each raw commodity

17 This is analogous to the textbook assumption of a “small” country that is too small to affect world prices with its policies. See Krugman et al. (2014).

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173

market j is identical and the long run supply is given by the linear supply curve Sj: xj ¼

r j −a b

ð1Þ

where rj is the price per unit of the raw commodity (the farmers' wage), a is the intercept and b is the slope. There are Nj identical oligopsonistic intermediaries that purchase the raw commodity from farmers in market j. For simplicity, the number of intermediaries Nj is exogenous. A given intermediary purchases xoj units of the commodity but, due to processing and transportation costs, sells only ξxoj units to final goods producers in the world market, where 0 b ξ b 1. No explicit labor costs are incurred by the intermediaries, however 1 − ξ units of the commodity ‘melt’ away after processing and transportation. To simplify notation, processing and transportation costs are the same for purchases from any raw commodity market j. It follows that an intermediary's marginal revenue from selling one unit of the commodity in the world market is ξpc and, from the supply curve Sj in Eq. (1), the efficient quantity of output is xj ¼ ξpcb−a. An intermediary's profit is given by o πm j


 o ¼ ξpc −r j x j −F m

or, equivalently,  ð2Þ

where Fm is a fixed cost and, from Eq. (1), rj depends upon the purchases of all Nj intermediaries xj = Njxoj . Since a small number of intermediaries confront the entire supply curve Sj, if an intermediary expands its purchases, given the purchases of the other intermediaries, it must pay a higher price on all units and not just the marginal unit. Consequently, its marginal cost curve is steeper than the supply curve Sj. In standard Cournot fashion, each intermediary purchases the profit maximizing quantity e xoj that equates its marginal cost with its marginal revenue, while treating the purchases of the other intermediaries as given.18 Since each intermediary's marginal cost curve is steeper than the supply curve in Eq. (1), in aggregate the intermediaries purchase less than the efficient quantity of the raw commodity x⁎j and the wage they offer to farmers is less than the efficient wage ξpc.19 Fig. 3a depicts the raw commodity market for the case where ξ = 1 and Nj = 1.20 In the absence of the FT program, the intermediary purchases the quantity xjo b x⁎j and offers farmers the wage rjo b ξpc. A number of FT contracts xfj are allocated to a given raw commodity market j. For simplicity, each raw commodity market that is covered by the program receives an equal share of the total number of FT contracts so that x fj ¼ 1nx f . Since the total number of FT contracts xf are a fraction of the world market, xfj b x⁎j . If the FT price rf is at least as large as the wage offered to farmers by the intermediaries rj, then the program is binding and xfj units of the raw commodity are sold to the FT intermediary.21 Hence, under the FT program, supply of the raw commodity in the conventional market is given by the residual supply curve SRj: 8 r −a > < j −x f j ; if r j ≤r f b x j ¼ r −a j > : ; if r j Nr f b 18

Cournot is the appropriate mode of competition since the intermediaries must buy the products before shipping them to the world market. 19 From Eq. (1) it follows that the marginal cost of a given intermediary is given by MC j ¼ a þ NNþ1bx j, which has NNþ1 times the slope of the supply curve Sj. If barriers to entry Fm were to hypothetically fall to zero and the number of intermediaries Nj were to become arbitrarily large, then MCj → rj and xj → x⁎j. 20 Since Nj = 1, there is a single monopsonistic intermediary. 21 The section Preliminaries (i), ‘The minimum binding FT price r f ,’ of Appendix A proves the existence of a unique minimum binding FT price r f b ξpc . In actuality, the program is binding since pc ≥ ξpc ≥ rj for all Nj, and the FT price rf exceeds the world price pc by at least the social premium. j

j

j

j

Fig. 3. a. Monopsonistic intermediary in the raw commodity market. Case: ξ = 1 and Nj = 1.

rj ¼

a þ bz j ; if r j ≤ r f a þ bx j ; if r j N r f

ð3Þ

where zj = xj + xfj is aggregate output of the raw commodity in market j. It follows from Eq. (3) that whenever the program is binding, the wage of unselected farmers is increasing in aggregate output zj. Under the FT program, the intermediaries in raw commodity market j confront the residual supply curve SRj in Eq. (3), and each intermediary treats xfj as given. The total quantity of the raw commodity optimally purchased by intermediaries is22 xe j ¼

N j ξpc −a−bx f j Nj þ 1 b

ð4Þ

and ξe x j units are sold in the world market. For a given pc, it follows from Eq. (4) that output in the raw commodity market x˜ j is decreasing in the number of FT contracts xfj. Also, output in the absence of the program e x jo is given by Eq. (4) and xfj = 0. The effect of the FT program on a given raw commodity market j is depicted in Fig. 3b, for a given pc = pco, and the case where ξ = 1 and Nj = 1. Under the FT program, the intermediary's marginal cost curve is given by MCj1, which corresponds to the residual supply curve SRj. From Eq. (3), the residual supply curve SRj is ‘shifted’ to the left of Sj by xfj units for all rj ≤ rf since xfj units of the raw commodity are sold to the FT intermediary whenever the program is binding. Since pco is unchanged by the program, the intermediary maximizes its profit by decreasing its purchases of the raw commodity to xe j1 . From Eq. (4) it follows that, given the optimal behavior of the intermediaries, aggregate output of the raw commodity is given by ze j ¼

N j ξpc −a 1 þ x Nj þ 1 f j Nj þ 1 b

ð5Þ

which, for a given pc, is increasing in the number of FT contracts xfj. Since each intermediary's marginal cost curve is steeper than the residual x j decreases by less than the number of FT supply curve SRj, output e contracts xfj under the program.23 The program squeezes the intermediaries since they reduce their purchases but, due to their market power,

22 Under the program, it follows from Eq. (3) that the marginal cost of a given intermediary is given by MC j ¼ a þ NNþ1bx j þ bx f j ; and its marginal revenue is given by ξpc. 23 From Eq. (4) it follows that in response to an increase in the number of FT contracts by xfj, output falls by NNþ1x f j . j

j

j

j

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which are also decreasing in the number of FT contracts xfj since e x j is decreasing in xfj. It directly follows that as the number of FT contracts xfj increases, the program succeeds in extracting more profit from oligopsonistic intermediaries. Intermediary profits in the absence of the program πem jo are given by Eqs. (4), (8) and xfj = 0. Referring again to Fig. 3b, in response to a given number of FT contracts xfj, aggregate output increases to ze j1 and the wage received by unselected farmers increases to e r j1 . The intermediary's spread decreases to ξpco −re j1 and since output falls to
 xe j1 , its operating profits decrease to ξpco −re j1 xe j1 .

Fig. 3. b. The effect of the FT program on the raw commodity market. Case: ξ = 1 and Nj = 1.

they are only partly displaced by the FT intermediary. Consequently, however, aggregate output ez j exceeds output in the absence of the program xe jo and is closer to the efficient level of output x⁎j .24 If barriers to entry Fm were to hypothetically fall to zero and the number of intermediaries Nj were to become arbitrarily large, then the level of output in the absence of the program xe jo would be equal to the efficient level x⁎j due to competition among intermediaries. From Eq. (4) it follows that output e x j would fall by the full number of FT contracts allocated to the raw commodity market and hence, from Eq. (5), aggregate output e z j would be equal to the level of output in the absence of the program xe jo . The intermediaries would be fully displaced by the FT intermediary and, from the perspective of the aggregate raw commodity market (conventional and FT), the FT program would have no effect on output. In this case, the program would preserve the efficiency of the raw commodity market and would serve only to transfer income to selected farmers.25 From Eqs. (3) and (5), the wage offered to farmers by the intermediaries is e rj ¼

 Nj 1
ξpc þ a þ bx f j : Nj þ 1 Nj þ 1

ð6Þ

The wage in the absence of the program e r jo is given by Eq. (6) and xfj = 0. Since aggregate output e z j in Eq. (5) is increasing in the number of FT contracts xfj, the wage offered to farmers that have not been selected to participate in the program er j is increasing in xfj. It directly follows that unselected farmers are better off under the program than in its absence. Since aggregate output ez j exceeds xe jo , the wage of unselected farmers er j exceeds e r jo . From Eqs. (4) and (6), the intermediaries' spread is Δm ¼ ξpc −er j ¼

b e x Nj j

ð7Þ

which is decreasing in the number of FT contracts xfj since, from Eq. (4), e x j is decreasing in xfj. From Eqs. (2) and (7), aggregate intermediary profits are πem j ¼

b 2 xe −N j F m Nj j

ð8Þ

23

From Eq. (4) it follows that in response to an increase in the number of FT contracts by xfj, output falls by NNþ1x f j . 24 From Eqs. (4) and (5) we have ez j ¼ e x jo þ N 1þ1x f j . 25 We shall examine this further in Section 3.1. j

j

j

Since output e x j falls under the program, it may seem that the program exacerbates the market failure due to the presence of the oligopsonistic intermediaries in the raw commodity market. From the perspective of the aggregate market (conventional and FT), however, the inefficiency due to the intermediary's presence is decreasing in aggregate output zj. Fig. 4a depicts the reduction in the distortion under the program for the case where ξ = 1 and Nj = 1. The number of FT contracts xfj offered by the program creates a ‘wedge’ between output in the raw commodity market xj and aggregate output zj, which simultaneously squeezes the intermediaries, reducing their output fromxe jo toxe j1, and reduces the distortion due to their presence by increasing total output from xe jo to ze j1 . The following proposition summarizes the effects of the FT program on a given raw commodity market. Proposition 1. For a given world price of the raw commodity pc, the greater is the size of the program xfj, the greater is the wage offered to farmers of the conventional raw commodity er j and the smaller are intermediary profits πem j . Proof. See Appendix A. ■ For a given pc, recall from Eq. (6) that the wage er j is increasing in the number of FT contracts xfj and, from Eq. (8), aggregate intermediary profits πem j are decreasing in xfj. It follows that the wage er j is greater under the program and intermediary profits πem j are smaller under the program than in its absence. Also, the larger is the program, the greater is the increase in the wage and the greater is the quantity of profits extracted from the intermediaries. The effects of the program summarized in Proposition 1 are due to the improved efficiency of the raw commodity market. The following proposition establishes that the FT program has a procompetitive effect on a given raw commodity market, which is increasing in the size of the program xfj. Proposition 2. In a given raw commodity market j, (i) the elasticity of residual supply Esj is increasing in the number of FT contracts xfj (ii) achieving full efficiency requires the number of FT contracts xfj to equal the efficient level of output x⁎j . From Eq. (3), whenever the program is binding, the elasticity of residual supply is given by Es j ¼

∂x j r j a þ bz j ¼ : bx j ∂r j x j

ð9Þ

It follows from Eqs. (4) and (5) that Esj is increasing in the number of FT contracts xfj, since zj is increasing in xfj and xj is decreasing in xfj. We can express the wage offered to farmers in Eq. (6) as er j ¼ ξpc −

1 ξp : N j Es j þ 1 c

ð10Þ

It follows from Eq. (10) that the intermediaries' mark down below marginal revenue is decreasing in the number of FT contracts xfj, since it is decreasing in Esj. Hence, as the number of FT contracts xfj increases, the wage er j moves up the supply curve toward the efficient level ξpc.

A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

175

From Eq. (10), however, achieving full efficiency in the raw commodity market requires the elasticity of residual supply Esj to approach infinity x j in Eq. (4), so that, from Eq. (9), output e x j must approach zero. From e this requires the number of FT contracts xfj to approach the efficient level of output in the raw commodity market x⁎j . I assume, however, that the number of FT contracts xfj is insufficient to fully displace the intermediaries and hence the program does not completely eliminate their market power. 3.1. Producer surplus The main objective of the FT program is to transfer income to farmers. In a given raw commodity market, selected farmers receive a premium of r f −er j , and they pay cooperative and certification costs c per unit of output xfj.26 It follows that their net transfer is given by
 T f j ¼ r f −re j x f j −cx f j :

ð11Þ

Since the FT program establishes both a FT price and an alternate distribution channel, the total transfer Tfj can be decomposed into a share that is due to the ‘fairness’ premium paid by consumers for FT products
 c T f j ¼ r f −ξpc x f j

ð12Þ

a share that is due to bypassing the oligopsonistic intermediaries
 m T f j ¼ ξpc −re j x f j

ð13Þ

less the total certification costs C f j ¼ cx f j where Tf j = Tfcj + Tfmj − Cf j. If rf N ξpc, then Tfcj is a transfer from consumers to selected farmers because consumers are willing to support a FT price rf that exceeds the efficient wage for the raw commodity ξpc. In this sense, we can think of rf − ξpc as a pure fairness premium, since selected farmers receive a wage in excess of what they would have earned if there were competition among intermediaries.27 The share Tfmj is a payment received by selected farmers because the FT intermediary does not extract a spread. If barriers to entry Fm were to hypothetically fall to zero and the number of intermediaries Nj were to become arbitrarily large then, since the wage offered to farmers er j in Eq. (6) would approach the efficient wage ξpc, Tfjm would approach zero and the total transfer to farmers Tfj would be equal to the transfer due to the fairness premium Tfcj net of z j in Eq. (5) would be equal certification costs Cfj. Since aggregate output e to the level of output in the absence of the program xe jo, the effect of the FT program on the raw commodity market would be equivalent to a transfer to selected farmers of Tfcj − Cf j.28 Aggregate producer surplus is given by PS j ¼

b 2 ze þ T f j 2 j

ð14Þ

which is the sum of baseline producer surplus that depends upon aggregate output e z j, and the transfer received by selected farmers Tf j. Baseline producer surplus accrues to both selected and unselected farmers and is the difference between the wage offered by the intermediaries er j and the minimum wage farmers are willing to accept, aggregated over 26 Producer organizations pay an annual certification fee that depends on the size of the organization, and hence the fee is positively correlated with output. See http://www.flocert.net/wp-content/uploads/2014/03/PC-FeeSysSPO-ED-25-en.pdf. 27 Note that because intermediaries extract a spread, it is possible for a binding FT price to be less than ξp c, so that Tfjc b 0. In actuality, however, rf N pc ≥ ξpc. 28 The overall efficiency of the program will be discussed in Section 5.

Fig. 4. a. Inefficiency in the raw commodity market. Case: ξ = 1 and Nj = 1: b. Producer surplus in the raw commodity market. Case: ξ = 1 and Nj = 1.

the sum of conventional and FT output, e z j . Producer surplus in the absence of the program PS jo ¼ 2b x˜ 2jo is given by Eqs. (5), (11), and (14) and xfj = 0. Fig. 4b depicts the effect of the FT program on aggregate producer surplus, for the case where ξ = 1 and Nj = 1. Baseline produce surplus increases since aggregate output increases to ze j1 and the wage received by unselected farmers increases to e r j1. Also, selected farmers receive the transfer Tfj, which is the sum of Tfcj and Tfmj , net of certification costs Cf j. Comparing Figs. 4a and b, it's clear that the increase in baseline producer surplus under the program and the transfer due to bypassing the intermediary Tfjm are entirely comprised of the reduction in the intermediary's profit πem j and the reduction in the distortion due to its presence in the raw commodity market. Consequently, these benefits directly result from the improved efficiency of the raw commodity market under the program.29 Moreover, given the structure of the raw commodity market, the only condition required for farmers to realize these benefits is the receipt of a number FT contracts xf j. In this section we've seen that the FT program has a procompetitive effect on a given raw commodity market and consequently farmers experience benefits that are due to its improved efficiency. The wage 29 Note that this observation does not require that transfers are given to farmers with high marginal costs, and Fig. 4b is depicted in this way only to facilitate a clear comparison with Fig. 4a.

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A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

offered to farmers by conventional intermediaries er j increases and selected farmers receive a transfer Tfjm because the FT intermediary does not extract a spread. Further, these benefits are increasing in the number of FT contracts allocated to a given raw commodity market xfj. Selected farmers receive an additional transfer Tfjc because consumers are willing to support a FT price rf that exceeds the efficient wage ξpc, and the total transfer received by selected farmers is reduced by certification costs Cfj. If there were perfect competition among intermediaries, farmers would benefit in aggregate by only Tfjc − Cfj since no further improvements could be made to the efficiency of the raw commodity market. 4. The final goods market In the final goods market, consumers purchase FT certified goods according to how they value their ethical quality relative to their price. The ethical quality produced by a firm is positively related to the wage it pays for raw materials. Since ethical quality is not discernible in the final characteristics of its product, FT certification facilitates the provision of ethical quality to the market. The existence of consumer preferences for ethical quality is revealed by actual purchases of FT certified goods and, using experiments and surveys, several empirical studies measure the premium consumers are willing to pay (Arnot et al., 2006; Didier and Sirieix, 2008; Loureiro and Lotade, 2005). Since consumers purchase FT certified goods despite that the purchases of a single individual can only have a negligible impact on farmers, it must be that consumers care about ethical quality through their own consumption. Different interpretations of the private benefit that results from purchasing environmentally or socially responsible products include social approval, a feeling of ‘warm glow’ satisfaction, and prestige (Andreoni, 1990; Becker, 1974; Benabou and Tirole, 2006). Since certification is costly, consumers' willingness to pay for ethical quality creates an incentive for firms to participate in the FT program. A firm's overall cost to certify its product, however, depends upon its organizational capacity to fulfill the numerous administrative tasks required by the program.30 Also, certified firms are required to offer pre-financing to farmers upon request and they incur the opportunity cost of these funds. I assume that firms differ according to their effective certification costs and consequently it is optimal for only some firms to certify their products. Building on Melitz (2003), I assume that a firm must make an initial investment to establish a basic production process before it can obtain an understanding of its organizational capacity and determine the desirability of undertaking certification.31 Due to this initial sunk cost, only a bounded number of firms enters the industry and ex-post profits are not dissipated to zero.32 4.1. Consumers

according to two levels of ethical quality: rf and r . Since consumers also value conventional goods, both certified and uncertified goods are produced in equilibrium. Products are also horizontally differentiated according to their brand. Consumers purchase some of each variety according to its price and how they value its ethical quality relative to other brands.33 If the price of a certified variety is less than the price of an uncertified variety, for instance, consumers continue to buy the uncertified variety but in a smaller quantity. Consequently, the consumption of certified and uncertified goods is continuous in the FT price rf.34 Specifically, there is a continuum of identical consumers I indexed by i. Consumers infer the level of ethical quality of any differentiated good by observing whether it has been certified by the FT program. Let V be a continuous set of horizontally differentiated varieties indexed by υ. For each variety υ, a representative consumer i weights the utility from consuming the quantity ci(υ) with the subjective function λ that serves to characterize how she privately values the ethical quality of variety υ. The weight λ(rj(υ)) depends upon the wage paid to farmers in raw commodity market j for the raw materials used to produce variety υ. I assume that λ is continuously differentiable and there are diminishing marginal returns to ethical quality so that λ′ N 0, λ″ b 0 and as rj → ∞, λ′ → 0. Also, λðr ÞN0 so that consumers value products that have a minimal level of ethical quality. The preferences of a representative consumer i are given by the CES utility function 2 n Z X Ui ¼ 4 j¼1

υ∈V

31 h
 iρ  ρ λ r j ðυÞ ci ðυÞ dυ 5

ð15Þ

where, for a given rf,  r j ðυÞ ¼

r f ; if variety υ is certified : r; if variety υ is uncertified

Maximizing Eq. (15) subject to the budget constraint Z υ∈V

pðυÞci ðυÞdυ ≤ Y i

determines the optimal consumption decision ci(p(υ)), which, aggregated over all consumers, yields the aggregate consumption of variety υ cðpðυÞÞ ¼


 pðυÞ−1 λp r j ðυÞ Y P 1−σ

ð16Þ

where Y = wL is aggregate income and L is the total number of workers. Since the varieties are substitutes, the elasticity of substitu1 N1. The expenditure weight tion σ ¼ 1−ρ

Consumers enjoy a private benefit from consuming products that are produced with raw materials purchased from farmers at above-market prices. I assume that consumers are unable to perfectly observe the wage paid to farmers in a given raw commodity market. For simplicity, they attribute a minimal level of ethical quality to uncertified goods r. Once the FT program establishes a FT price rf and some firms certify their products, final goods are vertically differentiated

is a measure of the ethical quality of variety υ, relative to its price. From Eq. (16) it follows that the share of income spent on a given

30 These include providing detailed reports of relevant stock and financial records, purchase and sales invoices, wastage, recipe sheets and product labels that need to be approved by the program. 31 In Melitz (2003), firms are heterogeneous in terms of their productivity, which permits an analysis of how exposure to international trade reallocates market shares and affects aggregate productivity. More generally, however, the paper establishes a tractable model of firm heterogeneity within a monopolistic competition framework. 32 Since participation in the program is costly, the program's existence relies on an imperfectly competitive final goods market structure. For an excellent discussion of this point in the wider context of firms practicing corporate social responsibility, see Besley and Ghatak (2007), pg. 1653.

33 The existence of heterogeneity in tastes across consumers suggests that the love of variety assumption that is typically used to model monopolistic competition is a good depiction of aggregate consumer behavior. 34 Hence not only is a monopolistically competitive final goods market structure an empirically accurate description of the final goods market (Nakamura and Zerom, 2010), and permits firms to earn profits necessary to cover certification costs, it also yields a tractable analysis.

3σ−1 2

 λ r j ðυÞ 5 λp r j ðυÞ ¼ 4 pðυÞ

ð17Þ

A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

variety υ is determined by λp(rj(υ)) relative to its aggregate, since the real price index P is given by P

1−σ

¼

n Z X j¼1

υ∈V


 λp r j ðυÞ dυ:

ð18Þ

Although consumers' valuation of the ethical quality for certified goods λ(rf) is increasing in the FT price rf, as we'll see below, the price of certified goods is also increasing in rf. I assume that the value consumers place on certified goods is strong enough to ensure that the aggregate consumption of FT products is initially increasing as the FT price rf is increased from the minimum binding level r f .35 From Eq. (16), then, it is necessary for λp(rf) to first increase as rf is increased from r f . Eventually, however, once the FT price rf is sufficiently large, the expenditure weight λp(rf) begins to decrease since λ′(rf) → 0, and hence there is a FT price at which λp(rf) is maximal. At this point, the higher price of certified goods outweighs further increases in their ethical quality. Once λp(rf) is decreasing in the FT price rf, from Eq. (16) it follows that the consumption of FT products is decreasing in rf. It's possible to extend the interpretation of the model to permit λ to encompass other notions of quality such as the actual quality of the product, or its environmental quality. In this case, for a given rf, if the overall quality of certified goods increases relative to that of conventional goods, then from Eq . (16) it follows that the relative demand for certified goods will increase. This demonstrates that the FT program's efforts to improve quality and to facilitate farmers' transition to organic farming work to increase its market share and thus the total quantity of FT contracts xf available to farmers. As first shown by Dixit and Stiglitz (1977), Ui can be thought of as a composite good with aggregate price P. Hence, from Eqs. (15) and (16), consumer welfare W is given by real income36 W¼

Y : P

ð19Þ

The CES utility function represents ‘love of variety’ preferences since the same level of expenditure spread out over more varieties increases welfare. 4.2. Firms Each differentiated product is produced by a single monopolistically competitive firm that is small relative to the size of the industry. Firms package and brand the commodity and then sell to consumers in the final goods market. They incur variable costs from hiring labor in the local market and purchasing raw materials. One unit of labor, at cost w, and one unit of raw materials, at cost pm, produces one unit of output. In equilibrium, the aggregate consumption of variety υ, c(p(υ)) in Eq. (16), is equal to the output of variety υ. From Eqs. (16) and (17), each firm will perceive itself as facing a downward sloping demand curve with constant elasticity σ,37 and each firm maximizes its profit σ by charging a markup over its marginal cost equal to σ−1 . Hence the

price of a given product variety υ is pðpm ðυÞÞ ¼ wþpρm ðυÞ and, from Eq. (16), each firm's operating profit is

π ðr ðυÞÞ ¼ ½pðυÞ−ðw þ pm ðυÞÞcðpðυÞÞ ¼


 λp r j ðυÞ Y σP

1−σ

35

:

ð20Þ

This assumption ensures interior optima for variables of interest. The conditions on λ are established in Appendix A under Preliminaries (iv), ‘Quasiconcavity of λp(rf) and xf.’ 36 Note that since expected profits are equal to zero due to free entry to the industry, social welfare is equivalent to consumer welfare in Eq. (19). 37 From Eqs. (16) and (17) we have cðpðυÞÞ ¼ pðυÞ PλðrðυÞÞ Y and since a given firm is small, it treats P as given. −σ

σ−1

1−σ

177

Since final goods producers that do not participate in the program purchase the commodity in the world market for pc per unit, the price of an uncertified good is given by pðpc Þ ¼

w þ pc : ρ

ð21Þ

From consumer demand in Eq. (16) and p(pc) in Eq. (21), it follows that the aggregate consumption of uncertified goods is given by C UL ¼

ð1−α ÞρY w þ pc

ð22Þ

where α is the share of income spent on certified goods. 4.3. The Fairtrade program The total number of FT contracts xf is determined according to the demand for the FT commodity by final goods producers, which is derived from consumer demand for certified goods. The FT intermediary purchases xf units of the raw commodity from farmers at the FT price rf, and then sells the commodity to final goods producers that choose to participate in the program. Analogous to the intermediaries' costs, 1 − δ units of the commodity melt away after processing and transportation, where 0 b δ b 1. The FT intermediary acts competitively by setting the final goods producers' price equal to its marginal cost to purchase and deliver one unit of the commodity. Participating firms pay the FT inr

termediary δf per unit since, to deliver 1 unit, it must purchase 1δ units from farmers at the cost rf. It follows that the price of a certified good is rf
 wþ δ p rf ¼ ρ

ð23Þ

which is increasing in the FT price rf.38 From consumer demand in Eq. (16) and p(rf) in Eq. (23), the aggregate consumption of certified goods is given by C L ¼

αρY r

wþ δf

. Since final goods producers require one

unit of raw materials to produce one unit of output, their demand for the FT commodity is equal to the aggregate consumption of certified goods CL. Hence, accounting for the FT intermediary's processing and transportation costs, for a given rf, the total number of FT contracts is xf ¼

1 αρY C ¼ : δ L wδ þ r f

ð24Þ

4.3.1. Certification Each firm's type is drawn independently according to the common h i distribution H, which is continuous over support φ; φ . The certification cost fc(φ) (measured in units of labor) is decreasing in a firm's type so that fc′(φ) b 0, and fc(φ) → 0 as φ→φ. Since participation in the program is voluntary, firms do not incur the certification cost fc(φ) unless they choose to certify their product. A firm is indifferent to certifying its product if and only if the additional profit from undertaking certification is equal to its certification cost. Hence the indifferent firm type φ* is   defined by π r f −πðr Þ ¼ w f c ðφ Þ or, from Eq. (20),

  λP r f −λP ðr Þ Y σP

1−σ

  ¼ wf c φ :

ð25Þ

For a given rf, high type firms that draw φ N φ* have a sufficiently small certification cost and optimally choose to certify their product. 38

Note that from Eq. (7) we can express the price of uncertified goods in Eq. (21)

as pðpc Þ ¼

er

wþ ξj þΔξm , ρ

which is analogous to p(rf ) in Eq. (23).

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Low type firms that draw φ b φ* optimally choose to sell their product uncertified.39 Free entry ensures a zero expected profit net of the entry fee F (measured in units of labor) so that, from Eq. (20), Z

φ

φ

λP ðr ÞY dHðφÞ þ σ P 1−σ

Z

φ

φ

0
 1 λP r f Y @ −w f c ðφÞAdHðφÞ ¼ wF σ P 1−σ

ð26Þ

and a bounded number of firms M enters the industry. Given the indifferent firm type φ*, the number of certified goods mL = (1 − H(φ*))M and the number of uncertified goods mUL = H(φ*)M can be determined. Also, from Eq. (18), we can express

P

1−σ


 ¼ mL λp r f þ mUL λp ðr Þ
    
   ¼ 1−H φ λp r f þ H φ λp ðr Þ M:

ð27Þ

After normalizing the wage w to 1, Eqs. (25) and (26) determine the equilibrium threshold firm type φ* and the real price index P as implicit functions of the FT price rf.40 The number of firms M can then be determined from Eq. (27). Aggregating expenditure in Eq. (16) over the number of certified goods mL yields the share of income spent on mL λp ðr Þ certified goods α ¼ P1−σ f or, from Eq. (27),
  ð1−H ðφ ÞÞλp r f
 α¼ ð1−H ðφ ÞÞλp r f þ Hðφ Þλp ðr Þ

ð28Þ

which, for a given rf, depends only on the threshold firm type φ*. The following proposition demonstrates that the optimal amount of ethical quality is provided to the final goods market whenever the FT price rf is chosen to maximize the share of income spent on certified goods α. As a single policy instrument, however, it cannot simultaneously be used to best correct the inefficiency that results from the intermediaries' presence in the raw commodity market. Proposition 3. For a given world price of the raw commodity pc, (i) welfare W is maximal in the FT price rf if and only if the share of income spent on certified goods α is maximal in rf (ii) the FT price rf that maximizes the share of income spent on certified goods α is greater than the FT price rf that maximizes the number of FT contracts allocated to a given raw commodity market xfj. Proof. See Appendix A. ■ Since firms voluntarily certify in response to incentives provided by consumers, the proportion of firms that choose to certify 1 − H(φ*) is increasing in consumers' willingness to pay for certified goods. It follows from the definition of the threshold firm type φ* in Eq. (25) that the proportion of firms that choose to certify 1 − H(φ*) is maximal if and only if the expenditure weight for certified goods λp(rf) is maximal. From the definition of α in Eq. (28), the share of income spent on certified goods α is maximal if and only if the proportion of firms that choose to certify 1 − H(φ*) is maximal. This is because consumers purchase a given quantity of each product variety so that the share of income 39

It follows from Eq. (25) that a necessary condition for certified goods to exist in the market is for λP(rf) to exceed λP ðr Þ. The section Preliminaries (i), ‘The minimum binding price floor r f ,’ of Appendix A develops a non-stringent condition on r that ensures some firms will certify. 40 As shown in Appendix A, Preliminaries (ii), there is a unique solution if the entry fee F is not too large. Also, as shown in Appendix A, Preliminaries (iii), the labor market clears.

spent on certified goods α is increasing in the proportion of firms that choose to certify 1 − H(φ*). It follows that α is maximal if and only if λp(rf) is maximal. Furthermore, consumer welfare W in Eq. (19) is maximal if and only if λp(rf) is maximal. Since the ethical quality of certified goods increases relative to their price whenever λp(rf) increases, the real price index P is decreasing in λp(rf).41 Since firms certify in response to consumer preferences for ethical quality, choosing the FT price to maximize ethical quality per dollar λp(rf) is equivalent to maximizing the share of income spent on certified goods α, and consumer welfare W. While the optimal amount of ethical quality is provided to the final goods market whenever the FT price rf is chosen to maximize the share of income spent on certified goods α, the greatest benefits to farmers in a given raw commodity market j are realized whenever the number of FT contracts xfj is as large as possible. From Eq. (24), the number of FT contracts xf is increasing in the proportion of income spent on certified goods α but decreasing in their price p(rf), so that the total number of FT contracts xf is maximized at a lower FT price than α. Since the number of FT contracts allocated to raw commodity market j, xfj, is a constant proportion of the total number of FT contracts xf, xfj is maximal whenever xf is maximal. Consequently, there is a fundamental trade-off between choosing the FT price to best restore efficiency to a given raw commodity market and to maximize consumer welfare W in the final goods market. 4.3.2. The optimal Fairtrade price The following proposition establishes the Pareto optimal FT price by comparing consumer welfare W in the final goods market with aggregate producer surplus PSj in a given raw commodity market. Proposition 4. For a given world price of the raw commodity pc, if farmers' δ certification costs cb δþr x f j whenever the FT price rf is such that α is maxf p imal, then the Pareto optimal FT price r f maximizes the share of income spent on certified goods α. Proof. See Appendix A. ■ The hypothesis of Proposition 4 is not restrictive since it is equivalent δ x2f j , which is to requiring total certification costs Cfj to be less than δþr f increasing rapidly in xfj. From Proposition 3(i) we have that consumer welfare W in Eq. (19) is maximal whenever the share of income spent on certified goods α is maximal. Also, from Proposition 3(ii), when α is maximal, the number of FT contracts allocated to a given raw commodity market xfj is decreasing in the FT price rf so that, from Eq. (6), the wage of unselected farmers er j is decreasing in rf. Since rf is increasing while er j is decreasing, the premium received by selected farmers r f −er j is increasing rapidly in rf. It follows that the net transfer received by selected farmers Tf j in Eq. (11) is increasing rapidly in rf if certification costs c are not unusually large. Although baseline producer surplus is decreasing, Tf j is increasing sufficiently rapidly to ensure that aggregate producer surplus PSj is maximized at a higher FT price than the share of income spent on certified goods α.42 Hence, from Proposition 3, PSj is maximized at a higher FT price than consumer welfare W. Taking consumers, and farmers collectively into account, the Pareto optimal FT price maximizes the share of income spent on certified goods α. An increase in the FT price beyond the level that maximizes α makes farmers collectively better off however it also makes consumers worse off. Since the share of income spent on certified goods α is a measure that is easily observed in the final goods market, Proposition 4 establishes a transparent rule for how to choose the FT price rf. 41 Referring to Eq. (27), the FT price rf affects P only directly through λp(rf). The indirect effect of rf on P through M is exactly offset by the indirect effect of rf on P that works   through average ethical quality ð1−H ðφ ÞÞλp r f þ Hðφ Þλp ðr Þ. This is because the firm with type φ* is indifferent to certification and hence a small change in φ* can have no effect on welfare W. 42 Once the FT price rf is large enough to ensure that the number of FT contracts xfj is sufficiently small, Tfj begins to decrease and hence PSj begins to decrease.

A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

179

In this section we've derived the total number of FT contracts xf from consumer demand for certified goods. We've seen that consumer welfare is maximal whenever the FT price rf is chosen to maximize the share of income spent on certified goods α. Since the number of FT contracts allocated to a given commodity market xf j is maximized at a lower FT price, there is a fundamental trade-off between maximizing consumer welfare and best restoring efficiency to a given raw commodp ity market. The Pareto optimal FT price rf maximizes the share of income spent on certified goods α because aggregate producer surplus in a given raw commodity market is maximized at a higher FT price than α. 5. Program efficiency To assess the overall efficiency of the FT program as a means to transfer income to farmers, I compare the FT program with a direct transfer to farmers equal to the premium consumers would have paid for certified goods under the program. I assume that consumers are indifferent to the means by which income is transferred to farmers. Specifically, they derive the same utility from paying a premium for a certified product, so that income is transferred to farmers through the program, and buying a conventional product and donating the same premium directly to farmers. In Section 3 we've seen that the FT program has a procompetitive effect on a given raw commodity market, which delivers benefits to farmers. Unlike a direct transfer, however, since the FT program affects final goods producers' marginal costs, final goods producers extract a markup on the transfer to farmers. An additional loss results because of the FT commodity's greater transportation and processing costs, which final goods producers pass on to consumers at a markup. Farmers must also pay certification costs under the program. From p(pc) in Eq. (21), p(rf) in Eq. (23) and CL in Eq. (24), consumers pay an excess of  


 1 1−δ 1−ξ c δT f þ rf − ξpc δx f pðr f Þ−pðpc Þ C L ¼ ρ δ ξ

ð29Þ

for certified goods, where the aggregate transfer due to the fairness premium Tfc = ∑nj = 1Tfcj. From Eq. (29) it follows that the premium consumers pay for certified goods can be decomposed into a fairness premium on the quantity they ultimately purchase43 and the excess transportation and processing costs for the FT commodity, both gross of the markup charged by final goods producers. The transportation and processing costs for the FT commodity are given by (1 − δ)rfxf since the FT intermediary purchases xf units valued at the FT price rf per unit, and the fraction 1 − δ dissipates.44 Also, the transportation and processing costs to deliver δxf units of the conventional commodity are (1 − ξ)pcδxf since conventional intermediaries must purchase 45

δx f ξ

units valued at ξpc per unit, and the fraction 1 − ξ dissipates. For a given FT price rf, the program is a more efficient way to transfer income to farmers than a direct transfer equal to the premium consumers would have paid for certified goods under the program if and only if ∑nj = 1PSj N ∑nj = 1PSjo + (p(rf) − p(pc))CL. Equivalently, from aggregate producer surplus PSj in Eq. (14), the excess payments for certified goods in Eq. (29), and applying the assumption of symmetry,46 we have      b
2 δ 1 1−δ 1−ξ m 2 c ze j −xe jo NC f j þ −1 T f j þ rf− ξpc δx f j : ð30Þ Tfj þ 2 ρ ρ δ ξ

Fig. 5. The benefits and the costs of the program relative to the direct transfer.

From Eq. (30) it follows that the program is a more efficient way to transfer income to farmers if and only if the benefits received by farmers due to the improved efficiency of a given raw commodity market under the program: the transfer due to bypassing the intermediaries Tfjm in Eq. (13) and the increase in baseline producer surplus under the program, which are depicted in Fig. 4b, exceed the total certification costs paid by farmers, and the excess payments by consumers for certified goods that are not received by farmers in a given raw commodity market: the final goods producers' markup on the fairness premium, and the excess transportation and processing costs for the FT commodity gross of the markup charged by final goods producers. Fig. 5 depicts the benefits of the program relative to the direct transfer B, given by the left hand side of Eq. (30), and the costs of the program relative to the direct transfer C, given by the right hand side of Eq. (30), as functions of xfj, for a given FT price rf. The benefits B are increasing in xfj at a diminishing rate and reach a maximum when xfj = x⁎j .47 This follows from Proposition 2, since the efficiency of the raw commodity market is increasing in the number of FT contracts xfj and is maximal whenever the FT program fully displaces intermediaries. If xfj exceeds x⁎j , then the benefits B are decreasing because output in the raw commodity market is getting further from the efficient level. Also, for a given FT price rf, the costs of the program C are increasing linearly in xfj.48 The greater is rf relative to ξpc, the greater is the slope of C since both the fairness premium Tcfj and the excess transportation and processing costs for the FT commodity are greater for a given xf j. As shown in Fig. 5, since C is linear while B is concave, for a given x′ fj ϵ(0, x⁎j ) there is a unique critical value of the fairness premium (r Cf − ξp c)′ that corresponds to the slope of C′ such that B N C if and only if rf − ξpc b (rCf − ξpc)′. Also, referring to Fig. 5, if the slope of C is less than the slope of CL, then B N C for all xfjϵ(0, x⁎j ) and if the slope of C exceeds the slope of CU, then B N C for all xfjϵ(0, x⁎j ). Hence there is a lower bound for the fairness premium r Cf −ξpc such that the program is the more efficient way to transfer income if r f −ξpc b r Cf −ξpc and there is an upper bound for the fairness premium r Cf −ξpc

43

From Eqs. (24) and (12) we have δTfc = (rf − ξpc)CL. The value of one unit of the Fairtrade commodity is given by rf since the fraction δ is r sold to final goods producers for the price δf . 45 The value of one unit of the conventional commodity is given by ξpc since the fraction ξ is sold to final goods producers in the world market for the price pc. 46 Recall that x f j ¼ 1n x f : 44

47

B¼ 48

From the definition of Tfjm in Eq. (13), and ez j in Eq. (5), and xe jo in Eq. (4), we can express
 2N þ1 ðξpc −aÞx f j −2b x2f j . ðN þ1Þ h i δ−ρξ From the definition of Tfjc in Eq. (12), we can express C ¼ 1−ρ ρ r f − ρξ ξpc þ c x f j : j

2

j

180

A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

whether small or large programs are more efficient than the direct transfer. It's interesting to note that if farmers' certification costs were comprised of a fixed component, then all program sizes generated by Λ

Fig. 6. The critical value of the fairness premium rCf − ξpc and the number of FT contracts xfj.

such that the direct transfer is the more efficient way to transfer income if r f −ξpc N r Cf −ξpc independent of the size of the program xfj. The following proposition defines these boundaries on the fairness premium and, utilizing the relationship between xf and rf in Eq. (24), demonstrates that there is a unique threshold FT price r′f such that Eq. (30) is satisfied for all rf b r′f.
 2N j þ1 ρ δ−ξ ρ ξpc −c and Λ j ¼ ðξpc −aÞ. Proposition 5. Define ε ¼ 1−ρ 2 ρξ ðN j þ1Þ 1−ρ If ε + Λj N 0, then there exists a unique threshold value of the fairness
 Λ premium r 0f −ξpc ∈ ε þ 2j ; ε þ Λ j such that the program is a more efficient way to transfer income to farmers than a direct transfer equal to (p(rf) − p(pc))CL if and only if rf − ξpc b r′f − ξpc. Proof. See Appendix A. ■ Fig. 6 depicts the number of FT contracts xfj as a function of fairness premium rf − ξpc, which is the FT price rf shifted down by ξpc units. It also depicts the critical value of the fairness premium rCf − ξpc as a function of the size of the program xfj. It follows from Fig. 5 that rCf − ξpc is decreasing in xfj because the benefits of the program B are concave in xfj while the costs C are linear in xfj. As shown in Appendix A, the upper bound for the fairness premium r Cf −ξpc corresponds to ε + Λj and the lower bound for the fairness premium r Cf −ξpc corresponds Λ

to ε þ 2j . From Fig. 6 it follows that there is unique threshold fairness
 Λ premium r0f −ξpc ∈ ε þ 2j ; ε þ Λ j such that program is a more efficient way to transfer income to farmers than the direct transfer if and only if rf − ξpc b r ′f − ξpc. For a given size of the program xfj, if the FT price rf required to generate xfj is too large, then the costs of the program C exceed the benefits of the program B relative to the direct transfer. Since the critical value of the Fairness premium rCf − ξpc is decreasing in xfj, it may seem that small programs are more likely to be more efficient than the direct transfer. While small programs that are generated by small FT prices rf b r′f are more efficient than the direct transfer, small programs that are generated by large FT prices that exceed r′f are less efficient than the direct transfer because their costs are too large relative to their benefits. Since xf j is single-peaked in rf, it's not possible to infer a threshold program size or to make general statements about

small FT prices r f b ξpc þ ε þ 2j would no longer be more efficient than the direct transfer. Referring to C′ in Fig. 5, if there is a fixed component to farmer certification costs, then C′ would have the same slope but a strictly positive intercept. Hence, whenever xfj is close to zero, the benefits of the program B are close to zero while the costs of the program C are strictly positive. In this case, the program's size xfj must be large enough if its benefits are to cover its fixed costs. Analogous to Proposition 5, there is a unique threshold value for the fairness premium r′f − ξpc and small programs that are generated by large FT prices that exceed r′f continue to be less efficient than the direct transfer. If rf − ξpc b r′f − ξpc, however, then only sufficiently large programs can be more efficient than the direct transfer. Although Proposition 5 must be qualified if farmers' certification costs are comprised of a fixed component, if the size of the program xf j is not too small, then the impact on Proposition 5 is of little consequence. If the model's parameters are such that ε and Λj are large, then the threshold fairness premium that maintains the efficiency of the program over the direct transfer is large since the program's benefits B are then large relative to its costs C. The benefits of the program B increase whenever the number of intermediaries Nj decreases. Since a smaller number of intermediaries Nj possess greater market power, the program yields greater benefits from improving the efficiency of the raw commodity market. The costs of the program C decrease whenever the dissipation rate for the FT commodity 1 − δ decreases relative to that of the conventional commodity 1 − ξ (or, equivalently, δ increases relative to ξ) since the excess transportation and processing costs for the FT commodity decrease. Costs c also decrease whenever the final goods producers' markup rate 1−ρ ρ decreases and the farmers' certification costs c decrease. The magnitude of farmers' certification costs c limit the extent of the fairness premium that can be efficiently transferred to farmers through the program, since ε is decreasing in c. If c is large enough to yield ε þ Λ j ≤r f −ξpc , then the fairness premium at the minimum binding FT price exceeds the upper bound for the fairness premium and hence the direct transfer is a more efficient way to transfer income to farmers for all r f N r f . Since r f −ξpc b 0,49 it's sufficient to require ε + Λj N 0 to ensure the existence of a threshold fairness premium r 0f −ξpc N r f − ξpc . Final goods producers' margins are the same on both certified and uncertified goods, since they charge a constant markup over their marginal costs ρ1. If the program were to require a lower margin on certified goods, then the costs of the program C would decrease relative to its benefits B, and its efficiency would improve for a given xfj. Since the profits of firms that certify would decrease, however, it follows from Eq. (25) that the proportion of firms that certify 1 − H(φ*) would decrease and hence, from Eqs. (24) and (28), the number of FT contracts xfj would decrease. In choosing the margin for certified goods, then, an improvement in the program's efficiency must be traded off with a smaller program that transfers less to producers.50 Proposition 5 can assist policy makers in determining whether the FT program should be utilized to transfer income to farmers. Given an estimate of the model's parameters, and the relationship

49 The section Preliminaries (i), ‘The minimum binding FT price r f ,’ of Appendix A shows that r f b ξpc : 50 Defining the markup for certified goods by ρ1 , it can be shown that as ρf → 1, so f that certified goods are priced competitively in the limit, the program is more efficient than the direct transfer for all xfj if c is not too large. Since π(rf) = 0, however, no firms will certify and xfj = 0.

A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

between xfj and r f , it is possible to estimate the threshold FT price r f ′. 51 Recall from Proposition 4 that the Pareto optimal FT price p p rf maximizes the share of income spent on certified goods α. If rf exp ceeds r′, f then a direct transfer of (p(rf ) − p(pc))CL results in a greater p increase in aggregate producer surplus than the program.52 If rf is less than r′, however, then the program is a more efficient way to transfer f income to farmers. If barriers to entry Fm were to hypothetically fall to zero and the number of intermediaries Nj were to become arbitrarily large, then the benefits of the program that are due to improving the efficiency of the raw commodity market B would approach zero. Since there would be perfect competition among intermediaries, the raw commodity market would be efficient and no further improvements could be made. As we've seen in Section 3.1, the effect of the FT program on each raw commodity market would be equivalent to a transfer to farmers of Tfjc net of certification costs. If there were no certification costs, no transportation and processing costs, and the final goods producers' markup rate were equal to zero, from Eq. (29) it follows that consumers would pay an excess of (p(rf) − p(pc))CL = Tfc for certified goods and, in aggregate, Tfc would be transferred to farmers.53 Analogous to Besley and Ghatak (2007), if there were perfect competition along the entire commodity supply chain, the program would be equivalent to a direct transfer to farmers. Recall from Section 4, however, that imperfect competition in the final goods market is necessary to ensure that some firms will earn a profit sufficient to cover their certification cost and to provide an incentive for firms to voluntarily certify their products. It follows that if Nj were arbitrarily large, then consumers would pay more than Tfjc under the program to transfer Tfjc to farmers in a given raw commodity market. Since Λj → 0, from Proposition 5 it follows that the threshold fairness premium would be defined by r ′f − ξpc = ε. Hence if ε ≤ 0, the transfer would be more efficient than the program for all binding FT prices.54,55 Analyzing this extreme case in which there is perfect competition among intermediaries serves to demonstrate that the superiority of the program relies on its ability to generate benefits by improving the efficiency of the raw commodity market. More generally, however, for a finite number of intermediaries Nj and a given rf, the program is a more efficient way to transfer income to farmers than the direct transfer if the market power of final goods producers is sufficiently small relative to the market power of intermediaries. Whenever market power is concentrated at the beginning of the supply chain, the program yields benefits from improving the efficiency of the raw commodity market, while the markup extracted by final goods producers is small. 5.1. Example: the global coffee crisis Given actual FT prices and historical data, the following example evaluates whether the FT program was more efficient than a direct transfer during the global coffee crisis that took place from 2000 to 2005, in which coffee prices reached historic lows.56 The example demonstrates that during this time period, a direct transfer would have been a more efficient way to transfer income to farmers than the FT program. I determine the values of ε and Λ using a simple back-of-the-envelope calculation and estimates taken from other studies. An estimate of
 As shown in Appendix A, rf′ is implicitly defined by r 0f −ξpc ¼ ε þ Λ j −2xΛ x f j r 0f . It follows from Proposition 5 that since rf′ b ε + Λj, a sufficient condition for the transfer to be more efficient than the program at the Pareto optimal FT price is ε + Λj b argmax α, which does not require an estimate of rf′. 53 From Eq. (29), since ρ = δ = ξ = 1, (p(rf) − p(pc))CL = Tcf . 54 From Eq. (7) it follows that as Nj becomes arbitrarily large, the intermediaries' spread Δm approaches zero and hence er j approaches ξpc. 55 From the definition of ε in Proposition 5, if the dissipation rate for the FT commodity 1 − δ is at least as large as for the conventional commodity 1 − ξ, it follows that ε ≤ 0. This is a likely case since, as we'll see in Section 5.1, FT importers pay an additional license fee. 56 This coffee crisis stemmed from the increased supply of Vietnamese coffee (robusta) onto world markets. See Talbot (2004), chapter 5 for an in-depth discussion of coffee crises. 51 52

j  j

181

the final goods producer's markup 1ρ is provided by Nakamura and Zerom (2010), which evaluates incomplete pass-through in the coffee industry. The authors estimate the Dixit–Stiglitz model using coffee retail and sales data from AC Nielsen for the period 2000 to 2004 and find the elasticity of substitution σ = 2.92, which implies that ρ = .657.57 Daviron and Ponte (2006) analyzes coffee value chains and, from the authors' own fieldwork data, provide rare information on the net margins that various actors make along a given chain as a proportion of the final retail price. For the case of the Uganda–Italy value chain for Robusta coffee (2001/2002), the total transportation costs are .16 USD for a pound of coffee,58,59 and the selling price to the supermarket chain is 1.81 USD per pound. Since processing and transportation costs for one unit of the raw commodity are given by (1 − ξ)pc, the data provided by Daviron and Ponte (2006) imply that ξ=.912. Similarly, using data the authors provide for the Tanzania–Italy value chain for 100% Arabica coffee (1999/2000), ξ=.931.60 Fair trade importers pay an additional license fee of .1% to .7% of the sales value (van Hilten, 2011), which implies that, on average, we can estimate that δ − ξ =−.004. Since producer certification fees were not introduced until 2004, c = 0. If we assume that a = 0, and, according to Footnote 8, Nj = 8, it follows that ε = − .012pc, ΛU = .367pc for Robusta coffee and ΛT = .374pc for Arabica coffee, where ξ is given by the Uganda and Tanzania estimates, respectively. From these estimates and Proposition 5 it follows that for Arabica coffee, during the early 2000's, the threshold value of the FT price r′f ∈ (1.12pc, 1.29pc). If the FT price was set at a lower premium than 12% (greater premium than 29%) over the world price of Arabica coffee, then the program was a more (less) efficient way to transfer income to farmers than the direct transfer. Given the FT price of 1.26 USD per pound of Arabica coffee that was in existence until June 2007, it follows that the direct transfer would have been a more efficient way to transfer income if the world price of Arabica coffee was less than .98 USD per pound. According to the ICO database, annual averages of the world price for Arabica coffee (averaged over Colombian milds, other milds, and Brazilian naturals) are less than .98 USD from 2000 to 2004.61,62 Similarly, for Robusta coffee, r ′f ∈ (1.08pc, 1.27pc). Given the FT price of 1.06 USD per pound of Robusta coffee that was in existence until June 2007, it follows that the direct transfer would have been a more efficient way to transfer income if the world price of Robusta coffee was less than .83 USD per pound. According to the ICO database, annual averages of the world price for Robusta coffee are less than .83 USD from 2000 to 2006.63 The evidence suggests that the FT prices for Arabica and Robusta coffee were set too high relative to the world price during this time period that was characterized by extremely low prices, and that the FT program is not the ideal mechanism to transfer income to farmers during crises. A FT price that covers farmers' production and living expenses far exceeds the efficient wage for the raw commodity when the world price is extremely low. In this section we've compared the FT program with a direct transfer to farmers equal to the premium consumers would have paid for certified goods under the program. We've seen that there is a unique 57

See Nakamura and Zerom (2010), page 1222, footnote 42. See Table 6.1. Uganda–Italy value chain for Robusta (home consumption, sale at supermarkets, 100% Robusta blend), 2001/2. The average exchange rate utilized: US$ 1 = ITL 1.743 (average from October 2001–September 2002). 59 The cost to process and transport the coffee from the farm gate to Kampala is .07 USD (it gets hulled, transported, dried, sorted and prepared for export), the cost of transporting from Kampala to Mombasa is .05 USD (clearing, forwarding, insurance and shipping charges), and the cost of transporting from Mombasa to the import harbor is .04 USD. 60 See Table 6.2 Tanzania–Italy value chain for Arabica (home consumption, sale at supermarkets, weighted prices depending on blend composition), 1999/2000. The average exchange rate utilized: US$ 1 = ITL 2.010 (average from October 1999–September 2000). 61 See http://www.ico.org/historical/2000-09/PDF/HIST-PRICES.pdf. 62 The annual averages differ from .98 USD by .08 USD in 2000 to .41 USD in 2002. In 2005 and 2006, the average price of Arabica coffee falls between the bounds of .98 USD and 1.13 USD. 63 The annual averages differ from .83 USD by .15 USD in 2006 to .55 USD in 2001. 58

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A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

threshold value of the fairness premium r′f − ξpc such that the program is a more efficient way to transfer income to farmers if and only if rf − ξpc b r′f − ξpc. For FT prices in excess of r′, f the costs of the program exceed its benefits, relative to the direct transfer. If there were perfect competition among intermediaries, since the program would not generate any benefits from improving the efficiency of the raw commodity market, the direct transfer would be a more efficient way to transfer income to farmers for all binding FT prices. 6. Conclusion This paper develops a theoretical model of the commodity supply chain to analyze the FT certification program as a voluntary mechanism to transfer income to farmers in developing countries. This extensive approach facilitates a comparison of the returns to farmers in a given raw commodity market with the welfare of consumers in the final goods market, and permits the Pareto optimal FT price to be determined. I assume that there are a small number of oligopsonistic intermediaries between a given raw commodity market and the world market. If consumers care about the ethical quality of goods, then a number of FT contracts that pay a premium over the market wage can be offered to farmers. Despite that unselected farmers do not participate in the program, their wage is greater under the program than in its absence. This is because the program decreases the intermediaries' market power, and hence the wage offered to farmers by the intermediaries approaches the efficient level. There is a fundamental trade-off, however, between choosing the FT price to best improve the efficiency of the raw commodity market (and hence to maximize the wage of unselected farmers), and to maximize the welfare of consumers. The model shows that the Pareto optimal FT price maximizes consumer welfare or, equivalently, the share of income spent on certified goods. This is because aggregate producer surplus is maximized at a higher FT price than the share of income spent on certified goods, since the transfer to selected farmers is increasing rapidly in the FT price. This presents a clear policy prescription since the share of income spent on certified goods is easily observed in the final goods market. The framework also permits a comparison of the FT program with a direct transfer to farmers equal to the premium that consumers would have paid for certified goods under the program. The FT program is a more efficient way to transfer income to farmers if and only if the FT price is not set too high above the efficient wage. If so, the markup extracted by final goods producers and excess transportation and processing costs for the FT commodity, in addition to farmers' certification costs, exceed the program's benefits that are due to improving the efficiency of the raw commodity market. Despite that consumers may be willing to support such a large FT price, the direct transfer results in a greater increase in aggregate producer surplus since it avoids the costs that are intrinsic to the program. If there were perfect competition among intermediaries, we've seen that the FT program would preserve the efficiency of the raw commodity market and would serve only to transfer income to farmers. Since consumers must pay a markup on the amount transferred to farmers through the program while the program would not provide any benefits from improving the efficiency of the raw commodity market, the direct transfer would be a more efficient means to transfer income to farmers than the program for all binding FT prices. The model demonstrates the importance of understanding how consumers trade off a product's ethical quality with its price, which is revealed by consumer demand for certified goods. Given this relationship and estimates of the model's parameters, we've seen that it's possible to infer the Pareto optimal FT price and an upper bound on the FT price that ensures the program's efficiency over a direct transfer. While historically, for a given commodity, there has been little variation in FT prices, powerful estimates could be obtained by data generated from experiments or consumer surveys. Estimates of the model's parameters could be obtained from current retail and sales data, world

market prices, supply elasticities, and information about transportation costs and the concentration among intermediaries. An empirical analysis of the model's propositions awaits future research. Acknowledgments I am grateful to Sam Bucovetsky, Gene Grossman, Brishti Guha, Anthony Heyes, Andrey Stoyanov, Timothy Van Zandt, and numerous conference and seminar participants for their helpful comments or suggestions. I would also like to thank a coeditor of this journal, Nathan Nunn, and two anonymous referees for their valuable suggestions. Appendix A Preliminaries The following argument demonstrates that after normalizing w = 1, the final goods market in Eqs. (25) and (26) can be described by the following system of equations:
 λp r f −λp ðr Þ L   ¼ fc φ σM Q

ðA1Þ

L −I ¼ F σM

ðA2Þ

where      
 Q ¼ H φ λp ðr Þ þ 1−H φ λp r f Z I¼

φ

φ

f c ðφÞdHðφÞ

ðA3Þ ðA4Þ


 δρλ r σ−1 ð Þ and λp ðr Þ ¼ and, from Eqs. (17), (21), and (23), λp r f ¼ δþr f f

σ −1 ρλðr Þ . We have that Eq. (A1) follows from Eq. (25) since, from 1þp c

Eq. (18), P

1−σ


 ¼ mL λp r f þ mUL λp ðr Þ ¼ QM:

ðA5Þ

φ λp ðr ÞL Also, Eq. (A2) is derived from Eq. (26) as follows. ∫ φ dHðφÞþ σ P 1−σ         λp r f L Hðφ Þλp ðr Þ þ ð1−Hðφ ÞÞλp r f φ ∫ φ −f c ðφÞ dHðφÞ ¼ F⇔ L−I ¼ σ QM σ P 1−σ

F⇔ σLM −I ¼ F: (i) The minimum binding FT price r f . n o Nj If r b min δpc ; N j þ1 ξpc , then there exists a unique r f such that   rbr f bξpc andr f ≥ er j r f for allr f ≥ r f . From Eq. (6), the program is binding     Nj ξpc þ N j1þ1 a þ bx f j or equivalently if and only if r f ≥re j r f ¼ N j þ1 xf j ≤

 Nj þ 1
ξp −a : r f −a −N j c b b

ðA6Þ

Define the right hand side of Eq. (A6) as RHS. We have that RHS is N þ1

linear in rf with positive slope jb . As shown in the proof of Proposition 3(ii) below, the left hand side of Eq. (A6), xfj, is quasiconcave in rf. The following argument shows that if r f ¼ r, xfj N 0 if and only if

A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

  r b δpc. From Eqs. (17), (21), and (23) it follows that if r f ¼ r, λp r f N     λp ðr Þ ⇔ p r f b pðpc Þ ⇔ r b δpc. From Eq. (25), λp r f Nλp ðr Þ ⇔ 1− H ðφ Þ N 0 and, from Eqs. (28) and (24), 1 − H(φ*) N 0 ⇔ α N 0 ⇔ xfj N 0. N

j ξpc . Consequently, at r f ¼ r, xfj N 0 Second, at r f ¼ r RHS b 0 if r b N j þ1 n o Nj and RHS b 0 if r b min δpc ; N j þ1 ξpc . It follows that there exists   a unique r f N r such that r f ≥ er j r f if and only if r f ≥ r f . Further, since

xfj ∈ (0, x⁎j ), where xj ¼ ξpcb−a , it follows from Eq. (A6) that r f ∈
 Nj 64 1 Hence the program is binding for some FT N j þ1 ξpc þ N j þ1 a; ξpc . prices rf b ξpc and all FT prices rf ≥ ξpc. As Nj → ∞, r f ¼ ξpc and all binding FT prices rf ≥ ξpc.

substituting into Eq. (A1) yields Ψ(φ*) = F, where

Z φ       λ ðr Þ
p þ f c φ 1−H φ − f c ðφÞdHðφÞ: φ λp r f −λp ðr Þ


 As φ →φ; Ψ→ f c φ λ

Hence λp(rf) is initially increasing if


 φ −∫ φφ f c ðφÞdHðφÞ , which, þ f c p ðr f Þ−λp ðr Þ
 since fc′(φ) b 0, is positive because f c φ N ∫ φφ f c ðφÞdHðφÞ. To ensure

 that Ψ φ NF, it's sufficient to require f c φ −∫ φφ f c ðφÞdHðφÞ N F. Also,

λp ðr Þ 0 ∂Ψ   Ψ is decreasing in φ* since ∂φ ð Þ b0. Fiþ 1−H φ  ¼ f c ðφ Þ λp ðr f Þ−λp ðr Þ  nally, as φ →φ, Ψ → 0 since fc(φ*) → 0. It follows that an equilibrium
 exists if F is not too large. We have that Ψ φ NF and ΨðφÞ ¼ 0 b F . λp ðr Þ

Uniqueness follows because fc′(φ*) b 0.

σ

P 1−σ

þ mUL

σ −1 λp ðr ÞL
φ þ M∫ φ f c ðφÞdHðφÞ þ M F: σ P 1−σ φ

which, using Eq. (A4), is equivalent to the free entry condition Eq. (A2). (iv) Quasiconcavity of λp(rf) and xf.

 λ rf (a) If λ r f N δþr f , then λp(rf) is quasiconcave in rf. Differentiating 0

dλp ðr f Þ dr f


 where Φ r f N 0 and is defined in Eq. (A22) below. We'll see in the proof of Proposition 3(ii) that Eq. (A9) ensures that λp(rf) is initially increasing sufficiently rapidly to permit xf to increase as rf is increased from r f . Comparing Eq. (A9) with part (a) above, Eq. (A9) implies that λp(rf) is quasiconcave. Comparative statics Differentiating the system of Eqs. (A1), (A2), (A3) and (A4) with respect to rf yields:66
 λ0p r f f 0 ðφ Þφ c d
 φ −Q M¼ c f c ðφ Þ λp r f −λp ðr Þ ^ M¼ −

ðA10Þ

I ^ I IþF 0



H ðφ Þφ

ðA11Þ 



  λp r f −λp ðr Þ Q

c

φ þ


  0 ð1−Hðφ ÞÞλp r f Q

f ðφ Þhðφ Þφ c ^ φ : I ¼− c I

ðA12Þ

ðA13Þ

Also, differentiating the Eqs. (28), (24), (4), (5), (6) and (8) with respect to rf yields:

Nj dxe j x ^ ¼− x dr f Nj þ 1 f j f dze j 1 x ^ ¼ x Nj þ 1 f j f dr f

ðA14Þ

dre j 1 bx ^ ¼ x dr f N j þ 1 f j f

ðA15Þ

N 0 if and only if



 λ rf : λ rf N δ þ rf 0

ðA8Þ

  λðr Þ λðr Þ Differentiating RHS, we have that drd δþr N0⇔λ0 r f N δþr . The hat notation indicates the percentage change in a given variable in response to a marginal increase in rf so that, for example, ^x ¼ drdx 1x. 65 66

64

ðA9Þ

ðA7Þ

Using Eq. (A5) we can express Eq. (A7) as σLM −∫ φ f c ðφÞdHðφÞ ¼ F,

Eq. (17) we have

. Define the left

Eq. (A17) and Eq. (A21) below, the number of FT contracts xf is quasiconcave in rf if

^ Q¼ −

From Eq. (16), the total revenue earned by a final goods producer is λ ðr ðυÞÞL pðυÞcðpðυÞÞ ¼ pP 1−σ and, from Eq. (20), workers earn the share 1− σ1 of total revenue. Hence the labor market clears if

L ¼ mL

1 δþr f

hand side of Eq. (A8) as LHS and the right hand side as RHS. We have LHS N 0 since λ′(rf) N 0, and LHS is decreasing in rf toward 0 since λ″(rf) b 0 and λ′(rf) → 0 as rf → ∞. Also, RHS N 0 and is increasing so

 λ rf 0 65 long as LHS N RHS. It follows that if λ r f N δþr f , then there exists a   unique r 0f ¼ arg maxr f λp r f and λp(rf) is quasiconcave in rf. (b) From

(iii) Labor market clearing.


 σ −1 λp r f L


 N

λ rf

2 3

 λ rf 1 þ 15 λ r f N4
 δ þ rf Φ r f ðσ−1Þ

A unique equilibrium exists in the final goods market if
 F b f c φ −∫ φφ f c ðφÞdHðφÞ . Solving Eq. (A2) for σLM and then






λ0 r f

0

(ii) Equilibrium in the final goods market.

    Ψ φ ¼ fc φ

183

Recall that if r f ¼ r f Eq. (A6) holds with equality.

f

f

f

f

f

f

184

A. Podhorsky / Journal of Development Economics 116 (2015) 169–185

dπem j 2b x^ ¼− x Nj þ 1 f j f dr f dx f 1 ¼ xf ^ α− δ þ rf dr f

ðA16Þ

! ðA17Þ


 0 0   λp r f H ð φ Þφ ^:  c þ
 −Q ^ φ α¼− 1−H ðφ Þ λ r p

ðA18Þ

f

Proof of Proposition 1. (i) From Eq. (6) it follows that er j is increasing x j is in xfj. Also, from Eqs. (4) and (8), πem j is decreasing in xfj since e r j ≥re jo and πem j ≤πem jo . decreasing in xfj. It directly follows that e e e dr dπ (ii) From Eqs. (A15) and (A16) it follows that x^f ¼ 0⇔ dr j ¼ 0⇔ drm j f

f

Preliminary

(iv)

above.

1 ^ ¼ δþr xbf ¼ 0⇔α N 0, f

Since

and,

from the proof of Proposition 1, α is quasiconcave in r f , it follows that arg maxr f x f b arg maxr f α. Proof of Proposition 4. The following argument demonstrates that δ x f j at r f ¼ arg maxr f α , then arg maxr f αb arg maxr f PS j . if c b δþr f Using the definition of rej in Eq. (3), and then differentiating
   dze x f j þ r f −a−bzej dxdr − Eq. (11) with respect to rf yields dTdr ¼ 1−bdr
 dx dze c ¼ x f j þ r f −a−bxej −NN þ2 þ1bx f j dr − c, where dr is given in Eq. (A14) fj

j

f

f

fj f

j

fj

j

j

f

f

ej

dz ¼ bzej dr and zej ¼ xej þ x f j. It follows that differentiating Eq. (14) yields dPS dr

 ^ − δþr1 − c , since, from þdTdr ¼ x f j þ r f −a − NNþ1 bxej −bx f j x f j α j

f

fj

f

j

j

f

f

^ − δþr1 . It follows that, when α ^ ¼ 0; dPS Eq. (A17), xc N 0 if c b δþrδ x f j . fj ¼ α dr j

f

f

f

d from Eqs. (A11) ^ and then QM, Proof of Proposition 3. (i) Solving for M c and hence from Eq. (A12) and (A13), we have ^ M ¼ Iþ1 F f c ðφ Þhðφ Þφ φ it follows that

Proof of Proposition 5. Define the left hand side of Eq. (30) with B, and the right hand side with C. From ez j in Eq. (5), er j in Eq. (6), and Tfjm in Eq. (13) and since xe jo is given by Eq. (4) and xfj = 0, we can express
 that B ¼ 2N þ1 ðξpc −aÞx f j −2b x2f j . Also, from the definition of Tfjc in ðN þ1Þ h i δ−ρξ Eq. (12), we can express C ¼ 1−ρ ρ r f − ρξ ξρc þ c x f j . Hence B ≥ C if


 rf d Q M¼α
 λp r f

r f −ξpc ≤ε þ Λ j −

¼ 0. Hence arg maxr f x f ¼ arg maxr f e r j ¼ arg minr f πem j . Proof of Proposition 2. Provided in the text of the paper.

λ0p

ðA19Þ

where the fact −

H0 ðφ Þφ ðλp ðr f Þ−λp ðr ÞÞ Q

   þ Iþ1 F f c ðφ Þhðφ Þφ ¼ 0 , which

follows from Eqs. (A1) and (A2), is utilized. From Eq. (A19) it follows d N 0 if and only if λ p ′(r f ) N 0 and arg max QM ¼ arg max that QM rf rf
 λp r f . From Eq. (A5), we can express P1 − σ = QM. It follows from
 Eq. (A19) that arg maxr f W ¼ arg maxr f QM ¼ arg maxr f λp r f . From Eqs. (A10) and (A19) it follows that
 λ0p r f c ¼ Ψ
 φ λp r f where Ψ ¼

j

2

j

and only if Λj x 2xj f j

ðA23Þ

h i ρ δ−ξ ρ 2N þ1 where ε ¼ 1−ρ ξpc −c and Λ j ¼ 1−ρ ðξpc −aÞ. When Eq. (A23) ρξ N þ1 j

ð

j

Þ2

holds with equality, it defines the critical value for the fairness premium rfc − ξpc as a function of xf j. From Eq. (A23) and as depicted in Fig. 5, it is Λ

decreasing linearly in xf j, and rfc − ξpc ranges from ε + Λj to ε þ 2j as xfj  increases from 0 to x j ¼ ξp b−a. Also depicted in Fig. 5 is xf j, which from the Preliminaries (iv), is quasi-concave in rf and, as rf → ∞, xf j → 0. From Preliminaries (i), we have that r f b ξpc . It follows that if r f −ξpc b ε þ Λ j ,
 then there exists an r′f such that r 0f − ξpc  ε þ Λ2 ; ε þ Λ j and B ≥ C if c

j

ðA20Þ

 f c ðφ Þ ð1−α Þλp ðr f Þþαλp ðr Þ f 0c ðφ Þφ λp ðr f Þ−λp ðr Þ

and only if rf ≤ r′.f The following argument demonstrates that r Cf −ξpc ¼ ε þ Λ j and r Cf −ξpc

b 0 since fc′(φ*) b 0. Hence, from

j

equal to the slope of B evaluated at x fj = 0. Differentiating B with   respect to x fj yields 2N þ1 ðξpc −aÞ−bx f j x ¼0 ¼ 2N þ1 ðξpc −aÞ; and j

Eqs. (A12), (A18) and (A20), we have
 λ0p r f ^ ¼Φ
 α λp r f

¼ ε þ Λ2 . Referring to Fig. 5, if C = C U, then the slope of C is j

2

ðN j þ1Þ

fj

1−ρ ρ

the slope of C is given by ðA21Þ

cause

1−ρ ρ

r f −δ−ρξ ξρc þ c ¼ ρξ

2

ðN j þ1Þ

r f −δ−ρξ ξρc þ c. The result follows beρξ

2N j þ1

ðN j þ1Þ

2

ðξpc −aÞ if and only if r f − ξp c =

ε + Λj. Similarly, if C = CL, then the slope of C is equal to the slope of the secant line through the origin and B evaluated at xfj = x⁎j or


where


 H 0 ðφ Þ λp ðr Þ f c ðφ Þ ð1−α Þλp r f þ αλp ðr Þ
 Φ¼− þ ð1−α Þ N 0: ð1−H ðφ ÞÞ Q f 0c ðφ Þ λp r f −λp ðr Þ ðA22Þ λ0 r ^ N 0⇔ p ð f Þ N 0 and arg maxr f α ¼ It follows from Eq. (A21) that α λp ðr f Þ   arg maxr f λp r f . Hence arg maxr f W ¼ arg maxr f α.

(ii) We have that xf is quasiconcave in rf. From Eqs. (A17) and (A21), λ0p ðr f Þ 1 1 δþr f ⇔Φ λp ðr f Þ N δþr f . Hence, to ensure that x f is increasing when r f ¼ r f , using the definition of λ p (r f ) in Eqs. (17) and
 2 3

equivalently
 B xj xj

B xj xj

. We have

2N j þ 1 1 ¼
2 ðξpc −aÞ Nj þ 1 2

and the result follows because

1−ρ ρ

r f −δ−ρξ ξpc þ c ¼ ρξ

2N j þ1 1

ðN j þ1Þ2 2

ðξpc −aÞ if

Λj 2

and only if r f − ξpc ¼ ε þ .

^N xbf N 0⇔α

(23), we require

λ0 r f


 N4
1

λ rf

Φ rf

ðσ −1Þ

1 þ 15 δþr , which is assumed in f

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