Working Paper. Middlemen, Non-Profits, and Poverty. Nancy H. Chau, Hideaki Goto, and Ravi Kanbur. WP September 2009

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1 WP Setember 2009 Working Paer Deartment of Alied Eonomis and Management Cornell University, Ithaa, New York USA Middlemen, Non-Profits, and Poverty Nany H. Chau, Hideaki Goto, and Ravi anbur

2 It is the Poliy of Cornell University atively to suort equality of eduational and emloyment oortunity. No erson shall be denied admission to any eduational rogram or ativity or be denied emloyment on the basis of any legally rohibited disrimination involving, but not limited to, suh fators as rae, olor, reed, religion, national or ethni origin, se, age or handia. The University is ommitted to the maintenane of affirmative ation rograms whih will assure the ontinuation of suh equality of oortunity.

3 Middlemen, Non-Profits, and Poverty Nany H. Chau Hideaki Goto Ravi anbur This version: August 2009 Abstrat: In many markets in develoing ountries, eseially in remote areas, middlemen are thought to earn eessive rofits. Non-rofits ome in to ounter what is seen as middlemen s market ower, and rih ountry onsumers ay a fair-trade remium for roduts marketed by suh non-rofits. This aer rovides answers to the following five questions. How eatly do middlemen and non-rofits divide u the market? How do the rie mark u and rie ass-through differ between middleman and non-rofits? What is the imat of non-rofits entry on the wellbeing of the oor? Should the government subsidize the entry of non-rofits, or the entry of middlemen? Should wealthy onsumers in the North ay a remium for fair trade roduts, or should they suort fair trade non-rofits diretly? JEL Classifiation: F15, I32, L3. eywords: Middlemen, Non-rofits, Poverty, Market Aess. Deartment of Alied Eonomis and Management, Cornell University, Ithaa, NY hy3@ornell.edu National Graduate Institute for Poliy Studies, Tokyo , Jaan. h-goto@gris.a.j Deartment of Alied Eonomis and Management and Deartment of Eonomis, Cornell University, Ithaa, NY sk145@ornell.edu

4 1 Introdution Middlemen, trading entrereneurs who link the bakwaters of develoing ountries to emerging markets nationally and eseially globally, seem to be universally reviled desite the eonomi servie they rovide. Without their aital and seialized knowledge, high ries in growing markets might be outside the reah of the small holder in the rural area, or of the home-based artisan in the urban slum. By bridging this ga, albeit for rofit, surely they hel to alleviate overty? And yet it is this rofit motive, and the laim that these middlemen make eessive rofits beause of market ower, that is at the root of muh of the onern. Thus, for eamle, MMillan, Welh and Rodrik (2004) study the ase of ashews in Mozambique, and reort that ashew growers only reeive 40 to 50 erent of the border rie, even after border taes are allowed for. They go on to note: it is lear that the marketing hannels for raw ashew nuts remain imerfetly ometitive. Farmers inomes are deressed not only by transort and marketing osts, but also by the market ower eerised by the traders. ( 120). The role of middlemen and market ower in determining rie ass throughs has been widely ommented uon. 1 Middlemen and their rofits attrat artiular attention in remote areas, where rural households arguably bear a double burden: high transort osts, and the market ower of middlemen (Goetz 1992, and Seton, ling and Carmen 1991). These etra margins, it would seem, render it all the more unlikely that households in disersed agriulture, for eamle, an rea the full benefits of globalization (Niita 2004, Hertel and Winters 2005). Remoteness of loation and the market ower of middlemen, it is thus suggested, are losely related. Many soial movements in develoing ountries address themselves to roviding an alternative hannel to the market for oor roduers. For eamle, the Self Emloyed Women s Assoiation (SEWA) India has set u the SEWA Trade Failitation Servie (STFC):...the artisan women though skilled in hand embroidery had to foribly migrate in 1 See for eamle Arndt et. al (2000), Hertel and Winters (2005), and Pokkrel and Thaa (2007). 1

5 searh of work, or undertake earth digging work. The trade of their old valuable embroidered trouso would tyially our during distressed time. This would our with traders and middlemen sine the artisans had aess to a very limited market... Lak of market information hindered artisans from building a strong relationshi with the buyers. With the inetion of STFC, integrated suly hain mehanism was reated and the rodution beame organized. (htt:// Some not-for-rofit organizations, in the fair trade business, romise a number of outomes, inluding an imroved outome for the imoverished roduers of the roduts being sold. Here is how this is aomlished aording to the Fair Trade Federation:...fair traders tyially work diretly with artisans and farmers, utting out the middle men who inrease the rie at eah level - enabling retail roduts to remain ometitively ried in reset to their onventional ounterarts, while more fairly omensating roduers. (htt:// One interretation of the above laim is that the fair trade organization essentially divides u the eessive rofit of the middlemen between the roduer and the onsumer. However, in many ases fair trade roduts sell for a remium omared to idential roduts but without the fair trade label. Moreover, in many ases suh non-rofits reeive diret suort, from governments and other donors, to arry out their mission of being middlemen but without the (eessive) rofits, heling to get more of the market rie into oor roduers okets (DFID 2009). 2 The jutaosition of middlemen trading for rofit and non-rofits with other objetives raises interesting and imortant analytial and oliy issues. Analytially, what does an equilibrium with middlemen and non-rofits look like? How reisely do the rie mark u as well as the rie ass through, from market rie to roduer rie, differ in the equilibrium with 2 See DFID (2009, ) for eamle, for one of the most reent government ommitments to suort fair trade through diret investment and rourements. 2

6 middlemen and non-rofits omared to the equilibrium with only middlemen? What reisely is the imat of non-rofits on overty when the full round of market reerussions, inluding entry and eit of middlemen and of non-rofits, is taken into aount? Should a government interested in overty redution subsidize the entry of non-rofits, or should it erhas subsidize the entry of middlemen? Should wealthy onsumers in the North ay a remium for fair trade roduts, or would the same amount of money be better used to subsidize fair trade non-rofits diretly? These are the questions to whih this aer is direted, and they are questions to whih we believe the literature rovides only a artial answer. Indeed, the literature has yet to deliver a theory of endogenous rie markus and variable rie ass throughs in a satial equilibrium where middlemen and non-rofits o-eist with free entry and eit. The develoment of suh a model is the first task of this aer. We begin with a framework in whih middlemen market ower interats with roduer loation to o-determine the degree of imerfet rie transmission. 3 Math frition à la Mortensen (2003) due to farmers imerfet knowledge about ries onstitute the reason for middlemen market ower in our setu. Equilibrium is haraterized by rie disersion among otherwise idential roduers. We thus deart from the multi-tiered marginalization aroah used for eamle in MMillan, Welh and Rodrik (2004), and onsider instead a setting that an aommodate heterogeneity in the distribution of the eort surluses between middlemen and roduers within a given region. In addition, we also deart from the familiar math frition setting by introduing a satial dimension to the model. This allows us to eamine how the nature of rie disersion, and the imlied degree of rie transmission imerfetion, vary with loation. Our findings are largely onsistent with the emirial observations already stated. At eah loation, middlemen market ower imlies an endogenous division of eort surlus between roduers and the middlemen. Aross loations and aounting for roduers oerating in inreasingly remote areas, middlemen market ower intensifies. This endogenous variation in middlemen market ower aross loation further ditates the etent of imerfet rie trans- 3 There is also a literature on the theory of middlemen as market intermediaries (e.g. Rubinstein and Wolinsky 1987). The emhasis of our work differs from this earlier literature in that we are interested in the role of non-rofit middlemen in influening the distribution of the gains from trade, and how this distribution varies endogenously along a satial ontinuum. 3

7 mission. Indeed, we find that roduers in more remote loations are more susetible to an unequal division of the size of the eort surlus. 4 Within this setting, we introdue non-rofits motivated by a onern for overty either on behalf of the final onsumers they serve via a rie remium, or the referenes of the nonrofits themselves. 5 These non-rofits at as an alternative intermediary other than traditional middlemen linking the world market and individual roduers. 6 Their onern for overty will be eressed in the form of a warm glow effet, whih takes effet whenever the non-rofit oerates in loations where overty is known to be ervasive. In our setu with math frition and satial differentiation, we eamine how the entry of non-rofit middlemen imats the distribution of roduer ries for any given loation, as well as how the imat of non-rofits is differentially felt aross loations. In doing so, we rovide answers to the questions osed above on the imat of non-rofits on rie ass-through and on overty. This framework also allows us to address the questions on oliy, seifially, on what if anything should a government, or rih onsumers, subsidize if the ultimate objetive is overty redution. The lan of the aer is as follows. Setion 2 sets u the framework and equilibrium with middlemen only. Setion 3 introdues non-rofits and haraterizes equilibrium when both tyes of intermediaries an enter. Setion 4 takes u the oliy questions who eatly should the government subsidize and what eatly should onsumers interested in fair trade subsidize? Setion 5 onludes. 4 These results also distinguish our setting from Gersovitz (1989), where the issue of agriultural taation with satial disersion is analyzed in the the absene of (for-rofit) middlemen market ower. 5 There is a longstanding literature on mied oligoolies, in whih welfare-maimizing ubli firms omete with rofit maimizing firms (Merrill and Shneider 1966, Harris and Wiens 1980). Most of these models entertain Cournot ometition (Matsushima and Matsushima 2003), and Cremer, Marhand and Thisse (1991) works with rodut differentiation in a Hotelling model. Our emhasis here is different in that non-rofits are neither rofit maimizing, nor do they maimize soial welfare. To our knowledge, our treatment based on math frition has likewise not been emhasized in the literature. 6 From an altogether different ersetive, Bardhan, Mookherjee and Tsumagari (2007) also study the issue of middlemen margin in a model of outsouring. Unlike our work, moral hazard and the imortane of quality form the motivation for the eistene of middlemen in their aer (Biglaiser and Friedman 1994). 4

8 2 The Model and Equilibrium with Middlemen 2.1 The Basi Setu We onsider a satially disersed eonomy, in whih rodution takes lae at a range of distanes [, ] away from a transort hub. At eah loation there is a large number of idential roduers, N. Eah roduer has a unit of outut for sale either domestially or as eorts. Any outut bound for eorts must be transorted to the hub. For eah unit eorted, let be the unit border rie, and the roduer rie. Outut not bound for eorts an be used for own-onsumtion or sold domestially. In either ase, the revenue equivalent of any outut not eorted is, with 0 <. 2.2 Middlemen: The Bertrand Benhmark Transortation is arried out by middlemen, who inur a loation-seifi transortation ost t er unit outut. 7 If free entry and fritionless Bertrand rie ometition revail among middlemen, the equilibrium roduer rie t is stritly loation-seifi at eah, as long as t is greater than the reservation value. All middlemen thus earn zero rofit: they sell outut at rie at the hub, after having inurred t as transortation ost, and t as ayment to roduers. This simle framework yields a stark set of reditions regarding the volume of total eort, the distribution of inome between middlemen and roduers, as well as the inidene of overty among roduers. In terms of eort volume, all roduers loated at ( )/t + o devote all outut to eorts. In what follows, we assume that < + o, and as suh there eist at least some loations where eorts generates stritly ositive surlus t > 0. To furthermore aommodate the ossibility of inomlete overage and loation as a binding onstraint on eorts for at least some roduers, we assume in addition that + o. The roduer rie imliations of Bertrand ometition are likewise straightforward. There is erfet one-to-one ass through of the net border rie ( t) to roduers, and the full eort surlus ( t ) at eah loation, aroriately aounting for oortunity ost, is atured by the roduer. Consequently, inequality in the distribution of revenue 7 A Samuelson ieberg tye transortation ost an similarly be imosed, by assuming for eamle that t = τ, τ > 0, without affeting the qualitative imliations of the model. 5

9 among roduers is a stritly inter-regional henomenon. At any given loation + o, all roduers earn identially t. Aross loations, roduer rie is dereasing in. For > + o, border rie is insuffiient to over the full ost t +, and roduers reeive the domesti value er unit. To eamine the overty imliations of eort, let denote the minimal roduer rie required to sustain rivate onsumtion at a level no less than an eogenously given overty line. We are artiularly interested in situations where rodution alone without the ossibility of eort is not suffiient to stage an esae from overty, or >. 8 With Bertrand ometition among middlemen, overty inidene as measured by the share of roduers living under the overty line is thus disontinuous along the loational ontinuum: for ( )/t o(< + o ), no one is oor, but immediately thereafter, every roduer is oor. In summary, there are two ritial threshold loations, o and + o. For o, eort omletely eradiates overty. For ( o, + o ), unit eort revenue lies stritly between and the overty line. Produers at loations even more distant than + o from the hub have effetively no aess to eort markets. Figure 1 summarizes, and shows the equilibrium roduer rie along the loation ontinuum. 2.3 Middlemen with Market Power We deart now from the Bertrand assumtion, where every roduer is erfetly aware of eah and every middlemen rie offer, and onsider instead an arguably more realisti senario in whih there is math frition between roduers and middlemen (Mortensen 2003). Seifially, at every loation, eah of an endogenous number (M ) of middlemen first hooses a rie offer from the range of feasible ries,. Let F () be the umulative distribution funtion of suh offers at loation. The middleman rooses an offer to one of the N roduers hosen at random. Eah roduer ranks any and all offers reeived this way, aets the highest offer, and rejets the rest. Math frition arises whenever roduers are not aware of the full set of rie offers. Indeed, let the likelihood that a roduer omes aross z = 0, 1, 2,... offers be given by a Poisson 8 If < instead, overty is a non-issue sine all roduers an live above the overty line by simly selling their roduts domestially at. 6

10 distribution with arameter λ = M /N, or, Pr(z; λ ) = e λ λ z /z!. 9 Sine the distribution of eah suh rie offer is F (), the umulative distribution of the maimal offer reeived is: e λ λ z H () F () z z! z=0 = e λ(1 F()). (1) Middlemen are fully ognizant of and an thus take advantage of the eistene of math frition. Eeted middlemen rofit aordingly embodies the middlemen margin t onditional on the rie offer, as well as the likelihood that out-ometes all other offers reeived by the roduer, H (): Π = ma H ()( t ) (2) where 0 is a fied ost er roduer ontated. Eeted middlemen rofit maimization imlies the following equilibrium rie offer distribution: F () = 1 λ ln ( ) t, f () = t 1 λ ( t ). (3) Naturally, F () = 0 for no roduer will aet a rie offer less than the domesti (reservation) value. Meanwhile, the highest rie offer given aross all middlemen + at loation an be found by setting F ( + ) = 1, or equivalently: + = (1 e λ )( t) + e λ, (4) a weighted average of the net border rie ( t), and the domesti value (). The relative weights deend only on the etent of middlemen market ower, as given by the ratio λ = M /N. As λ, F () uts unit mass on lim λ + = t. In ontrast, as λ 0, + tends to the domesti rie. In addition to the rie offer distribution F (), middlemen market ower λ has an imortant bearing also on the realized distribution of roduer ries. Whenever λ > 0, where H () = e λ H () = e λ(1 F()) = e λ ( t ). (5) t gives the fration of roduers who are left out of eort markets, and H () H () the fration for whom outut is bound for eorts, and who feth a rie at 9 As is well-known, the Poisson distribution is the limit of the binomial distribution with arameter λ as the number of trials aroahes infinity. 7

11 or less from their middlemen. With the distribution of realized roduer ries from (5), it an be easily seen that all middlemen in fat earn idential eeted rofits anywhere along the domain [, + ]: H ()( t ) = e λ ( t ) = H ()( t ). To asertain entry inentives, therefore, it suffies to onsider one suh rie, say. Endogenous entry imlies e λ ( t ) = (6) whenever there is ositive number of middlemen M = λ N > 0. It follows therefore that in equilibrium, 10 λ = M /N = ma{ln(( t )/), 0} H () = ma{, 0}. t (7) From (6) and (7), equilibrium middlemen market ower λ is determined by the interlay between entry ost, and the eort surlus t. Evaluated at the market determined λ N = M, any eeted inrease in eort surlus with one additional middleman, H ()( t ), is equated to the ost of doing so,. Thus, equilibrium middlemen entry is in fat onstrained effiient given math frition and ositive entry osts. 11 As a seial ase, onsider the ase of ost free entry = 0. From (7), middlemen market ower vanishes (λ ), and the Bertrand outome revails. More generally for > 0, the ratio λ = M /N inreases with border rie refleting more intense ometition among middlemen, and dereases with distane refleting instead a deeening of middlemen ower along the loation ontinuum. In the end, with ositive entry ost, eort is ositive only in the range ( )/t +. In omarison with the Bertrand outome, + o = ( )/t > +, middlemen market ower robs roduers in loations ( +, + o ] their aess to eort markets. 10 The assoiated maimal rie offer is thus + = ma{ t, }. 11 It an be readily verified that λ as dislayed in (6) maimizes total roduer and middlemen revenue net of entry ost at eah loation N [( t)(1 H ()) + H () λ ]. 8

12 2.4 Produer Prie of Eorts and Pass Through Aart from endogenous middlemen market ower, math frition additionally gives rise to endogenous roduer rie of eorts, deending on loation. At any given loation with ositive eort, average roduer revenue onditional on reeiving at least one aetable offer (E ) is a weighted average of the net border rie ( t) and the domesti value : E + dh () 1 H () = (1 γ )( t) + γ < t. (8) where γ λ e λ /(1 e λ ). Sine t reresents net surlus available from eorts, the share that goes, on average, to middlemen is thus: t E t = γ λ e λ 1 e λ γ thus atures the etent of unequal division of the eort surlus between middlemen and roduers. Evidently, this division deends systematially on middlemen market ower λ, and as suh the division of surlus varies endogenously along the loational ontinuum. From (7), it is straightforward to onfirm that γ rises with distane for middlemen market ower strengthens with distane. smaller slie of the eort surlus. Produers at farther away loations are aordingly left with a Using (6) and (7), the average roduer rie of eorts with endogenous entry an now be eressed as: E = t ln( t t ) t. (9) Thus, a mark u t E > 0 revail whenever entry ost is stritly ositive > 0. The size of this marku, aounting for endogenous entry, is stritly inreasing in the net border rie t. 12 Intuitively, a higher net border rie enourages entry (λ ) and simultaneously 12 To see the intuition here, note that whereas Nλ = M number of middlemen enter at ost in equilibrium, and the number of middlemen with ositive average marku gross of fied ost ( t E ) is equal only to the number of roduers with ositive sales N(1 H ()) = N(1 e λ ). The rest Nλ N(1 e λ ) fail to strike a suessful math desite having inurred the fied ost, for their rie offers are outbid by that of other middlemen. Equation (9) essentially requires that with endogenous entry, ( ) λ t E = Nλ = N(1 e λ )( t E ). 1 e λ Thus, the equilibrium size of the marku t E is just high enough to justify the entry of the marginal middlemen, aounting fully for the ossibility of negative rofits at subsequent to entry in ase of a failure to math. 9

13 inreases the number of middlemen who fail to strike a suessful math Nλ N(1 e λ ) as they are outbid by other middlemen. To justify this risk, the mark u t E for those who sueed in striking a math must also rise in tandem. Turning now to the issue of ass through of border rie to the average loal roduer, what role does distane lay? Seifially, the average revenue of all roduers at an be eressed simly as the weighted average: ER = (1 H ())E + H () = t (1 + λ ). (10) where λ = ln( t ) ln from (4). The etent of border rie ass through an be asertained by evaluating the resonsiveness: ER ( t) = 1 t = 1 e λ < 1. (11) Thus, the revenue of the average roduer at loation rises less than one for one with net border rie. But even more imortant, the etent of this imerfet ass through worsens endogenously with distane from (7), all the way u until the oint is reahed where + o and thus λ = 0. Produers loated here and beyond are by definition untouhed by fores of eort markets. Figure 2 illustrates, and shows the range of middlemen rie offer [, + ] at eah loation, as well as the average revenue of all loal roduers along the loation ontinuum. 2.5 Intra- and Inter-regional Poverty With rie disersion both within region through H (), and aross regions as H () varies with, the inidene of overty has both an intra- and an inter-regional dimension. These are shown in Figure 3, for three suessively more remote regions (from H 1 to H and then to H 2 ), and aordingly three roduer rie distributions that an be rank ordered in the sense of first order stohasti dominane. To have a diret gauge on overty, resetively define P m,α and P,α as the overty of roduers who gain aess to eort markets through middlemen, and the overty of all other roduers at loation. We adot the Foster-Greer-Thorbeke (1984) overty indiator: P m,α = min{, + } ( ) α ( ) dh () α 1 H () = P,α (12) 10

14 where ( )/ is the overty ga ratio, and α 0 arameterizes the etent of overty aversion. Naturally, overall overty at loation an be eressed as: P,α = (1 H ())P m,α + H ()P,α. (13) As shown, of the two grous of roduers living under the overty line: (i) H () = e λ oor beause they fail to eort and (ii) H (min{, + }) H () = e λ (min{, + } )/( t min{, + }) remain oor desite eort. Between the two, roduers who fail to eort are oorer sine P,α P m,α whenever α 0. As long as some roduers are non-oor, or + >, a small inrease in the border rie, all else equal, alleviates both these soures of overty. Furthermore, heightened ometition between middlemen (an inrease in λ ) brings relief to both H () and H ( ) H (). In the limit, as λ or as 0 aroahing the Bertrand outome, the first soure of overty H () vanishes with the disaearane of math frition as long as the net border rie t eeeds the overty line, while the measure of the seond H ( ) H () likewise aroahes zero, sine no middlemen an offer less than the full t and get away with it without math frition. Inter-regional differenes in overty arise for two reasons in our setu. are First, remote loations are naturally disadvantaged for the net border rie ( t) is lower there. But seond, remote loations are in fat made doubly worse off for middlemen market ower also deeens along the loational ontinuum from (7). Taken together, overty worsens with distane, and indeed from (13), the overty indiator an be re-eressed to reflet diretly the imat of loation on overty: P,α = ᾱ ( ) α 1 t d. for loations where there are at least some roduers who are non-oor. The threshold distane, all it, beyond whih roduers are universally living below the overty line is reahed when the maimal rie offer + an no longer over, or equivalently min{, + } = +. From (4) and (7), ( ) e λ ( t ) /t = ( )/t (14) t = o. 11

15 Consequently, middlemen market ower deeens the inidene of overty along both the intensive (P,α > 0) and etensive ( < o) margins (Figure 2). For >, all roduers are oor, and thus, P,α = ᾱ + ( ) ( ) α 1 + α t d + and P,α ontinues to worsen with distane (say from H to H 3 in Figure 3). Heneforth, we assume that eeeds at least the lower bound, in order to eamine the set of fators that effet hanges along the etensive margin. We have so far demonstrated loation as a key determinant of middlemen market ower. In addition, we have demonstrated the imliations of suh a link in terms of mark us and ass through, as well as intra-and inter-regional overty. In this ontet, how does the introdution of non-rofits imat middlemen market ower along the loational ontinuum? And what about the related issues of mark u and ass through, as well as intra- and inter-regional overty? 3 Non-rofits Like rofit-maimizing middlemen, we heneforth inororate non-rofits who similarly serve roduers by bringing outut to eort markets at transortation ost t. But unlike rofitmaimizing middlemen, they are additionally motivated by the loation-seifi imliations of middlemen market ower both on overty as well as on ries. We inororate these onerns by a loation seifi rie remium n > 0, where n is the valuation ut by the non-rofit on urhase of outut at loation. Our restrition on n is mild, and our objetive is simly to ature a onern for roduers in loations otherwise haraterized by high mark us and / or isolation from world markets. Seifially, we assume n = a where a 0 atures the overall strength of the overty and riing onerns of the non-rofit. In what follows, we further assume that the deendene of the rie remium on is not overly strong, so that the net border rie aounting for transortation osts, t, ontinues to indiate remoteness as a deterrene to eorts, or equivalently n t = (t a) is dereasing in. 13 The (money equivalent) gains to a non-rofit who serves a 13 The linearity of the rie remium in assumed here an be easily relaed to aommodate any monoton- 12

16 roduer loated at, and offers roduer rie, is thus also loation-seifi n t = + a t. As will be seen below, this simle modifiation gives rise to a rih array of ossible imliations. But first in terms of interretation, the rie remium an be thought of as the money equivalent utility gains to a non-rofit simly by virtue of serving faraway roduers, who reviously saw a large art of the eort surlus atured by middlemen. Alternatively, a non-rofit middleman an also be thought of as but another rofit maimizing middleman, who has aess to foreign onsumer demand that embodies a onern for loation, via a revised shedule of border ries n = + a. We take the fied ost aliable to non-rofits n to be stritly greater than, in order to aount for any non-rofits ost disadvantage relative to longstanding middlemen, and other non-trivial osts of monitoring and ertifiation to justify the final onsumer rie remium Equilibrium with Middlemen and Non-Profits Denote F n (),, as the umulative distribution of rie offers inlusive of both nonrofits and middlemen. In analogous fashion as when there are only middlemen, let H n () = e λn (1 F n()) be the umulative distribution of the realized roduer rie distribution, where λ n is now the ratio (m n +M n )/N, and m n and M n resetively denote the endogenous number of non-rofits and middlemen. The roblem of a non-rofit is otherwise similar to that of a middlemen: they aount for the net (rie remium augmented) gains from serving a roduer ( n t ), adjusted aroriately to reflet the likelihood of suessfully striking a math, H n (), in the fae of ometing rie offers from other middlemen: π n = ma H n ()( n t ) n (15) Π n = ma H n ()( t ). (16) ially inreasing funtion a() without affeting the results to follow, as long as t a is inreasing in and distane ontinues to deter eort. 14 The oosite senario where n < an be easily inferred from the analysis to follow. 13

17 Sine the remium adjusted gains from a math is higher for a non-rofit n t > t for any given rie offer, it is straightforward to show that the equilibrium range of non-rofit rie offers, if non-emty, is always higher than that of rofit-maimizing middlemen. 15 another way, the entry of non-rofits effetively onfines rofit maimizing middlemen to servie roduers who are not mathed with non-rofits. Aordingly, let ˆ be an endogenous rie offer threshold, dividing the range of middlemen and non-rofit rie offers. F n (ˆ ) thus gives the share of rie offers from rivate rofit maimizing middlemen (M n /(m n + M n )), and 1 F n (ˆ ) the share from non-rofits. For any ˆ, (15) imlies F n () = 1 ( ) t λ n ln t and otherwise with > ˆ for non-rofits, (15) and (16) give F n () = F n (ˆ ) + 1 λ n ln ( n t ˆ n t Put (17) ). (18) The threshold ˆ is determined via (17) as soon as the share of middlemen at loation, F n (ˆ), is known. This imortant share is endogenized here by way of simultaneous endogenous entry of rofit maimizing middlemen and non-rofits resetively: e λn ( t ) = e λn (1 F n (ˆ)) ( t ˆ ) =, (19) e λn (1 F n (ˆ )) ( n t ˆ ) = e λn (1 F n ()) ( n t ) = n (20) where the marginal non-rofit λ n (1 F n (ˆ )) = m n /N equates the rie remium augmented eeted eort surlus e λn (1 F n (ˆ )) ( n t ˆ ) and the ost of entry n from (20), and the marginal middlemen λ n = (m n + M n )/N then equates the eeted eort surlus (e λ ( t )) with the ost of entry from (19). Thus for interior solutions F n (ˆ ) (0, 1), the threshold rie offer dividing middlemen and non-rofits is: ˆ = t ak 1 k (21) 15 To see this, suose that n and are solutions to (15) and (16) resetively. By virtue of rofit maimization, it must be the ase that with it follows that n. n t n n t Hn ( ) H n ( n ) t n t, a 0, 14

18 where k denotes the ratio of fied osts / n < 1. Clearly, the higher the rie remium a, the narrower the range of middlemen rie offers [, ˆ ]. Meanwhile, the greater the non-rofit s (fied) ost disadvantage n / = 1/k, the higher the middlemen s maimal rie offer. These show interestingly the tendeny for middlemen to otimally harge a higher mark u on average to roduers they ontinue to serve, the higher the non-rofits rie remium. At the other end of the rie offer setrum, the maimal non-rofit rie offer is given by: n+ = + a t n (22) from (20) evaluated at F n ( + ) = 1. The larger the rie remium, the higher of ourse will be the maimal non-rofit offer in equilibrium. Finally, from (19) and (20), the number of non-rofits (m n ) and the number of middlemen (M n ) at an interior equilibrium are resetively, 16 m n = Nλ n (1 F n a (ˆ )) = N ln( n ) (23) M n + m n = Nλ n = N ln( t ). (24) 3.2 Produer Prie of Eorts and Pass Through Deending on the rie remium, fied osts, as well as the eort surlus, it follows from (23) and (24) that there are three ossible equilibrium onfigurations, resetively when there eist only middlemen, only non-rofits, and when the two oeist: Proosition 1 Uon introduing non-rofits with rie remium a t( n )/( ), roduers are served 1. entirely by middlemen at loations losest to the hub < ( n )/a 2. by a mi of both middlemen and non-rofits, for [( n )/a, ( n )( )/(a+ ( n )t)) 16 Suh an alloation is one again onstrained effiient in the resene of math frition and ostly entry, in the sense that national welfare, as measured by the sum of eeted roduer revenue, eeted middlemen and non-rofit gains from serviing roduers at entry ost and n, N[( n t)(1 H n (ˆ ))+( t)(h n (ˆ ) H n ()) + H n () λ n λ n (1 F n (ˆ ))( n )], an be shown to be maimized eatly by hoie of m n and M n as shown in (19) and (20). 15

19 3. entirely by non-rofits, for [( n )( )/(a+( n )t), ( n )/(t a)]. Produers at even farther away loations are not served by either middlemen or non-rofits. In what follow, we disuss eah of these ases in detail No Non-Profits, Only Middlemen With no non-rofits in equilibrium, m n = 0. From (23), this ours whenever: a n a 1 (). (25) or equivalently, whenever non-rofits fail to out-omete middlemen thanks to a rie remium too small to over the added fied ost n. Naturally, this ours at loations suffiiently lose to the hub where the rie remium is the lowest, sine: 17 a a 1 () n a 1 (a). Region I of Figure 4 illustrates all (, a) ombinations onsistent with this equilibrium. Here, the distribution of realized ries are unaffeted by the entry of non-rofits (H 1 in Figure 5). Consequently, the average rie of eorts, the resonsiveness of average roduer revenue to world rie hanges, along with intra-regional overty, all remain untouhed by the ossibility of non-rofit entry No Middlemen, Only Non-Profits At the other etreme, there are no middlemen, M n remium is suffiiently high: = 0, or from (23) and (24), the rie t t ˆ a n t a 2 (). (26) In loational terms, a no-middlemen equilibrium alies at distant loations: a a 2 () (n )( ) a + ( n )t 2 (a). 17 The range of equilibrium rie offers with non-emty suort ([, (1 e λn )( t) + e λn ]) remains the same as before, while middlemen market ower ontinues to be given by (λ n = M n N ln, 0} = M ). N = ma{ln( t ) 16

20 Note in addition that loations too distant ( n )/(t a) n+ (a) are beyond the reah of even non-rofits, sine the remium adjusted border rie + a is too small to over osts (t + n + ). These two restritions are illustrated in Figure 4 by region III inluding all ombinations of (, a) bounded resetively to the left and right by shedules 2 (a) and n+ (a). As shown, region III an be further divided into two arts. The first art [ 2 (a), + ) reresents all loations wherein non-rofits take over and middlemen are omletely dislaed. The seond inlude all other loations where non-rofits now serve as brand new links to eort markets where reviously none eisted. What differene do non-rofits make? We demonstrate in what follows (i) a level effet on the average roduer rie of eorts, and (ii) a ass through effet on the resonsiveness of loal roduer revenue to world rie hanges. To see the first, the maimal rie offer by a non-rofit is at n+ = + a t n. (27) from (20). n+ is thus greater than the orresonding maimal middlemen rie offer + = t sine in [ 2 (a), + ) must be greater than 1 (a), or, a > n from (25). Furthermore, the equilibrium non-rofit to roduer ratio is λ n = mn N = ma{ln( + a t ) ln n, 0} (28) from (20). This is likewise stritly greater than the middlemen to roduer ratio λ = ma{ln( t ) ln, 0} in the absene of non-rofits. Finally, from (20), the equilibrium realized rie distribution aounting for endogenous entry is simly (H 4 in Figure 5): H n () = n + a t whih lies uniformly below H () = /( t ) in the absene of non-rofits rovided that > 2 (a). Eah of these observations reinfore one another, and together they imly a higher average roduer rie of eorts with non-rofits: 18 n+ (29) E n = 1 H n () dhn () = + a t λn n 1 e λn E. (30) 18 The roof of inequality (30) is relegated to the Aendi. 17

21 as well as a higher overall average roduer revenue aross all roduers E n R = (1 H n ())E n + H n () ER. (31) Furthermore, with a higher revalene of non-rofits to roduer than middlemen to roduers (λ n > λ 0) from (28): E n R t = 1 e λn > 1 e λ = ER t. (32) Evidently, the entry of non-rofits imroves the resonsiveness of loal roduer revenue to border rie hanges as well Co-eistene Turning finally to the ase where m n > 0 and M n > 0, non-rofits and rivate rofit maimizing middlemen oeist when a is in the intermediate range, a (a 1 (), a 2 ()) for fied loation, or equivalently, ( 1 (a), 2 (a)) for fied a. Region II in Figure 4 illustrates the intermediate loations, and rie remium ombinations onsistent with this range. With o-eistene, the diret imat of non-rofit entry on rivate middlemen an be seen in two regards. The first onerns entry. From (10) and (11), we note that interestingly, λ n = mn + M n N = ln( t ) ln() = M N = λ. All else onstant, therefore, the entry of one more non-rofit has the effet of diretly dislaing a middleman. The seond onerns riing. The revised realized roduer rie distribution aounting for λ n above is iee-wise ontinuous, with H n () = = t = H () if ˆ n n t H () otherwise. so that the umulative H n () remains stritly unhanged in the range of middlemen ries ˆ, but the fration of roduers reeiving higher ries in the non-rofit range inreases with the entry of non-rofits. Prie distribution shedules H 2, H and H 3 in Figure 5 illustrate. Naturally, the entry of non-rofits raises the imlied average rie of eort: E n = ˆ 1 H n () d n+ t + = E + a (1 (1 + mn /N)e mn /N ) 1 e (mn +M n )/N 18 ˆ 1 H n () d n + a t > E

22 whenever m n > 0. Similarly, the imlied average loal roduer revenue E n R = (1 H n ())E n + H n () = ER + a(1 (1 + m n /N)e mn /N ) > ER also eeeds ER. By ontrast, however, note from (23) that sine the equilibrium number of non-rofits deends stritly on the rie remium a relative to the inrement in entry ost n, it follows that E n R t = ER t and thus the etent of imerfet ass through remains unhanged desite the entry of nonrofits as long as middlemen market ower λ n remains unhanged at λ. In summary, Region I in Figure 4 ehibits invariane desite the ossibility of non-rofit entry. Produers in these loations are too lose to the hub and aordingly the rie remium is to low to justify the entry of non-rofits. Region II resents the intermediate range where middlemen and non-rofits o-eist. As disussed, overall roduer revenue rises thanks to the entry of non-rofits, but the degree of border rie ass through remains untouhed. The final region III enomasses loations where non-rofit omletely dislae middlemen, and loations where non-rofit failitated eort where isolation from world markets was the norm. At these loations, both overall roduer revenue, and the etent of border rie ass through imrove with non-rofits. Figure 4 reveals additionally that regions II and III are non-emty as long as the rie remium is large enough to guarantee that non-rofits are viable at least at + the least remote distane without ometition from middlemen or a + ( n ), equivalently a t( n )/( ). It follows that Proosition 2 At the national level, averaging aross all loations [, ], the introdution of non-rofits with rie remium a t( n )/( ) 1. gives rise to a first order stohastially dominating shift in the roduer rie distribution as H n () H () for all, 2. raises the average roduer rie of eorts sine E n E for all, and 19

23 3. imroves the resonsiveness of average loal roduer revenue, inlusive of eorting and non-eorting roduers, to border rie hanges sine E n R / ( t) ER / ( t) for all. 3.3 Intra- and Inter-regional Poverty Inidene The overty imliations of non-rofits are illustrated in Figure 5, in whih a family of roduer rie distributions is shown going from distanes nearest to the hub, to more remote loations deeer into the hinterland. Of artiular interest is the utoff distribution H. For loations loser to the hub relative to H, the oor are served by middlemen only, and non-rofits offer a rie higher than the overty line, or ˆ t + ak/(1 k) n (a). (33) Sine the oor remains untouhed by non-rofits, the introdution of non-rofits at these loations naturally leave overty unhanged at: P n,α = ᾱ ( ) α 1 t d = P,α. By ontrast, for loations further into the hinterland than H, either some (for [ n (a), 2 (a)), or all of the oor ( [ 2 (a), n+ (a))) will be served by non-rofits. At all loations where there are at least some non-oor, n+, overty delines with the entry of non-rofits: P n,α = ᾱ ᾱ ( ) α 1 H n ()d ( ) α 1 H ()d. = P,α whih follows sine H n () first order stohastially dominate H () from Proosition 1. In the aendi, we disuss all of the remaining ases, deending on (i) whether all roduers are oor, and (ii) whether middlemen and non-rofits o-eist. But in all: Proosition 3 At the national level, averaging aross all loations [, ], the introdution of non-rofits 20

24 1. redues overall average overty (P,α n P,α ) for all if a t( n )/( ), and remains unhanged otherwise, 2. ushes bak towards the hinterland the threshold loation beyond whih all roduers are oor if in addition a t( n )/( ); otherwise the threshold loation remains unhanged. To see the seond art of the roosition, note that the maimal non-rofit rie offer + a t n from (27) is below the overty line n t a n (a) = t (34) if and only if a t( n )/( ) as stated based on (14). With the hel of (33) - (34), Figure 6 illustrates the full array of ossibilities in our model of middlemen and non-rofits. Deending on the size of the remium a, there are two main lasses of outomes. 19 The first lass involves a at relatively low levels, between t( n )/( ) and t( n )/( ). In this range of rie remia, non-rofit an emerge and do so in regions II n,alloor m,alloor where they o-eist with middlemen, and III n,alloor where non-rofits only serve as roduers link to eort markets. Imortantly, with rie remia this low, in no loation are non-rofits able to rie above the overty line. The seond lass of ases involves relatively high rie remia a t( n )/( ). For eah a in this range, there are as many as five distintive equilibrium middlemen-nonrofit onfigurations, deending on whether middlemen and non-rofits oeist (regions I, II or III), and whether at least some of the roduers served are non-oor. Interestingly, therefore, at a given rie remium, a, the mean overty of roduers served by non-rofits aross all loations: P n α = 2 (a) 1 (a) min{, n+ } ˆ [( )/ ] α dh n ()d + n+ (a) 2 (a) 2 (a) 1 (a) 1 Hn (ˆ )d + n+ (a) 2 (a) min{, n+ } 1 H n ()d [( )/ ] α dh n ()d may well be higher or lower than the mean overty of roduers served by middlemen: (35) P m α = 1 (a) min{, + } min{,ˆ} [( )/ ] α dh n ()d [( )/ ] α dh n ()d + 2 (a) 1 (a) 1 (a) 1 H n ()d + 2 (a) 1 (a) Hn (ˆ ) H n ()d (36) 19 An additional lass has a smaller than t( n )/( ) and as shown in Figure 5, a is too small for non-rofit to ever emerge in equilibrium. 21

25 sine there are regions (say II n,alloor m,alloor ) where non-rofits offer stritly higher ries omared to middlemen in the same loation, but there are also loations (say, III n,alloor ) where some non-rofits offer stritly lower ries omared to middlemen in other loations (say, region I n,someoor ). These an be ontrasted against the average overty of roduers who ontinue to have no aess to eort markets, P α = [( )/ ]α H n ()d Hn ()d ( ) α =. (37) In what follows, we offer an observation omaring the three. Lemma 1 For all a t( n )/( ) where either middlemen, non-rofits, or both an emerge in equilibrium deending on loation, overty among non-eorting roduers is the greatest but the overty ranking between roduers served by middlemen and non-rofits is in general ambiguous: Pα ma{pα m, Pα n }. In the seial ase of overty head ount with α = 0, and rie remia in the range a [t( n )/( ), t( n )/( )] 1 = P0 = P0 n > P0 m all non-eorting roduers and all roduers served by non-rofits are oor, but some roduers served by middlemen are not. There are two oosing fores at work here. With a rie remium, non-rofits do indeed offer higher ries (Proositions 2 and 3). But with overty aversion, non-rofits tend to work in remote loations where roduers are oorer (Proosition 1). Consequently, the relative overty of roduers served by middlemen and non-rofits is indeed ambiguous. As we will see, however, this artiular ranking turns out to be key in the determination of overty reduing strategies. 4 Poliy for Poverty Redution We have by now seen the full range of ossibilities in the absene of government interventions, in terms of the equilibrium share of middlemen and non-rofits, the imat of non-rofits on mark 22

26 u and ass through, as well as the equilibrium overty imliation of non-rofits. We now address a final set of questions: Should a government interested in overty redution subsidize non-rofits, or should it erhas subsidize middlemen? And should onsumers interested in overty redution ay a remium on urhases from a non-rofit, or should they subsidize the fied osts of the non-rofits? 4.1 What Should Government Subsidize? With three grous of roduers served resetively by middlemen, non-rofits, and no intermediaries at all, there are three orresonding diret mehanisms of intervention: (i) a subsidy on eorts mediated by middlemen s m ; (ii) a subsidy on eorts mediated by non-rofits s n, and (iii) a subsidy on roduts for domesti sales s, or equivalently, a rie suort guarantee for all roduers who do not eort. The first otion effetively raises the border rie for middlemen from to + s m. The seond otion effetively raises the remium adjusted border rie faing non-rofits from n to n + s n. The final otion raises roduers oortunity ost of eorts from to + s. The revised eeted rofits of non-rofits and middlemen are: π n = ma H n ()( n + s n t ) n, Π n = ma H n ()( + s m t ). Sine the oortunity ost of eort faing roduers is now + s in the resene of domesti rie suort, the minimum rie offer from any middlemen must now be + s. Like before, let ˆ be the rie offer threshold searating non-rofits and middlemen, the distribution of middlemen rie offers ˆ, aounting for the three subsidies is: F n () = 1 λ n ln ( + s m t s + s m t ). (38) Thus, an inrease in s m shifts the rie offer distribution via a first order stohastially dominating hange, refleting an on average higher offer from middlemen to roduers. Likewise, an inrease in s has a similar effet, literally sine the minimum offer rises in tandem with s. Now for non-rofit rie offers with > ˆ, F n () = F n (ˆ ) + 1 ( n λ n ln + s n ) t ˆ n + s n, (39) t 23

27 and as suh an inrease in the subsidy s n shifts the rie offer distribution again via a first order stohastially dominating hange, raising the average non-rofit rie offer even further. Eah of these observations are imortant from a distributional standoint, sine the overty head ount H n ( ) ultimately deends on the rie offer distribution F n () : H n () = e λn (1 F n ()). Now, the threshold rie offer ˆ searating middlemen and non-rofits is determined one again obtained by observing that with simultaneous and endogenous entry of rofit maimizing middlemen and non-rofits: e λn ( + s m t s ) = e λn (1 F n (ˆ)) ( + s m t ˆ ) =, (40) e λn (1 F n (ˆ)) ( n + s n t ˆ ) = e λn (1 F n ()) ( n + s n t ) = n (41) and thus for interior solutions where F n (ˆ ) (0, 1) where middlemen and non-rofits o-eist: M n + m n N ˆ = t (a + sn )k + sm 1 k 1 k m n ( a + s N = λn (1 F n n s m ) (ˆ )) = ln n ( = λ n t + s m s ) = ln. (42) Evidently, any differene in s n s m > 0, refleting oliy disrimination favoring non-rofits, diretly imats non-rofit entry and thus the equilibrium number of non-rofits m n. Meanwhile, any differene in s m s, will diretly imat middlemen entry, and thus the equilibrium number of middlemen, at onstant s n s m. For any given rie remium a > t( n )/( + s m s ) in Figure 6 so that non-rofits emerge in some loations, 20 let β m, and β n denote the share of roduers served by middlemen and non-rofits resetively, aross all loations: β m = β n = 1 (a) 1 H n ()d + 2 (a) 1 (a) Hn (ˆ ) H n ()d, 2 (a) 1 (a) 1 Hn (ˆ )d + n+ (a) 2 (a) 1 H n ()d. 20 Figure 6 shows equilibrium onfiguration when all three subsidies are evaluated at zero. 24

28 We an now eress overall overty, aounting for all loations, as: P α = β m Pα m + β n Pα n + (1 β m β n )Pα, and the budget ost B of the three subsidies as: B m + B n + B = [β m s m + β n s n + (1 β m β n )s ]( )N (43) where B i = s i β i ( )N, i = m, n,. Consider therefore a small inrease in subsidy budget B n diretly towards subsidizing non-rofits, s n β n ( )N. In the aendi, we show that starting from s n = 0, the marginal imat of a small inrease in the non-rofit subsidy budget on total overty P α : P α B n = α N( ) P α 1 n (44) is roortional to the overty indiator Pα 1 n among roduers served by non-rofits. This ehoes Besley and anbur (1988), where the national overty imat (P α ) of a regional food subsidy is shown to highest by targeting a region with the highest P α 1. This very insight ontinues to hold desite several key differene between setus: the revalene of both intraand inter-regional heterogeneity in roduer inome here, and the fat that middlemen, nonrofits, or both, an and do artake in the inome gains made ossible by the orresonding subsidy rogram beause of imerfet ass through. In similar fashion, the marginal imat of a middlemen subsidy, and a domesti rie suort are resetively given by: αp m α 1 αp α 1 P α B m = N( ) and P α B = N( ). From Lemma 1, we know that the relative ranking of Pα 1 m, and P α 1 n is in general ambiguous for any given rie remia, and thus the relative ranking of the marginal imats of a non-rofit subsidy and a middlemen subsidy is aordingly ambiguous. But for the seial ase of α = 1, we know from Lemma 1 that in fat 1 = P0 = P 0 n > P 0 m based on the overty head ount, we have thus: Proosition 4 The marginal imats of resetively a small inrease in s n, s m, and s on the overall overty ga ratio P 1 an be ranked as follows: P 1 B = P 1 B n > P 1 B m 25

29 if the rie remium is in the range a [t( n )/( ), t( n )/( )]. Interestingly, and intuitively, with an objetive to minimize overall overty (P 1 ) at α = 1, one way to maimize the marginal imat of the subsidy rogram (44) is to target non-rofits, if the rie remium a is small and in fat all roduers served by non-rofits are living below the overty line. Alternatively, the marginal imat of a domesti rie suort is similar in magnitude, beause roduers who do not have aess to eort markets are likewise oor aross the board. 4.2 What Should Consumers Subsidize? In this final setion, we investigate whether subsidizing rodution via a rie remium n > is a sensible strategy for onsumers interested in raising the welfare of roduers at large. A natural andidate to omare with is a subsidy on non-rofit entry. Thus, let S a and S k reresent resetively subsidies to sulement the non-rofit remium from a to a + S a, and subsidized non-rofit entry, so that the fied ost is redued from n to n S k. Denote m n (a) = 2 (a) 1 (a) n+ λ n (1 F n (a) (ˆ ))Nd + λ n Nd 2 (a) as the total number of non-rofits aross all loations at given a. The budget osts of the two subsidies an now be eressed as: B a = Nβ n ( )S a, Bk = m n (a)s k. where Nβ n ( ) as before gives the total number of roduers served by non-rofits. Consider therefore a small inrease in the diret entry subsidy, starting from S k = 0, the assoiated imat P α B k = βm Pα n m n (a) n whereas the marginal overty imat of a small inrease in B n has already been shown to be P α B a = α N( ) P α 1. n The relative effetiveness of the two redues to the sign of the differene P α B k P α B a (45) 26