CREATION OF MARINE RESERVES AND INCENTIVES FOR BIODIVERSITY
CONSERVATION
QUACH THI KHANH NGOC
Nha Trang University, Nha Trang, Vietnam
Email: [email protected]
ABSTRACT. Despite a number of benefits, marine reserves provide neither incentives for
fishermen to protect biodiversity nor compensation for financial loss due to the designation of
the reserves. To obtain fishermen’s support for marine reserves, some politicians have
suggested that managers of new marine reserves should consider subsidizing or compensating
those fishermen affected by the new operations. The objective of this paper is to apply
principal-agent theory, which is still infrequently applied to fisheries, to define the optimal
reserve area, fishing effort, and transfer payments in the context of symmetric and
asymmetric information between managers and fishermen. The expected optimal reserve size
under asymmetric information is smaller than that under symmetric information. Fishing
efforts encouraged with a transfer payment are always less compared to those without
payment. This reflects the fact that as the manager induces the fishermen to participate in the
conservation program, the fishermen will take into account their effects on fish stock by
decreasing their effort. Examples are also supplied to demonstrate these concepts.
KEY WORDS: asymmetric information, biodiversity conservation, bioeconomics, marine
reserve, principal-agent
1. Introduction. As a measure against uncertainty and the management failure of fisheries
and other marine resources (for references, see e.g. Flaaten and Mjølhus [2005] and Lauck et
al. [1998]), the establishment of a well-managed network of marine reserves has been
receiving considerable attention. Despite a number of benefits from the creation of marine
reserves, they do not provide any incentives for fishermen to join in the effort to protect
biodiversity. Compensation for the financial loss to fishermen is needed. Lack of
compensation may lead to opposition to marine reserves from the local fishermen, and this
opposition is also one of the major barriers to reserve establishment (Gell and Roberts
[2003]). If the costs incurred from the presence of marine reserves outweigh the benefits
accruing to the fishermen, they may have few incentives to support conservation. As long as
fishermen believe them to be their detriment, experience suggests that marine reserves will be
economically unviable and unsustainable. Therefore, providing incentives and appropriate
management arrangements are necessary to enhance the sustainability of fisheries and insure
the needed support from the fishermen.
Due to limited fishing ground access, establishing marine reserves may initially be
costly to local fishermen. Fishermen may need compensation for the loss of a significant
proportion of their former fishing grounds at least until other livelihood options have been
secured. Compensation is also necessary when options for fishing in other areas are limited or
when the fishermen have limited opportunities to develop an alternative income (Gell and
Roberts [2003]). From the managers’ point of view, often providing compensation payment
to fishermen is not aimed to make them leave the sector. To the contrary, it helps them adjust
to a new system of closure or enable them to continue fishing elsewhere (O’Brien et al.
[2002]).
The notion of compensation is more commonly dealt with in agriculture and
environmental services. The main reason why compensation by a transfer payment has been
suggested by conservation practitioners is that it can benefit low-income agents by improving
cash flow and diversifying sources of household income. Furthermore, the agents under the
payment approach may determine the best way to meet their own goals rather than being
subsidized to conduct predetermined activities, as is the case under the indirect approach
(Ferraro and Kiss [2002]). Indirect approach included programs that provide alternative
sources of products, incomes or social benefits to encourage communities to cooperate, or
encourage local communities to conserve biodiversity.
The compensation plan has just recently been considered by fishery managers. Several
compensation payment schemes for fishermen affected by marine reserves have been
conducted in the United States of America and Australia. In the United States, upon
establishment of the marine national monument in 2006, a financial compensation program to
bottomfish permit holders has been implemented (Wood and Nelson [2009]). In Australia, the
State of Victoria conducted a compensation scheme to cover increased fishing costs and
reduced catch yields. However, the managers in Victoria readily recognize that even without
the limits, compensation claims should be minimal (O’Brien et al. [2002]).
Technically, compensation not only aims to rectify fishermen’s economic loss.
Managers may also use it as an incentive to induce a particular response or behavior from
fishermen in keeping with their biodiversity conservation objectives. Incentive measures have
long been used by governments to manipulate the way that macro and sectoral economies
work. It is, however, only recently that they have been applied to biodiversity conservation
(Emerton [2000]). The basic aim of setting in place economic incentives for biodiversity
conservation is to influence people’s behavior by making it more desirable for them to
conserve rather than to degrade or deplete biodiversity in the course of their economic
activities.
One of the main issues that managers face when designing the payment scheme as an
economic incentive is asymmetric information. Asymmetric information occurs when
fishermen possess better information about fishing activities than managers. To solve this
problem, often the principal-agent model is applied. The central issue investigated through
principal-agent theory is how to get the agent to act in the principal’s best interests when the
agent both has an informational advantage and has different interests. For this purpose,
managers often propose a contract for the payment scheme. There are two important
information asymmetries related to contracts: hidden information and hidden action.
Hidden information (adverse selection) occurs when the principal and agent negotiate
the contract. The agent has superior knowledge about the cost or the production technology
used. Taking advantage of his superior position, the agent can inflate costs in order to
maximize profit. This case is particularly relevant in capacity adjustment situations and in
effort regulation, where the aim is to distribute capacity reduction or effort in an efficient
manner (Frost et al. [2001]).
Hidden action (moral hazard) arises after a contract has been negotiated. The agent’s
behavior is not observable by the principal; the principal does not know how the agent will
act after the contract has been signed. Illegal landings, discards, and poaching are viewed as
moral hazard problems in fisheries because often the individual catches cannot be observed
by a manager.
There are only a few papers which apply the principal-agent model to fisheries.
However, this method is well known from studies in environmental and agricultural
economics, which have a strong resemblance to fisheries economics (see Spulber [1988]; Wu
and Babcock [1995]; Smith [1995]; Bourgeon et al. [1995]; Jebjerb and Lando [1997]).
Jensen and Vestergaard [2002a] used the principal-agent model to examine the case of two
types of fishermen (low cost and high cost) and investigate the optimal efforts for them. The
manager did not know if the agent belonged to a low-cost or high-cost group, so an adverse
selection problem arose. Jensen and Vestergaard [2002a] assumed that the manager paid
fishermen a subsidy and collected the revenue from their fishing activity. Fishermen bore the
cost of fishing. A resource restriction expressing that natural growth rate must be equal to
aggregate catches was introduced as a new feature of the principal-agent problem.
As expected, they showed that the high-cost agent’s effort was smaller under an
asymmetric information situation than under a full information situation. However, the lowcost agent had to be allowed greater effort under the asymmetric information situation than
under the full-information situation. This result contradicted standard principal-agent theory.
In standard principal-agent theory, the low-cost agent is allowed the same level of effort in
both the symmetric and asymmetric cases. The reason for this is that steady stock is assumed
as the manager’s objective. The low-cost agent must apply greater effort under the
asymmetric information to satisfy the resource restriction. However, the aggregate effort is
smaller under the asymmetric information situation, and as a result, steady stock was found
greater in the asymmetric information situation than in the full information situation.
Their paper can be seen as a solid contribution to fisheries management. It
investigated the principal-agent analysis as a useful tool in fisheries due to its abilities to take
into account a huge information requirement and to handle the asymmetric information (one
of the main characteristics of the relationship between managers and fishermen).
In another work, Jensen and Vestergaard [2002b] applied the principal-agent model to
study an EU tax on fishing efforts as an alternative to the system of Total Allowable Catches
(TACs). Again, it was assumed that there are two types of fishermen, low-cost and high-cost
type. The EU lacks information about the costs of individual fishermen, so low-cost
fisherman may pretend to be high-cost fisherman. They concluded that the tax could secure
the correct revelation of the type of fishermen and help to correct market failure.
Furthermore, they showed that there were some advantages of tax compared to TACs. TACs
are normally based on a maximum sustainable yield concept thus TACs do not incorporate
the differences in information between EU, Member States, and fishermen. TACs also neither
take into account the differences in efficiency between fishermen nor lead to economic
efficiency. However, EU tax may solve these problems as in their principal-agent analysis,
the EU tax consists of the marginal value of fish stock, an information rent and a value of
marginal tax revenue.
The objective of this paper is to apply the principal-agent model to define the optimal
reserve area, fishing effort, and transfer payment in the context of symmetric and asymmetric
information between managers and fishermen. The principal-agent model is not widely
applicable to fisheries because, although the fish resource is common property, governments
do not pay the fishermen to exploit the fish stock in the same way as the owner of a property
would. However, by using subsidies or payments as economic incentive to induce a particular
response or behavior from the fishermen for restrictions on fishing activity, or in our case,
with the creation of a marine reserve, the manager establishes a conservation program by
which he could provide transfer payments to the fishermen to compensate their economic loss.
The fishermen in turn agree to participate in the program and adjust their activities to
facilitate biodiversity conservation. The principal-agent model is a reasonable method to
apply. The reason for this is that the compensation payment is often subject to asymmetric
information between fishermen and the manager, and the principal-agent model can capture it.
Consequently, it may help to improve the effectiveness of conservation program and make it
less expensive to implement.
The manager’s purpose through the conservation program is to raise fishermen’s
income (redistributive objective), limit the social costs due to distortionary taxation, and
obtain the beneficial effects of the marine reserve. To investigate and understand these issues,
a question of the management regime should be addressed. We assume that regardless of
whether there is a marine reserve or not and whether the manager compensates the fishermen
or not, the fishery is open access.
The paper is organized as follows. Section 2 describes the basic model and its basic
characteristics. Section 3 presents our main analysis of the regulation of the incentive
payment program under both full information and asymmetric information. Finally, section 4
discusses the findings and concludes the paper.
2. The basic model without a marine reserve. We start with the traditional model for
fisheries in order to provide input to the model by adding the presence of marine reserve. Let
X be the fish population and H be the aggregate harvest. The model for the exploitation of
biological resources:
X  G X   H ,
(1)
where G X  is the function representing the natural growth of the population. For simplicity,
we assume a quadratic relation between the fish population and its growth. We use a
quadratic growth model since it is a commonly used growth model in the fisheries. Following
this growth model, the population will grow slower as it approaches the maximum capacity
and grow faster when it is relatively small. Also, from the biological resource management
point of view, the quadratic growth model can tell us for each population size, the maximize
amount that can be harvested without depleting the underlying stock of the resource under
consideration. Therefore, when aggregate harvest exceeds the natural growth, (1) will be
negative, implying that a collapse of the fish population will occur. In contrast, when
aggregate harvest is less than the natural growth, (1) will be positive, and the fish population
will increase. The population only remains constant when aggregate harvest rate equals
natural growth rate, G X   H .
If we assume a constant price p per unit of harvesting and assume an aggregate cost
function of fishing CE  , then the profit function from the fishery is:
(2)
  TR  TC  pH  CE  ,
where E is aggregate fishing effort. The aggregate cost function is assumed to be increasing
and convex in E so
C
 2C
 0 and 2  0 .
E
E
Theoretically, in an open access fishery effort tends to reach a bionomic equilibrium
at which the average revenue equals the marginal cost ARE   MCE  (Flaaten [2008]) and
we believe that it is approximately the way fisheries behave in reality. Therefore, a level of
effort either greater or smaller than open access effort cannot be maintained indefinitely. At a
level of effort greater than open access effort, some fishermen may lose money and withdraw
from the fishery. At a level of effort smaller than open access effort, some fishermen may
earn a profit, additional fishermen will be attracted to participate in the fishery, and the effort
tends to increase.
In contrast, maximizing the resource rent, the profit in excess of that needed for
payment of capital and labor, requires that equilibrium effort is at a level where marginal
revenue equals marginal cost, MRE   MC E  . The equilibrium effort under-maximizing
the resource rent regime is smaller than that under the open access regime, which helps to
maintain a larger stock than under the open access.
Here, we assume that the fishing industry consists of n fishermen. The rate of
harvesting of fisherman i is assumed to be proportional to both the level of the biomass and
the level of his fishing effort hi  qei X where
hi
 0 . q is the catchability coefficient, and
ei
n
n
i 1
i 1
ei is the fishing effort of the fisherman i . Note that H   hi and E   ei .
With respect to the individual fisherman, under open access condition the fisherman i
will behave so as to maximize his own profit with respect to his effort and disregard the user
cost of fish stock. The profit function for each individual fisherman is:
 i  phi ei , X   ci ei  ,
(3)
where cei  is the effort cost for fisherman i with positive, non-decreasing marginal costs:
ci
 2ci
 0,
 0.
ei
ei2
The first order condition for profit maximization can be expressed as follows:
(4)
p
hi ci

.
ei ei
Condition (4) states that to maximize profit, each fisherman’s marginal productivity of
effort should equal his marginal cost of effort. Note that (4) is the fisherman’s behavior under
open access situation while condition ARE   MCE  , discussed previously is open access
equilibrium at the fishery level.
3. The model with a marine reserve. Consider a fishery habitat with a marine reserve and
fishery area. A fraction m , m 0,1, of the whole area is set aside as a marine reserve, and
consequently 1  m is the size of the outer area. When m  0 , there is no marine reserve and
m  1 implies that the whole area is a reserve.
Since the marine reserve will restrict the area for harvesting, following Arnason
[2001], we assume that the marine reserve will negatively impact on the harvest. The harvest
function can be written as follows:
H  H E ,m, X  ,
where
H
 0.
m
It should be noted that an increase in the size of the reserve is followed by an equal
reduction in the outer area. Because of this, the diffusion rates between the sub-areas are
specified as dependent on the size of the respective areas. If
H
 0 , the fish density inside
m
the reserve and outside the reserve is the same. Consequently, there is no diffusion between
the sub-areas. If
H
 0 , the change of the reserve’s size affects the harvest implying that
m
the fish density inside and outside the reserve is different. Thus, there is imperfect diffusion
between inside and outside the reserve.
We assume that the marine reserve also influences the cost function, contrary to
Arnason [2001]. This is because the marine reserve limits the area for fishing. The fishermen
may have to travel further for fishing or their choice of fishing ground may be limited.
Consequently, their costs may increase. The aggregated cost function affected by a marine
reserve can be expressed by the function CE ,m and we assume that
C
 0.
m
In this case, the expected rent from the fishery with respect to effort, reserve size, and
resource population will be:
(5)
  pH E ,m, X   CE ,m .
The creation of a reserve often helps to obtain greater fish stocks. As a result, the
growth may be affected by the reserve. We assume that the growth function G X ,m is a
function of population stock and the size of the reserve, which positively affects the
population growth, so G / m is positive. The change of population per unit of time can be
represented as:
(6)
X  G X ,m  H E ,m, X  .
3.1 Without the transfer payment. As noted previously, the main aim of transfer payments is
to influence the fishermen’s behavior to favor biodiversity conservation. We will first
investigate the fishermen’s behavior without the transfer payment, and then see how their
behavior changes when the manager compensates them for their loss due to the reserve.
We assume that the fisherman’s cost function is given by cij  j , m ,eij  which is
expanded from the fisherman’s cost function in section 2 but adding effects of cost parameter
and marine reserve.  j is a cost parameter reflecting various aspects of the fisherman’s
efficiency and eij is the effort level exerted by fisherman i with cost parameter j . As
previously, we suppose that the cost function is increasing in effort, so
and increasing in reserve size,
cij
m
cij
eij
 0 and
 2cij
eij2
 0,
 0 . We assume that the fisherman has complete
information about his cost function. However, the manager is unable to observe it.
The harvest function for fisherman i with the creation of marine reserve is assumed
as a function of fishing effort, reserve size and population stock, hij eij ,m , X  . It is assumed
hij
eij
0,
hij
X
 0 , and
hij
m
 0 . The economic model depends on the catch and the cost
related to fishing, so the objective profit function of the individual fisherman i is:
 ij  phij eij ,m , X   cij  j ,m ,eij  .
(7)
As with the case without the reserve, we assume that without the transfer payment the
fisherman disregards his effect on the resource stock. He wants to decide his effort according
to the following first order condition:
p
(8)
hij
eij

cij
eij
.
The first order condition provides the best response function for harvesting based on
the level of effort. Maximum profit for fisherman i is obtained by equalizing his marginal
productivity of the effort with his marginal cost of effort, since  j is a cost parameter and m
is determined by the manager. When p
hij
eij

cij
eij
the fisherman tends to increase his effort
and vice versa.
Without the transfer payment, each fisherman defines optimal effort for his harvesting
activity on the basis of equation (8). Since the fisherman disregards the resource restriction,
his effort will be larger than in the optimal case with the resource restriction taken into
account. Thus, by moving from the effort level that the fisherman determines from the profit
maximization to the optimal effort level, the welfare of society, i.e. the value of the goods and
services from marine reserves and fishing activity procured total costs of providing them,
increases.
3.2 With the transfer payment. With the transfer payment, the manager’s objective is to
maximize social welfare with respect to the reserve area, the transfer payment, and resource
restriction. The model is now comprised of the principal (the manager), who provides the
compensation payment, and the agents (fishermen), who receive payment and are assumed to
support the principal’s conservation program. Although the manager cannot observe the
characteristic of the fishermen (the cost parameter  j ), we suppose that he knows its density,
which is given by f  j   0 . For simplicity, we assume that there are only two types of
fishermen, 1 and 2 with  2  1 .
As discussed previously, asymmetric information is one of the main challenges faced
by the manager when designing a transfer payment scheme. Fishermen can attain higher
payments by inflating costs. In this case, they use their private information to extract
information rent, the payment above the minimum payment necessary to induce the
fishermen to support the conservation objectives, from the manager. Although the manager
has incomplete information about the cost of fishing, he wants to increase his expected return
by deciding upon a level of transfer payment with incentives that maximizes social welfare –
the objective of the manager – and induces the fisherman to report his true cost information.
Both the manager and fisherman are assumed to be risk-neutral. Risk neutrality means
that they are indifferent in the choice between a certain outcome and a gamble that give the
same expected payoff as the certain outcome. If the manager and fisherman are risk-neutral,
the manager is assumed to maximize expected welfare while the fisherman maximizes his
expected profit or income.1
In a standard principal-agent theory, an agent has only one source of income: payment
from the principal. Agents in this study receive income from the manager’s payment and their
production activity profits. The question thus naturally arises whether there has been an
increase in the number of fishermen participating in the fishery due to the transfer program.
The manager understands that the transfer payment will attract more fishermen due to the
open access regime. We assume that the manager avoids this state by having an entrance
license system, by which the number of fishermen will be kept constant before and after the
creation of the marine reserve, with or without a transfer payment program.
3.2.1 Full information model. When the fishermen’s cost of fishing is known by the manager,
he has full information. Given full information, a first best solution can be obtained by a least
cost set of payment schemes that get the fishermen to support the conservation program. The
creation of the reserve can provide a number of benefits for society. These benefits include
biodiversity conservation, ecosystem services, i.e, protection of reefs provides protection
against coastal erosion and increase assimilative capacity for pollutants; opportunities for
tourism and recreation, and education and research (Becker and Choresh [2006]).
It is assumed that the social benefits from the marine reserve depend on reserve size.
Unlike the voluntary incentive contract for biodiversity conservation in agriculture where
managers offer a volunteer contract for each type of agent and the agent chooses area and size
1 If the manager and the fisherman are risk averse, the manager’ program becomes the maximization of the expected utility of social welfare
and the fisherman’s program is the maximization of expected utility of profit or income.
of land for protection himself, the fisheries manager decides to set a fraction of the total area
as the reserve, and compensates the fishermen for the decrease in catch. The difference is
easy to understand. Agricultural land is almost all held in individual private ownership so the
farmer actively determine his activity. In fisheries, private ownership of the resource or
fishing areas is not possible so the manager will determine the area for reserve and the area
for harvest. With a reserve size equal to m , we assume that Bm is a function of the social
benefits from the reserve. We further assume that Bm is increasing and concave with the
B
2B
 0,
size of the reserve,
 0 , B0  0 .
m
m2
The manager provides the fisherman with a transfer payment Tij eij  and this payment
is an expense on the society’s budget. Because informational asymmetries are also a reality,
the manager may not be able to regulate or allocate fishing activities. For example, a manager
wants to control catch yields through effort management in order to maximize economic
welfare. He can observe fishing effort but he cannot observe catch per day for each vessel.
Consequently, he cannot observe the link between effort and harvest. Regulations, therefore,
must be made contingent on the observable variable, such as number of vessels, days at sea,
or size of vessel to help the manager get correct information (Frost et al. [2001]). In this
setting, the transfer payment in this paper is assumed to be paid on the basis of the
individual’s effort.
The expected income of the fisherman now includes his profit from fishing and the
payment from the manager:
(9)
I ij  phij eij ,m , X   cij  j ,m ,eij   Tij eij .
For individual fisherman, he will have an incentive to operate to maximize his
expected income. Since his expected income now consists of the rent from fishing activity
and the transfer payment from the manager, the first order income maximization condition of
fisherman i then becomes:
(10)
p
hij
eij

cij
eij
 Tij' eij   0 ,
We can arrange (10) as follow:
Tij' eij    p
(11)
hij
eij

cij
eij
.
The first order condition for maximizing the fisherman’s expected income indicates
that the marginal transfer of the fisherman’s effort is equal to negative marginal productivity
of effort plus the marginal cost of effort, or equal to negative marginal rent from fishing.
The manager represents society, therefore instead of maximizing fishermen’s
expected income, he wants to maximize social welfare with the payment scheme. Social
welfare is defined by social benefits from biodiversity conservation of marine reserve
deducing total cost of public funding plus total expected income of the fishermen. Social
welfare can be written as follows:
W  Bm   1   Tij eij    I ij ,
n
(12)
2
i 1 j 1
n
2
i 1 j 1
 is distortion tax or the cost of collecting T,   0 , and n is the number of fishermen.
With full information, the manager can observe the costs of the fisherman. He chooses
the transfer payment and reserve size that maximize social welfare with respect to the
participation constraint and resource restriction. Participation constraint ensures that the
fishermen will participate in the conservation program, since the income from fishing and the
transfer payment is at least as high as the income level that the fisherman obtains outside the
program. Thus, the fisherman will be no worse off than when there are neither reserves nor
transfer payments. This constraint is also called an individual rationality constraint, because,
if violated, no rational fisherman would participate. Following Jensen and Vestergaard
[2002a], a resource restriction is introduced. This is different from the standard constraints in
the principal-agent problem. For fisheries, this constraint should be included in the maximum
problem, as it can ensure that the fishermen’s catches are not exceeding the natural growth of
the fish stock. The reason why we set up the resource restriction by equalize natural growth
rate to the catch yields is that we focus on condition for the steady state, that is on what
happens in a fishery in long-run equilibrium where the stock is stable over time.
Substitute (9) into (12) and rearrange the social welfare, the first best solution is
determined by the following program:


Max W  Bm   phij eij ,m, X   cij  j ,m,eij   Tij eij 
n
(13)
2
i 1 j 1
subject to:
(14)
phij eij ,m , X   cij  j ,m ,eij   Tij eij   u0 ,
(15)
G X ,m   hij eij ,m, X   0 ,
n
2
i 1 j 1
(16)
0  m  1.
u0 is the reservation utility of a fisherman if he conducts alternative activities instead
of participating in conservation program. Reservation utility is often assumed to depend on
the type of the agent. However, for simplicity in this paper we assume that u0 is the utility of
the best alternative of the fishermen including low-cost and high-cost type to the conservation
program. The manager then maximizes the social welfare subject to 3 constraints,
participation constraint (14), resource restriction (15) and constraint guaranteeing that the
extent of the reserve will range from 0 to 1 (16).
The manager’s most important tasks are how to determine the transfer payment that
induces possible actions by the fisherman and assign the reserve size m to maximize social
welfare. Since the manager wants the payment to be as small as possible to avoid distortions
in the economic signals to the fishermen, the participation constraint (14) will be binding. If
the constraint (14) didn’t bind, the manager would be paying too much to the fisherman. The
manager only needs to provide a payment to the fisherman in such a way that the fisherman
would still accept the contract and the manager would get the greatest utility, which is known
as the Pareto Optimum. From this perspective, the optimal transfer to fisherman i , type j is:
(17)
Tij eij   u0   phij eij ,m , X   cij  j ,m ,eij 
From (17) it is easy to see that the transfer depends on the stock density, effort of the
fisherman, the reserve size, and the cost of fishing. The size of reserve m is an exogenous
parameter decided by the manager. The greater the reserve size, the higher the transfer
payment the fisherman receives. The transfer equals the difference between the reservation
utility and the profit from fishing.
Substituting equation (17) into (13), we can obtain a new social welfare function:

W  Bm   1    phij eij ,m, X   cij  j ,m,eij   u0
n
(18)
2

i 1 j 1
subject to (15) and (16).
This problem can be solved using Kuhn-Tucker theory. To characterize the optimal
mechanism for the conservation program, let us state two propositions (see Appendix 1 for
proof).
Proposition 1: The optimal reserve size under perfect information is defined by
hij cij  B / m

  G n 2 hij 


.

p



 


m m 
1 
1    m i 1 j 1 m 
i 1 j 1 
n
(19)
2
 is the Lagrange multiplier for the resource restriction. The optimal reserve size is
defined by equalizing the aggregate marginal loss for the fisherman caused by the marine
reserve to the marginal benefits of the reserve (including a marginal increase for society
benefits
B
, and a marginal increase for the stock size) adjusted by the marginal cost of
m
public funding 1    . In other words, we can say that the marginal rate of substitution
between the total benefits for society and the total cost must be equal to the fisherman’s
marginal loss per unit of reserve. As  increases, the marginal loss of the fisherman due to
the reserve decreases. The size of the reserve is smaller and the area for fishing larger, so less
conservation is achieved.
Proposition 2: Under full information, the optimal fishing effort that the manager wants the
fishermen to exert in order to satisfy his objective to maximize the social welfare is always
smaller than the fishermen’s effort without the transfer payment:
(20)
p
hij
eij

cij
eij

 hij
.
1   eij
(20) expresses the optimal level for fishermen that will help the manager obtain social
welfare maximization. Without the payment program, the fisherman i produces at a point
p
hij
eij

cij
eij
and does not take into account the externality associated with the fish
population. His effort, because of this, will be too great. The proposition 2 tells us that when
the manager compensates the fisherman by a transfer payment, the manager wants the
fisherman to exert the effort level where his marginal revenue, p
private cost of fishing,
account,
cij
eij
hij
eij
, equals his marginal
, plus the marginal cost of taking the manager’s objective into
 hij
 hij
. The presence of the factor
requires a decrease in the
1   eij
1   eij
fisherman’s effort, since it makes the marginal cost of fishing increase compared to the case
without a transfer payment.
The manager wants to use the transfer payment to adjust the individual fisherman’s
effort under an open access situation through adhering it to his objective of social welfare
maximization. By substituting (20), the effort level of the fishermen that maximizes social
welfare, into (11), the effort level that maximizes the fishermen’s income, we get lemma 1
Lemma 1: An optimal transfer that satisfies both the manager’s objective to maximize social
welfare and the individual fisherman’s objective to maximize his income by inducing the
fisherman to exert the optimal effort level in equation (20) is
Tij' eij   
(21)
 hij
 0.
1   eij
By setting marginal transfer payment at a satisfying level (21), the manager may
induce the open access fishermen to exert the optimal fishing effort that is lower than his
fishing effort under open access and without the transfer payment. The payment scheme at
least helps the manager to protect the fish population by reducing the fisherman’s effort, and
this contributes to the biodiversity conservation objectives of the manager.
The marginal payment is negative, so the manager should reduce transfers as effort
increases. Otherwise, the fishermen may increase their effort to obtain a larger transfer. The
fishermen face the trade-off between the increase in fishing effort and the decrease in transfer
payment. The marginal payment also includes  , a measure of the value of a marginal
increase in the fish stock, so it can capture the part of externality associated with fish stock.
An example
We now illustrate the full information model with the following example, and try to
investigate more characteristics of the program. With the specific functional form, we derive
optimal effort and the condition for the population stock to obtain this level of effort.
We assume the social benefit function and functions for natural population growth,
total harvest, and total cost as follows:
(22)
Bm  m  m2 ,
(23)
Gm, X    1  mX  X 2 ,
(24)
hij eij ,m , X   1  m eij X ,
(25)
1
cij  j ,m ,eij   1  m  j eij  eij2 ,
2
where  ,  and   0 are scaling parameters.
This example meets the assumptions: Bm  0 , Gm  0 , hm  0 , cm  0 .
As before, in the case without a transfer payment, the individual fisherman’s decision
is to adjust his effort until the marginal revenue equals marginal cost. Thus the fisherman’s
effort is:
(26)
eij  p1  m X  1  m  j .
With a transfer payment, from the first order condition (20), the optimal effort of the
fisherman under full information case is given by:
 

eij*   p 
1  m X  1  m  j .
1  

(27)
Comparing (26) and (27), it suggests that the existence of a transfer payment, offered
by the manager regardless of the fisherman’s type, implies the fisherman’s effort reduction.
As mentioned previously, we assume that there are only two types of fishermen. From
(27), the corresponding effort for each type can be written as:
(28)
 

ei*1   p 
1  m X  1  m 1 ,
1  

(29)
 

ei*2   p 
1  m X  1  m  2 .
1  

The only difference in optimal effort of two types of fishermen is their private costs.
The cost of the type 2 fisherman is higher than that of the type 1 fisherman, 2  1 , so this
leads to ei1  ei 2 . From this result, the effort analysis can be extended to n types of fishermen.
Since the difference in effort of different types of fishermen is due to the cost parameter, it
will follow the pattern that the fisherman with a higher cost parameter will exert the lower
optimal fishing effort and vice versa.
For the size of the reserve, it can be derived from the first order condition (19):
(30)
m
1
2
n
2
n
2














X


e
X

1


p

e
X


e

.


ij
ij
j
ij


i

1
j

1
i

1
j

1




The size of the reserve under full information is chosen based on the marginal change
of fish stock and the marginal economic loss of the fishermen due to its change.
3.2.2 Adverse selection model. Let us now turn to the second best situation where information
is asymmetric. Under asymmetric information, we suppose that the manager has some
information, but he does not know either the cost parameters of the fisherman or if the
fisherman belongs to the low-cost type or high-cost type group. The management solution
under full information thus cannot apply in the system with asymmetric information if the
aim is to obtain optimal social welfare.
When the manager has imperfect information about the fishermen’s costs, a
conservation program may be expressed as a relation between the fishing effort and the
transfer paid to fishermen. Since the conservation program will provide a transfer payment,
the low-cost type may mimic the high-cost type because of the benefit of its action. In order
to minimize the cost for this program, the manager must now offer a payment that satisfies
the fishermen’s reservation utility, and an incentive to induce the fishermen to reveal their
economic type. So, in addition to the participation constraints, the incentive compatibility
constraints are formulated in order to make the fishermen truthfully reveal their information.
These constraints are designed so that the income for the agents from reporting their true cost
types is higher than the income from reporting a false type. The incentive compatibility
constraint is also called self-selection constraints. From such constraints, the manager will
provide payment schemes in which one fisherman’s payment depends on both his own type
and the revealed type of other fishermen.
The single-crossing property is assumed to be fulfilled so that the agent with a higher
cost parameter also has higher marginal costs ( ce 2 ,e,m  ce 1 ,e,m for all e ). The
fishermen will participate in the conservation program instead of keeping fishing and not
taking into account their fishing effects on the fish stock if it is profitable for them, i.e. the
transfer payment received is greater than the losses due to the effects from the reserve.
Despite the fact that the manager is unsure about the type of the fisherman, he attaches
the probability of a low-cost type fisherman as s and that of a high-cost type fisherman as
1  s . With the transfer payment, the manager wants to maximize social welfare:
n
(31) W  Bm    s phi1 ei1 , m , X   ci1 1 , m , ei1   Ti1 ei1   1  s  phi 2 ei 2 , m , X   ci 2  2 , m , ei 2   Ti 2 ei 2 
i 1
subject to:
(32)
phi1 ei1 ,m, X   ci1 1 ,m,ei1   Ti1 ei1   u0 ,
(33)
phi 2 ei 2 ,m, X   ci 2  2 ,m,ei 2   Ti 2 ei 2   u0 ,
(34) phi1 ei1 ,m, X   ci1 1 ,m,ei1   Ti1 ei1   phi 2 ei 2 ,m, X   ci1 1 ,m,ei 2   Ti 2 ei 2  ,
(35) phi 2 ei 2 ,m, X   ci 2  2 ,m,ei 2   Ti 2 ei 2   phi1 ei1 ,m, X   ci 2  2 ,m,ei1   Ti1 ei1  ,
n
(36)
G  X ,m    shi1 ei1 ,m , X   1  s hi 2 ei 2 ,m , X   0 ,
i 1
(37)
0  m  1.
Constraints (32) and (33) are participation constraints. Constraints (34) and (35) are
incentive compatibility constraints to ensure that each agent will prefer the contract that is
designed for him. Constraint (34) ensures that the low-cost fisherman’s income from
reporting his true type is higher than his income from reporting a false type, and similarly for
the high-cost fisherman in constraint (35).
Adding (34) and (35), we immediately have:
(38)
ci 2 2 ,m,ei1   ci 2 2 ,m,ei 2   ci1 1 ,m,ei1   ci1 1 ,m,ei 2  .
(38) is known as the single crossing property as it states that the agent with a higher
total cost also has a higher marginal cost. From Varian [1992], page 457 we know that the
single crossing property implies that ei1  ei 2 . The single crossing property is an
implementation ability condition that is necessary for the implementation ability of the
conservation program. The single crossing property enables us to considerably reduce the set
of incentive constraints and allows for separate the contracts or the types of the fishermen.
In the standard adverse selection model with two types of agent, the high-cost agent
has a binding participation constraint and the low-cost agent has a binding incentive
compatibility constraint. It also follows that rule in our case for the optimal payment. The
proof is in Appendix 2.
(39)
(40)
Ti1 ei1   u0   phi1 ei1 ,m, X   ci1 1 ,m,ei1   ci 2 2 ,m,ei 2   ci1 1 ,m,ei 2  ,
Ti 2 ei 2   u0   phi 2 ei 2 ,m, X   ci 2  2 ,m,ei 2  .
The second best solution is necessarily incentive compatible, so the optimal contract
is different from the first best one. The payment scheme is now separating, which means that
fishermen with different cost parameters will be allocated different payment schemes. The
participation constraint of the high-cost fisherman binds in both the symmetric and
asymmetric case. He will always receive the payment equal to his reservation utility minus
his profit. The low-cost type, however, will receive the payment that includes the reservation
utility minus the profit plus the information rent equal to ci 2 2 ,m,ei 2   ci1 1 ,m,ei 2  . The
information rent keeps him from imitating the high-cost agent and, as mentioned above, it is
the information cost for the manager.
By substituting (39) and (40) into (31), social welfare can be defined by the following
program:
(41)
n
W  Bm    s1    phi1 ei1 , m , X   ci1 1 , m , ei1    ci 2  2 , m , ei 2   ci1 1 , m , ei 2   u0 
i 1
n
  1  s 1    phi 2 ei 2 , m , X   ci 2  2 , m , ei 2   u0 
i 1
subject to (36) and (37).
We set up the Lagrange problem and use the Kuhn-Tucker condition to solve for the
optimal solution. The following propositions can be derived from the optimal program (see
Appendix 3):
Proposition 3: The optimal reserve size under asymmetric information is smaller than that
under full information due to the presence of an incentive cost
 
n
hi1
 s  p m
i 1
(42)


ci1 
h
c 
s  ci 2 ci1 


  1  s   p i 2  i 2  


m 

m

m
1
   m
m 


B / m


1 
1 
 G  n hi1
h  
  s
1  s  i 2  


m

m
m  
 i 1

.
(42) is the optimal reserve size under asymmetric information. Under full information
situation, the reserve area is chosen without any uncertainty. The asymmetric information
situation reveals that the probability of each agent s and 1  s will affect the reserve size.
Although the manager decides the size of the area for the marine reserve in both the full and
asymmetric information models, there is still a difference between the two. An optimal
program under asymmetric information requires that the optimal reserve size is defined by
equalizing the expected marginal loss of the marine reserve plus the incentive cost to the
marginal social benefit and expected marginal increase of the population stock adjusted by
the marginal cost for social funding. The reserve size in the second best solution is different
from that of first best one. The social benefit of the reserve due to this is different between
the two information schemes.
Proposition 4: Under asymmetric information, the optimal effort for both types of fishermen
with the conservation program that the manager expects them to exert to maximize social
welfare is always smaller than the effort of fishermen under open access without the
conservation program.
p
(43)
(44)
p
hi1 ci1
 hi1


,
ei1 ei1 1   ei1
 ci 2 ci1 
hi 2 ci 2
 hi 2






.
ei 2 ei 2 1   ei 2 1   1     ei 2 ei 2 
(43) and (44) are the optimal effort levels that the manager wants the low-cost and
high-cost fisherman respectively to exert to obtain social welfare maximization. The optimal
efforts for two types of the fishermen are defined by equalizing their marginal revenue to
their marginal cost. These effort levels are smaller than those under open access without the
conservation program. Distortions are due to the presence of the factor
cost fisherman and the factor
 hi1
for the low1   ei1
 ci 2 ci1 
 hi 2
s



 for the high-cost
1   ei 2 1  s 1     ei 2 ei 2 
fisherman. These terms represent the marginal cost of the fishermen when they take into
account the manager’s objectives. This cost is the additional cost to the fisherman’s private
cost of fishing and makes the marginal cost increase compare to the case without the transfer
payment.
Comparing expression (43) and (44) with expression (20) will help us investigate
more the characteristics of the first best and second best fishing effort.
Lemma 2: With asymmetric information about the cost parameters, the effort for the highcost fisherman is smaller than that with full information. However, the effort of the low-cost
fisherman must be greater than that under full information.
Proof. See Jensen and Vestergaard [2002a].
The effort of the high-cost fisherman under asymmetric information decreases
compared with that under full information due to the presence of incentive costs. The effort
of the low-cost fisherman looks the same as in the full information situation. However, it is
not the case. We assume that the manager always wants to control the fisheries in a steadystate equilibrium stock. The decrease in effort of high-cost fisherman must allow a greater
effort of low-cost fisherman to fulfill the resource restriction. With the steady resource
restriction, Jensen and Vestergaard [2002a] showed that since the effort for the high-cost
fisherman is smaller compared to the first best solution, the effort for the low-cost fisherman
must be greater than that under the first best case to satisfy the resource balance constraint.
They further stated that the reasons for this are firstly, the Lagrange multiplier for resource
restriction is the interaction between the first order condition for stock size and the first order
condition for effort, so it may be different between the model of symmetric and that of
asymmetric information. Secondly, the optimal stock size could also be different between the
models.
In our paper, the Lagrange multiplier for resource restriction shows the interaction
between the first order condition of effort and the first order condition for reserve size, so 
may be different between the two models. As found by Jensen and Vestergaard [2002a], the
effort of the high-cost fisherman under asymmetric information is smaller, but the effort of
the low-cost fisherman must be greater than that under full information.
The presence of the low-cost fisherman requires an incentive for him to reveal his true
type. Marginal incentive costs
 ci 2 ci1 
s
are added in the first order

1  s 1     ei 2 ei 2 
condition for the high-cost fisherman as a measure to correct revelation of the low-cost one.
Here, the payment scheme proposed decreases the effort of the high-cost fisherman to reduce
the information rent paid to the low-cost fisherman. We know that compensating the low-cost
type with a higher payment than that paid under symmetric information is one way to
improve the program. However, it should be noted that only improving the compensation
program by changing the low-cost type without altering the high-cost type contract is not the
best solution for the principal. Information rent to the low-cost fisherman not only depends
on his private effort, but also on the effort of the high-cost fisherman. The greater the effort
of the high-cost fishermen, the larger is the rent for the low-cost type. Because of this, the
marginal payment with the second best solution will be different from the first best solution.
In the full information situation, the manager wants to use the transfer payment to
induce the fishermen to follow his objective. Substitute (43) and (44) into (11), we have
lemma 3 for optimal transfer payment.
Lemma 3: The optimal transfer payment for the two types of fishermen that satisfies
social objectives and the fishermen’s perspective:
Ti1' ei1   
(45)
Ti'2 ei 2   
(46)
 hi1
 0,
1   ei1
s
  ci 2 ci1 
 hi 2

 

0 .
1  s 1    ei 2 ei 2  1   ei 2
The marginal transfer payments in (45) and (46) may help the manager adjust the
fishermen’s fishing effort from open access level to optimal fishing effort level. In order to
induce the high-cost fisherman to reduce his effort, there will be a correction term under
asymmetric information
we know that
 ci 2 ci1 
s

 0 (due to the single crossing property,
1  s 1     ei 2 ei 2 
ci 2 ci1

 0 ). The marginal payment for the high-cost fisherman is seen to
ei 2 ei 2
be larger in absolute value compared to the full information case. This means that the highcost fisherman under asymmetric information case will receive less than full information case
when he increases his fishing effort to the same level.
From the solution in lemma 3, we see that the marginal transfer payment for both
types of fishermen is strictly decreasing in ei for any ei  0 . In his choice of optimal effort,
the fisherman will take into account the fact that the effort level influences their income,
including the revenue from fishing and the transfer from the manager. To increase his
received payment, the fisherman, whether of a high-cost or low-cost type, should choose a
low effort level.
An example
We can investigate the characteristics of the program under asymmetric information with this
example. All related function forms are the same as in the full information case.
With the transfer program, the effort of the fishermen:
(47)
(48)
 

ei*1   p 
1  m X  1  m 1 ,
1  

 
s

1  m 2  1  .
ei*2   p 
1  m X  1  m  2 
1  s 1   
1  

Comparing above expressions with the expression under the no transfer payment
framework (26), it shows that fishermen’s effort under asymmetric information is smaller
than that of the case without a transfer payment.
The area of the reserve is computed as follows:
(49)
n


 n

1 
    X   sei1 X  1  s ei 2 X   1     s pei1 X  1ei1   1  s  pei1 X   2 ei1 
2 
i 1


 i 1
 .

1   n
  s    2 ei 2  1ei 2 
2   i1

m
We can see that the reserve size is not now the same as with the full information case,
since it is affected by a correction term representing the effect of information rent,
1
2
  n

s   2ei 2  1ei 2   0 . The correction term provides an extra effect on

  i 1
determination of reserve size. It makes the reserve size under asymmetric information
different from that under full information case.
4. Discussion and Conclusions.
The international workshop on factors of unsustainability
and overexploitation in fisheries, Bangkok 2002 (FAO [2002]), concluded that the primary
reason for unsustainability is the lack of appropriate incentives. Five others factors were
identified: high demand for a limited resource; poverty and lack of alternative sources of
income; complexity and inadequate knowledge; lack of effective governance; and
interactions of the fishery sector with other sectors and the environment. Managing with the
use of economic incentives relative to marine reserves is an interesting question to study.
Economic incentives from a conservation program can be designed to reduce fishing effort,
improve biodiversity performance, while simultaneously providing a compensation payment
to fishermen.
The model is simple as it involves only two types of agent. Nevertheless, while
maintaining reasonably simple assumptions, the model points out important characteristics of
the optimal contracts and the differences between symmetric and asymmetric information.
The main feature of the model is related to the introduction of resource restriction in the
standard principal-agent theory. It ensures that the harvest will not exceed the natural
population growth. The introduction of a resource restriction within the biodiversity
conservation benefit function can be seen as a first step in making the link between the
fishermen's decision to fish and the ecological contribution of the reserve. The effort of
fishermen under the symmetric and asymmetric information frameworks is always smaller
than that without the transfer payment. This reflects the fact that as the manager induces the
fishermen to participate in the conservation program, the fishermen will take into account
their effect on fish stocks by decreasing their effort. More precisely, with resource restriction,
no fisherman will be allowed to catch more when the conservation program is implemented
than when it is not implemented.
There are several objectives associated with a conservation program. Two main
objectives commonly cited are: to supply biodiversity conservation at least cost which aims
to minimize budget for society, and to provide income redistribution for low-income agents
(Ferraro [2007]). From these objectives, it is clear that the idea of offering different payments
to different types of fishermen is important in the area of fishery management with the
presence of a marine reserve. The payment scheme may be expensive to implement if it is
affected by asymmetric information due to the fact that the fishermen may use their private
information to extract information rents from the manager. Reducing information rent
becomes an important task for fisheries managers attempting to maximize social welfare from
their limited budgets. The manager cares about information rent because when they pay it,
they obtain less biodiversity value than they could obtain if the opportunity cost of
conserving biodiversity is observable. Furthermore, the conservation programs are funded by
tax, and it leads to market distortions associated with taxation. Thus, society could benefit
more if the payments only compensate the fishermen’s opportunity costs of program
compliance. As a result, the high-cost fisherman receives the reservation value in both the full
information and the asymmetric information. The low-cost fisherman, however, receives his
reservation value plus additional information rent within the asymmetric information. The
difference in the payment is due to the fact that the manager knows that there is no incentive
for the high-cost fisherman to misrepresent his cost status.
A natural question to ask here is what the principal should do to decrease the
information rent? It has been shown above that the information rent depends on the reserve
area and the effort of the high-cost agent. The principal will adjust the incentive payment to
follow the effects of the information rent. The size of the reserve and the effort of the highcost agent positively impacts the information rent, so under asymmetric information these
parameters are adjusted by a factor that represents the effect of information rent. This is why
under asymmetric information the size of the reserve and the effort of the high-cost fisherman
are less than those under full information. The size of the reserve and the high-cost agent’s
effort are smaller because the manager trades off social welfare for information rents.
For fishermen, they will select the payment that maximizes the sum of the profit from
fishing and the transfer payment for conservation. The transfer must increase when the
fishermen’s activities become more restricted, otherwise there would be no incentive to
participate in the program. As the size of the reserve increases, or as the fishermen manage to
decrease their effort, the conservation payment for them must be increased.
The low-cost fisherman is more efficient than the high-cost one. In both the
symmetric and asymmetric information cases, the optimal effort of the low-cost fisherman is
always greater. Otherwise, he would report high cost parameters and the information rent
paid to avoid misreporting would be too high. From the social perspective, it is easy to
explain, since it will be optimal for social welfare if the efficient agent is allowed to produce
more than the inefficient one.
It may be very costly for the manager to monitor the different cost of fishing between
fishermen. The implementation of a monitoring system whereby a monitoring official is
stationed with every fisherman to determine the payment, or to set a fixed payment for every
fisherman would be too costly. An incentive payment is a good measure to correct this
problem. Furthermore, incentive payment programs can help to increase the social surplus
from fishery production and biodiversity conservation. Often the opportunity costs for not
destroying the resources are relatively low and compensation schemes may be suitable
investments for changing people’s behavior in favor of protecting the area.
While the analysis of principal in this paper may be useful for evaluating if the
transfer payment is able to support biodiversity conservation objectives, limits associated
with application of principal agent model in this context should be mentioned here. The
application of the principal-agent model in this study allows us to set up differentiated
payments as incentive for biodiversity conservation and reduce the information rent.
However for biodiversity conservation projects related to agriculture and forestry sectors,
especially in low and middle-income nations, the managers seem averse to payment
differentiation (Ferraro [2007]). One of the main reasons for this is that agents often perceive
differentiated payments as unfair or manipulated to satisfy political constituencies or
corruption rather than to meet conservation goals. Since the fishery sector, as mentioned
above, can resemble the agriculture and forestry sectors, we also raise this as a possible
problem for fishery sector if the incentive payment is implemented.
Given the informational and technical complexity of the principal-agent approach, our
model has not dealt with some factors that may be important in contracting initiative for
biodiversity conservation such as: administrative cost that often takes from 5 to 25 percent of
the operating budget (Ferraro and Simpson [2002]), and enforcing fishing areas once they are
claimed due to the establishment of marine reserves. These issues should not be ignored and
may become interesting concepts for studies in the future.
Potential obstacles to implementing a transfer payment program also arise. The
transfer payment often requires an ongoing financial commitment to maintain the link
between investment and conservation objectives. Social conflicts may exist if other
stakeholders (non-fishing groups), who are also affected by marine reserves but do not
receive payment. Also, the loss of biodiversity for other areas may increase if the fishery
suffers from a lack of appropriate management and control rules following the presence of
transfer payments.
Acknowledgement. The author is very grateful to Norwegian Agency for International
Development Cooperation (NORAD), Project SRV2701 for financial funding, Ola Flaaten,
Niels Vestergaard, two reviewers and the editor for valuable comments and suggestions.
Thanks also to Claire Armstrong and Siv Reithe for helpful discussions on the topic.
APPENDIX 1
Full information – Proposition 1 and 2
The optimal problem for society is:
2
i 1 j 1
subject to

W  Bm   1    phij eij ,m, X   cij  j ,m,eij   u0
n
(A1)

G X ,m   hij eij ,m, X   0 ,
n
(A2)
2
i 1 j 1
(A3)
0  m  1.
To set up the Lagrange for the problem, the first order conditions will be:
(A4)
 G n 2 hij 
 h c 
L B n 2 
   0,

  1    p ij  ij    
 

m m i 1 j 1 
 m m 
 m i 1 j 1 m 
(A5)
n
2 
 B

 h c 
 G n 2 hij 
     0 ,
  1    p ij  ij    
 
m  0 , m
 m i 1 j 1 

 m m 
 m i 1 i 1 m 
  0 , 1  m  0 ,  1  m  0 ,
(A6)
 h c 
h
L
 1    p ij  ij    ij  0 ,
 e
eij
eij 
eij
ij

where  is the Lagrange multiplier associated with the participation constraints, and  is the
multiplier associated to the constraint m  1 .  is the user cost of the resource when we
solve the maximization problem. We can see it as the shadow price of the resource stock.
Condition (A5) helps us to define the optimal size of the reserve, and condition (A6)
helps us to find out the optimal fishing effort. It should be note that m  1 is not the optimal
reserve size, since when m  1 the fishing effort will be equal to 0. We assume that the effort
is larger than 0 so m  1. From this case, we find from (A5) that   0 .
The fraction of marine reserve will be decided by this equation:
 G n 2 hij 
 h c 
B n 2 
  0,
  1    p ij  ij    
 

m i 1 j 1 
 m m 
 m i 1 j 1 m 
(A7)
(A7) is arranged as follows:
n
2

hij
cij 
   p m  m  
(A8)
i 1 j 1


B / m
  G n 2 hij 
.

 
1 
1    m i 1 j 1 m 
And the effort of fishermen under full information is defined by:
(A9)
p
hij
eij

cij
eij

 hij
.
1   eij
APPENDIX 2
Participation and self-selection constraints for asymmetric information
Rearranging the participation and incentive compatibility constraints of the low-cost
fisherman, we can rewrite them as follows:
Ti1 ei1   u0   phi1 ei1 ,m, X   ci1 1 ,m,ei1  ,
(A10)
(A11) Ti1 ei1    phi 2 ei 2 ,m, X   ci1 1 ,m,ei 2   Ti 2 ei 2    phi1 ei1 ,m, X   ci1 1 ,m,ei1  .
Manager wants the transfer Ti1 to be as small as possible, so one of these constraints
will be binding.
Due to the single crossing property, it is easy to show that:
ci 2 2 ,m,ei 2   ci1 1 ,m,ei 2  ,
(A12)
or
 ci 2 i 2 ,m,ei 2   ci1 1 ,m,ei1 .
(A13)
From (A13) and the participation constraint of high-cost fisherman, we will have:
(A14) phi 2 ei 2 ,m, X   ci1 i1 ,m,ei 2   Ti 2 ei 2   phi 2 ei 2 ,m, X   ci 2 i 2 ,m,ei 2   Ti 2 ei 2   u0 .
Since phi 2 e2 ,m, X   ci1 1 ,m,ei 2   Ti 2 ei 2   u0 , the expressions in the first bracket of
equation (A11) are larger than u0 , (A10) cannot be binding. This means that the incentive
compatibility constraint is binding for the low-cost fisherman:
(A15) Ti1  phi 2 e2 ,m, X   ci1 1 ,m,ei 2   Ti 2   phi1 ei1 ,m, X   ci1 1 ,m,ei1 
For the high-cost fisherman, the participation and incentive compatibility constraints
are below:
(A16)
phi 2 ei 2 ,m, X   ci 2 2 ,m,ei 2   Ti 2 ei 2   u0 ,
(A17) phi 2 ei 2 ,m, X   ci 2 2 ,m,ei 2   Ti 2 ei 2   phi1 ei1 ,m, X   ci 2 2 ,m,ei1   Ti1 ei1  .
One of two above constraints will be binding for the purpose of minimizing the
budget for society. We assume that constraint (A17) is binding. Substituting the binding
incentive compatibility constraint of the low-cost fisherman (A15) into the incentive
compatibility constraint for the high-cost fisherman (A17), we obtain:
(A18)
phi 2 e2 , m, X   ci 2  2 , m,e2   Ti 2  phi1 e1 , m, X   ci 2  2 , m,e1   phi 2 ei 2 ,m, X 
 ci1 1 , m,ei 2   Ti 2   phi1 ei1 , m, X   ci1 1 ,m,ei1 
,
From (A18), we have:
ci1 1 ,m,ei 2   ci1 1 ,m,ei1   ci 2 2 ,m,ei 2   ci 2 2 ,m,ei1 .
(A19)
(A19) violates the single cross property. The participating constraint of the high-cost
fisherman will be binding. The optimal transfer for the high-cost fisherman is:
Ti 2  u0   phi 2 ei 2 ,m, X   ci 2 2 ,m,ei 2 .
(A20)
Inserting (A20) into (A15), the optimal transfer for the low-cost fisherman reads:
(A21) Ti1 ei1   u0   phi1 ei1 ,m, X   ci1 1 ,m,ei1   ci 2 2 ,m,ei 2   ci1 1 ,m,ei 2 
APPENDIX 3
Asymmetric information – Proposition 3 and 4
The maximum problem for the manager is:
n
(A22)
W  Bm    s1    phi1 ei1 , m , X   ci1 1 , m , ei1    ci 2  2 , m , ei 2   ci1 1 , m , ei 2   u0 
i 1
n
  1  s 1    phi 2 ei 2 , m , X   ci 2  2 , m , ei 2   u0 
i 1
subject to
n
(A23)
G  X ,m    shi1 ei1 ,m , X   1  s hi 2 ei 2 ,m , X   0 ,
i 1
(A24)
0  m  1.
We set up the Lagrange problem and solve it for the optimal solution. It is the same as
the full information:  is the Lagrange multiplier for resource restriction and  is the
multiplier for the constraint of the reserve area.
(A25)
n

L B
c 
c 
c 
 h
 h
 c

   s 1    p i1  i1   1  s 1    p i 2  i 2   s  i 2  i1 
m m i 1 

m

m

m

m

m
m 





,
n
 G
h  
 h
 
   s i1  1  s  i 2      0
m  
 m i 1  m
(A26)
(A27)
(A28)
(A29)
m0
n
 B

c 
c 
c  
 h
 h
 c
   s 1    p i1  i1   1  s 1    p i 2  i 2   s  i 2  i1  

m 11 
m 
m 
m  
 m
 m
 m
m
 0,
n


 G
hi 2  
 hi1
  s
 1  s 
  

  
m  


 m i 1  m
  0 , 1  m  0 ,  1  m  0 ,
 h
L
c 
h
 s1    p i1  i1   s i1  0 ,
e1
ei1
 ei1 ei1 
 c
 h
L
c 
c 
h
 s  i 2  i1   1  s 1    p i 2  i 2    1  s  i 2  0 .
e2
ei 2
 ei 2 ei 2 
 ei 2 ei 2 
That is similar to the full information. Since the effort is larger than 0, the reserve size
must satisfy the condition m  1 . Due to this, we also find from (A27) that   0 . The
optimal reserve size will be defined by the equation:
n

B
c 
c 
c  
 h
 h
 c
   s 1    p i1  i1   1  s 1    p i 2  i 2   s  i 2  i1  
m 
m 
m   .
 m
 m
 m
(A30) m i 1 
n
 G
h  
 h
  
   s i1  1  s  i 2    0
m  
 m i 1  m
From (A30), we can derive the optimal area for the reserve:
 
n
hi1
ci1 

hi 2
ci 2 
s  ci 2
ci1 
 s  p m  m   1  s   p m  m   1    m  m 
i 1

(A31)
B / m
  G  n hi1
h  

  s
1  s  i 2  

1 
1    m  i 1 m
m  
.
The optimal efforts for two types of fishermen under asymmetric information are
defined from (A28) and (A29) as follows:
p
(A32)
(A33)
p
hi1 ci1
 hi1


,
ei1 ei1 1   ei1
 ci 2 ci1 
hi 2 ci 2
 hi 2
s





.
ei 2 ei 2 1   ei 2 1  s 1     ei 2 ei 2 
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