Institute for Economic Studies, Keio University
Keio-IES Discussion Paper Series

Trophy Hunting Restrictions and Land Use in Private Land Conservation Areas:
A Bioeconomic Analysis
Zijin Xie
22 March, 2023
DP2023-007
https://ies.keio.ac.jp/en/publications/22464/

Institute for Economic Studies, Keio University
2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
ies-office@adst.keio.ac.jp
22 March, 2023

Trophy Hunting Restrictions and Land Use in Private Land Conservation Areas:
A Bioeconomic Analysis
Zijin Xie
Keio-IES DP2023-007
22 March, 2023
JEL Classification: Q57, Q2, Q26
Keywords: Bioeconomic modeling, Lion hunting; PLCA, Tourism, Trophy hunting,
Wildlife conservation

Abstract
This study investigated how bans/restrictions on trophy hunting affect wildlife
conservation in private land conservation areas (PLCAs). We developed a bioeconomic
model to examine wildlife and land utilization in a fixed-size PLCA with a land manager.
We calibrated the model for the lion-hunting industry in PLCAs in South Africa. The
model simulates the impact of trophy-hunting restrictions on the lion population
under different management scenarios. We demonstrated that restrictions on trophy
hunting would be effective if wildlife-based tourism is an alternative land use to trophy
hunting. However, the restrictions on trophy hunting will negatively affect the wildlife(lion) population if alternative land use is not wildlife-based. Although wildlife-based
tourism is considered a positive alternative to trophy hunting, it is more vulnerable toexternal shocks than trophy hunting. Our results suggest that international
bans/restrictions on trophy hunting should be cautiously imposed, particularly in thecontext of the global pandemic, which has had a devastating effect on wildlife-based
tourism.

Zijin Xie
Faculty of Economics, Keio University
2-15-45, Mita, Minato-ku, Tokyo 108-8345, Japan
xiezijin@keio.jp

Acknowledgement : This research was supported by the JST SPRING (grant number
JPMJSP2123). The author also appreciates the support of the 2020 SEEPS Research
Fund for Graduate Students. This study was presented at the 2021 Annual Conferenceof the Society for Environmental Economics and Policy Studies.

Trophy Hunting Restrictions and Land
Use in Private Land Conservation Areas:
A Bioeconomic Analysis
Zijin Xie∗
Faculty of Economics, Keio University

Abstract
This study investigates how bans/restrictions on trophy hunting affect wildlife
conservation in private land conservation areas (PLCAs). We develop a bioeconomic model to examine wildlife and land utilization in a fixed-size PLCA witha land manager. We calibrate the model for the lion-hunting industry in PLCAs
in South Africa. The model simulates the impact of trophy-hunting restrictions
on the lion population under different management scenarios. We demonstratethat restrictions on trophy hunting would be effective if wildlife-based tourism is
an alternative land use to trophy hunting. However, the restrictions on trophy
hunting will negatively affect the wildlife (lion) population if alternative land use
is not wildlife-based. Although wildlife-based tourism is considered a positive
alternative to trophy hunting, it is more vulnerable to external shocks than trophy hunting. Our results suggest that international bans/restrictions on trophy
hunting should be cautiously imposed, particularly in the context of the global
pandemic, which has had a devastating effect on wildlife-based tourism.
Keywords: Bioeconomic modeling; Lion hunting; PLCA; Tourism; Trophy
hunting; Wildlife conservation∗

Faculty of Economics, Keio University, 2-15-45, Mita, Minato-ku, Tokyo 108-8345, Japan. E-mail:xiezijin@keio.jp1

1Introduction
The debate over whether trophy hunting should be banned gained momentum

after the iconic animal—Cecil the lion—was hunted by an American trophy hunterin 2015. The incident was widely reported and sparked international outrage overtrophy hunting on social media, which led to campaigns against trophy hunting. Underpublic pressure, some developed countries that are the main markets of the trophyhunting industry have implemented several bans or restrictions on the import of wildlife
trophies1 .
However, scientists have consistently expressed concerns regarding bans or restrictions on trophy hunting and their transportation. The trophy-hunting industry has
been a significant financial stimulant for Sub-Saharan countries and has contributed
to the conservation of large areas of natural habitats (Lindsey et al., 2007). Several
studies have highlighted that an outright ban on trophy hunting will accelerate the lossof biodiversity due to the loss of the main financial resource for conservation2 .
Trophy hunting remains vital for private land conservation areas (PLCAs) as theprimary source of financial income (Parker et al., 2020; Taylor et al., 2020). In South
Africa, the area classified as PLCA is twice that of state-owned protected areas (Parker
et al., 2020). The trophy-hunting industry incentivizes careful wildlife managementin PLCAs because high-quality wildlife trophies are extremely profitable. Although
the contribution of trophy hunting toward wildlife conservation remains controversial,
Lindsey et al. (2007) and Cooney et al. (2017) documented several successful conservation cases under PLCAs in South Africa, which were attributed to the trophy-hunting
1

France and Australia immediately stopped importing and exporting lion trophies in 2015, and the
UK imposed a strict ban on trophy-hunting imports in 2021 (Manning, 2021).
2
See for example Di Minin et al. (2016) and Sills et al. (2019).

2

industry.
Therefore, it is believed that a ban or restrictions on trophy hunting may impede
wildlife conservation in PLCAs. For PLCAs that do not receive government grants, any
forms of ban or restriction on trophy hunting would eliminate the landowner’s financial
incentive for wildlife management, which increases the risk of extensive habitat loss andpoaching.
Consequently, it is essential to understand how bans and restrictions on trophy
hunting affect wildlife conservation in PLCAs. Notably, Parker et al. (2020) interviewed
PLCA landowners about their attitude toward a potential ban on trophy hunting.
They found that 90% of the interviewees claimed that a blanket ban on trophy hunting
would negatively impact their livelihood, and 63% would change their wildlife-based
land use (i.e., trophy-hunting area) to other non-wildlife-based land uses (e.g., livestock
farming or cultivation). Naidoo et al. (2016) demonstrated that a blanket ban on trophy
hunting will render a large conservation area unprofitable and decrease the number ofcommunal conservancies in Namibia. However, these studies only discussed the effectof a potential outright ban on trophy hunting. However, research on the impact ofexternal restrictions on trophy hunting, such as restricting the import and export of
wildlife trophies, on wildlife conservation in PLCA remains scarce. Although some
African countries—such as Kenya—have imposed a complete ban on trophy hunting,external restrictions on trophy hunting led to a significant loss of profits for othercountries that rely on revenue from trophy hunting—such as South Africa (Ngounou,
2022). Therefore, this study focuses on the effects of exogenous restrictions instead ofa blanket ban.
This study addresses the effect of an external ban or restrictions on trophy hunting3

(hereafter referred to as trophy-hunting restrictions) on the imports of wildlife trophies
and wildlife conservation in PLCAs. We examine a fixed-size PLCA with any of thefollowing land-use types: (1) land used for wildlife-based tourism and trophy hunting
and (2) land divided for agriculture and trophy hunting. First, we develop a theoreticalmodel to describe the management of PLCA for each land-use type. In addition, thePLCA managers may or may not share property rights with wildlife populations3 .
Thus, we consider two property rights regimes. Then, we compare the effect of trophyhunting restrictions on the lion trophy-hunting industry in PLCAs in South Africa,
considering the above-mentioned land-use types and property rights regimes.
The numerical analysis reveals that the impact of trophy-hunting restrictions on
wildlife conservation depends on alternative land use. Particularly for the second landuse type, external trophy-hunting restrictions are expected to decrease wildlife (lion)
populations in the long term because it can be optimal for land managers to reduce thehunting area’s size under such restrictions, irrespective of whether they share property
rights. Therefore, if alternative land use is not wildlife-based, reducing hunting area
causes habitat loss, decreasing wildlife populations.
Our work contributes to the bio-economic literature on trophy hunting and protected area management. While we focus on the effect of trophy-hunting restrictions,previous studies have modeled protected area management with trophy hunting and/or
poaching behaviors of locals. For example, Skonhoft and Solstad (1998) suggested thatgiving property rights to locals can reduce their poaching behavior, which increases
wildlife populations. In a series of related studies, Johannesen and Skonhoft (2005),
Johannesen (2006), Fischer et al. (2010), and Winkler (2011) focused on introducing
economic incentives to prevent locals from poaching. In particular, they explore the ef3

The owners and managers of a PLCA could be different (Stolton et al., 2014).

4fect of a benefit-sharing protected area management scheme that transfers a part of the
profits from tourism and/or trophy hunting to locals4 . Although Winkler (2011) and
Rondeau and Bulte (2007) considered hunting as land use for wildlife habitats, theirmain focus was on promoting wildlife conservation by preventing wildlife poaching. In
this study, we do not explicitly include the poaching behavior of locals but focused on
managing a PLCA under trophy-hunting restrictions.
The remainder of this paper is organized as follows. Section 2 discusses a theoretical model that describes management in a PLCA. Section 3 describes the model’s
application to the lion trophy-hunting industry in PLCAs in South Africa. Section 4
discusses the results and concludes the study.

2

The Model
Let us consider a fixed-size PLCA with a land manager. This PLCA has two typesof land uses: (1) land used for trophy hunting and tourism and (2) land used for trophy
hunting and agricultural activities5 . Regardless of the land-use type, the manager
optimizes profits by delimiting the area for trophy hunting and tourism/agriculture.

2.1

Land-use type 1: PLCAs with trophy hunting and tourism
We first consider the case wherein the fixed-size area is split into regions for hunting

and tourism. The manager delimits the size of the hunting and tourism area, which
directly affects the corresponding revenue. In addition, we assume that tourism and4

Such a management scheme is called integrated conservation development projects (ICDPs) orcommunity-based natural resource management (CBNRM).
5
According to Parker et al. (2020), trophy hunting is not the only source of income for PLCAs.
Revenue from trophy hunting accounts for an average of 36% of the total revenue. Other income
resources include eco-tourism and agriculture.

5

hunting activities are limited to their respective areas, even though wildlife can roam
freely across the two regions6 .
The land manager, who maximizes the present value of the net profits from trophy
hunting and tourism, has the following objective function:max{Ht }∞
0

π=
=

∞
X
t=0
∞
X

ρt [(1 − c)R(ht ) + W (Vt , Xt )]ρt [(1 − c)R(αHt ) + W (L − Ht , Xt )]
(1)

t=0

s.t.

Xt+1 − Xt = F (Xt ) − αHt , X0 > 0 given, Rh > 0, Rhh < 0, ht ≡ αHt ,Vt ≡ L − Ht , WV > 0, WV V < 0, WX > 0, WXX < 0, FX ⋛ 0, FXX < 0(1 − c)R(ht ) refers to the benefit from trophy hunting during period t; ht ≡ αHt isthe offtake for wildlife quota, and Ht is the size of the hunting area7 . Trophy-hunting
restrictions are modeled by assuming that restrictions can decrease the benefit of trophy
hunting (increased c) or offtake rate of the hunting quota (decreased α)8 . Furthermore,
W (Vt , Xt ) is the income from tourism, which is a function of the size of the area for
tourism denoted by Vt ≡ L − Ht and wildlife populations in the PLCA denoted by
Xt 9 . The profits from trophy hunting and tourism change according to the change inwildlife stock Xt+1 − Xt —the difference between bio-growth F (Xt ) and the hunting
quotas αHt . Additionally, ρ represents the discount factor, and ρ ≡ 1/(1 + δ), whereδ denotes the capital interest rate.
6

We assume that although wildlife can migrate freely between the two regions, they are evenly
distributed throughout the conservation area. There are studies on wildlife migration between management borders (e.g., Johannesen (2007)).
7
Quota-setting methodology remains problematic for the trophy-hunting industry due to the lackof transparency (Lindsey et al., 2013). Hurt and Ravn (2000) mentioned that hunting quotas areusually based on the following: “(i) size of the area, (ii) type of habitat, (iii) density of species, and(iv) offtake in the previous year” (p. 308). For simplicity, we assume that the hunting quota ht isbased on the size of the hunting area Ht .
8
Trophy import restrictions affect wildlife species profitability. Limiting the offtake rate of hunting
quota is also a form of restriction (IUCN, 2016).
9
In period t, wildlife population in the tourism area is Xt /L ∗ Vt .

6

The Lagrangian for this problem is as follows:

L =

∞
X

ρt {(1 − c)R(αHt ) + W (L − Ht , Xt ) + ρλt+1 [Xt + F (Xt ) − αHt − Xt+1 ]} (2)t=0The first-order conditions for the manager are as follows:∂L= ρt {(1 − c)αRht − WVt − αρλt+1 } = 0∂Ht∂L= ρt {WXt + ρλt+1 (1 + FXt )} − ρt λt = 0∂Xt∂L= ρt {Xt + F (Xt ) − αHt − Xt+1 } = 0∂ρλt+1

(3)
(4)
(5)

(3) implies that a profit-maximizing manager expands hunting land until the marginal
net benefit of hunting (1 − c)αRht − WVt equals the discounted shadow price of thewildlife stock in period t + 1 for trophy hunting. (4) reveals that for optimal management, the shadow price λt equals the marginal net benefit WXt with the discounted
marginal benefit of an unharvested unit of stock in the next period ρλt+1 (1 + FXt ).
(3)∼(5) imply a steady state where Xt+1 = Xt = X ∗ , Ht+1 = Ht = H ∗ , andλt+1 = λt = λ∗ . Consequently, in steady-state equilibrium, (3)∼(5) can be written as
follows:(1 − c)αRh − WV = αρλ(6)ρλ(δ − FX ) = WX

(7)

F (X) = αH

(8)Rearranging (6)∼(8) and using the definition of the discount factor ρ ≡ 1/(1 + δ), we

7derive the fundamental equation of renewable resources

WX+ FX = δ.
(1 − c)αRh − WV /α(9)The LHS of (9) is referred to as the resource’s rate of return, which is the sum of themarginal stock effect (the ratio of marginal net hunting revenue to marginal tourism
revenue) and marginal growth rate (Conrad, 2010). (9) indicates that the resource’s
rate of return should be equal to the interest rate under optimal management. Furthermore, (6)∼(8) imply that dX/dc > 0 and dX/dα < 0 if FX < 0 and WXV are
sufficiently small, ceteris paribus. See Appendix.

2.2

Land-use type 2: PLCAs with trophy hunting and agriculture
In cases where land is used for trophy hunting and agriculture, the manager max-

imizes the sum of the revenue by determining the size of the area for hunting andagriculture. Thus, the following defines the problem for the manager:

max∞ π ={Ht }0∞X

ρt [(1 − c)R(ht ) + Q(At , Xt )]

t=0

=

∞
X

ρt [(1 − c)R(αHt ) + Q(L − Ht , Xt )]

t=0

s.t.

Xt+1 − Xt = F (Xt , Ht ) − αHt , X0 > 0 given, Rh > 0, Rhh < 0,At ≡ L − Ht , QA > 0, QAA < 0, QX < 0, QXX < 0,
FX ⋛ 0, FXX < 0, FH > 0

8

(10)

Q(At , Xt ) is the revenue from agricultural production, which is a function of the sizeof the agricultural land At and wildlife stock Xt . We consider that QXt < 0 because
wildlife stock causes damage to agricultural production in farms near the predator’s
habitat. The wildlife stock changes according to the bio-growth function F (Xt , Ht ) andthe hunting quotas αHt . Notably, the bio-growth function depends on the wildlife stock
Xt and size of the hunting land Ht 10 . This implies that the expansion of agriculturalland reduces the ability of the land to support wildlife. In addition, we suppose thatthe land used for hunting can be converted into farmland immediately without cost(and vice versa).
The Lagrangian for this problem is as follows:

L =

∞
X

ρt {(1−c)R(αHt )+Q(L−Ht , Xt )+ρλt+1 [Xt +F (Xt , Ht )−αHt −Xt+1 ]} (11)t=0

The first-order conditions are as follows:∂L= ρt {(1 − c)αRht − QAt − ρλt+1 (α − FHt )} = 0∂Ht∂L= ρt {QXt + ρλt+1 (1 + FXt )} − ρt λt = 0∂Xt∂L= ρt {Xt + F (Xt , Ht ) − αHt − Xt+1 } = 0∂ρλt+1

(12)
(13)
(14)

(12) implies that under conditions of optimum management, the marginal net benefitof trophy hunting equals the discounted shadow price of the wildlife stock in the next
period multiplied by the net marginal effect of hunting land on the dynamics of thewildlife stock. According to (13), the shadow price of the wildlife stock in period t
10

We assume that the bio-growth function F is a logistic function, which depends on Xt , the intrinsic
growth rate of wildlife, and carrying capacity. Since the carrying capacity of wildlife is positively
associated with the size of wildlife habitat (Griffen and Drake, 2008), the size of the agricultural area
negatively affects the carrying capacity.

9equals the marginal wildlife damage on agricultural production QXt along with thediscounted marginal benefit of an unharvested unit of the stock in the next period
ρλt+1 (1 + FXt ).
(12)∼(14) imply a steady state, where Xt+1 = Xt = X ∗ , Ht+1 = Ht = H ∗ , andλt+1 = λt = λ∗ , solving(1 − c)αRh − QA = ρλ(α − FH )(15)

ρλ(δ − FX ) = QX

(16)

F (X, H) = αH

(17)Thus, we can derive the fundamental equation of renewable resources:

QX+ FX = δ.
(1 − c)αRh − QA /(α − FH )(18)

Ceteris paribus reveals that the impact of hunting restrictions on steady-state
wildlife populations can be ambiguous. The comparative static results and derivations
are presented in the appendix. In the next section, we numerically show the asymmetricpath of how X0 converges with X ∗ under trophy-hunting restrictions11 .

3

Numerical Application
This section applies the theoretical model with specific function forms to a numer-

ical simulation of lion trophy hunting in South Africa.
Trophy hunting generates enormous revenue for the conservation of wildlife andcorresponding habitat in Southern African countries. Lion trophies, one of the most
11

Also known as the optimal path approach method (Conrad, 2010).

10valuable wildlife trophies, are significantly profitable for South Africa—the world’s
largest exporter of lion trophies (Lindsey et al., 2012). However, the global publiccondemned the lion trophy-hunting industry, especially after Cecil the lion was killed.
Importing lion trophies has been banned in some developed countries, including Australia, France, and the UK. PLCA managers turn to ecotourism and livestock farming
as alternative land uses in the face of a ban on trophy hunting (Parker et al., 2020). Thelion trophy-hunting situation is similar to the problem of PLCA management discussed
in the previous section.

3.1

Functional forms and parameterization
The revenue from trophy hunting, that is, R(ht ), depends on selling the hunting

quotas represented by ht = αHt . We assume that the hunting revenue under the
restriction on the trophy price during period t is given by:(1 − c)R(αHt ) = (1 − c)PH (αHt )γ(19)

where PH is the per-unit price of the hunting quota, c represents the exogenous restrictions on the trophy price, and γ is the production elasticity of hunting quotas ingenerating revenue.
For revenue from tourism, extant literature suggests that increasing the densityof the lion population Xt /L and tourism area Vt = L − Ht increases tourism revenue
W (L−Ht , Xt ) for PLCAs (Clements et al., 2016; Naidoo et al., 2011). Thus, we assume11

that tourism revenue takes the following form:

W (L − Ht , Xt ) = PW (L − Ht )θ (Xt /L)1−θ(20)

where PW is a scaling factor, and θ is the production elasticity of the land area thatgenerates tourism revenue.
In cases where the land is unsuitable for tourism, we postulate that livestock
farming is the alternative land use to hunting. Since agricultural production Q(At , Xt )depends on the size of the farmland At = L − Ht , its proportion D(Xt , At ) will be
destroyed by predators Xt . For simplicity, we postulate that the proportion of agricultural products damaged by wildlife D is a linear function of Xt and At , which isD(Xt , At ) = dXt At . Thus, we define revenue from agricultural production as follows:

Q(At , Xt ) = PA (1 − dXt At )(At )µ , with At = L − Ht(21)

where PA is the price of agricultural products (i.e., a scaling factor for farming productivity), d denotes the proportion of agricultural products destroyed by wildlife, and µ
is the production elasticity of farmland.
The lion population has grown according to a logistical growth function.

F (Xt ) = rXt (K − Xt )(22)

where r refers to the intrinsic growth rate, and K represents the carrying capacity. Since
the carrying capacity is associated with habitat size, we define K as a linear functionof habitat size. In other words, for land-use type 1, the bio-growth function can be12written as F (Xt ) = rXt (ϕL − Xt ) and for land-use type 2, it becomes F (Xt , Ht ) =rXt (ϕHt − Xt ), where ϕ is the size of the lion population per unit of land can support.
Subsequently, we can apply the model to lion trophy hunting in PLCAs, withplausible parameter values. In South Africa, lion hunts are generally sold as all-inclusive
hunt packages with a mid-price of US$ 30542 ± 3523 (Lindsey et al., 2012). Thus, weestablished the trophy price of PH = 3.3 (10 thousand US$). Lion trophy exports fromSouth Africa averaged 758 trophies in 2009–2010 (Lindsey et al., 2012), and the sizeof the hunting land was estimated at 160,000 km2 (Lindsey et al., 2007). Accordingly,
we estimate an offset rate of α = 758/16000 ≈ 0.004 lions/km2 .
For revenue generated from lion tourism, Clements et al. (2016) estimated therelationship between tourism income and lion density using survey data from 71 PLCAs
managers in South Africa. Following this empirical study, the elasticity of lion density
for generating tourism revenue is 1 − θ = 0.55, and the scaling factor for tourism
productivity is PW = 1 (10 thousand US$).
Compared with the wildlife-based revenue from hunting and tourism, income fromagricultural production constitutes a relatively small portion of PLCAs’ total revenue(Parker et al., 2020). Even though economic data for agricultural production in PLCAs
are challenging to find, an estimate of the impact of several factors on agricultural
production in sub-Saharan countries is provided by Barrios et al. (2008). They showthat the production elasticity of land is 0.539∼0.576; therefore, we set µ = 0.558.
We assume a scaling factor for agriculture of PA = 0.2 and a wildlife damage rate of
d = 0.00001.
Finally, Miller and Funston (2014) reported that the lion population in South
Africa’s small reserves grew at a rate of 1∼2. Thus, we set the lion growth rate as13

Table 1: Parameter values
Economic

Sourceparameters

Biological andSourceharvest parameters

PH = 3.3

Lindsey et al. (2012)

L = 300

Parker et al. (2020)

γ = 0.9-

r = 0.015

Miller and Funston (2014)

PW = 1Clements et al. (2016)

ϕ = 0.12

Hayward et al. (2007)

1 − θ = 0.55

Naidoo et al. (2011)

X0 = 15

Clements et al. (2016)

PA = 0.2-

δ = 0.01-µ = 0.558

Barrios et al. (2008)

α = 0.004

Lindsey et al. (2012)

d = 0.00001-

r = 0.015. Hayward et al. (2007) estimated the carrying capacity of large carnivores
in South Africa as 0.12 lions /km2 , so ϕ = 0.12. Moreover, the size of the PLCA land
ranged from 0.1∼543.8 km2 in South Africa (Parker et al., 2020); thus, we assume that
the PLCA’s land area is L = 300 km2 . The density of the lion population in different
PLCAs vary according to the available prey, with an average value of 0.048 million/km2 (Clements et al., 2016). Accordingly, we assume X0 = 0.05 ∗ 300 = 15 lions.
Table 1 summarizes the parameter values.

3.2

Results

3.2.1

Land-use type 1

We first consider the case wherein the manager has property rights over lions
under land-use type 1. Here, the land manager determines Ht while considering thelion population’s dynamics. Substituting the parameter values in Table 1 into (1), we
use Solver to numerically derive the approach paths of Xt under different scenarios.
For tractability, we assume that trophy-hunting restrictions decrease the offtake rate
α or the price of hunting quota PH (i.e., increase c).
14

Figure 1 depicts the approach paths for different scenarios. In the absence oftrophy-hunting restrictions, we observe that Xt → 33.72 as t → 19 (grey line). However, after imposing restrictions, Xt → 33.79 as t → 21 if PH is reduced by 30%(dashed line), and Xt → 34.97 as t → 17 if α = 0.002 (dotted line). This implies thattrophy-hunting restrictions positively affect the lion population.

Figure 1: Approach paths of Xt under land-use type 1, wherein the manager has
property rights over lions

We also consider the case wherein the manager does not have property rights
over lions. In this case, the manager is a myopic harvester who does not consider thelion population’s dynamics while determining Ht . In other words, a myopic manager’s
problem can be stated as follows:

max π = (1 − c)R(ht ) + W (Vt , Xt )Ht(23)
= (1 − c)R(αHt ) + W (L − Ht , Xt )This myopic manager determines Ht based on the first-order condition of (23), whichis (1 − c)αRht = WVt . Given that X0 = 15, we can solve for H0 by substituting the15parameter values in Table 1 into this first-order condition. Subsequently, X1 can bederived from the interactive map X1 = F (X0 ) − αH0 . We repeat this process t = T
times to derive the lion population’s dynamics.
Figure 2 depicts the approach paths of Xt . The gray line represents the approach
path of Xt in the absence of trophy-hunting restrictions. In Figure 2, we observe thatthe gray line is below the dashed line (the approach path of Xt when the quota price
PH is reduced by 30%) and the dotted line (the approach path of Xt when the offset
rate α becomes 0.002). This implies that any decrease in the value of α or PH will also
increase the value of Xt .
The effect of trophy-hunting restrictions when property rights are taken away fromthe manager is the same as in the previous case. In the presence of trophy-hunting
restrictions, it is optimal for a manager to convert hunting land into land for tourism
activities. Thus, the number of hunting quotas decreases with the size of hunting land,consequently increasing the lion population.

Figure 2: Approach paths of Xt under land-use type 1, wherein the manager has noproperty rights over lions16

3.2.2Land-use type 2

Here, we consider land-use type 2, wherein the land is divided into areas for
hunting and agricultural activities. The management problem when the manager has
property rights over lions is denoted by (10). The parameter values in Table 1 aresubstituted into (10) to numerically solve the problem and derive the approach pathof Xt . Figure 3 depicts the approach paths of the lion population Xt . With an initial
lion population X0 = 15, figure 3 shows that Xt → 28.88 as t → 21 in the absenceof hunting restrictions (gray line). However, Xt → 25.96 as t → 30 when the price of
quotas PH decreases (dashed line) and Xt → 24 as t → 34 if the offset rate is reduced
to α = 0.002 (dotted line).

Figure 3: Approach paths of Xt under land-use type 2, wherein the manager has
property rights over lions

For the case in which the manager has no property rights over lions, the optimal

17

problem becomes as follows:

max π = (1 − c)R(ht ) + Q(At , Xt )Ht(24)
= (1 − c)R(αHt ) + Q(L − Ht , Xt )The first-order condition implies that the optimal hunting area size at time t satisfies(1 − c)αRht = QAt . The approach paths for Xt are shown in Figure 4. This implies
that if the price of hunting quota or offtake rate decreases, Xt corresponds with alower lion population (Xt → 26.97 as t → 27 if PH is reduced by 30% (dashed line);
Xt → 26.69 as t → 24 for α = 0.002 (dashed line) compared to when there are no
hunting restrictions (Xt → 29.13 as t → 20, grey line). Furthermore, a comparisonof Figure 3 and Figure 4 shows that the manager’s possession of the property rights
over lions does not necessarily ensure a higher lion population under land-use type
2. A summary of the steady-state values of the lion population for different cases ispresented in Table 2.

Figure 4: Approach paths of Xt under land-use type 2, wherein the manager has noproperty rights over lions

18

Table 2: Summary of the results
Land-use type

Steady-state lion population X ∗Manager with

Figureproperty rights? No restrictionsa Lower PH b Lower αc references
1. Trophy hunting

Yes

33.719

33.79

34.97

Fig 1

& tourismNo

33.718

33.78

34.96

Fig 2

2. Trophy hunting &

Yes

28.88

25.96

24.03

Fig 3

livestock farming

No

29.13

26.97

26.69

Fig 4

a

PH = 3.3 and α = 0.004.
The value of PH is reduced by 30%.
c
The value of α is reduced by 50%.
b

4Conclusion and Discussion
Whether trophy hunting should be banned remains a matter of controversy. In

this study, we developed a bioeconomic model to explore the impact of trophy-hunting
restrictions on wildlife populations in the context of a fixed-size PLCA and two landuse types. The land is divided into areas for hunting and tourism activities in thefirst land-use type. In the presence of trophy-hunting restrictions, managers can turnhunting areas into tourism areas, which still serve as wildlife habitats. In land-use type2, we consider agricultural production (livestock farming) as an alternative land use
to trophy hunting. In other words, the manager may convert the hunting area into
an area for agricultural activities in the presence of trophy-hunting restrictions. The
numerical simulation results suggest that if alternative land use is not wildlife-based,
then any restriction on trophy hunting can negatively affect wildlife populations.
Our results reveal that trophy-hunting restrictions improve wildlife conservation
when the hunting area is converted into an area for tourism activities; however, tourism
is particularly sensitive to external conditions (Lindsey et al., 2007), such as travel
restrictions due to the COVID-19 pandemic. Travel restrictions due to the pandemic
19

have caused massive shocks to wildlife-based tourism, which is one of the principal
sources of revenue for protected areas in African countries. For example, protectedareas in South Africa experienced a 90% reduction in tourism revenue during 2020
(Gibbons et al., 2021). Owing to the decrease in income, the budget for conservation
has declined, causing a reduction in anti-poaching efforts, increasing human-wildlife
conflicts, and bushmeat hunting (Gibbons et al., 2021). This problem has been further
exacerbated for private conservation areas owing to the need for more government
grants.
The COVID-19 pandemic induced financial losses of up to USD 58 million in theprivate wildlife industry of South Africa in 2020 (van der Merwe et al., 2021). The
cancellation of ecotourism and trophy-hunting tours has negatively affected privately
owned reserves. Researchers believe that PLCA landowners are more likely to sellor convert wildlife habitats into other land uses in the face of an uncertain future of
wildlife-based tourism (Spenceley, 2021).
Although the recovery of the ecotourism industry remains elusive in the short run,some sub-Saharan countries, such as Botswana and South Africa, announced re-opening
the trophy-hunting season in 2021. Compared with photographic tourism, the trophyhunting industry can generate massive profits from fewer visitors (Lindsey et al., 2007).
In addition, Biggs et al. (2020) mentioned that trophy hunters may be more willing tovisit reserve areas because they are more resilient to risk circumstances. Consequently,
trophy hunting is significant for solving the immediate financial difficulties private
reserve areas faced during the pandemic. Therefore, international trophy-hunting bansand restrictions should be cautiously issued, especially during/after the pandemic.
While several people continue to believe that trophy hunting is brutal and unneces-20

sary, they do not recognize it as a conservation tool for wildlife habitats in low-income
countries. Opponents of trophy hunting argue that it should be replaced by photographic tourism, which can generate sustainable revenue and conserve wildlife habitats. Indeed, photographic tourism does generate higher total benefits compared totrophy hunting. However, many visitors have caused over-tourism, negatively impacting the local culture and ecosystem in sub-Saharan countries (Séraphin et al., 2020).
Furthermore, as mentioned previously, some remote reserve areas are unsuitable for
ecotourism. Banning trophy hunting can preserve wildlife from trophy hunters; however, finding alternatives to trophy hunting that can provide revenue for conserving
wildlife remains difficult.

Acknowledgements
This research was supported by the JST SPRING (grant number JPMJSP2123).
The author also appreciates the support of the 2020 SEEPS Research Fund for Graduate Students. This study was presented at the 2021 Annual Conference of the Society
for Environmental Economics and Policy Studies.

Appendix
In the case where land is used for hunting and tourism, comparative static results
are derived by taking the total differential of (6), (7), and (8). The total differentiation
yields
 

 


dρλ
0
H∗
0
−α
FX
 

 


 

 


(A1)
 −α
LHH LHX   dH  = αRh  dc +  ψ1  dα
 

 


dX
0
0
FX − δ LXH LXX
{z
}
|
[J]

21

where
LHH = α2 (1 − c)Rhh + WV V < 0
LHX = −WXV
LXX = WXX + ρλFXX < 0 for FX − δ < 0
ψ1 ≡ –(1 − c)Rh − (1 − c)αHRhh + ρλ

(A2)
(A3)
(A4)
(A5)

at steady state. We define the first term of (A1) as the matrix [J]; then, the determinantof [J] must be positive if FX (FX − δ) > 0 and WXV is sufficiently small. If we assume
that |J| > 0 and FX − δ < 0, then (A1) implies that dX/dc > 0 and dX/dα < 0(otherwise, the signs of dX/dc and dX/dα could be ambiguous).
For land-use type 2, the steady-state value was obtained from (15)∼(17). The
total differentiation yields


 

 
0
FH − α FX
dρλ
0
H∗


 

 


 

 
(A6)
FH − α LHH LHX   dH  = αRh  dc +  ψ2  dα


 

 
FX − δ LXH LXX
dX
0
0
{z
}
|
[R]

where
LHH = (1 − c)α2 Rhh + QAA + ρλFHH
LLX = −QXA + ρλFXH
LXX = QXX + ρλFXX > 0 for FX − δ < 0ψ2 ≡ –(1 − c)Rh − (1 − c)αHRhh + ρλ

(A7)
(A8)
(A9)
(A10)

We set the first term of (A6) to [R]. However, the sign of |R| is ambiguous. If
we assume that |R| > 0 and FX − δ < 0, then dX/dc < (>)0 and dX/dα ≷ (<)0 if
FH − α > (<)0.

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