Journal of Envronmental Economcs and Management 4, 97 309 Ž 001. do:10.1006 jeem.000.1164, avalable onlne at http: www.dealbrary.com on Common Pool Resource Appropraton under Costly Cooperaton 1 Nancy McCarthy Internatonal Food Polcy Research Insttute, 033 K Street, NW, Washngton, DC 0006; and Internatonal L estock Research Insttute E-mal: n.mccarthy@cgar.org and Elsabeth Sadoulet and Alan de Janvry Un ersty of Calforna at Berkeley, Berkeley, Calforna 9470; and Gannn Foundaton of Agrcultural Economcs E-mal: sadoulet@are.berkeley.edu, alan@are.berkeley.edu Receved February 17, 1999; revsed January 31, 000; publshed onlne February 13, 001 In addton to the usual fxed costs, we ntroduce varable costs n a communty s effort to cooperate n extractng from a common pool resource. Usng a standard supervson mechansm, these varable costs are shown to be an ncreasng functon of ndvdual members ncentves to default. The model explans why we frequently observe communtes that all cooperate and have relatvely smlar resource endowments, and yet acheve very dfferent levels of extracton. 001 Academc Press I. COOPERATION IN APPROPRIATING COMMON POOL RESOURCES Because of the pervasveness of common pool resources CPR and recurrent observaton of ther msuse, dentfyng the determnants of appropraton of these resources has generated consderable nterest n many branches of the socal scences. These resources are characterzed by jont access by a fnte set of users and by rvalry n appropraton. When a communty member decdes ndvdually on appropraton of a common pool resource, he generates negatve externaltes on others by reducng supply avalable to them. These externaltes are, however, not taken nto account n the ndvdual s proft maxmzaton calculus, leadng to overuse of the resource. 3 Ths feature of CPR has been used to explan a varety of adverse envronmental phenomena such as overgrazng and desertfcaton, deforestaton, sol eroson n watersheds, overdraft on underground aqufers, and overfshng. Observatons n the feld, however, show great varaton n the qualty of common pool resource management. Whle the lterature tends to assocate 1 The authors are grateful for comments receved from Antono Cccone, Ethan Lgon, and Leo Smon. To whom correspondence should be addressed. 3 We do not dscuss here the other aspect of a common pool resource, namely provson and the ncentve to under-provde as ndvdual actons create postve externaltes on others. For provson problems n CPR, see Baland and Platteau 3 and de Janvry et al. 11. 97 0095-0696 01 $35.00 Copyrght 001 by Academc Press All rghts of reproducton n any form reserved.
98 MCCARTHY, SADOULET, AND DE JANVRY over-explotaton of resources wth lack of cooperaton and effcency n resource management wth cooperaton ŽOstrom 4, Bromley 8, Baland and Platteau., our own observatons suggest a whole range of ntermedate levels of msuse, even among communtes that seem to cooperate. The key questons rased by these observatons are: How do some communtes succeed n effcently usng ther CPR? What explans what appear to be ntermedate levels of cooperaton? Turnng to theory, three types of nterpretatons have been proposed to explan why communtes may use ther CPR effcently. The frst s that the decson on appropraton may correspond to non-cooperatve games where the outcome of ndvdual actons happens to be dentcal to a cooperatve outcome. In the Assurance Game, for nstance, both the cooperatve and non-cooperatve outcomes can be supported n equlbrum ŽBardhan. 4. These partcular payoff structures, however, characterze only a subset of rather specfc stuatons of CPR appropraton. The second nterpretaton calls on repeated games wth trgger strateges where the Folk Theorem apples. The long-term perspectve s approprate for communty affars snce there s usually consderable stablty n membershp. However, callng on trgger strateges that requre ether excluson of access to the CPR or reversal to non-cooperaton may have appeal n the olgopoly lterature but s less useful n explanng communty behavor: n most tradtonal communtes, the threat of excluson from the CPR s not credble, and the threat of revertng to non-cooperaton when many members are nvolved would be too costly to too many others to be credble. The thrd nterpretaton s that effcency n resource use s obtaned by cooperaton ŽOstrom 4, McKean 1, Bromley 8, Berkes and Folke 6.. Cooperaton, however, requres acton by the communty to defne rules and to montor and enforce them. As these actons ental costs, cooperaton wll be observed whenever the benefts of cooperaton exceed the costs. The prospect for cooperaton hence mportantly depends on the factors that ncrease the expected gans from cooperaton ŽOstrom 4, Wade 3, Olson 3, Bendor and Mookherjee 5, Bardhan 4.. On the cost sde, there s a large lterature on how these costs vary and on how they affect the potental for cooperaton ŽSandler et al. 6 and references cted theren.. Much of the lterature takes the communty as gven and consders costs of negotaton, supervson, and enforcement as fxed at the communty level. Analyses focus on the factors that lower montorng costs ŽWade 3, Hrschman 15. or ncrease the ablty to enforce rules ŽHrschman 15, Johnson and Lbecap 16, Besley and Coate 7, Seth and Somanathan 9, Seabrght 8.. Note that snce these costs are fxed, they do not affect the optmum level of extracton, as cogently argued by a number of researchers ŽSeabrght 8.. Ths theory can thus explan contrasts n extracton between non-cooperatng and cooperatng communtes, but not the ntermedate levels of extracton mentoned above. Buldng on the mportance of keepng groups small for effcency purposes, a branch of the lterature looks at the determnaton of the optmal number of frms when there are costs n contanng membershp. In Caputo and Lueck 9, 10, communtes must ncur explct costs for excludng potental exploters. Assumng that costs of excluson decrease wth membershp sze Žor equvalently ncrease wth the number of potental exploters to exclude., and that externaltes and effcency costs ncrease wth membershp sze, the communty settles for an optmal number of members. These results are akn to those found n the lterature
COMMON POOL RESOURCE APPROPRIATION 99 on the olgopolstc explotaton of a natural resource, although n ths case the nature of the cost s qute dfferent. 4 Whle these excluson mechansms are mportant n the area of commercal explotaton of resources, they are often not an opton n tradtonal communtes where extracton from the CPR s a rght for all members of the communty. It suggests, however, that whenever feasble, subcoaltons of members wth control over a porton of the CPR mght lead to better management Že.g., n the case of Mexcan ejdos see Wlson and Thompson 33.. Nonetheless, once the sze of the communty has been decded, the level of resource extracton depends only on whether the members act cooperatvely or non-cooperatvely. When excluson from the communty s not possble, communtes only have the opton of engagng n explct supervson and puntve actons to ensure complance wth the cooperatve agreement. A smlar problem s found n the lterature on the enforcement of polluton standards ŽVscus and Zeckhauser 31, Harrngton 13, Harford and Harrngton 1.. The ndvdual cost to a frm of respectng a polluton standard ncreases wth the severty of the standard. As each frm balances the expected punshment from not complyng wth the cost of complance, t chooses whether to comply or not. For a gven enforcement mechansm Žchar- acterzed by the probablty that a non-complyng frm would be caught and the penalty t would then have to pay., the regulator selects the optmal standard whch leads to the lowest expected level of polluton. In equlbrum, the lowest polluton level s obtaned wth a mx of frms that abde by the standard and frms that prefer not to abde and rsk payng the penalty. Whereas n the polluton abatement lterature, outcomes are partal n the sense that some fully cooperate whereas others fully do not cooperate, we are nterested here n an outcome where all members agree to cooperate at a level above the costless cooperaton outcome. In ther game of provson of nvestment n a CPR, Caputo and Lueck 9, 10 assume a reduced form for the enforcement mechansm, whereby the cost of enforcng any agreed upon aggregate level of nvestment s an ncreasng functon of the level of nvestment. Addng to the prce of the nvestment good, ths enforcement cost reduces the optmal level of nvestment. In ths paper, we consder the management of common property pastures n the context of Mexcan ejdos. In these communtes, all members have access rghts, and hence the communtes do not have the opton of excludng. We conceptualze the enforcement mechansm as n the polluton control lterature,.e., wth explct expendtures by the communty and a resultng probablty of catchng cheatng members. We let the communty choose both the expendture on enforcement and the standard of extracton to maxmze aggregate welfare. In addton, we do not allow for asymmetrc treatment of herders, where the standard could be set at the ndvdual level or where only a fracton of the communty would abde by the cooperatve agreement. Ths s because ejdos have a relatvely strong governance 4 In the context of non-cooperatve commercal exploters that sell on a non-compettve market, the welfare cost of reducng membershp to only one frm s the monopolstc behavor of the frm. Hence, the optmum les between a small number of frms whch may under-explot the resources to capture the monopoly rent on the market, and a large number of frms whch wll over-explot the resources because of the standard CPR externalty problem ŽMason and Polasky 18 ; Mason et al. 19, and the references cted theren.. These models also use non-cooperatve games, whle here we focus on understandng sub-optmal management of resources n cooperatve games.
300 MCCARTHY, SADOULET, AND DE JANVRY structure based on deep-rooted egaltaran prncples that do not easly allow for dfferental treatment of members. We show that the optmal soluton corresponds to enforcement expendtures that ncrease wth the ncentves of ndvdual members to cheat, themselves an ncreasng functon of the tghtness of the standard, as assumed by Caputo and Lueck 9. The resultng optmal extracton of the resource s an ntermedate level between what would be obtaned under a fxed cost cooperatve regme and a non-cooperatve regme. The ntuton behnd ncorporatng ncentves to cheat nto the determnaton of an optmal agreement was n fact presented by Stgler 30. In that artcle, he assumes that olgopolsts wsh to collude, and that the successfulness of colluson wll depend on the problems n polcng a collectve agreement. He notes that f the enforcement s weak, however f prce-cuttng s detected only slowly and ncompletely the conspracy must recognze ts weakness: t must set prces not much above the compettve level so the nducements to prce-cuttng are small ŽStgler 30, p. 46.. The model developed thereafter, however, focuses on determnng how prce-cuttng mght be determned, but does not return to how an optmal collusve prce mght be set, gven ncentves to cheat. The model developed below explans the optmal agreed-upon level of extracton, and thus why we observe a wde range of qualty of common pasture management, from extreme over-explotaton n communtes where cooperaton fals to relatvely poorly managed resources where cooperaton s obtaned at hgh costs, and well-managed resources where cooperaton s obtaned at low cost. For any hgher varable cost of enforcement, communtes optmally choose to cooperate at a less strngent level of extracton. In Secton II, we develop a model of costly cooperaton when there are two dentcal communty members; n Secton III, we extend the model to any number m of dentcal communty members. Secton IV concludes wth a dscusson of some polcy mplcatons of the model. II. TWO-PLAYER MODEL OF COSTLY COOPERATION The overall decson process on appropraton from a CPR s a two-stage game, where a cooperatve agreement on the level of extracton and on the enforcement mechansm s chosen n the frst stage, and members ndvdually choose ther effort levels n the second stage. Usng backwards nducton, the cooperatve agreement n the frst stage s chosen based on the ncentves to devate determned n the second-stage non-cooperatve game. Costs are borne n the begnnng of the perod, whereas returns are realzed at the end of the perod. In the partcular case of common property pasture that we develop n ths paper, the terms of the cooperatve agreement nclude the number of anmals that each member can graze, the resources spent by the communty on supervson and enforcement, and the penalty mposed on members caught cheatng. II. A. The Second-Stage: Non-Cooperat e Choce of Ind dual Efforts Consder a two-person game over the number of anmals Ž n, n. 1 to graze on a common property pasture of gven sze H. We assume that the herders are homogenous, rsk-neutral proft-maxmzers, and that each herder has a constant
COMMON POOL RESOURCE APPROPRIATION 301 margnal cost of stockng anmals, c. Productvty of forage for each ndvdual s a decreasng functon of the total number of anmals stocked; thus, a crowdng externalty captures the negatve effect of addng an addtonal head of cattle on the total weght for all anmals stocked. However, each ndvdual only nternalzes that porton of the negatve externalty accrung to hm. The proft from grazng s wrtten bž n1 n. Ž n 1, n. pn a cn ; 1,, Ž 1. H where p s the prce of lvestock products, n a bn Ž n. H 1 s a commonly used cattle weght producton functon Žsee Hart et al. 14., a s the pasture productvty coeffcent, and b the pasture senstvty to stockng coeffcent. Each of the two players contemplates two strateges: one s to cooperate and graze the number of anmals agreed upon n a jont maxmzaton, n n, and the other to not cooperate and graze the number of anmals consstent wth ndvdual maxmzaton gven the number of anmals grazed by the other player: a c p n 0 j n Ž nj. arg max H ;, j 1,; j. b Let us call n 00 the Nash non-cooperatve soluton when nether player cooperates: a c p 00 n H. 3b II.B. Incent es to Cooperate or to Defect and Costs of Enforcement Profts at the Nash non-cooperatve soluton are lower than those obtanng from jont-maxmzaton. Hence, there are ncentves for ndvduals to act collectvely to secure rents from jontly owned resources. Incentves to cooperate are smply the addtonal revenues receved when movng from the non-cooperatve level to a cooperatvely agreed upon level of extracton n: I C Ž n, n. Ž n 00, n 00.. On the other hand, as explctly captured n Prsoner s Dlemma games, there are ncentves for a person not to cooperate. If he beleves that all others wll cooperate, then hs best response s to not cooperate, and to add more anmals. Ths s the ncentve to cheat, whch s equal to the dfference between the proft of optmally cheatng and the proft obtaned by abdng by the agreement Žgven that the other person cooperates.: I Ch n 0 Ž n., n Ž n, n.. We can show that the ncentve to cheat s always non-negatve, / 9 bp a c p Ch I ž H n 0. 4 H 3b
30 MCCARTHY, SADOULET, AND DE JANVRY FIG. 1. Incentves for cooperaton and non-cooperaton. Fgure 1 llustrates these ncentves and choces. Incentves to cooperate and to cheat are null at the non-cooperatve level n 00. Thus, f the group agrees to cooperate at the level of the non-cooperatve game outcome, then the gans from ths agreement are zero and clearly ncentves to cheat are also zero. As the group lowers ts chosen cooperatve level of extracton, gans from cooperatng are ncreasng, though at a decreasng rate a result that derves drectly from the concave specfcaton for the proft functon. On the other hand, the ncentves to cheat are ncreasng at an ncreasng rate. To capture the potental gans from cooperaton, the group as a whole can set up an enforcement mechansm. We characterze ths enforcement mechansm by ts cost, whch ncludes a fxed cost,, and expendtures, C, spent on montorng ndvdual herders behavor, and the penalty K mposed on the herders caught cheatng. That enforcement of an agreement requres specfc costs to supervse each ndvdual, and not only an overall fxed cost, s justfed n the case of common pastures when the number of anmals grazng n large communal lands has to be montored. The more effort the communty puts nto ths montorng, the hgher s the probablty that any cheatng ndvdual wll be caught. If probž C. s the probablty of beng caught f cheatng, then ndvdual wll choose not to cheat f and only f probž C. K 1 probž C. I Ch 0. Ths defnes the mnmum expendture level that the communty has to ncur to prevent from cheatng. It s an ncreasng functon of the ncentve to cheat I Ch. To smplfy the analytcs of the problem, we choose a smple montorng technque wth C probž C.. 1 C
COMMON POOL RESOURCE APPROPRIATION 303 The ndvdual wll thus abde by the cooperatve level, n,fc I Ch K, and 0 Ch act non-cooperatvely, n n,fc I K. j II.C. The Frst Stage: O erall Welfare Due to Cooperaton and Cooperat e Equlbrum In the frst stage, the members cooperatvely choose the enforcement levels Žresources and C to expend n montorng, and penalty K to mpose to a member caught cheatng. and the number of anmals, n, that maxmze the aggregate welfare of the group. The aggregate welfare s equal to the sum of all ndvdual profts, net of the costs ncurred for reachng an agreement, and enforcng the rules and regulatons. In addton, we only consder equlbra that can be sustaned wthout explct transfers between ndvduals, as such transfers are not observed n the contexts that we consder. 5 The cooperatve soluton n s enforceable wthout explct transfer only f there s a postve proft gan from Ž. Ž 00 00 cooperaton, n, n n, n., for each producer. The group s problem s then ½Ý j Ý 5 max Ž n, n. C n, K, C s.t. ½ n f C I Ch K, n n0 Ž n j. otherwse, Ž n, n. Ž n 00, n 00.,, j 1,, j. The soluton to ths problem s to set the penalty K at a very hgh level and to nduce cooperaton wth mnmum cost and correspondng probablty of catchng a cheater. Yet, n real settngs, a very hgh penalty cannot be extracted and hence the threat s not credble. The group then sets up the penalty at the maxmum level, K max, that can be credbly extracted from ndvduals. Gven the response functon of ndvdual members, the group retans only two possble values for C, ether not to spend any resources and let the members cheat, or to spend the mnmum amount I Ch K max that ensures cooperaton. 6 Correspondngly, the fxed cost wll only be spent f supervson s undertaken. Substtutng these values n the problem above, the group s cooperatve level for the number of anmals s gven by n arg max W Ž n, n. I Ch 1Ž n n 00. ½ Ý ž Ý / 5 n 00 00 s.t. n, n n, n, 1,, 5 Dsregardng the possblty of secondary transfers s classcal n the lterature on local cooperatve behavor. See Ostrom and Gardner 5 and Seabrght 7. In any case, n the symmetrc problem consdered here, one can show that no soluton would nvolve transfer. 6 In equlbrum, resources wll be spent to prevent cheatng, so that no cheatng should be observed. In ths one perod game, we assume that f cheatng s observed durng the perod, the member wll pay the penalty, and then play at the cooperatve level.
304 MCCARTHY, SADOULET, AND DE JANVRY Ž 00 where 1 K s the unt cost of enforcement, and 1 n n. max s the ndcator functon that takes value 1 f n n 00 and 0 otherwse. Ths parameter s dmensonless; t measures the resources that have to be spent to prevent one player from cheatng per unt of gan he would obtan by cheatng. The costs parameters and capture the group s ablty to defne rules, montor the behavor of ts members, and enforce rules. Consequently, they are a functon of the soco-economc characterstcs of the group Žsze of the group, observablty of actons, socal captal to retalate, etc.. and the characterstcs of the resource Ž well-defned boundares, abundance, etc.. that were dentfed n Secton I as factors determnng the ablty to cooperate. Soluton of the problem gves the enforceable cooperatve soluton, ž / a c p 1 Ž 3. a c p n H H Ž. f max, 4b 1 Ž 9 8. 4b a c p 00 n n H f max, 3b 1 Ž 3. n where 1 Ž 9 8. n s overgrazng, defned as the costly cooperatve opt- 0 mum stockng relatve to the optmal level of stockng n 0 that would be obtaned f cooperaton had no varable cost, and / Ž a c p. 1 4 max p H ž 4b 3 3 s the maxmum fxed cost that the communty can bear. Ch We represent on Fg. 1 the varable cost of cooperaton, I Ž the curve can le below or above the ncentve curve dependng on the unt cost.. The graph llustrates a very ntutve pont: for agreements to cooperate at levels just slghtly below the non-cooperatve outcome, gans to ths agreement are relatvely large at the margn, whereas ncentves to devate from ths pont are relatvely low at the margn. However, margnal gans to cooperaton near the fxed-cost cooperaton outcome are nearly flat Žclearly they are zero at the fxed-cost cooperaton outcome., whereas the margnal gans to devate are at ther hghest over the relevant range Žstockng rates between the non-cooperatve and fxed-cost cooperatve outcomes.. Snce welfare s equal to the dfference between the gan n profts from cooperatng and the varable cost of enforcng cooperaton ŽEq. Ž.., the optmal level of cooperaton n s obtaned when these margnal effects balance each other. Expresson Ž. 3 shows that the enforceable level of cooperaton s ndependent of the level of fxed cost, and that t les between the fxed-cost cooperatve equlbrum Ž as calculated n standard cooperatve models. and the non-cooperatve equlbrum: a c p a c p 00 n0 H n n H. 4b 3b 4 Ths gves the range of varaton for overgrazng: 1. 3 Ž 3.
COMMON POOL RESOURCE APPROPRIATION 305 As the unt enforcement cost tends to 0 Žwhch occurs when the communty s more effectve n enforcng the contract wth hgher penalty K or a more effcent montorng technque,., the communty can tend to perfect cooperaton. Conversely, wth hgher unt enforcement cost, the costly cooperaton soluton s much closer to the non-cooperatve soluton. Furthermore, snce the maxmum fxed cost, max, s a decreasng functon of the unt enforcement cost,, cooperaton breaks down for lower values of the fxed cost as ths cost ncreases. If, ndvdual proft gans from cooperaton are max /ž / Ž a c p. 4 00 00 Ž n, n. Ž n, n. p Hž, Ž 4. 8b 3 3 and the overall welfare s ž / Ž a c p. 1 4 W p H. Ž 5. 4b 3 3 II.D. Comparat e Statcs on the Costly Cooperaton Soluton Expresson Ž. 3 shows that overgrazng ncreases wth the unt cost of enforcement and, for a very hgh unt enforcement cost, tends to the non-cooperatve level. Both the non-cooperatve number of lvestock, n 00, and the costly cooperaton a c p level, n, are ncreasng functons of b H. Indvdual proft gans from coopera- ton Ž. 4 and overall welfare gans Ž. 5 decrease wth the unt costs of enforcement and, for very hgh unt enforcement costs, tend to zero. Profts under both non-cooperaton and cooperaton, ndvdual proft gans from cooperaton Ž. 4, ncentves to cheat, and overall welfare gans from cooperaton Ž. 5 are all ncreas- Ž a c p. ng wth p b H. Ths shows that gans from cooperaton are larger on pastures wth better qualty forage and that are less fragle, when product prces are hgher, for more effcent lvestock producton, and when the magntude of the resource over whch cooperaton occurs s greater. Yet, as seen n Ž. 3, the level of overgrazng s unaffected by these varables and parameters. III. MODEL WITH MORE THAN TWO MEMBERS In ths secton, we expand the model to nclude any number of members, m. Membershp, however, remans an exogenous varable. The choce varables thus reman the expendtures on enforcng the agreement and the stockng level. As all herders are assumed dentcal, we also restrct ourselves to symmetrc solutons and do not allow for the communty to arbtrarly desgnate herders on whch the contract wll be enforced whle others are allowed to cheat. Hence, only the two solutons of a costly cooperaton agreement respected by all herders or non-cooperaton are consdered. The ncentve to cheat for any one member s the gan that could be made by cheatng, gven that all other members abde by the agreed cooperatve level.
306 MCCARTHY, SADOULET, AND DE JANVRY Extendng the formulaton of the last secton s qute straghtforward. It leads to the followng enforceable cooperatve soluton, a c p 1 Ž m 1. a c p n H H Ž. f max, mb 1 Ž 1 m. Ž m 1. mb a c p 00 n n H f max, Ž m 1. b where / Ž a c p. m 1 m max p H ž b 4Ž m 1. m 1 s the maxmum fxed cost that the communty can afford, and s the level of overgrazng compared to the fxed-cost cooperaton level. The total stockng level under cooperaton s therefore a c p 1 Ž m 1. N mn H. b 1 Ž 1 m. Ž m 1. As n the two players case, n ncreases wth the enforcement cost and always les between the fxed-cost cooperaton Ž obtaned for 0. and the non-cooperatve levels, for any level of m. We note that dn dm 0, but that dn dm 0, as s the case under a non-cooperatve game. As the number of herders ncreases, the total stockng level N approaches the non-cooperatve stockng level Ž Fg... The communty welfare gan from enterng nto ths cooperatve agreement s the sum of the ncrease n profts for the ndvdual herders net of the enforcement costs, Ý Ý W 00 I Ch Ž a c p. 1 4m Ž m 1. p H, b 1 Ž m 1. 4m FIG.. Cooperatve soluton as a functon of the number of members.
COMMON POOL RESOURCE APPROPRIATION 307 where and 00 are profts at the cooperatve and non-cooperatve level of stockng. Fgure llustrates the evoluton of the equlbrum as the number of members n the communty ncreases. Welfare gans are represented gross of the fxed cost. If there were no varable cost of enforcement Ž 0., the welfare gan of cooperaton would monotoncally ncrease wth the sze of the communty Ž curve 1 on Fg... Ths s because the externalty mposed by non-cooperatve behavor ncreases wth the number of herders, and hence, as seen n the left-hand sde of the fgure, the non-cooperatve stockng level N 00 ncreases wth the sze of the communty. Yet, when one ncludes the varable enforcement costs, the stuaton s dfferent. At the gven cooperatve level, N 0, the beneft for one ndvdual to cheat would ncrease wth the remanng numbers of cooperatng members. Hence, varable enforcement costs would ncrease. Ths nduces an optmal relaxaton of the standard,.e., an ncrease n the cooperatve level to N Ž left-hand sde of graph.. As the optmal stockng level ncreases, the proft gans from cooperaton Ž curve 3. are not as hgh as when the lower level of stockng level N 0 can be mantaned. We thus see that the welfare gan from cooperaton ncreases and then decreases as the sze of the communty ncreases Ž curve 4.. Ths result ndcates that, when a fxed cost needs to be ncurred to enforce cooperaton, only communtes not too small and not too large wll choose the cooperatve soluton Ž between A and B.. In small communtes, the externaltes of non-cooperaton are not too hgh and t s not worthwhle ncurrng the fxed cost of gettng organzed. 7 In very large communtes, as the ncentve for ndvdual herders to cheat s very hgh, the cooperatve level s set at a hgh level and the benefts from cooperaton are not suffcent to justfy ncurrng the fxed cost. Cooperaton thus breaks down. To summarze, the model developed above provdes a framework for analyzng cooperatve appropraton levels that are between the jont-maxmzaton and the Nash non-cooperatve solutons. The dea of partal success n cooperaton has been analyzed by a number of authors, though most of the emprcal evdence s anecdotal ŽBaland and Platteau, Ostrom 4, Oakerson.. Three studes whch attempt to measure the extent of cooperaton show varyng degrees of success. In Lopez 17 and Ahuja 1, the authors measure the degree of success communtes have n managng the fertlty of agrcultural land n Cote ˆ d Ivore, where land n fallow produces a postve externalty on land n ndvdually cultvated plots by helpng restore fertlty. There s hence a socal optmum n the allocaton of communty land between fallow and ndvdual plots. Results from both studes suggest that some communtes cooperate, and that, n general, the degree of success n management les between the outcomes assocated wth non-cooperatve and wth fxed-cost cooperatve behavor. In McCarthy et al. 0, we estmate stockng rates across nne Mexcan ejdo communtes wth common property pastures. In a frst econometrc model, communtes are ether fully cooperatng or not; n a second, an ndex measurng the degree of cooperaton s constructed. Results show that the ndex measurng the degree of cooperaton has more explanatory power than a dchotomous cooperate not cooperate specfcaton, ndcatng that there are ndeed dfferent qualtes of cooperaton among these communtes. 7 One could argue that the fxed cost tself s small n small communtes, and hence cooperaton may stll be proftable.
308 MCCARTHY, SADOULET, AND DE JANVRY IV. CONCLUSION We have developed a theory of cooperaton that ncludes an explct and costly mechansm of supervson and enforcement. Under farly mld assumptons on ths mechansm, we show that the optmal level of costs of montorng and enforcng the agreed upon rules for appropraton of the CPR depends on the ncentves that members have to defect, and on unt costs that capture the group s ablty to montor and enforce ts rule. Introducton of these varable costs, as opposed to the fxed costs of enforcement usually consdered n the lterature, drastcally modfes the outcome of the group-level maxmzaton problem. As n the fxed-cost case, cooperaton may break down f unt costs are too hgh. However, f an nteror soluton can be reached, the group optmally chooses a unque level of appropraton that les somewhere between the non-cooperatve level and the costless Žor fxed-cost. cooperatve level. The level of over-appropraton thus obtaned s an ncreasng functon of the unt costs of enforcement. Ths helps explan why cooperatng communtes wth smlar endowments and facng dentcal market condtons may choose dfferent levels of resource appropraton. Among cooperatng communtes, the qualty of cooperaton wll thus mprove wth communty features and polcy nterventons that help reduce the varable costs of cooperaton. On the other hand, we also show that hgher proftablty Ždue to qualty of the resource or the prce of the commodty. leads to greater gans from cooperaton, yet does not affect the degree of over-appropraton because t smultaneously ncreases the ncentve to cheat. The model s hghly stylzed, but ths s an nterestng result that contradcts much of the current thnkng on common-pool resource management. Thus, ncreasng market access and effectve prces, and reducng producton costs, should not affect the degree of over-use, even though they ncrease the gans from cooperaton, all else equal. Furthermore, we show that the qualty of cooperaton and hence the benefts of cooperaton at frst ncrease and then decrease as the number of members ncreases. Hence, nether very large communtes nor very small communtes wll fnd cooperaton economcally feasble, a regularty commonly observed n the emprcal lterature. REFERENCES 1. V. Ahuja, Land degradaton, agrcultural productvty and common property: Evdence from Cote ˆ d Ivore, En ron. De elop. Econom. 3, 7 34 Ž 1998... J.M. Baland and J.P. Platteau, Haltng Degradaton of Natural Resources: Is There a Role for Rural Communtes? Cambrdge Unv. Press, Cambrdge, UK, 1996. 3. J.M. Baland and J.P. Platteau, Wealth nequalty and effcency n the commons: The unregulated case, Oxford Econom. Papers 49, 451 48 Ž 1997.. 4. P. Bardhan, Analytcs of the nsttutons of nformal cooperaton n rural development, World De elop. 1, 633 640 Ž 1993.. 5. J. Bendor and D. Mookherjee, Insttutonal structure and the logc of ongong collectve acton, Amer. Polt. Sc. Re. 81, 19 154 Ž 1987.. 6. F. Berkes and C. Folke Ž Eds.., Lnkng Socal and Ecologcal Systems: Management Practces and Socal Mechansms for Buldng Reslence, Cambrdge Unv. Press, Cambrdge, UK, 1998. 7. T. Besley and S. Coate, Group lendng, repayment ncentves and socal collateral, J. De elop. Econom. 46, 1 18 Ž 1995.. 8. D. Bromley Ž Ed.., Makng the Commons Work: Theory, Practce, and Polcy, Insttute for Contemporary Studes Press, San Francsco, CA, 199.
COMMON POOL RESOURCE APPROPRIATION 309 9. M. R. Caputo and D. Lueck, Modelng common property ownershp as a dynamc contract, Natur. Resour. Modelng 8, 5 45 Ž 1994.. 10. M. R. Caputo and D. Lueck, A theory of natural resource use under common property rghts, mmeo, Unversty of Calforna at Davs, 000. 11. A. de Janvry, N. McCarthy, and E. Sadoulet, Endogenous provson and appropraton n the commons, Amer. J. Agrcultural Econom. 80, 658 664 Ž 1998.. 1. J. D. Harford and W. Harrngton, A reconsderaton of enforcement leverage when penaltes are restrcted, J. Publc Econom. 45, 391 395 Ž 1991.. 13. W. Harrngton, Enforcement leverage when penaltes are restrcted, J. Publc Econom. 37, 9 53 Ž 1988.. 14. R. H. Hart, M. Samuel, P. Test, and M. Smth, Cattle, vegetaton, and economc responses to grazng systems and grazng pressure, J. Range Management 41, 8 87 Ž 1989.. 15. A. Hrschman, Ext, Voce, and Loyalty, Harvard Unv. Press, Cambrdge, MA, 1970. 16. R. Johnson and G. Lbecap, Contractng problems and regulaton: The case of the fshery, Amer. Econom. Re. 7, 1005 10 Ž 198.. 17. R. Lopez, The tragedy of the commons n Cote ˆ d Ivore agrculture: Emprcal evdence and mplcatons for evaluatng trade polces, World Bank Econom. Re. 1, 105 131 Ž 1998.. 18. C. F. Mason and S. Polasky, The optmal number of frms n the commons: A dynamc approach, Canad. J. Econom. 30, 1143 1160 Ž 1997.. 19. C. F. Mason, T. Sandler, and R. Cornes, Expectatons, the commons, and optmal group sze, J. En ron. Econom. Management 15, 99 110 Ž 1988.. 0. N. McCarthy, A. de Janvry, and E. Sadoulet, Land allocaton under dual ndvdual-collectve use n Mexco, J. De elop. Econom. 56, 39 64 Ž 1998.. 1. M. A. McKean, Management of tradtonal common lands Ž Irach. n Japan, n Makng the Commons Work: Theory, Practce, and Polcy Ž D. Bromley, Ed.., Insttute for Contemporary Studes Press, San Francsco, CA, 199.. R. Oakerson, Analyzng the commons: A framework, n Makng the Commons Work: Theory, Practce, and Polcy Ž D. Bromley, Ed.., Insttute for Contemporary Studes Press, San Francsco, CA, 199. 3. M. Olson, The Logc of Collectve Acton: Publc Goods and the Theory of Groups, Harvard Unv. Press, Cambrdge, MA, 1965. 4. E. Ostrom, Governng the Commons: The Evoluton of Insttutons for Collectve Acton, Cambrdge Unv. Press, New York, 199. 5. E. Ostrom and R. Gardner, Copng wth asymmetres n the commons: Self-governng rrgaton systems can work, J. Econom. Perspect. 7, 93 11 Ž 1993.. 6. T. Sandler, J. Cauley, and J. Tschrhart, Toward a unfed theory of nonmarket nsttutonal structures, Austral. Econom. Papers 4, 33 54 Ž 1983.. 7. P. Seabrght, Managng local commons: Theoretcal ssues n ncentve desgn, J. Econom. Perspect. 7, 113 134 Ž 1993.. 8. P. Seabrght, Is cooperaton habt formng? n The Envronment and Emergng Development Issues Ž P. Dasgupta and K. G. Maler, Eds.., Clarendon, Oxford, UK, 1994. 9. R. Seth and E. Somanathan, The evoluton of socal norms n common property resource use, Amer. Econom. Re. 86, 766 788 Ž 1996.. 30. G. J. Stgler, A theory of olgopoly, J. Polt. Economy 7, 44 61 Ž 1964.. 31. W. K. Vscus and R. J. Zeckhauser, Optmal standards wth ncomplete enforcement, Publc Polcy 7, 437 456 Ž 1979.. 3. R. Wade, Vllage Republcs: Economc Condtons for Collectve Acton n South Inda, Cambrdge Unv. Press, Cambrdge, UK, 1987. 33. P. N. Wlson and G. D. Thompson, Common property and uncertanty: Compensatng coaltons, Econom. De elop. Cultural Change 41, 99 318 Ž 1993..