E C O L O G I C A L E C O N O M I C S 6 2 ( 2 0 0 7 ) 4 6 1 – 4 7 2

ava i l ab l e a t www.sc i enced i rec t . com

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ANALYSIS

The economics of wildlife farming and endangeredspecies conservation

Richard Damaniaa, Erwin H. Bulteb,c,⁎aWorld Bank, Washington DC, USAbDepartment of Economics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, NetherlandscDevelopment Economics Group, Wageningen University, Netherlands

A R T I C L E I N F O

⁎ Corresponding author. Department of EconoE-mail address: rdamania@worldbank.org

0921-8009/$ - see front matter © 2006 Elsevidoi:10.1016/j.ecolecon.2006.07.007

A B S T R A C T

Article history:Received 21 November 2005Received in revised form12 June 2006Accepted 6 July 2006Available online 28 August 2006

There is growing concern that the traditional “protectionist” approach to conservation isexpensive and insufficient to deliver the desired environmental outcomes. “Supply side”policies to conserve endangered species have drawn support. By generating supplies fromcaptive-bred animals, wildlife commodity prices are expected to fall, thereby lowering theincentive to poach species in the wild. Supply side policies, however, often neglect theinstitutional framework withinwhich thewildlife trade takes place, and ignore the potentialstrategic responses of economic agents. Adopting a model that captures imperfectcompetition between traders and farmers, we analyze the effect of supply side policiesand conclude that under some circumstances these policies may contribute to furtherdevastation of wild stocks. We derive conditions under which captive breeding contributesto conservation, and discuss implications for policy makers.

© 2006 Elsevier B.V. All rights reserved.

Keywords:PoachingPreservationStorageTrade banLaunderingSmugglingPrice competitionQuantity competitionTiger farmsBear farms

1. Introduction

Protecting endangered species is expensive. The opportunitycost of conserving habitat may be high (and could escalatefurther as the human population in the vicinity of protectedareas increases), and protecting animals from poaching in-volves substantial additional costs. Estimates of theamounts required to prevent poaching range from US$200to $500 per hectare in Africa (e.g., Parker and Graham, 1989;Burton, 1999), and often-times exceed actual expenditures

mics, Tilburg University,(R. Damania), e.h.bulte@u

er B.V. All rights reserved

on enforcement (e.g. Dublin et al., 1995). Since many of theworld's threatened high-profile species are found in devel-oping countries with limited resources and tight budgetconstraints (e.g. tigers in Asia, elephants and rhinos in Africaand South Asia), it is no surprise that enforcement expen-ditures lag behind recommended rates. As a result, manyspecies demanded on markets suffer from intense poachingpressure.

Given these difficulties, conservationists have looked foralternativeways to conservewildlife (e.g. VanKooten and Bulte,

P.O. Box 90153, 5000 LE Tilburg, Netherlands.vt.nl (E.H. Bulte).

.

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2000). Economists have proposed a consistent set of recom-mendations, which flow naturally from first principles in eco-nomics. Rather than trying to keep poachers out of protectedareas at enormous costs - driving up prices on black markets,possibly increasing the incentive to hunt - alternative “supply-side” policies have been proposed. Stated simply, the recom-mendation is to flood the market for wildlife commodities withcaptive-bred varieties and other alternatives. This will depressprices and make poaching unprofitable, thus allowing wildpopulations of endangered species to recover. The supply sidesolution appears to have gained considerable popular support.For example, an influential publication provocatively asserts: “Ifthe global captive population of tigersweremanaged like a cashcrop… in no time the domestic tiger would be an importanteconomic resource and poaching wild tigers would be about asprofitableashunting forheneggs inthe jungle” (Asiaweek, 1993).

Captive breeding has been recommended as a way to en-sure a steady supply of bear bile, tiger bones and rhino horn,thus protecting wild bears (Mills et al., 1995), tigers (Sieden-sticker et al., 1999) and black rhinos (Brown and Layton, 2001).Similar policies have been recommended to curb the buoyantillegal trade in live endangered species such as birds andreptiles (Commonwealth of Australia, 1998). There are at leasttwoalternativeways to generate additional supplies and lowerwildlife prices. First, prices can be depressed by developingclose substitutes for commodities obtained from the wild.1

Second, as a possible temporary solution, prices may belowered by sales from stockpiles. Kremer and Morcom (2000),for example, have proposed the use of stockpiled ivory as aninstrument to manipulate poaching intensity, and Brown andLayton (2001) describe how sales of stockpiled rhino hornmight help address poaching of black rhinos.2

For the analysis that follows, it does not matter which type ofpolicy is considered. Since trade in most endangered species iseither regulated or banned by CITES,3 a key decision common toall approaches iswhether segments of the (international) trade incommodities shouldbe legalizedso that the legal tradecancrowdout the illegal trade. For concreteness the discussion is cast intermsofpoachingandcaptivebreeding, butwebelieve theresultsare sufficiently general to spill over to the other cases as well.

To our knowledge, the supply side approach to conserva-tion has not been subjected to close scrutiny. Moreover,conservationists appear to be reluctant to adopt thesepolicies without further analysis. In light of the uncertaintiesthat surround this issue, themain objective of this paper is to

1 For instance in a recent study Von Hippel and Von Hippel(2002) compared the (legal) trade in three wild animal products(velvet from reindeer antlers, harp seal and hooded seal penises)that are prescribed as aphrodisiacs in traditional orientalmedicine. Between 1988 (the year that Viagra went on sale) and2000, trade in all three commodities plummeted by 70%. Theauthors suggest that the availability of a less expensive andscientifically endorsed substitute has virtually eliminated de-mand for the wild animal product.2 A possible alternative approachmaybe to influence demand for

wildlife commodities, through publicity campaigns. It is oftenargued that burning stockpiled ivory by former Kenyan presidentDaniel arapMoi in 1989 had a profound effect on demand for ivory.3 Currently trade in about 30,000 species is subject to regulations

(Appendix II) or banned (Appendix I).

evaluate the prospects of supply-side policies for conserva-tion. We extend the basic model to better capture the truemarket situation, and demonstrate that supply-side policiesmay be counterproductive. Specifically, assumptions withrespect to demand (preferences forwildlife commodities), theinstitutional framework and responses of commodity tradersare very important.

The organization of the paper is as follows. In Section 2 wepresent the conventional model and discuss its implicit as-sumptions. In Section 3 we extend the basic model by intro-ducing imperfect competition. InSections4and5wediscuss theimplications of captive breeding in this context, and discuss theconditions under which the supply side approach is likely tosucceed or fail. In Section 6 we apply the theory to the case ofrhino farming. The conclusions and policy implications ensue.

2. The simple model and some caveats

2.1. The basic poaching model

In this section we sketch the basic model spurring theoptimistic belief that supply side policies can contribute toconservation of endangered species. The model is based onthe assumption of “poachers”, harvesting an animal popula-tion under conditions of open access (e.g., Berck and Perloff,1984; Bulte and van Kooten, 1999). Individual poachers do nothave property rights to the resource, and typically act as staticoptimizers. Entry in the “poaching sector” takes place as longas the returns to poaching for themarginal entrant exceed thereturns to effort elsewhere in the economy, and exit occurswhen the reverse is true.4 Assume that the marginal cost ofpoaching effort increases in effort, and that individuals cansupply one unit of effort (so that aggregate effort is identical tothe number of poachers). Increasing marginal poaching costsare caused, for example, if individuals have to be attractedfrom other increasingly profitable alternative occupations.Denoting U as the net payoff from poaching for the marginalpoacher, the dynamics of aggregate poaching effort E aredefined as (suppressing time notation):

E: ¼ gU ¼ g½dðsqÞ=dE−dðWE/Þ=dE�; ð1Þ

where Ė=dE /dt or a derivative with respect to time, η is anadjustment parameter; s is the net price received by poachersper unit harvested (paid by commodity traders); q is the totalquantity harvested; and WN0 and ϕN1 are cost parameters.We assume ϕ=2 in what follows. Note that the specification inEq. (1), unlike the standard model by Gordon (1954), does notimply complete rent dissipation even though there is freeentry—differential opportunity costs of time imply theexistence of positive inframarginal rents for poachers whocan supply effort at low cost. Also note that, for simplicity, wehave omitted the probability of being caught and penalizedfrom the analysis — a central feature in many models ofpoaching. If poachers are risk neutral this does not affect the

4 See Bulte and Horan (2003) for a model where poaching andthe alternative activity are ecologically and economically inter-connected (see also Schulz and Skonhoft, 1996).

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qualitative nature of the results — it means that we are omit-ting an expected return term, that has a similar effect as theopportunity cost of poaching.

In conventional poaching studies harvesting is typicallydescribed by a Schaefer production function, q=σxE, where σis a catchability coefficient and x represents the wildlife stock(Milner-Gulland and Leader-Williams, 1992a; Bulte and vanKooten, 1999). Assuming that biological growth of the resourceis described by a logistic function, the dynamic system iscomplemented by the differential equation:

x: ¼ gðxÞ−q ¼ rxð1−x=kÞ−rxE; ð2Þ

where g(x) describes the biological growth of the resource, r isthe intrinsic growth rate and k is the carrying capacity. Thesteady state of the dynamic system is at the intersection of theE.=0 isocline (defining zero profits) and the x

.=0 isocline

(defining zero net growth), and the steady state populationof the endangered species is defined as:

x* ¼ zrksr2kþ zr

; ð3Þ

where z=2W. Observe that dx⁎/dsb0. Decreasing the price forthe poached commodity s rotates the Ė=0 isocline down-wards. As a result, the steady state effort level declines and thesteady state wildlife stock rises. This implies fewer peoplechasing more animals.5

2.2. The basic model: wildlife commodity traders as pricetakers

How does poaching respond to changes in demand or supplyfrom other sources? To analyze this question, we distin-guish between poachers and traders (or middlemen). Inves-tigations suggest that the illegal trade in wild animalproducts is organized and controlled by a relatively smallnumber of traders, while poaching and trapping may becarried out by subsistence forest dwellers under open accessconditions. Milner-Gulland and Leader-Williams (1992b:199), for example, write: “There are relatively few middle-men, who effectively control the exploitation of the wildliferesource. There is evidence that a single dealer controlledmost of the hunting in Luangwa Valley [Zambia]. Theorganized part of the poaching industry is probably operatedby this dealer much like any other business with exclusiverights in its territory.”

First assume the simple case where wildlife traders,trafficking the poached commodity across borders, are pricetakers on international markets. That is, traders are monopso-nists when it comes to purchasing wildlife commodities frompoachers but sell their output elsewhere (say, on Asianmarkets) taking prices as given. Assuming instantaneous entry

5 The effect on harvesting in the steady state is ambiguous.Harvesting would be ambiguously affected even if both effort andstocks went up (or down). This is due to the backward bendingsupply curve that is implied by the logistic growth function(Copes, 1970). See Berck and Perloff (1985) for an analysis of theimpact of backward bending supply on the profitability of captivebreeding (fish farms).

and exit of poachers so that the marginal entrant never earnsany rent, the equilibrium effort and harvest rates for a givenprice s are defined as:

E* ¼ srx=z;and ð4Þ

qw ¼ rEx ¼ ðsr2x2Þ=z ð5Þ

In Eq. (5), the superscript w refers to taken from the wilds.Price-taking wildlife traders maximize the following function:

Cw ¼ Pqwp −sqwp ; ð6Þ

where P is the exogenous market price per unit of output.Substituting Eq. (5) in Eq. (6) and maximizing with respect to syields as an optimal trader-poaching price s⁎=P /2, so that:

qwp ¼ ðPr2x2Þ=2z: ð7Þ

From Eq. (7) is clear that any policy or shock that reduceswildlife commodity prices will also reduce poaching (dqpw /dPN0). Captive breeding policies (promoting additional supply)or consumer awareness campaigns (shifting demand) there-fore both contribute to conservation of wild stocks, assummarized in Proposition 1.

Proposition 1. Ceteris paribus, the introduction of farmedanimal products will decrease the level of poaching relative tothat which occurs in the absence of farming for any given wildlifestock if commodity traders are price takers.

2.3. Two implicit but important assumptions

The reasoning above is incomplete as it rests on two implicitassumptions that do not hold in many cases. First, it isassumed that there exists a stationary downward slopingdemand functionalongwhich theadditional supply of captive-bred products will depress prices. A number of studies castdoubt on the validity of this assumption. Much of theinternational trade in wildlife commodities is regulated byCITES. While these trade restrictions are circumvented on aroutine basis by criminal networks, there is evidence thatsmuggling is easier when illegal supplies may be “laundered”and sold under the cover of legal supplies (e.g. Fischer, 2004).6

Legal supplies from captive-bred animals may also increasedemand by lowering the social and legal sanctions forconsuming wildlife products (Servheen, 1995; Nowell, 2000).Furthermore, as noted byMeacham (1997), when commoditiesfrom the wild and farms are perceived as different products,with farmed varieties perhaps lacking the potency of the wildproducts, the legally available farmed commodity may arouse

6 This potential problem is one of the main reasons why theivory trade ban is still in place, even though in parts of Africaelephant densities exceed environmentally sustainable levelsConservationists are concerned that poached ivory from, sayEastern Africa or Asia may be sold under the cover of legal ivoryoriginating in Southern Africa where elephants are plentifu(Dobson and Poole, 1992).

.,

l

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the interest ofnewconsumersandeventually stimulatedemandfor the authentic product — a “stepping stone” argument.

Perhaps of greater significance is the other strong assump-tion thatwildlife traders are price takers, or that themarket forwildlife commodities is perfectly competitive. As notedearlier, the illegal trade in endangered species and wildlifecommodities is spatially controlled by a small number oforganized and often criminal groups (e.g., Meacham, 1997;Galster et al., 1994; Galster and Elliot, 2000; WPSI, 2001;Commonwealth of Australia, 1998). Traders act as an inter-mediate agent between poachers and consumers or retailers,setting prices for poachers and determining the quantities torelease on the market.7

Evidence suggests that markets for wildlife commoditiesare characterized by supernormal profits and imperfectcompetition, possibly giving rise to strategic behavior. Theglobal illegal trade in wild animals is measured in the billionsof dollars, and law enforcement authorities suggest that incountries such as India the profitability of the trade is secondonly to that of narcotics (IUCN, 2000; Wildlife Trust of India,2001; WCS, 2002).8 Owing to the clandestine nature of theillegal trade more precise estimates are unavailable.

In the analysis below we analyze the implications ofrelaxing the assumption of a perfectly competitive marketfor wildlife commodities. The remaining effects (launderingeffect and changing consumer preferences) are captured byassuming that the inverse demand curve for wildlife com-modities may shift as a result of captive breeding. Hence,given a level of supply, the “net” price that the traders receive(that is, the market price minus transaction costs) mightincrease.9 The resulting ambiguous effect on residual demand

7 Such criminal networks possibly exploit economics-of-scale insmuggling as the illegal trade in wildlife is often accompanied bytrade in narcotics, arms, gems, and people (WPSI, 2001; Galster etal., 1994; Milner-Gulland and Leader-Williams, 1992b).8 A certain fraction of these profits may be lost because the

incumbent trader attempts to deter entry by others (think ofcostly “cocaine wars”), or transfers part of the rent as a bribe topolicy makers or forest officials. It may also be objected that theserents are purely a reflection of the risk premium required toengage in illegal activities. The evidence suggests that this seemsunlikely for the trade in some wildlife commodities. For instance,no trader has ever been convicted for dealing in illegal tiger partsand the penalties are low (US$500) compared to the payoffs fromthe sale of products from each tiger (US$2500–10,000) (WPSI,2001). Moreover, only two tiger poachers have ever been convictedin India (the main source of tiger bones and organs) despite aflourishing illegal industry in tiger poaching (WTI 2001). Thissuggests that the potential risks (and, hence the required riskpremium) of conviction and apprehension are low. Recentsimulation work suggests tiger survival is likely less caused byrent-dissipation through bribing or by the protection afforded byofficial conservation agencies, than by the difficulty in locatingthese animals in dense tropical forests (Karanth and Stith, 1999;Damania et al., 2003).9 While this assumption is convenient and logical for the case of

changing consumer preferences, the “laundering effect” is morenaturally captured by assuming that the marginal costs curve(supply curve) has shifted out. However, since the qualitativeresults are identical, we simplify the exposition by assuming thatall effects may be combined into the shifting (inverse) demandcurve.

for commodities from the wild is consistent with actualexperience of captive breeding. For example, Meacham(1997:169) argues the laundering effect has caused the (near)extinction of the wild crocodile in Thailand. “There was a wildcrocodile population in Thailand once, but it virtually ceasedto exist within a few years of the crocodile farms starting.” Incontrast, according to Mills et al. (1995) widespread bearfarming in China in the 1990s has stabilized Chinese prices forbear bile, while prices have increased substantially elsewherein Asia.

3. An imperfect competition model

We characterize the case where traders sell output onimperfectly competitive markets by developing a stylizedthree-stage game. In the first stage the traders of wild animalproducts set the remuneration to be paid to poachers. In thefollowing stage the poachers determine the harvest of wildanimals, taking as given the prices set by the traders. In thefinal stage the traders sell the wild animal products toconsumers. For the second stage in the game, the basemodel presented above is directly applicable.

For analytical tractability the results are based on twosimplifying assumptions. First, we adopt the stylized assump-tion of competition between a single wildlife trader andfarmer—a standard duopoly model. The assumption ofduopolistic competition is admittedly a strong one: whilewildlife traders may act as monopsonists in certain countries,they likely face some competition from other traders oninternational commodities. However, it is well known that thequalitative results apply more generally (albeit in a dilutedform) to situations of oligopolistic trade more relevant for theproblem at hand.10 Even with several players and spatialarbitrage of commodities, traders can retain some degree ofmarket power. When the trade is clandestine, markets arelikely imbued with informational imperfections conducive totraders accruing market power through the existence of in-formational rents. A necessary condition for the qualitativeresults in this paper to spill over to the oligopoly context is thattrade in animal products generates positive profits—a condi-tion that is supported by all the evidence that we have beenable to retrieve.11 The case of imperfect competition on themarket for illegal commodities is well documented and hasbeen briefly discussed above. More surprising, perhaps, isevidence that captive breeding of some species is also subjectto increasing returns to scale (be it through fixed costs, infor-mational asymmetries or regulation-see Mills et al. (1995) forsupport of this notion). We distinguish cases where compe-tition in the retail markets involves price setting (Bertrand

10 We have an appendix available on request in which wedemonstrate how the results are affected by assuming oligopo-listic competition in the farming or trading sector (the simula-tions presented in Section 6 also confirm this finding).11 We already discussed that trading wildlife commodities isprofitable. Mills et al. (1995) report that captive breeding of bearsis also a profitable activity, generating rates of return in the rangeof 70%–90%. One explanation for the existence of such profits isregulation that restricts entry in this sector.

12 Note that this is the same equilibrium outcome that even-tuates when traders set s (instead of qw) in the final stage of thegame to maximize profits taking account of the optimumresponse in Eq. (12).

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competition) and quantity setting (Cournot competition) bythe two suppliers.

Second, because the trader lacks formal property rights andis uncertain about future access to the resource (eitherbecause of greater future policing, or perhaps the risk ofbeing displaced by rivals), we follow the conventional assump-tion in the open access literature that the trader solves a staticoptimization problem, maximizing profits in every period.

3.1. The no-farming equilibrium: trader as a monopolist

As a benchmark for future comparison, consider first theequilibrium when there is no captive breeding program andthe (sole) trader is a monopolist. Given the sequential natureof events, the trader will determine the price paid for eachharvested animal, taking account of the poachers' optimalresponses and demand in the downstream retail market. Bybackward induction we begin by solving the final stage of thegame.

We develop the model assuming a linear inverse demandfunction for the trader in the retail market as this assumptionallows us to operationalize different substitution possibilitiesin a relatively straightforward manner below:

Pm ¼ am−bwqw; ð8Þ

where Pm is price of wild animal products and qw is output ofwild animal products, αm, βwN0 are parameters (the super-script m refers to monopoly, the superscript w refers toproducts taken from the “wild”). The trader's payoff functionis given by:

Cm ¼ ðam−bwqw−c−sÞqw; ð9Þ

where s is the remuneration paid to poachers for each unit ofharvest, c represents all the costs associated with thetransportation and final sale of wild animal products. Theoutput level that maximizes profits is defined by the first-order condition:

ACm

Aqw¼ am−2bwqw−c−s ¼ 0: ð10Þ

Solving for the optimal output level:

qewm ¼ am−c−s

2bw: ð11Þ

In the second stage, as noted above, poachers determinethe harvest of wild animals, taking as given the remunerationrate set by the trader and the in situ stock:

qwp ¼ ðsr2x2Þ=z: ð12Þ

To ensure that the harvest of wild animals is sufficient tomeet the needs of the traders, the remuneration paid topoachersmust satisfy the condition: qpw= q̃m

w. Equating Eqs. (11)and (12) and solving yields the equilibrium remuneration paidto poachers:

sm ¼ zðam−cÞ2bwr2x2 þ z

: ð13Þ

Finally, using Eq. (12) the equilibriumharvest ofwild animalswhen there is no captive breeding program is defined by12:

qm ¼ ðam−cÞr2x22bwr2x2 þ z

: ð14Þ

Assuming an interior steady state exists, it may be foundnumerically by equating the monopolist's optimal harvestwith natural growth: qm=g(x). Note that this implies solving athird-order polynomial when g(x) is a logistic function.

4. Captive breeding, imperfect competitionand conservation

4.1. Demand functions

Whencaptive-bredanimalproductsare introducedto themarket,the inverse demand for poached wild animals is modified to:

Pi ¼ awðqFÞ−bwqw−gqF; ð15Þ

where qF is the supply of captive-bred farmed animal productsand qw is the supply of commodities from the wild. To ensurepositive output levels over some ranges it is assumed that αi(q j)Nβ i (i,j=w,F; i≠ j).Observe that γ is a measure of the degree ofsubstitutability between the products. When γ=β i the goods areperfect substitutes. We assume γ≤β i (i=w,F), so that the ownprice effects on demand are no less than the cross price effects(alternatively, one could consider the case of vertically differen-tiated products where the legal produce is always preferred tothe illegal one — ceteris paribus). Captive breeding redistributesdemand to the legal sector, captured by the term γqF, and mayalsoaffect “laundering costs”or consumerpreferences (capturedby the argument qF in the demand curve's intercept αw(qF) whereAαw /AqFN0). For analytical tractability we treat αw(qF) as aparameter αw in what follows, but we consider the comparativestatics with respect to this parameter in detail. That is, we takethe casewithout demandshifts as a benchmark, and explore theconsequences of Aαw/AqFN0 later.

Analogously, the inverse demand for farmed animalproducts is:

PF ¼ aF−bFqF−gqw: ð16Þ

Rearranging Eqs. (15) and (16), the direct demand functionsmay be expressed as:

qw ¼ aw−bwPw þ ePF;and ð17Þ

qF ¼ aF−bFPF þ ePW ; ð18Þ

where ai=(αiβ j−αjγ) / (β iβ j−γ2), bi=β j / (β iβ j−γ2), e=γ / (β iβ j−γ2)for i,j=w,F and i≠ j.

It is possible to consider the Nash equilibrium thateventuates when players are allowed a free choice of theinstruments of competition-prices or quantities. If the firmscan pre-commit to either competing in prices or quantities,

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the dominant strategy can be shown to be quantity compe-tition. However, with asymmetric players there exist circum-stances under which firms have an incentive to defect fromthis strategy. In the absence of a credible commitment deviceit is difficult to rationalize how any agreement with an illegalsupplier can be enforced. For that reason we consider bothcases in what follows–though we return to this issue in theConcluding section13.

4.2. Cournot competition in the retail market

Webegin by considering the effects of Cournot competition (i.e.competition through quantity setting) the farm sector and thetraders in the final stage of the game. The farm sector's andwildlife trader's payoff functions are given by, respectively:

CF ¼ ðaF−bFqF−gqw−mÞqF and Cw ¼ ðawbwqw−gqF−s−cÞqw; ð19Þ

where ν denotes production costs of captive breeding. UnderCournot competition each supplier sets output levels, taking itsrival's output as given. Differentiating Eq. (19) with respect toown output (qF and qw, respectively) and solving yields thereaction functions:

rFðqwÞ ¼ aF−gqw−m2bF

; and rwðqFÞ ¼ aw−gqF−s−c2bw

: ð20Þ

Solving Eq. (20), output levels for a given s are:

qe Fc ¼

2bwðaF−mÞ−gðaw−s−cÞð4bFbw−g2Þ and

qewc ¼ 2bFðaw−s−cÞ−gðaw−mÞ

ð4bFbw−g2Þ :

ð21Þ

Substituting Eq. (21) in Eq. (19) gives the Cournot reduced-form profit function for w:

Ce wc ¼ bw

2bFðaw−s−cÞ−kðaw−mÞð4bFbw−g2Þ

!2

: ð22Þ

The trader sets the level of remuneration (s) paid topoachers to maximize Eq. (22) subject to the condition thatq̃cw=qpw. Equating Eqs. (12) and (21), the optimal remuneration

under Cournot competition is:

sc ¼ wð2bFaw−gðaF−mÞ−2cbFÞr2x2Dþ 2wbF

; ð23Þ

where Δ=4βFβw−γ2. Substituting in Eq. (21), equilibriumsupplies under Cournot competition are:

qFc ¼r2x2ð2aFbw þ gðaw−cÞ−2bwmÞ þwðaF−mÞ

2bFwþ r2x2D;and ð24Þ

qwc ¼ r2x2ð2awbF−gðaF−mÞ−2bFcÞ2bFwþ r2x2D

: ð25Þ

The following Lemma compares poaching levels before andafter the introduction of captive breeding, when the para-

13 In an Appendix available from the authors we provide a formalanalysis of different forms of competition, based on work byKreps and Scheinkman (1983).

meters of the demand function are held constant. All proofsare in Appendix A.

Lemma 1a. For any given wildlife stock, poaching levels in anequilibriumwith captive breeding will be lower than those withoutcaptive breeding, if the introduction of captive-bred animal productshas no impact on the parameters of the original inverse demandfunction for wild animal products. (i.e. qm

wNqcw if αm=αw).

Intuitively, under Cournot competition each firm max-imizes profits taking as given its rival's output. Thus, comparedwith the monopoly case, the introduction of a substituteproduct lowers the (residual) demand for wild animal parts.Thus, themarket share and profitability of wild animal tradingdecline and poaching levels fall. Lemma 1a suggests thatgreater competition in themarket forwild animal productswillhave the desired effect of reducing poaching levels.

The following Lemma describes the effects of varying de-mand in themarket forwildanimalparts. Enhancedpossibilitiesfor laundering illegal commodities or changing consumer pref-erences will shift demand out. Demand variations may thusoccur either through changes in the level of demand (i.e. αw).

Lemma 1b. If the intercept of the demand curve for wildcommodities increases, poaching levels will increase for any givenwildlife stock.

This outcome accords entirely with intuition. Higherdemand increases the payoffs from trading in wild animalparts and hence poaching levels increase. Lemmas 1a and 1bsuggest the following result, which is consistent with conven-tional wisdom:

Proposition 2. The introduction of farmed animal products willreduce poaching if the demand for wild animal products isunchanged and competition in the retail market occurs throughCournot competition.

To assess the generality of this conclusion it is clearlynecessary to determinewhether these results continue to holdwhen competition occurs through price setting.

4.3. Bertrand competition in the retail market

Consider next the case when competitors in the retail marketset prices (i.e. there is price competition with differentiatedproducts). Using the direct demand functions in Eqs. (17) and(18), the farmer's and trader's payoff functions are given by,respectively:

CF ¼ ðPF−mÞqF and Cw ¼ ðPw−s−cÞqw; ð26Þ

where qF= (aF−bFPF+ePw) and qw=(aw−bwPw+ePF). Differentiatingwith respect to ownprice (PF and Pw) and solving yields the pricereaction functions:

RFðPwÞ ¼ aF þ ePw þ bFm2bF

; and

RwðPFÞ ¼ aw þ ePF þ bwðcþ sÞ2bw

:

ð27Þ

Fig. 1 –An example with 3 equilibria (vi-a and vi-c are stable,and vi-b is unstable).

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Solving Eq. (27) for a given s gives the equilibrium prices:

PFB ¼ 2bwðaF þ mbFÞ þ eðaw þ ðsþ cÞbwÞ4bwbF−e2

;

PwB ¼ 2bFðaw þ ðsþ cÞbwÞ þ eðaF þ mbFÞ4bwbF−e2

:

ð28Þ

Solving, for the equilibrium level of s as described above:

sB ¼ wbwðbFð2aw þ emÞ þ eaF þ cðe2 þ 2bwbFÞÞX

; ð29Þ

where Ω=σ2x2(4bFbw−e2)+wbw(2bFbw−e2). Substituting Eqs.(28) and (29) into the demand function for w:

qwB ¼ r2x2bw½bFð2aw þ em−2bwcÞ þ eðcþ aFÞ�X

: ð30Þ

Lemma 2a compares poaching levels before and after theintroduction of captive-bred animal products.

Lemma 2a. With Bertrand competition, poaching levels in anequilibrium with captive breeding will exceed poaching levelswithout captive breeding for any given wildlife stock, if theintroduction of captive-bred animal products has no impact on theparameters of the demand function for wild animal parts (i.e.qBwNqcw if αm=αw).

The intuition for this result is the following. In the absenceof captive breeding the trader, as a monopolist, maximizesprofits by restricting supply. In contrast, when playerscompete by setting prices there is intense competition in themarket, inducing an expansion in output levels and aconsequent increase in poaching levels. This finding suggeststhat if captive breeding results in aggressive competition inthe retail market, it will increase poaching levels and thereforebe counterproductive. It appears that this facet of competitionhas been overlooked in proposals to introduce captivebreeding programs.14

Lemma 2b. With Bertrand competition, if the intercept of theinverse demand function for wild animal products increases, thelevel of poaching increases for any given wildlife stock.

Lemmas 2a and 2b combine to suggest the following result.

Proposition 3. The introduction of farmed animal products willincrease the level of poaching relative to that which occurs in theabsence of farming for any given wildlife stock, if the demand for

14 It is useful to compare the effects of product differentiation onBertrand and Cournot equilibria. Mills et al. (1995) suggest thatbile from farmed bears (and even animal bile from differentspecies) has gained greater acceptance over the last decade. Inour specification of demand, the term γ measures the degree ofproduct differentiation. By inspection of Eqs. (25) and (30), notethat as γ→0, the demands become more independent so thatqcw→qmw and qBw→qmw (in the extreme case of independent goodsthe outcome converges to the monopoly equilibrium derived inSection 3). Thus, as the degree of substitutability increases, asappears to have occurred with bear bile (Mills et al., 1995), theeffects of strategic interaction will become more pronounced overtime.

wild animal products is either unchanged or increases andcompetition in the retail market occurs through Bertrandcompetition.

Proposition is an example of the fact that a monopolist —even if it is a trader in wildlife commodities — can be a con-servationist's best friend (Solow, 1974; see also Buchanan,1969).

Finally, in case of Bertrand competition between farmerand trader and if farmed and wild output are perfectsubstitutes (γ=β), the usual Bertrand result applies. Withasymmetric costs, the more efficient producer will drive outthe higher cost producer (Tirole, 1988: 211). If farmers are ableto undercut traders, all poaching will cease in equilibrium.However, since the costs of raising species like bears, tigersand rhinos are considerable (a tiger eats some 2000–3000 kg ofmeat per annum, and the price paid to poachers, s, is typicallyin the range of $15–25), we conclude that the reverse is morelikely to happen for many charismatic species in the absenceof government intervention.

5. Steady states of the myopic Cournot andBertrand competition models

We now consider the interaction between myopic harvestingby poachers and stock regeneration. Assuming that theinitial stock corresponds with the monopolist's steady stateas discussed in Section 3, does captive breeding promote orundermine long-run wildlife abundance? To answer thisquestion, we first need to explore how many steady statesmay exist in the long run. Note that Eqs. (14), (25) and (30)define harvest functions q that are increasing and concavein stocks (x), and start from the origin (x=0, q=0). We canunambiguously “rank” the poaching functions; for a givenwildlife stock x, the harvest function for price competition(Cournot competition) is located above (below) the monopolyharvest function: qB(x)NqM(x)NqC(x), ∀xN0. The growth func-tion g(x) is also concave starting from the origin. Wedistinguish between 2 cases: for x→0, it may hold that q′(x)Ng′(x), or it may the case that q′(x)bg′(x). If the reduced-form harvest function q intersects the growth curve g(x)from below (above), the resulting steady state is stable(unstable).

If q′(x)Ng′(x), the poaching function is steeper than thegrowth function for low values of x. There may be (i) noequilibria (if q(k/2)NMSY), (ii) a single bifurcation point (if q(x)

Table 1 – Captive breeding and steady state rhino stocks inthe wild: base models

Competitionform

Low stableequilibrium

Unstableequilibrium

High stableequilibrium

No farming 2625 7346 90,030Cournot – – 91,370Bertrand 0 8480 83,470

468 E C O L O G I C A L E C O N O M I C S 6 2 ( 2 0 0 7 ) 4 6 1 – 4 7 2

and g(x) are tangent at intermediate levels of abundance), or (iii)two interior equilibria (one stable and one unstable). The casewhere q′(x)bg′(x) is more interesting for out purposes because itcorrespondswith the rhino case studybelow. Ifq′(x)bg′(x) holds,the growth function is steeper than the harvest function for lowvalues of x. Depending on the parameters, there may be (iv) asingle equilibrium, (v) a steady state and a bifurcation point, and(vi) three interior equilibria. The latter case is illustrated in Fig. 1.Note that q now (vi-a) first cuts g(x) from below (stableequilibrium, xbk /2), next (vi-b) q(x) cuts g(x) from above(unstable, xbk/2), and finally (vi-c) q(x) cuts g(x) from below(stable, xNk/2).

Our main results with respect to long-run wildlife abun-dance and captive breeding are summarized in Proposition 4.

Proposition 4. The stable steady state wildlife population thatresults with Cournot (Bertrand) competition is unambiguouslylarger (smaller) than the wildlife stock without captive breeding.Steady state harvesting is ambiguously impacted.

This result is readily derived from Fig. 1 if we imagine thatthe displayed harvest function q represents the monopolycase, and that Bertrand (Cournot) competition is representedby slightly moving q up (down)-recall, optimal harvestingunder Bertrand (Cournot) competition is strictly greater(smaller) for a given in situ stock. As a result, for stableequilibria where q cuts g(x) from below it must hold that thenew steady state occurs strictly to the left of the initialequilibrium under price competition (corresponding withsmaller stocks). Similarly, the new stable steady state occursstrictly to the right of the initial equilibrium with Cournotcompetition.15

16 That is we solve the equation sqp−wE2=0 for x=2600.Thisequation was solved for a range of values of c=(50, 500) and thenumber of traders n=(1, 20). The resulting solution for w rangedfrom w=(2.18, 7.6). We adopt the mid-point and set w=5. Varyingthe value of w had little qualitative impact on the results. Milner-Gulland and Leader-Williams (1992a) analyze the poaching inZambia, and assume that poaching costs are proportional to the

6. Empirical application: rhino farming

In this section we demonstrate the relevance of our analysisby applying the model to the case of rhino poaching andfarming in Africa. We calibrate the models using dataprovided by Milner-Gulland and Leader-Williams (1992a,b)and Brown and Layton (1997, 2001). We have incorporated afew simplifications consistent with the theoretical specifica-tions above, and therefore stress that the quantitativeresults must be considered an approximation. Specifically,we adopt the following three simplifying assumptions. (1)Rhino growth is described by a logistic growth function, asopposed to the skewed growth function common in theecological literature: g(x)=0.16x(1−x /k) where k=100,000animals is the carrying capacity or the historical level ofabundance according to Dublin and Wilson (1998). (2) The(inverse) demand function for rhino horn is assumed linear-we have fitted a line through the price-quantity observationsprovided by Brown and Layton (2001), yielding p(q)=6182−2.13q, where q is the number of rhinos supplied and whereevery rhino carries 3 kg of horn. In the absence of any dataon substitutability, we have arbitrarily set γ=0.75, though we

15 Because the growth function is non-monotone in wildlifeabundance x the impact of captive breeding on the equilibriumharvest level is ambiguous.

consider the effect of varying this parameter. (3) We have setthe poaching cost parameter z so that the no-farming modelyields a steady state that is roughly comparable to thecurrent population of rhinos.16 Recent evidence suggests thatthe wild population of rhinos is not being over-harvested toextinction, but rather that the population stabilizes at thehistorically low level of about 2600 animals, see Dublin andWilson (1998). Finally, as a proxy for farming costs we usedehorning costs data provided by Brown and Layton and letv=$1000. Table 1 summarizes representative results for thebase cases of monopoly and duopolistic competition, whichserves as a theoretical benchmark for the results that follow.

As is evident from Table 1, the “no farming” (or monopo-listic trader) scenario is qualitatively consistent with Fig. 1 andallows for 3 interior steady states. In contrast, the Cournotmodel has a single (stable) steady state at a high level ofabundance and the price competition model has an unstableand a single stable equilibrium.

Table 1 suggests that captive breeding may have dramaticimplications for rhino abundance, given that currently thesystem is at the low stable equilibrium of the no farmingmodel (note that to arrive at that steady state, starting fromthe carrying capacity level, some exogenous shock musthave hit the system, temporarily depressing levels ofabundance below the unstable stock size). If the trader andfarmer engage in Cournot competition, increased competi-tion from farmed substitutes would result in a dramatic andstable recovery to near carrying capacity levels, likelyrendering captive rhino breeding into one of the largestconservation successes of all times. On the other hand, thenumerical results indicate that Bertrand competition dra-matically increases the likelihood of extinction. The lowsteady state equilibrium is pushed down and vanishes,suggesting the complete demise of the rhino population(while there are two other possible steady states, there areno trajectories to lead the system towards these equilibria,starting from the low stable equilibrium).

number of expeditions. If we calibrate our specification using themicro-data provided by Milner-Gulland and Leader-Williams, weobtain a value of w that is very close to the one used in thenumerical model. The qualitative results are unaffected if we usethis parameter instead.

Table 2 – Robustness check

# Agents Cournot model Bertrand model

#Farmers

#Traders

Low stableequilibrium

Unstableequilibrium

High stableequilibrium

Low stableequilibrium

Unstableequilibrium

High stableequilibrium

Analysis 1: varying the number of players0 10 2170 20,540 77,310 – 34,870 66,9200 100 2143 20,860 77,000 – – –2 2 – – 88,540 – 10,520 82,30010 2 – – 89,460 – 9033 82,820100 2 – – 89,970 – – –10 10 3392 12,300 84,310 – 22,360 84,81020 10 3498 11,960 84,540 – 33,440 72,25030 10 3599 11,650 84,750 – – –10 20 3318 13,340 83,270 – 26,250 75,89010 30 3295 13,180 82,890 – – –50 50 3441 13,730 82,830 – – –

Analysis 2: increasing the substitutability parameter (γ=0.9)0 1 2625 7346 90,030 2625 7346 90,0300 10 2170 20,540 77,310 – 34,870 66,9200 100 2143 20,860 77,000 – – –1 1 – – 91,840 – 8489 83,2902 2 – – 89,260 – 10,340 82,00010 2 – – 90,560 – 11,310 81,290100 2 – – 91,020 – – –10 10 0 9814 85,270 – 29,070 69,44030 10 0 7849 85,890 – – –10 30 0 11,750 83,700 – – –50 50 0 12,470 83,100 – – –

Analysis 3: increasing the cost of trading poached output (c=500)0 1 3218 5939 90,080 3218 5939 90,0800 10 2405 16,110 81,490 – 12,410 90,8500 100 2364 18,360 79,300 – – –1 1 – – 92,180 – 9548 92,62010 2 – – 90,460 – 9833 92,760100 2 – – 90,950 – – –10 10 0 9522 86,190 – 3095 75,73030 10 0 8875 86,510 – – –10 20 4102 10,590 85,310 – 60,770a

10 30 4049 10,960 84,990 – – –50 50 4302 10,550 85,150 – – –

Base Case Parameter values: c=50; w=5, ν=1000; α=6182, β=2.13, γ=0.75.a Indicates bifurcation point.

17 We also considered numerous other simulations (not re-ported) such as changes in farming costs, the slope and theintercept of the demand function. The main conclusions of themodel were unaffected by these changes.

469E C O L O G I C A L E C O N O M I C S 6 2 ( 2 0 0 7 ) 4 6 1 – 4 7 2

The form of competition thus significantly affects theharvest level, shifting steady states as discussed above, butpossibly triggering discontinuous jumps from one steady stateto another. We believe these numerical results clearly demon-strate that the behavioral underpinnings of wildlife marketsshould be of theutmost importance to policymakers—there is alot to win or lose. But without sufficient understanding of themarket, it is extremely hard to predict what outcome mightemerge. How robust are these findings with respect to keyassumptions about the number of participants and demandparameters?

As a robustness check we consider the effects of varyingthree assumptions. First, as noted earlier, the assumption of aduopolisticmarket is a highly contrived depiction of real worldmarket structures. Hence, in the simulations we investigatewhether the qualitative predictions of the model are sensitive

to variations in the number of players in the market (we haveformally solved the oligopoly model with n farmers and mtraders in an appendix available from the authors). Inaddition, we explore the consequences of varying the substi-tutability parameter γ and the cost of trading poachedcommodities. Representative results are summarized inTable 2.17 We emphasize that it is difficult to identify themost realistic depiction of the rhino horn trade— the numberof farmers is as yet unknown but will likely be the result offuture policy choices, the substitution parameter is unknown,and the type of competition that eventuates is also unknown.

470 E C O L O G I C A L E C O N O M I C S 6 2 ( 2 0 0 7 ) 4 6 1 – 4 7 2

Thereforewe viewTable 2 as an overview of possible scenarios(and a plea for follow up research), rather than as a clearprediction of what will happen when farming commences oras a guide to policy-making.

The results for Cournot competition are on the left handside of Table 2. There are two notable features. First, for anygiven number of wildlife traders, an increase in the numberof competitors from the farm sector leads to stable equilibriawith higher rhino numbers—a result consistent with Prop-osition 1. Second, for any given number of farmers, anincrease in the number of wildlife traders lowers rhinostocks. This is a consequence of the well-known result thatunder Cournot competition as the number of playersincreases, aggregate industry output converges to theperfectly competitive output level. Hence, even though anincrease in the number of traders results in each traderproducing less, the aggregate harvest of wild rhinos rises, sothat stocks decline.

Turning next to Bertrand competition. Consistent with thepredictions of the model the simulations suggest that anincrease in either the number of traders or farmers inducesmore aggressive competition and leads to lower rhino stocks.Extinction occurs as the number of competitors (whetherfarmers or traders) increase. For instance with 30 farmers and10 traders the rhino population is hunted to extinction.Moreover, in all the simulations where extinction does notoccur, there are two equilibria— a low unstable one and a highstable equilibrium. The stable equilibrium is declining mono-tonically in the number of competitors, thus greater compe-tition has detrimental environment consequences under pricecompetition.

Table 2 also presents results for the case where theparameter of substitutability γ is increased to 0.9. Thequalitative features of the equilibrium are unaffected. How-ever, with greater substitutability between farmed and wildproducts, the stable Cournot equilibrium populations arehigher than those reported in Table 1. Conversely, underBertrand competition, stable equilibria have lower stocks andas expected extinction occurs more rapidly as competitionfrom the farmed sector rises.

Finally we acknowledge the possibility that the introduc-tion of captive supplies may have an impact on the costparameter of the illegal traders. This impact is difficult todetermine a-priori: the introduction of captive suppliesmight facilitate laundering of wild supplies and thus lowertraders' costs (Fischer, 2004), but a captive breeding programmay also weaken the relative bargaining position of tradersvis-à-vis the retailers, or damage the supply infrastructure insome other way (raising costs). The bottom part of Table 2considers the effects of a ten-fold increase in traders' costsfrom $50 to $500 per rhino horn (the qualitative results oflower trading costs are just opposite to those presentedhere). The simulations suggest that the qualitative resultsare largely unaffected. Increasing the cost of trading wildcommodities lowers harvests under both Cournot and pricecompetition and thus generally leads to higher stocks. Thistherefore renders captive breeding more effective in protect-ing rhino stocks. However, if competition is sufficientlysevere, the population still remains vulnerable to extinctionunder price competition.

7. Discussion and conclusions

While strategic trade theories have gained a firm foothold inenvironmental economics since the mid-1990s (e.g., Ulph,1996), similar analyses have not been widely conducted inrenewable resource economics. Perhaps this reflects the factthat imperfect property rights, free entry and rent dissipa-tion are pervasive problems in renewable resource systems,rendering strategic considerations less important. The sim-ple textbook case of open access, however, neglects impor-tant aspects of commercial poaching of wild animals. Inreality, the illegal trade in wild animals generates substan-tial rents that accrue, not to poachers in the field, but furtherup the supply hierarchy to criminal networks specialized intrafficking illegal commodities across borders.

Imperfect competition thus is also at the heart ofcommercial endangered species poaching, and failure toacknowledge this fact could have detrimental consequencesfor wildlife. This paper has highlighted the potential dangersof introducing supply side policies (such as captive breeding)without carefully scrutinizing the microeconomic structureof the market, together with the dynamic effects on resourcestocks. The analysis reveals that captive breeding may bedetrimental if it induces aggressive competition, and wheth-er this occurs will depend critically upon the form ofcompetition that eventuates in the market. The picturebecomes more complex when we allow for the possibilitythat consumer preferences are likely unstable and thattransaction costs of the illegal trade are affected when aparallel legal trade develops.

Of course it is possible that certain agents withobjectives other than making profits commit to producinga certain output level of wildlife commodities in captivity,refusing to play any strategic game with oligopolisticsuppliers from the wilds. Such parties, which might includeconservation agencies, would simply reduce residual de-mand for traders, and thereby reduce harvesting from thewilds. Alternatively, if a sufficiently close farmed substitutefor the wild product exists, then in the extreme case allprofits from wildlife harvesting could be eliminated byflooding the market with substitute products to such anextent that the price of wild products falls below harvestcosts. It is of course an open question whether commitmentto certain output levels is feasible, or whether such astrategy would be more cost effective than the traditional“protectionist” approach of providing greater security forwild animals against poachers.

Turning to one of the key simplifications in this paper, werecognize that the assumption that the trader does not careabout future payoffs is an extreme one. While it appearsreasonable to assume that tenure insecurity as faced by thetrader will translate into higher discount rates, the assumptionof an infinite discount rate is clearly a limiting case.With a finitediscount rate, an open loop dynamic duopoly model would beappropriate. Note that, unlike most other multiple agentresourcemodels, an open loop solutionwill be subgameperfect,because in the current model there is no interaction via thewildlife stock (the only state variable in the model) and thefarmer is a normal profit maximizing firm solving a static

471E C O L O G I C A L E C O N O M I C S 6 2 ( 2 0 0 7 ) 4 6 1 – 4 7 2

optimization problem.18 One may assume that the tradermaximizes the net present value of profits (subject to theequation of motion for the wildlife stock and the farmer'sresponse), and solve for the open loop solution using themaximum principle. For a discussion of features of the openloopequilibriumand the results of a static game, seeMason andPolasky (1997).

Turning to policy formulation, we found that simple rules ofthumb might not exist in the complex world of imperfectcompetition on output markets. However, two importantobservations are in order. First, assuming a government isconcerned about the farmer's revenues and in situ abundance ofthewildspecies, it is trivial to showthis impliesanoptimal trade-off between revenues and conservation at the margin. UnderCournot competition, captive breeding discourages poaching, sothat this may call for government subsidies to breeders. Incontrast, constraining output (e.g. by taxing farmers) may beoptimal under Bertrand competition, because the governmentwouldprefer anoutput (price) level that is lower (higher) than theprivate breeder would choose. An appendix where we derivethese results formally isavailable fromtheauthorsupon request.

Finally, policy makers can promote conservation bymanipulating the rules of the game. In a final Appendix(available from authors) we extend the analysis by Kreps andScheinkman (1983) to the case of differentiated products, anddemonstrate that when one supplier is constrained in theability to increase output, then the output will approximatethe Cournot equilibrium, even though players compete bysetting prices.19 This is an important result for policy makers;while restricting harvests from wild stocks is difficult andexpensive, it appears that policy makers can reach theirconservation objectives by restricting output from the farmingsector instead — freezing it at some preferred level of output(recalling that larger quota imply better conservation results).

Acknowledgments

The authors would like to thank the conference participants atthe EuroConference on “The International Dimension ofEnvironmental Policy”, Acquafredda di Maratea, Italy, seminarparticipants at the Resources for the Future and UniversityCollege London. Bulte would like to thank the Royal DutchAcademy of Arts and Sciences (KNAW) and the EU sponsoredBIOdiversity and Economics for Conservation (BIOECON)project (ENVK2-CT-2000-00086) for the financial support.

19 In the absence of policy intervention a similar outcomeemerges if the farming sector can only slowly adjust quantities,which is appropriate when quantity is interpreted as capacity toproduce (e.g. Varian, 1992; p.301). This is likely of relevance forfacilities producing wild species like tigers and bears (but not allwild animals, of course).

18 In effect, like List and Mason (2001), we assume that one of theplayers does not behave in a truly strategic manner. Whilefarmers rationally compete on output markets, they do notconsider the effect of their supply on future wildlife stocks (and,hence, on future supply of their competitor). Allowing for suchconsiderations (appropriate when international organizationssuch as the WWF would commence captive breeding programs)and solving for the Markov perfect equilibria would be extremelycomplicated because of the nonlinear state equation.

Appendix APROOFS

Proof of Lemma 1a. If the original parameters of demand areunaffected by the introduction of a substitute product, thenαm=αw and β m=βw. Substituting these conditions in Eq. (11)and manipulating, it can be seen that qmw ≤qcw if:

vz m̂ ¼ r2x2ð2bwaF þ gðaw−cÞÞ þ aFwðwþ r2x2bmÞ : ðA1Þ

Substituting Eq. (A1) in Eq. (21) it can be verified that qcF≤0 ifv≥ ν̂. Since qcFN0 by assumption, it follows that qmwNqcw. □

Proof of Lemma 1b. From straightforward differentiating Eq.(22) it can be verified that ∂qw /∂βwb0, ∂qw /∂αwb0. □

Proof of Lemma 2a. If the parameters of the demand functionfor wild animal parts are unchanged then am=aw and bm=bw.From Eq. (11) poaching levels in the absence of captive

breeding may be expressed as: qm ¼ r2x2ðaw−bwcÞ2r2x2þwbw . Comparing

with Eq. (27), it can be seen that qBwbqmw if:

v N meu−r2x2ðeaw þ 2bwaF þ eb cÞ−wbwðaweþ bwaFÞð2r2x2 þ bwwÞbFbw b0 ðA2Þ

Observe that Eq. (A2) is negative. Since ν≥0 by definition, itfollows that qBwbqmw. □

Proof of Lemma 2b. By differentiation of Eq. (27): ∂qBw /∂awN0,∂qBw /∂bwb0. □

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