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Subsistence farming, poaching and ecotourism Social versus communal welfare maximization in wildlife conservation Ralph Winkler School of Politics, International Relations and the Environment, Keele University Research Centre for Environmental Economics, University of Heidelberg January 2006 Abstract: We develop a bio-economic model of open access land and wildlife exploitation, which is consistent with many farming and hunting societies living in close proximity to protected areas in developing countries. We investigate if, and to what extent, integrated conservation and development projects (ICDPs) such as non-invasive ecotourism, can increase both the level of habitat and wildlife conservation and the welfare of the local communities. We show that, although ecotourism increases the incentive to conserve habitat and wildlife, in general the socially optimal level of conservation cannot be achieved, because of externalities and information deficits. We show how a social planner can achieve the socially optimal level of habitat and wildlife conservation by a more encompassing tax/subsidy regime. Keywords: bio-economic modelling, competing land-use, conservation, ecotourism, poach- ing JEL-Classification: Q56, Q57, Q26, Q24 Correspondence: Ralph Winkler School of Politics, International Relations and the Environment Keele University, Keele Staffordshire, ST5 5BG, United Kingdom phone: +44 1782 583745, fax: +44 1782 583592, email: [email protected] I am grateful to Marco Orsini, John Proops and Alessandro Stanchi for valuable comments on an earlier draft. Financial support by the European Commission under the Marie Curie Intra-European Fellowship scheme, No. MEIF-CT-2003-501536, is gratefully acknowledged.

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Subsistence farming, poaching and ecotourismSocial versus communal welfare maximization in wildlife conservation

Ralph Winkler∗

School of Politics, International Relations and the Environment, Keele UniversityResearch Centre for Environmental Economics, University of Heidelberg

January 2006

Abstract: We develop a bio-economic model of open access land and wildlife exploitation,which is consistent with many farming and hunting societies living in close proximity toprotected areas in developing countries. We investigate if, and to what extent, integratedconservation and development projects (ICDPs) such as non-invasive ecotourism, canincrease both the level of habitat and wildlife conservation and the welfare of the localcommunities. We show that, although ecotourism increases the incentive to conservehabitat and wildlife, in general the socially optimal level of conservation cannot beachieved, because of externalities and information deficits. We show how a social plannercan achieve the socially optimal level of habitat and wildlife conservation by a moreencompassing tax/subsidy regime.

Keywords: bio-economic modelling, competing land-use, conservation, ecotourism, poach-ing

JEL-Classification: Q56, Q57, Q26, Q24

Correspondence:Ralph WinklerSchool of Politics, International Relations and the EnvironmentKeele University, KeeleStaffordshire, ST5 5BG, United Kingdomphone: +44 1782 583745, fax: +44 1782 583592, email: [email protected]

∗ I am grateful to Marco Orsini, John Proops and Alessandro Stanchi for valuable comments on anearlier draft. Financial support by the European Commission under the Marie Curie Intra-EuropeanFellowship scheme, No. MEIF-CT-2003-501536, is gratefully acknowledged.

1 Introduction

Protected areas have been and still are the single most important strategy to protect andconserve natural habitats and wildlife (Swanson and Barbier 1992). However, in manydeveloping countries the establishment of protected areas often excluded local commu-nities from land and wildlife utilization to which they formerly had access. Thus, manyprotected areas act directly against the economic interests of the local population. Inaddition, the protection of many natural reserves is poorly enforced by the government,because of the vast areas involved and the poor financial situation of the park man-agement (e.g. Kiss 1990). As a consequence, illegal land and wildlife utilization, such asslashing and burning forests for agricultural use, and hunting game animals for meat, arewidespread. Thus, protected areas often fail to achieve their aim of protecting naturalhabitats and endangered animal species (Barrett and Arcese 1995, Gibson and Marks1995).

These shortcomings of the traditional approach to protected area management, oftenreferred to as the ‘fences and fines’ approach, have become increasingly apparent and re-cently resulted in the development of so-called ‘integrated conservation and developmentprojects’ (ICDPs), which include the local population in the wildlife management to gaintheir cooperation and support. Although there is widespread agreement that the involve-ment of the local communities is a crucial necessity for successful ICDPs, many ICDPshave failed (or are likely to fail) to achieve their aimed goal due to design errors. Barrettand Arcese (1995, 1998) argue that ICDPs which solely depend on wildlife harvest areprone to fail in the long-run, due to population growth and the strong correlation in thestochastic outputs of both crop production and wildlife harvest. Furthermore, there isample evidence that only a small fraction of the ICDPs revenues reach the local com-munities and, thus, incentives for the local population to change habits are small (e.g.Barrett and Arcese 1995, Bookbinder et al. 1998, Gibson and Marks 1995, Wells et al.1992). In addition, Wells et al. (1992), Ferraro (2001), and Ferraro and Kiss (2002),among others, question the assumption that local people voluntarily refrain from poach-ing if they receive transfers. In fact, economic reasoning (i.e. the opportunity costs oflabor as the main determinant for labor distribution among different activities) suggeststhat new income sources are complements to existing activities rather than substitutes.

This paper investigates the interdependencies between local subsistence farming andhunting communities, and the abundance of habitat and wildlife under a benefit-sharingICDP in a dynamic bio-economic model. As a prime example for an ICDP, which hasgained a lot of interest recently among both scholars and practitioners (e.g. Goodwin1996, Isaacs 2000), we focus on sharing ecotourism1 revenues, earned by a state managedtourism enterprize, with the local population as a prime example for ICDPs.

1 In this paper ecotourism is understood as any type of non-invasive tourism that has the viewingand/or enjoyment of nature as its primary purpose (e.g. Goodwin 1996, Naidoo and Adamowicz2005). As an example, it includes activities such as birdwatching and photo safaris but excludesactivities such as trophy hunting. The emphasis on non-consumptive uses of habitat and wildlife isin line with Barrett and Arcese (1995, 1998), who argue that ICDPs which solely depend on wildlifeharvest are unlikely to be viable in the long-run.

1

Our bio-economic model consists of a fixed size of land, which has two alternative uses.In its pristine state the land is the habitat of an animal species, which can be hunted forgame meat. In addition, the land can be turned into agricultural land, which yields cropproduction. The local subsistence farming and hunting communities distribute a fixedlabor endowment between the three activities of farmland production (i.e. the clearingof land for agricultural use), farmland cultivation and hunting. In addition, there is astate owned enterprize which earns revenues from ecotourism, which depends on theabundance of both pristine land and wildlife. Although, the state is supposed to exhibitwell defined property rights of both land and wildlife, it is unable successfully to enforcethem. Thus, de facto the local communities face an open access regime with respect toland and wildlife.

Our bio-economic model is most closely related to Bulte and Horan (2003), and Smith(1975), who consider pressure on wildlife conservation due to hunting and habitat loss,but do not explicitly investigate ICDP schemes. While the existing theoretical literatureon the effects of ICDPs rather concentrates on the competition in wildlife harvest be-tween the locals and the ecotourism enterprize (e.g. Barrett and Arcese 1998, Johannesenand Skonhoft 2005, Skonhoft and Solstad 1998), we focus attention to the problem ofhabitat loss due to externalities, which stem from the public good property of land andwildlife. Thus, we abstract from the nuisance argument for poaching that wandering an-imal herds interfere with agricultural production (e.g. Johannesen and Skonhoft 2005).Moreover, we assume that in the socially optimal long-run stationary state no huntingis optimal. This is in line with Barrett and Arcese (1998), who argue that under thelocal conditions given in many developing countries wildlife harvest is not profitable formost animal species. This also justifies the strict anti-poaching policy of many protectedareas. Obviously, our assumptions better fit with forest than rangeland reserves (e.g.Bookbinder et al. 1998, Naidoo and Adamowicz 2005).

Ideally, distributing ecotourism revenues to the local communities creates an incentivescheme which results in a ‘win-win’ situation in which (i) natural habitats and wildlife areprotected, and (ii) the income of the local population is increased and, thus, poverty andhardship is alleviated. Although we can show that the distribution of ecotourism revenuesgives incentives for increased habitat and wildlife conservation, even full distribution ofecotourism revenues leads to lower habitat and wildlife conservation than the socialoptimum suggests. The reasons are externalities due to the open access regime and/orlack of knowledge of the local communities about the ecological foundations of the animalreproduction. However, we show that a more encompassing tax/subsidy regime, whichis financed by ecotourism revenues, can achieve the socially optimal level of habitat andwildlife conservation.

The paper is structured as follows. In section 2 we explain in detail the bio-economicmodel. The preferences and knowledge of both the state and the local communities areoutlined in section 3. In addition, we introduce the fiscal tools the state commands inorder to influence the behavior of local communities. In section 4 the social optimallong-run outcome is derived and discussed. In section 5 we show that, in general, welfaremaximization of the local communities does not lead to the socially optimal outcome.Furthermore, we show how the state can implement the long-run social optimum by an

2

optimal tax/subsidy regime. Finally, section 6 concludes.

2 The bio-economic model

The aim of this paper is to investigate, if, and to what extent, the sharing of ecotourismrevenues to the local communities creates incentives for increased environmental protec-tion and conservation. To this end, we introduce a bio-economic model which capturesthe trade-offs between agricultural production, hunting and ecotourism. In contrast tomost of the existing literature on ICDPs, the local population is not treated as one ho-mogenous group, but split up in N identical local communities.2 In line with traditionalreasoning, the elders of each community are supposed to decide over the groups actions(Marks 1984). Thus, although we abstract from conflicting interests within the communi-ties, we consider the externalities that the action of one community can impact on othercommunities. In order to identify a possible gap between the welfare maximization ofindividual communities and the social optimum, we distinguish in the following betweenthe state and the community. The state represents the government of the society, whichis supposed to act as a social planner, i.e. it maximizes the welfare of a representativecommunity. The community refers to a representative community, which is supposed tomaximize its own welfare only.

The N communities are living on an area of land of size 1, which is originally in its(homogenous) pristine state called wilderness W . The wilderness is the habitat of anative animal species called buffalo B. Each community is considered to command thesame fixed amount of labor normalized to 1 at any time t, which can be assigned tothree different activities:

1. convert wilderness into farmland,

2. cultivate the farmland to produce food,

3. and hunt buffalo for consumption.

As all communities are identical, so are the labor shares of farmland conversion l1, farm-land cultivation l2 and hunting buffalo l3. In addition, the labor restriction is supposedto hold with equality:

1 = l1 + l2 + l3 . (1)

Let f be the amount of farmland each community cultivates. Then the total amount offarmland F = N · f . Thus, at any time t the remaining amount of wilderness equals thetotal size of land minus the total size of farmland: W = 1 − F .

2 For the sake of simplicity, we do not consider growth of the population. Thus, the number of individ-uals within each community is supposed to be constant, and the number of communities is given bythe constant exogenous parameter N .

3

Each community can convert wilderness into farmland according to the following equa-tion of motion:3

f = G(l1) − δf , (2)

where G is the production function of farmland, which is supposed to solely depend onlabor input l1. Moreover, without constant effort, farmland turns back into wilderness atthe constant deterioration rate δ. G is considered to to be a linear process with constantreturns to scale:

G(l1) = α1l1 , α1 > 0 . (3)

Thus, the amount of labor needed to convert an additional unit of wilderness equals1/α1, no matter what is the level of farmland which has already been converted fromwilderness. This amounts to the assumption that wilderness is homogeneous.

Farmland can be cultivated to produce consumption according to the following Cobb-Douglas production function P :

P (f, l2) = α2fβl1−β

2, α2 > 0 , 0 < β < 1 , (4)

where l2 is the amount of labor assigned to the cultivation of farmland, α2 is a scalingfactor for the overall productivity of farming, and β and 1 − β are the production elas-ticities of farmland and labor in the cultivation of farmland. Thus, farmland cultivationdepends positively on farmland and labor input (P1 > 0, P2 > 0), and exhibits constantreturns to scale.

In addition, communities can produce consumption by hunting buffalo. Hunting Hdepends on the abundance of buffalo B and the amount of labor assigned to huntingl3. As in the Gordon-Schafer model, H is supposed to depend linearly on the buffalopopulation and to exhibit constant returns to scale with respect to labor:

H(B, l3) = α3B l3 , α3 > 0 , (5)

where l3 is the amount of labor assigned to hunting and α3 is a scaling factor for theoverall productivity of hunting.

The buffalo population lives in the wilderness, reproduce according to the reproductionfunction R and is reduced by the total amount of hunting N H:

B = R(B,W ) − N H(B, l3) . (6)

The reproduction function R is supposed to be a logistic growth function, which dependson the size of the buffalo population B and the size of the buffalo habitat wilderness W :

R(B,W ) = ǫB

[

1 − (1 − θ)B

W − θ

]

, ǫ > 0 , (7)

3 Throughout the paper derivatives with respect to time will be denoted by dots (˙). In addition,derivatives of functions which solely depend on one variable will be denoted by primes (′), and partialderivatives of functions with more than one variable with subscript numbers, where the number

indicates the variable: dZdt

= Z, dZ(x)dx

= Z ′, d2Z(x)dx2 = Z ′′, ∂Z(x1,...,xn)

∂xi= Zi,

∂2Z(x1,...,xn)∂xi∂xj

= Zij .

4

where ǫ measures the reproductive capabilities of buffalo, and θ is the crucial levelof habitat size where the buffalo population becomes extinct. In fact, the equilibriumlevel of the buffalo population crucially depends on the level of wilderness remaining.Abstracting from hunting, the equilibrium level of the bison population is 1 if W = 1,and it is 0 if W ≤ θ. Thus, the buffalo population is eradicated once wilderness reachesthe threshold θ.

Finally, the state can generate revenues by offering ecotourism activities. The primeincentive for tourists to engage in ecotourism activities is the excitement created byvisiting pristine nature and wildlife environments. Thus, the main determinant for thesuccess of ecotourism is supposed to be the level of wilderness W and the abundance ofbuffalo B. Ecotourism revenues E in terms of consumption units are determined by thefollowing Cobb-Douglas function:

E(W,B) = α4WγB1−γ , α4 > 0 , 0 < γ < 1 , (8)

where α4 is a scaling factor for the overall productivity of ecotourism, and γ and 1 − γare the production elasticities of wilderness and buffalo in creating ecotourism revenues.

The total consumption C, which the whole society produces, equals N P plus N Hplus the revenues from ecotourism E:

C = N P (f, l2) + N H(B, l3) + E(W,B) . (9)

Note that as all communities are identical and all production functions exhibit constantreturns to scale with respect to farmland f and the labor shares l1, l2 and l3, totalconsumption is independent of society’s distribution of total farmland F and the totallabor shares N l1, N l2 and N l3 among individual communities.

The consumption c for each community is the sum of farmland cultivation P andhunting H plus a share −τ0

Nof ecotourism revenues:

c = P (f, l2) + H(B, l3) −τ0

NE(W,B) , (10)

where 0 ≥ τ0 ≥ −1 determines which percentage of ecotourism revenues the statedistributes among the communities. Thus, a negative τ0 transfers incentives for natureand wildlife protection, created by ecotourism revenues, from the society as a whole tothe communities.4

3 Social and communal preferences and knowledge

For deriving the social optimum, the state is supposed to maximizes the welfare of arepresentative community. The welfare of each community U is the discounted streamof instantaneous welfare V over an infinite time horizon:

U =

0

V (c) exp(−ρt) dt , (11)

4 τ0 is considered to be negative to be consistent with the normal convention that positive parametersindicate taxes, while negative parameters indicate subsidies/transfers.

5

where ρ denotes a constant discount rate. The instantaneous welfare function V dependspositively on community consumption c. Furthermore, V exhibits positive but decreasingmarginal increments with respect to consumption (V ′ > 0, V ′′ < 0).

Communities are considered to be of one of two types. Sophisticated communities arewell acquainted with the equation of motion of the buffalo stock (6) and its depen-dencies on the buffalo stock itself, the habitat size W and the total level of huntingN H. Moreover, they are aware that buffalo are driven to extinction, once wildernessreaches the threshold θ. In contrast, naive communities are completely ignorant aboutthe ecological foundations of the buffalo population and its dependance on habitat sizeW and the total level of hunting N H. As a consequence, naive communities take thelevel of buffalo population B as exogenously given at any time t. Obviously, both thesophisticated and the naive community represent rather extreme cases of knowledge orthe lack of it. In fact, they rather constitute the boundaries of a continuum of imper-

fect knowledge. Nevertheless, the analysis of theses extreme cases gives valuable insightsinto the dependence of the long-run outcome on the ecological knowledge of the localcommunities.

The state has perfect knowledge and perfect foresight of the model world (in partic-ular the repercussions of economic activity on the development of wilderness and thebuffalo population), the communities’ preferences, knowledge and maximization ratio-nale. Moreover, we assume that the state is aware that the welfare maximization of eachcommunity does not necessarily lead to the social optimal outcome (as will be shown insection 4 and 5), and it makes an effort to achieve the social optimum by state inter-ventions. However, the state’s options to interfere with communal welfare maximization,despite distributing ecotourism revenues, are limited.

First, the labor shares the communities assign to the three processes of farmlandproduction, farmland cultivation and hunting can neither be controlled by the statedirectly nor be taxed or subsidized separately. Second, we assume that the state cancontrol directly neither the hunting of buffalo nor the conversion of wilderness intofarmland. Moreover, the outcome of hunting is not directly observable and, thus, cannotbe taxed or subsidized, while the size of farmland is observable and, thus, can be taxed orsubsidized. In addition, the output of farmland cultivation is observable and, therefore,eligible for taxation or subsidization. In summary, the state commands three instrumentsto interfere with individual welfare maximization:

1. sharing ecotourism revenues E,

2. taxing/subsidizing output of farmland cultivation P , and

3. taxing/subsidizing the size of cultivated farmland f .

4 The socially optimal level of farming, hunting and wildlife

conservation

As outlined in the previous section, the state seeks to achieve the social optimum forthe society. That is, the state maximizes the welfare of a representative community and,

6

thus, solves the following maximization problem:

maxl2,l3

0

V (c) exp(−ρt) dt (12a)

subject to

c = P (f, l2) + H(B, l3) +1

NE(W,B) , (12b)

f = G(l1) − δf , (12c)

B = R(B,W ) − H(B, l3) , (12d)

1 = l1 + l2 + l3 , (12e)

W = 1 − N f , (12f)

l3 ≥ 0 . (12g)

Obviously, the welfare of a representative community will be higher the higher is thepercentage of ecotourism revenues which the state distributes to the communities. Thus,in the social optimum all ecotourism revenues will be distributed to the communities,i.e. τ0 = −1. Note that as hunting is linear with respect to labor (5), positive hunting isnot necessarily optimal at all times along the optimal path or in the long-run stationarystate. Thus, one has to check explicitly for corner solutions, where l3 = 0 (12g). Notefurther that farmland production G is also a linear process. Therefore, also the amountof labor assigned to farmland production l1 can be zero at some time along the optimalpath. However, this can only happen if the initial level of farmland f0 is bigger thanthe size of farmland f ⋆ in the long-run stationary state. Moreover, as the marginalproductivity of farmland cultivation with respect to farmland tends to infinity for verysmall sizes of farmland, farmland cultivation and, thus, also farmland production willbe strictly positive in the long-run stationary state. As we concentrate on the long-runstationary state, we do not explicitly check for the corner solutions, where l1 = 0.

Inserting (12b), (12e) and (12f) yields the following current-value Hamiltonian H:

H = V (c) + qf [G(l1) − δf ] + qB [R(B,W ) − H(B, l3)] + qll3 , (13)

where qf and qB are the shadow prices for the two state variables farmland and bison,and ql is the slackness variable for the non-negativity constraint for the amount of laborl3 (12g). The shadow price qf (qB) indicates how much the welfare of the representativecommunity would increase along the optimal path, if the level of farmland (buffalo)would be increased by a marginal unit.

7

4.1 Necessary and sufficient conditions for an optimal solution

The necessary conditions for an optimal solution are:

∂H∂l2

= V ′(c)P2(f, l2) − qfG′(l1) = 0 , (14a)

∂H∂l3

= V ′(c)H2(B, l3) − qfG′(l1) − N qBH2(B, l3) + ql = 0 , (14b)

∂H∂f

= −qf + ρqf = V ′(c)[P1(f, l2) − E1(W,B)] − δqf

− N qBR2(B,W ) , (14c)

∂H∂B

= −qB + ρqB = V ′(c)

[

H1(B, l3) +1

NE2(W,B)

]

+ qB [R1(B,W ) − H1(B, l2)] . (14d)

For presentational convenience the arguments of all functions will be dropped in thefollowing, safe for the time argument in integral equations. As shown in Appendix A.1the Hamiltonian H is strictly concave if hunting is not too productive (i.e. α3 is nottoo high), which will be assumed in the remainder of the paper. Then, the necessaryconditions are also sufficient if, in addition, the following transversality conditions hold:

limt→∞

qf exp(−ρt) f = 0 , limt→∞

qB exp(−ρt) B = 0 . (14e)

The necessary conditions (14c) and (14d) are ordinary first order differential equationswhich can be solved unambiguously by taking the transversality conditions (14e) intoaccount:

qf (t) =

t

{V ′(t′) [P1(t′) − E1(t

′)] − N qB(t′)R2(t′)}

× exp[−(ρ+δ)(t′−t)] dt′ , (15)

qB(t) =

t

V ′(t′)

[

H1(t′) +

1

NE2(t

′)

]

× exp

[

−ρ(t′−t) −∫ t′

t

[N H1(t′′) − R1(t

′′)] dt′′

]

dt′ . (16)

Thus, the shadow price of farmland qf equals the net sum (taking into account thediscount rate ρ and the deterioration rate δ) of all present and future contributions tothe welfare of the representative community of an additional marginal unit of farmland.These contributions are the compound of the welfare gain due to farmland cultivationand the welfare loss from reduced ecotourism revenues due to the reduction of wildernessand the welfare loss induced by the impact of habitat loss on the buffalo population. Notethat the total loss of wilderness dW for a marginal increase df of farmland size equalsdW = −N df . Thus, the total impact of wilderness reduction on ecotourism revenuesfor each community equals N 1

NE1 and the total impact of habitat loss on the buffalo

population equals N qBR2.

8

Analogously, the shadow price of buffalo qB equals the net sum of all present and futurecontributions to the representative community’s welfare of an additional marginal unitof buffalo. These contributions are the compound of the welfare gain due to increasedconsumption from hunting buffalo, as hunting becomes more productive if buffalo aremore abundant, and the increased revenues from ecotourism, due to an increased buffalopopulation. Again, the discount rate ρ and the buffalo dynamics have to be taken intoaccount.5

From equation (16) it is obvious that the shadow price of buffalo qB is positive alongthe optimal path as it is the discounted sum of a non-negative (H1) and a strictlypositive ( 1

NE2) term. Moreover, as can be seen from equation (14a) the shadow price of

farmland is strictly positive along the optimal path if farmland production G is positive,i.e. l1 > 0. As already argued, this is always the case in the long-run stationary stateand also true for the transition path if the initial level of farmland f0 is smaller than thesize of farmland in the long-run stationary state f ⋆.

Furthermore, from the necessary conditions (14a) and (14b) one derives the followingequality conditions, which hold along the optimal path and determine the optimal laborshares l1, l2 and l3 for the three activities farmland production, farmland cultivation andhunting:

V ′P1 = qfG′ = (V ′ − N qB)H2 + ql . (17)

Thus, as long as l3 > 0 (which implies ql = 0) holds, the welfare gain due to theproductivity of an additional marginal unit of labor employed in all three activities hasto be equal along the optimal path. As H2 = α3B is independent of the amount of labor l3assigned to hunting and decreases with decreasing buffalo population, it is possible thathunting is not optimal for some times along the optimal path and in the stationary state,if α3 is small enough. In this case the marginal labor productivity of hunting is smallerthan the marginal labor productivity of farmland cultivation and farmland production(i.e. (V ′ − N qB)H2 < V ′P1 = qfG

′) and, thus, no hunting takes place (l3 = 0).

4.2 Stationary state and comparative static analysis

In the following we analyze the long-run equilibrium, the stationary state, of the econ-omy. In fact, we assume that α3 is such that hunting is not optimal in the long-runstationary state. This assumption is motivated by the observation that hunting is oftenprohibited in reserves. If it is the case that hunting is not optimal, this justifies the nohunting policy from a social planner’s point of view.

In the stationary state qf = qB = f = B = 0 holds. Taking into account that l⋆3

= 0 ashunting is supposed not to be optimal in the long-run stationary state, from equations(14c) and (14d) one derives the following equations for the shadow prices of farmlandq⋆f and buffalo q⋆

B at the stationary state (a ‘⋆’ indicates that the function is evaluated

5 Note that R1 − N H1 is the partial derivative of the right hand side of equation (12d) and, thus, isthe equivalent to the deterioration rate −δ in the case of farmland.

9

at the stationary state values):

q⋆f =

V ′⋆(P ⋆1− E⋆

1) − N q⋆

BR⋆2

ρ + δ, (18a)

q⋆B =

V ′⋆E⋆2

N(ρ − R⋆1)

. (18b)

Inserting equations (18a) and (18b) into the necessary condition (14a) yields, togetherwith the equations of motions for farmland (12c) and buffalo (12d), the following threeimplicit equations for the three unknowns l⋆

2, f ⋆ and B⋆:

P ⋆2

G′⋆=

P ⋆1− E⋆

1

ρ + δ− E⋆

2R⋆

2

(ρ + δ)(ρ − R⋆1)

, (19a)

f ⋆ =G⋆

δ, (19b)

R⋆ = 0 . (19c)

Taking into account that l⋆1

= 1−l⋆2

one derives the following equations for the stationarystate variables from equations (19b) and (19c):

l⋆1

= 1−l⋆2, l⋆

3= 0, f ⋆ =

α1(1 − l⋆2)

δ, W ⋆ = 1−N α1(1 − l⋆

2)

δ, B⋆ = 1−N α1(1 − l⋆

2)

δ(1 − θ). (20)

Inserting these equations into equation (19a) and taking into account that R⋆1

= −ǫ andR⋆

2= ǫ

1−θone derives the following implicit function Z(l2) with Z(l⋆

2) = 0:

Z(l2) =α2

α1

(

α1(1−l2)

δl2

)β [

1 − β

(

1+δl2

(δ+ρ)(1−l2)

)]

+α4

(δ+ρ)(1−θ)×

(

(1−θ)[δ−N α1(1−l2)]

(1−θ)δ−N α1(1−l2)

)γ [

(1−γ)ǫ

ρ+ǫ+

γ[(1−θ)δ−N α1(1−l2)]

δ−N α1(1−l2)

]

. (21)

Although l⋆2

cannot be determined explicitly, it is shown in Appendix A.2 that theexistence, uniqueness and stability of the stationary state is guaranteed, if the discountrate ρ is sufficiently small or the minimum habitat size θ for the buffalo population tosurvive is sufficiently high, which is assumed in the following. Thus, for all feasible initialconditions the optimal path converges to the stationary state in the long-run.

The comparative static results can be determined from equations (20) and (21) andare summarized in Table (1). As can be seen from the comparative static results withrespect to the technological parameters α1, α2 and α4, an increase in consumption doesnot necessarily imply higher levels of habitat and wildlife conservation. This result isin line with Wells et al. (1992), Ferraro (2001), and Ferraro and Kiss (2002), amongothers, who argue that new sources of income are complements to existing activitiesrather than substitutes. Obviously, in a society where preferences solely depend on thelevel of consumption there is no unambiguous link between higher consumption andthe conservation of habitat size or wildlife. The society will exploit given resources inorder to maximize consumption levels. This is most obvious for farmland production.

10

l⋆1

l⋆2

f ⋆ W ⋆ B⋆ G⋆ P ⋆ E⋆ c⋆

α1 − + ? ? ? ? ? ? +α2 + − + − − + + − +α4 − + − + + − − + +γ ? ? ? ? ? ? ? ? ?δ ? ? ? ? ? ? ? ? ?ρ ? ? ? ? ? ? ? ? ?ǫ + − + − − + + − ?θ ? ? ? ? ? ? ? ? ?N + − + − − + + − −

Table 1: Comparative static results for the social optimal stationary state. A ‘?’ impliesthat the sign is ambiguous.

An increase in α1 (i.e. for given amount of labor l1 more farmland is produced) leadsto higher consumption but the impact on farmland size and, thus, on habitat size andwildlife abundance are ambiguous. A higher α2 (i.e. for given amounts of labor l2 andfarmland f more output is produced) leads to higher levels of farmland, and lowerhabitat size and buffalo population. As a consequence, policy measures such as increasingfarming technology increase the consumption level but lead to lower habitat and wildlifeconservation. However, an increase in α4 (i.e. for given levels of wilderness W and buffaloB more revenues from ecotourism are generated) creates in fact a ‘win-win’ situation: itincreases the level of consumption, habitat size and wildlife abundance. Thus, ecotourismhas at least the potential for a successful ICDP.

Another interesting result, although not very surprising, is that an increase in thenumber of communities N increases farmland size, and reduces habitat size and buffalopopulation. Thus, increasing human population increases the pressure on habitat andwildlife.

5 Farming, hunting and wildlife conservation under communal

welfare optimization under different tax/subsidy regimes

As the state holds the property rights for both the land itself and the buffalos livingon it, the ‘command and control’ approach to implement the socially optimal outcomewould be to prohibit land use above the optimal level F ⋆ and to restrict the huntingof bison to the optimal level H⋆ as calculated in the previous section. In the long-runequilibrium this would result in a natural reserve of size W ⋆ with a buffalo populationof B⋆ and, as hunting is supposed to be sub-optimal in the long-run stationary state,a complete ban of hunting. However, in line with Bulte and Horan (2003), Johannesenand Skonhoft (2005), and Skonhoft and Solstad (1998), among others, we assume thatde jure and de facto property rights differ in that the property rights cannot be enforced.As a consequence, the communities face an open access regime with respect to both landuse and buffalo hunting.

11

In the following, we show that, in general, the open access outcome does not coincidewith the the social optimum, because of externalities and/or lack of knowledge. There-fore, we discuss the outcome of communal welfare maximization for two cases: (i) thesophisticated communities have perfect knowledge of both the economic and the eco-logical foundations and interdependencies, and (ii) the naive communities do not knowhow the buffalo population is influenced on habitat size and hunting and, thus, takethe buffalo population as exogenously given. We assume that the state knows if thecommunities are sophisticated or naive and tries to achieve the socially optimal path bya tax/subsidy regime. As outlined in section 3, the state’s possibilities to intervene arelimited to taxes/subsidies on the output of farmland cultivation and the size of farmland.In addition, the state can share revenues from ecotourism.

The sophisticated community i maximizes its welfare by solving the following optimalcontrol problem:

maxli2,li3

0

V (ci) exp(−ρt) dt (22a)

subject to

ci = P (f i, li2)(1 − τ1) + H(B, li

3) − τ2f

i − τ0

NE(W,B) , (22b)

f i = G(li1) − δf i , (22c)

1 = li1+ li

2+ li

3, (22d)

B = R(B,W ) −N

j=1

H(B, lj3) , (22e)

W = 1 −N

j=1

f j , (22f)

lj3

≥ 0 , (22g)

where τ0 denotes the share of the ecotourism revenues the state pays to the community,and τ1 and τ2 are the tax/subsidy-rates on farmland cultivation and the size of farmland.

Introducing pf and pB for the shadow prices of farmland and buffalo, and pl as theslackness variable for the non-negativity condition for li

3(22g), the Hamiltonian Hi reads:

Hi = V (ci) + pf i

[

G(li1) − δf i

]

+ pB

[

R(B,W ) −N

j=1

H(B, lj3)

]

. (23)

12

5.1 Necessary and sufficient conditions for an optimal solution

Thus, the necessary conditions for an optimal solution are:6

∂Hi

∂li2

= V ′(ci)(1 − τ1)P2(fi, li

2) − pf iG′(li

1) = 0 , (24a)

∂Hi

∂li3

= V ′(ci)H2(B, li3) − pf iG′(l1) − pBH2(B, li

3) + pl = 0 , (24b)

∂Hi

∂f i= −pf i + ρpf i = V ′(ci)

[

(1 − τ1)P1(fi, li

2) − τ2 +

τ0

NE1(W,B)

]

(24c)

− δpf i − pBR2(B,W ) ,

∂Hi

∂B= −pB + ρpB = V ′(ci)

[

H1(B, li3) +

τ0

NE2(W,B)

]

+ pB

[

R1(B,W ) −N

j=1

H1(B, lj3)

]

. (24d)

Note that the necessary conditions for the naive community are derived by setting pB = 0and neglecting condition (24d). Thus, the optimal solution of the naive community caneasily be derived from the optimal solution of the sophisticated community by settingpB = 0.

Analogously to the derivation of the social optimum in section 4, these necessaryconditions are also sufficient, if the Hamiltonian is strictly concave and, in addition,corresponding transversality conditions hold. Under these conditions, the shadow pricespf i and pB can be solved to yield:

pf i(t) =

t

{

V ′(t′)

[

(

1 − τ1(t′))

P1(t′) − τ2(t

′) +τ0(t

′)

NE1(t

′)

]

− qB(t′)R2(t′)

}

× exp[−(ρ+δ)(t′−t)] dt′ , (25)

pB(t) =

t

V ′(t′)[

H1(t′) − τ0

NE2(t

′)]

× exp

[

−ρ(t′−t) −∫ t′

t

[

N∑

j=1

H1(t′′) − R1(t

′′)

]

dt′′

]

dt′ . (26)

Thus, the shadow price of farmland pf i is lower (higher) the higher (lower) the tax(subsidy) on the output on farmland cultivation τ1, the higher (lower) is the tax (subsidy)on farmland size τ2 and the higher is the share of ecotourism revenues −τ0 distributedto the local communities. The shadow price of buffalo pB is higher the higher the shareof ecotourism revenues −τ0 distributed to the local communities, but it is not directlyaffected by taxes/subsidies τ1 and τ2 on the output of farmland cultivation and thesize of farmland. For the naive community the shadow price of buffalo pB = 0 and,

6 In this section the term ‘optimal’ means optimal with respect to the community’s maximizationrationale as described by equations (22a)–(22g). As will be shown this does not necessarily correspondto the ‘social optimum’ derived in section 4.

13

thus, the shadow price of farmland pf i is higher for the naive than for the sophisticatedcommunity, because the negative impact of habitat loss on the buffalo population is notconsidered.

Furthermore, from the necessary conditions (24a) and (24b) one derives the followingequality conditions, which hold along the optimal path and determine the optimal laborshares l1, l2 and l3 for the three activities farmland production, farmland cultivation andhunting:

V ′P1(1 − τ1) = pfG′ = (V ′ − pB)H2 + pl . (27)

Thus, as long as l3 > 0 (which implies pl = 0) holds, the welfare gain due to theproductivity of an additional marginal unit of labor employed in all three activities hasto be equal along the optimal path. Analogously to section 4, it is possible that huntingis not optimal, at least for some times, along the optimal path. However, dependingon the number of communities N (which determines the extend of the externalities notconsidered by the communities), the tax/subsidy regime and whether communities aresophisticated or naive, hunting can be more or less favorable compared to the socialoptimum.

5.2 Distribution of ecotourism revenues only

First, assume that the taxes are set to zero (τ1 = τ2 = 0) and the state only distributesrevenues from ecotourism to the communities (0 < τ0 ≤ −1). Compared to no stateinterventions at all (τ0 = 0), this increases the shadow price of buffalo (in case of thesophisticated community) and reduces the shadow price of farmland. According to theconditions (27), which determine the distribution of labor among the three activities, thisdecreases the incentives to hunt and to produce farmland. Thus, compared to no stateintervention, the optimal labor share of hunting l3 (if it was not zero already) and theoptimal share of farmland production l1 decrease, while in the optimum a higher shareof labor l2 is assigned to the cultivation of farmland. As a consequence, independent ofwhether communities are sophisticated or naive, the higher is the share of ecotourismrevenues distributed to the local communities the higher is the level of habitat and buffalopopulation, both along the optimal path and in the long-run stationary state. Moreover,it is obvious that the consumption level of the community is higher the higher the shareof ecotourism revenues distributed to the communities. From this perspective, sharingecotourism revenues can be claimed to be a successful ICDP measure, as they create thedesired ‘win-win’ situation of increasing welfare, and wildlife and habitat protection.

However, even if all ecotourism revenues are distributed among the communities(τ0 = −1), the welfare maximization of the sophisticated community differs from thesocial optimum if N > 1. That is, because the community does not take into accountthe externalities which it own actions imply on the other communities. Comparing thenecessary conditions (24a)–(24d) with the necessary conditions (14a)–(14d) in the socialoptimum, we can identify two externalities. First, the community only considers the wel-fare loss of hunting due to a reduction of the buffalo population on its own welfare (24b).Second it considers only its own welfare loss from farmland expansion due to habitat

14

reduction, which impacts negatively on ecotourism revenues and the buffalo population(24c).

The naive community always fails to achieve the social optimum, even if N = 1.This is because it does not take into account its own welfare loss both of hunting dueto the reduction of the buffalo population and of farmland expansion due to habitatloss. Moreover, even under full sharing of ecotourism revenues the naive community canunintendedly drive buffalo to extinction, because of their lack of knowledge about theecological foundations of buffalo reproduction and, in particular, the critical habitat sizeθ for which buffalo become extinct. Thus, if the critical habitat size θ and the welfaregain from alternative land use (i.e. farmland production and cultivation) is sufficientlyhigh, the naive community decreases habitat size to such an extent that buffalo becomeextinct, which implies that also ecotourism ceases to create revenues. Obviously, thatis not in the interest of the local communities and only happens because of the lack ofknowledge of the naive community.

By comparing the conditions for the optimal distribution of labor among the threedifferent activities in the social optimum and under communal welfare maximizationwith full sharing of ecotourism revenues, one derives that incentives for hunting undercommunal welfare maximization are always higher compared to the social optimum innaive communities and are higher compared to the social optimum in sophisticatedcommunities if N > 1. Moreover, incentives are higher for naive than for sophisticatedcommunities. In addition, as shown in Appendix A.3, the level of habitat and wildlifeconservation under communal welfare maximization is always smaller than in the socialoptimum (except for N = 1 in the case of sophisticated communities).

In summary, sharing of ecotourism revenues increases incentives for habitat and wildlifeconservation for both sophisticated and naive communities, but due to externalitiesand/or lack of knowledge, the social optimum is not achieved. In general, in the long-runstationary state the level of habitat and buffalo population is below the socially optimallevel. Moreover, sharing ecotourism revenues can still lead to such extreme outcomes asthe extinction of the animal species if communities are naive.

5.3 Taxation/subsidy regime to implement the socially optimal long-runstationary state

In the following, we show how the social optimum can be achieved by a using all threeavailable intervention mechanisms τ0, τ1 and τ2. In the long-run stationary state, thefollowing equations for the shadow prices of farmland p⋆

f i and p⋆B hold:

p⋆f i =

V ′⋆[

P ⋆1(1 − τ1) − τ2 + τ0

NE⋆

1

]

− p⋆BR⋆

2

ρ + δ, (28)

p⋆B =

−V ′⋆ τ0N

E⋆2

ρ − R1

. (29)

Obviously, the equations for the naive community can be achieved by setting p⋆B = 0.

Comparing the conditions for optimal labor distribution in the social optimum (17) and

15

under communal welfare maximization (27), we achieve the following conditions, whichhave to hold for both to be equal:

(V ′⋆ − p⋆B)H⋆

2

1 − τ1

= (V ′⋆ − N q⋆B)H⋆

2, (30)

p⋆f iG′⋆

1 − τ1

= q⋆fG

′⋆ . (31)

These two equations allow us to solve for the optimal taxes/subsidies τ1 and τ2 dependenton the share of ecotourism revenues τ0 for both the sophisticated and the naive commu-nity. Denoting the taxes/subsidies with superscripts ‘soph’ and ‘naive’ for the sophisticatedand the naive community, we derive:

τ soph1

= − E⋆2(N + τ0)

N(ρ − R⋆1− E⋆

2)

, (32)

τnaive1

= − E⋆2

ρ − R⋆1− E⋆

2

, (33)

τ soph2

=(N + τ0)[E

⋆1(ρ − R⋆

1) + E⋆

2R⋆

2]

N(ρ − R⋆1− E⋆

2)

, (34)

τnaive2

=E⋆

1(N + τ0)(ρ − R⋆

1) + E⋆

2(NR⋆

2− τ0)

N(ρ − R⋆1− E⋆

2)

. (35)

Note that τ1 is negative and τ2 is positive. This result is intuitive. In order to giveincentives to decrease the labor shares l1 and l3 for farmland production and hunting,the state subsidizes the output of farmland cultivation (this gives incentives to increase l2and l1 and decrease l3), and taxes farmland production (this gives incentives to decreasel1 and increase l2 and l3).

Moreover, the social optimum can even be achieved, if no ecotourism revenues aredistributed to the local communities. However, the subsidy τ1 and the tax τ2 have to behigher (in absolute terms) the less ecotourism revenues are shared. Thus, although shar-ing ecotourism revenues is an effective tool to increase the income of the local populationit is rather ineffective in promoting habitat and wildlife conservation, in particular, ifthe number of local communities N is large and, thus, externalities are high.

A mechanism, which achieves both goals, increasing the welfare of local communitiesand promoting wildlife conservation, is achieved by using ecotourism revenues to financethe subsidy/tax regime as defined by equations (32)–(35). Thus, the following budgetconstraint has to hold:

τ1P⋆ + τ2f

⋆ +τ0

NE⋆ = 0 . (36)

Inserting τ1 and τ2 for the sophisticated and the naive community yields for the shareτ0 of ecotourism revenues, which ensures a balanced state budget:

τ soph0

= − N E⋆2(f ⋆R⋆

2− P ⋆) + E⋆

1f ⋆(ρ − R⋆

1)

ρ − R⋆1(E⋆

1f ⋆ + E⋆) + E⋆

2(f ⋆R⋆

2− P ⋆ − E⋆)

, (37)

τnaive0

= −N E⋆2(f ⋆R⋆

2− P ⋆) + E⋆

1f ⋆(ρ − R⋆

1)

(ρ − R⋆1− E⋆

2)(E⋆

1f ⋆ + E⋆)

. (38)

16

However, in the case that ecotourism revenues are low and the subsidies on the outputof farmland production outweigh the taxes on farmland size by far, the transfers ofecotourism revenues τ0 can change from a subsidy to a tax. Although such a solutionis viable from a purely economic point of view, it is doubtful that such a tax/subsidyregime can find the support of the local communities. Thus, additional funds eitherfrom other state incomes or from international aid have to be secured to implement theoptimal tax/subsidy regime.

6 Conclusion

Habitat and wildlife conservation in developing countries by the creation of protectedareas, which excludes the local population from formerly possible land and wildlife uses,are likely to fail because the state rarely has the means to enforce its property rights.More promising are integrated conservation and development projects (ICDPs), whichaim to increase both wildlife and habitat conservation and the income of the local com-munities. To scrutinize if and to what extent ecotourism can achieve both goals, we haveinvestigated the interdependencies between local subsistence farming and hunting com-munities, and the abundance of habitat and wildlife under benefit-sharing ICDPs in adynamic bio-economic model. Our model differs from the existing theoretical literatureon the effects of ICDPs in three aspects. (i) We focus on revenues from non-consumptive

uses to promote habitat and wildlife conservation (e.g. ecotourism). Thus, there is nocompetition in wildlife harvest between the locals and the ecotourism enterprize. (ii)We treat the local population not as one homogenous group, but explicitly allow forexternalities, due to the de facto open access regime, by considering N individual com-munities. (iii) We investigate how the knowledge about the ecological foundations of thereproduction of the animal species influences the communities’ decisions.

Our main findings are that, under reasonable assumptions (no hunting is optimalin the long-run stationary state and the discount rate is sufficiently small), the levelof habitat and the size of the animal population is higher the higher is the share ofecotourism distributed to the local communities. Thus, sharing ecotourism revenuesis in fact a tool to promote both conservation and development goals. However, thelong-run habitat size and buffalo population are, in general, lower than in the socialoptimum. This is a result of the externalities induced by the public good propertiesof land and wildlife and/or the lack of knowledge about the ecological foundations ofthe reproduction of the animal species. Both the externalities induced by the publicgood properties of land and wildlife and the lack of knowledge induce incentives for thereduction of wilderness for agricultural use and increased hunting. Thus, hunting canbe optimal from the point of view of individual communities, although it is not optimalin the social optimum. This can explain why poaching is a widespread observation inmany protected areas and also ICDPs fail to create an incentive structure that eliminatespoaching. Sharing ecotourism revenues as a the sole fiscal instrument is not sufficientto tackle this multitude of ‘market failures’ and, in addition, cannot necessarily preventextreme outcomes such as the extinction of the buffalo population in the case of naive

17

communities.Nevertheless, we show how the social optimum can be achieved by a more encompass-

ing regime of taxes and subsidies. In fact, by subsidizing crop production and taxingland use the optimal level of habitat and wildlife conservation can be achieved, indepen-dent of the share of ecotourism revenues distributed to the local communities. Thus, inour combined regime we separate to some extent the conservation and the developmentpart of the ICDP. While the subsidy on agricultural output and the tax on land useensure that the conservation goal is achieved, the revenues from ecotourism fund thistax/subsidy regime and raise the income of the local population.

A strong assumption in our model, which can hardly be justified in the long-run,is that we do not consider the growth of the human population. In fact, Barrett andArcese (1998) argue that population growth is the main factor why ICDPs, which createrevenues solely from wildlife harvest, are not viable in the long-run. A non-growingecological resource distributed among an increasing number of heads must eventually failto satisfy the needs of the local population. Although in our model the revenues createdfrom the ICDP do not depend on wildlife harvest, also the funds created by ecotourismare likely to be bounded from above. Thus, at least in the long-run the revenues createdby ecotourism have to be complemented by other means to raise income. Barrett andArcese (1998) suggest projects to improve the technology of farmland cultivation. Asthe land size for agricultural use is fixed in their model, an increase in technology doesnot give incentives to increase the size of farmland as is the case in our model. However,improving technology in farmland cultivation combined with increased taxes on farmlandsize are possible solutions to reduce the pressure on habitat and wildlife even if humanpopulation increases. In summary, the thorough investigation of the link between theeffectiveness of ICDPs and population growth is one of the main tasks for future research.

18

Appendix

A.1 Strict concavity of the Hamiltonian

As hunting enters the Hamiltonian H (13) with a positive sign as a source of consumptionpossibilities and with a negative sign as it diminishes the buffalo population, strictconcavity of the Hamiltonian is not granted in general. Thus, one has to check for thestrict concavity of the Hamiltonian directly.

The Hamiltonian H is strictly concave if and only if for all leading principal minorsof its Hessian H the following condition holds:

(−1)kDk > 0 , k = 1, . . . , 4 , (A.1)

where Dk a the kth leading principal minor of the Hessian of the Hamiltonian H.7 Recallthat the following conditions hold:

G′ > 0 , G′′ = 0 ,P1 > 0 , P11 < 0 , P2 > 0 , P22 < 0 , P12 > 0 , P11P22 − P 2

12= 0 ,

H1 > 0 , H11 = 0 , H2 > 0 , H22 = 0 , H12 > 0 , H11H22 − H2

12< 0 ,

E1 > 0 , E11 < 0 , E2 > 0 , E22 < 0 , E12 > 0 , E11E22 − E2

12= 0 ,

R1 ⋚ 0 , R11 < 0 , R2 > 0 , R22 < 0 , R12 < 0 , R11R22 − R2

12= 0 .

(A.2)

The Hessian of the Hamiltonian H reads:

H =

V ′P22+V ′′P 22

V ′′P2H2 V ′P12+V ′′P2(P1−E1) V ′′P2(H1+ E2

N)

V ′′P2H2 V ′′H22

V ′′H2(P1−E1) (V ′′−NqB)H12+

V ′′H2(H1+ E2

N)

V ′P12+ V ′′H2(P1−E1) V ′(P11+NE11)+ −V ′E12−NqBR12+

V ′′P2(P1−E1) V ′′(P1−E1)2+N2qBR22 V ′′(P1−E1)(H1+ E2

N)

V ′′P2(H1+ E2

N) (V ′′−NqB)H12+ −V ′E12−NqBR12+ qBR11+V ′ E22

N+

V ′′H2(H1+ E2

N) V ′′(P1−E1)(H1+ E2

N) V ′′(H1+ E2

N)2

.

(A.3)

Taking the conditions (A.2) into account, the leading principal minors D1, D2 and D3

can be simplified to yield:

D1 = V ′P22 + V ′′P 2

2< 0 , (A.4)

D2 = V ′V ′′P22H2

2> 0 , (A.5)

D3 = V ′V ′′P22H2

2(N2qBR22 + V ′NE11) < 0 . (A.6)

The 4th principal minor D4 (which is also the determinant of the Hessian of the Hamil-tonian) is a quadratic equation in H12 = α3, which has to be positive for the Hamiltonianto be strictly concave.

D4 = α2

3A + α3B + C , (A.7)

7 The kth leading principal minor of a symmetric n × n matrix A is the determinant of the matrixobtained by deleting the n − k last rows and columns of A.

19

with

A = (V ′ − qB)2[V ′V ′′(2P12P2(P1 − E1) − P11P2

2− P22P

2

1) − (A.8)

−(N2qBR22 + NE11V′)(P22V

′ + P 2

2V ′′)] ,

B = 2H2V′V ′′(V ′ − qB){(NqBR12 + E12V

′)[P12P2 − (P1 − E1)P22] − (A.9)

−(H1 +E2

N)(N2qBR22 + NE11V

′)P22} ,

C = qBH2

2P22V

′2V ′′(R11NE11 + N2R22E22 − 2NR12E12) . (A.10)

According to the conditions (A.2), A < 0, B R 0 and C > 0. Thus, the Hamiltonian His strictly concave if α3 ∈

(

0,−(B +√

B2 − 4AC)/2A)

.8 Frankly speaking, the Hamil-tonian H is concave as long as hunting H is not too productive.

A.2 The socially optimal stationary state

The stationary state is given by Z(l⋆2) = 0, where Z equals:

Z(l2) =α2

α1

(

α1(1−l2)

δl2

)β [

1 − β

(

1+δl2

(δ+ρ)(1−l2)

)]

+α4

(δ+ρ)(1−θ)×

(

(1−θ)[δ−N α1(1−l2)]

(1−θ)δ−N α1(1−l2)

)γ [

(1−γ)ǫ

ρ+ǫ+

γ[(1−θ)δ−N α1(1−l2)]

δ−N α1(1−l2)

]

.(A.11)

Z is monotonously decreasing, i.e. Z ′ < 0, if:

ǫ

ρ + ǫ

W ⋆

W ⋆ − θ> 1 . (A.12)

This condition holds either if the discount rate ρ is small enough or the critical habitatsize θ is high enough. In addition, the following two conditions for Z hold:

liml2→0

Z = +∞ , liml2→∞

Z = −∞ . (A.13)

Thus, condition (A.12) is a sufficient condition for the existence of a unique stationarystate.

The comparative static results can be derived from the equations (20) by using theimplicit function theorem. Thus, the partial derivatives of l⋆

2with respect to � =

α1, α2, α4, γ, δ, ρ, ǫ, θ,N are given by:

∂l⋆2

∂�= −∂Z/∂�

∂Z/∂l⋆2

(A.14)

8 Note that A, B and C are functions of the state and control variables and thus change along theoptimal path. For local strict concavity of the Hamiltonian around the stationary state it is sufficientto evaluate A, B and C at the stationary state. This guarantees a non-empty neighborhood aroundthe stationary state in which the Hamiltonian is strictly concave. For global concavity, lower boundsfor A, |B| and C, which hold along the optimal path, guarantee strict concavity of the Hamiltonianglobally along the optimal path.

20

As outlined above ∂Z∂l⋆

2

< 0 if condition (A.12) holds. For ∂Z∂�

one derives:

∂Z

∂α1

> 0 ,∂Z

∂α2

< 0 ,∂Z

∂α4

> 0 ,∂Z

∂γ=? ,

∂Z

∂δ=? ,

∂Z

∂ρ=? ,

∂Z

∂ǫ> 0 ,

∂Z

∂θ=? ,

∂Z

∂N< 0 .

(A.15)

A.3 Habitat size and wildlife abundance under communal welfare maximization

In the socially optimal stationary state the following conditions hold:

V ′P2 = qfG′ > (V ′ − N qB)H2 . (A.16)

Under communal welfare maximization, the following relationship between the shadowprices hold in the socially optimal stationary state:

pB ≤ qB , pf > qf . (A.17)

As a consequence, the following conditions hold in the socially optimal stationary state:

V ′P2 < pfG′ . (A.18)

Defining X1 = V ′P2, X2 = pfG′ and X3 = (V ′− pB)H2 one can show that the following

conditions at the socially optimal stationary state hold for the sophisticated community:

∂X1

∂l1> 0 ,

∂X1

∂l2< 0 ,

∂X1

∂l3= 0 ,

∂X2

∂l1< 0 ,

∂X2

∂l2> 0 ,

∂X2

∂l3< 0 ,

∂X3

∂l1< 0 ,

∂X3

∂l2= 0 ,

∂X3

∂l3< 0 ,

(A.19)

and that the following conditions at the socially optimal stationary state hold for thenaive community:

∂X1

∂l1> 0 ,

∂X1

∂l2< 0 ,

∂X1

∂l3= 0 ,

∂X2

∂l1< 0 ,

∂X2

∂l2> 0 ,

∂X2

∂l3> 0 ,

∂X3

∂l1< 0 ,

∂X3

∂l2= 0 ,

∂X3

∂l3< 0 ,

(A.20)

As a consequence, in the long-run stationary state under communal welfare maximiza-tion the labor share for farmland production l1 is higher, the labor share for farmlandcultivation l2 is lower, and the labor share for hunting l3 is higher or equal than theaccording labor share in the socially optimal stationary state. Thus, communal welfaremaximization leads to less habitat W and a lower buffalo population B than the socialoptimum suggest.

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