Abstract Steady state and dynamic management models are developed for analyzing the Malaysian marine fisheries. These models originate from the theoretical concepts of the natural resource economics namely the open access, limited entry and the intertemporal fishery models. Such management models are deemed necessary because of the need to sustain the depleting resource and degrading environment. Marine fisheries had been managed under open access for a long time before government intervention took effect sometime during the 1960s. Open access and government intervention during the earlier phase of economic development contributed to the immediate pressure on fisheries. Community development programs geared to alleviate poverty among the fishermen apparently contradicted the effort of sustaining fisheries. Even today this fundamental management objective of sustainable development of fishery resource is not fully adhered to. This study suggests that ability to sustain fishery requires government intervention that can direct resource use to steady state or intertemporal optimal levels.

1. Introduction

The management of capture fisheries from the natural resource perspective is somewhat recent in Malaysia. Earlier, development of fishing industry was primarily concerned with poverty eradication among fishermen, which was in contrast with the resource management issue. Some of the socioeconomic programs advocated during the initial development plans were in contradiction with the sustainable fisheries objectives. In an attempt to raise the income of fishermen, larger vessels and productive gears were proposed such that higher catch would be possible with the application of modern technology. Even at the end of last decade, modernization of the fishing industry was in fact the goal of many economies. Malaysia is not an exception. It is now being less emphasized with the realization of the importance of resource for the future and specifically with the depletion of coastal fisheries becoming a reality. Nowadays, deep-sea fishing becomes the ultimate goal for increasing production to meet rising demand; this activity is also envisaged as an alternative to reduce encroachment of the foreign vessels in the Malaysian exclusive economic zone.

Many fisheries policies adopted today are the result of past mismanagement blended with successful programs and experiences adopted from developed nations. The advancement of the industrialization era and the depletion of major natural resources lend support to management awareness among the developing nations. Early resource economists and fisheries biologists had studied the causes for resource depletion and probably contributed to the development of the basic concepts for the latter generation of economists to investigate. The tragedy of the common had long been recognized because of the difficulty involved in effective implementation and enforcement of laws. Despite international effort to alleviate resource overexploitation of the marine fisheries, the problem had in fact surged causing some 30% and 40% overexploitation of fisheries beyond maximum sustainable yield (MSY), respectively (FAO [1997]). In fisheries management, concepts like common property resource, undefined property rights, open access, limited entry, intertemporal optimization, and sustainability as understood by economists and biologists are some of the useful concepts that are being adopted by fisheries economists to this day. This paper intends to investigate some of these concepts, in particular, open access, limited-entry steady state, and intertemporal management as they apply to the Malaysian fisheries.

2. Steady-state fisheries models

There are a number of steady-state fisheries models developed by the marine biologists to investigate the relationship between fisheries population and its production growth. Nonetheless, the catch–effort function that is derived from the surplus production model is perhaps most used in fisheries economics because of its simplicity and is useful in deriving concepts relevant to their interpretations. For some there is a close resemblance between the fisheries biological model and the well-established production functions applied to agriculture and biology in economics. We will be focusing on the surplus production model and to relate this stock-growth fisheries formulation to the catch–effort fisheries model, which is widely used among marine economists. The steady-state fisheries model developed here will be extended further to incorporate the problem of externalities in resource economics before the dynamic fisheries model is investigated.

3.1 Surplus production equation The steady-state fisheries model is built on the biological relationships discussed in the preceding section. When little is known about specific biological factors affecting the growth rate of fisheries population, a simplified stock-growth relationship could be constructed that yields a positive rate of growth or surplus production (Hannesson [1978]). With a given environment and a limited food supply, marine biologists generally believe that the underexploited fish population will eventually tend to increase toward the maximum carrying capacity. As fisheries population grows from their initial population stock, surplus production is subsequently generated, which increases at a decreasing rate. Surplus production diminishes at the point of maximum stock corresponding to the MSY because recruitment and growth of the fisheries population will just offset natural mortality. Beyond the point of MSY, the rate of growth of the fisheries stock becomes negative as does the surplus production. This simple stock-growth relationship is known as the surplus production model.

Let us define the natural growth rate of the fisheries population as F(xt) that takes into consideration the unknown variables affecting the fisheries including recruitment, growth of parent population, and natural mortality of the original biological formulation. While ht represents the level of fishing harvest due to fishing effort applied to the resource, the rate of change in fisheries population over time can be represented as


Harvest level h(t), which depends on effort application and fishery stock, can be broken into several operators representing distinctive types of fishing methods such as between different fisheries jurisdictions of exclusive economic zones (EEZs) involved in the industry at time t. In the absence of fishing harvest, the change in the undisturbed fisheries population would simply be equal to dx/dt=F(xt) because there is a zero impact of fishing effort on fisheries stock. It was in reference to the above per time rate of change of the fisheries stock of equation (1) that Graham [1935] first formulated the surplus production model. According to Graham the undisturbed fisheries population, which he referred to as population biomass, would exhibit an instantaneous percentage rate of change per time directly proportional to the difference between the maximum carrying capacity and the population biomass itself. If x(t) denotes the population biomass at time t and xc is the population maximum carrying capacity, Graham's formulation can be translated as


where t is time and k is a constant denoting the degree of proportionate rate of change in population biomass per unit of time and the difference between maximum carrying capacity and the population biomass. This is because dx/dt=F(xt) for the undisturbed fisheries population and by transferring the stock variable of equation (2) to right-hand side the following surplus production model is obtained as in (3),


The stock-growth fisheries equation above is a bell-shaped quadratic function with two conditions in which the growth rate would be reduced to zero. First, when population stock approaches zero the growth rate will be forced to zero. Second, when the size of population stock builds up to the level of the maximum carrying capacity, the growth rate of the fisheries population would also be equivalent to zero, which is easily observable from equation (3) above. Equating the first differentiation of the natural growth rate, F(xt), with respect to the population stock, xt, and setting the result to zero yields the desired level of the fisheries population size associated with the maximum sustainable population size, xm. This maximum population stock is xc/2. Substituting this value into the right-hand side of the stock-growth function of equation (3), the maximum natural population growth rate or the maximum surplus production is obtained, which should be equal to kxc/4.

3.2 Catch–effort equation The derivation of catch–effort equation requires that the undisturbed fisheries stock be subjected to fishing mortality with the application of some forms of fishing effort. For discussion the over time stock-growth equation in (1) above is referred. However, the fisheries stock is managed in an equilibrium condition whereby the rate of growth of the fisheries population, F(xt) is equivalent to the rate of harvest, that is, the catch per time ht. In other words, the steady-state assumption is required in the management of the exploited fisheries, which means the rate of population growth is constantly offset by an equal rate of harvest as such the change in stock over time is continuously maintained at zero. This steady-state assumption is interchangeably used to imply a static or temporal management of the fisheries resource.

Besides the stock-growth equation, the fisheries production function is needed in which catch is mathematically a function of fishing effort, Et, and fisheries stock, xt. As evident from empirical investigations of fisheries studies, Hannesson[1978, p. 102] noted, “it is usually assumed that a given level of fishing effort will take a constant proportion of the population biomass to which it is applied.” Thus the relevant production function for single and several operators can be presented as in equations (4.1) and (4.2), respectively.


where q is a constant representing the catchability coefficient of the fishing effort. For a given stock the magnitude of q should be equal to ht/Etxt implying that the coefficient varies with the variation in these policy variables. Holding catch at any constant level, an increase in either fishing effort or stock will decrease the catchability coefficient. An estimate of q is necessary, say through some techniques associated with fishing effort on the rate of harvest, to obtain an approximation of fisheries stock. More often than not stock is unknown, which makes it difficult to use the production function directly in the formation of the fisheries policy. In the production function above, fishing effort and stock are directly related to catch; however, a maximum sustainable catch does not exist for the function. Equating the right-hand side of equation (3) to the right-hand side of equation (4.1) yields the equilibrium population stock, xe,


Substituting the right-hand side of equation (5) into the production function (4.1) yields the steady-state catch–effort function,


where α=qxc and β=q2/k. The catch–effort function is identified as the Schaefer model after the fisheries biologist M.B. Schaefer [1954, 1957]. With limited data information on the population stock, one could still apply the steady-state catch–effort function. Although exposed to many criticisms especially in estimation errors the function could provide relevant answers to the fisheries management problems such as the MSY, economic sustainable yield (ESY) and open-access fisheries. The catch–effort function is simple yet very useful in applied fisheries because it can be extended to answer some of the relevant issues in fishery economics like the externalities and the multiple-fleet optimal fishing operation.

Dividng through (6) by fishing effort, Et, effort productivity (ht/Et) is obtained which is a linear function and decreases as effort increases. Many researchers used this catch per unit effort equation in the estimation of parameters in their studies, and they were significantly different from zero (O'Rourke [1971], Sagura [1973], Anderson [1977]). In economic investigations, the number of trips and sometimes the number of vessels themselves or vessel tonnage and horsepowers were used to represent fishing effort, whereas the body weight of fish caught usually in tonnage was used to represent the rate of harvest.

The level of maximum sustainable effort, Em, is α/2β and the corresponding the maximum sustainable catch, hm, is α2/4β. For the economic sustainable effort, E0, and economic sustainable catch (ESC), h0, we need to have the input–output price ratios. Supposing per unit input cost and per unit output price is represented by c and p, respectively, the economic sustainable effort should be equal to (α– c/p)/2β and ESC should be (α– c/p)2/4β. The economic sustainable effort and catch refer to the level of economic operation that could yield the maximum economic rent to the operator if fisheries were to be managed or property right is assigned to a firm. In production economics these concepts would be synonymous with the optimal condition of profit maximization firm.

One of the serious criticisms of the catch–effort fisheries function or the Schaefer's model is its equality assumption between the surplus production and the catch. This model provides little direct insight into the possible relationship that may exist between efforts and catch when catch is not equal to surplus production over any observed time interval of fishing activity. Moreover, the catch–effort function is most directly applicable to a fisheries stock defined over a fixed geographical area such that in-migration and out-migration of the fish cannot occur. The steady-state model does not account for the possible changes that may take place in the underlying variables of importance including effort, catch, fisheries stock population, and government policy over time.

Despite above criticisms, Schaefer's model continues to be applied both in biology and economic studies. Crutchfield and Pontecorva ([1969]; see also Howe [1979]) used Schaefer's model to explain the biological production relationships of the salmon fishery in their research. O'Rourke [1971] adopted the catch–effort function to estimate and analyze the economic potential of the California trawl fishery using annual landings of catch against the number of trawl vessels to derive cost and revenue curves and the related optimality condition. Similarly, Sagura [1973] employed the model to estimate the optimal effort that should be applied to the Peruvian Anchoveta. Tomkins and Butlin [1975] discussed various forms of the modified Schaefer's model in their studies for the open-access commercially exploited Manx Herring fishery, and Angello and Anderson [1977] extended the model to study the production relationships among interrelated fisheries stock of different species.

The application of catch–effort fisheries model was tested by Uhler [1980] to assess the accurateness of this function in predicting useful policy variables, namely fish population, catch and fishing effort whereby the stock abundance xt=ht/Et catchability coefficient is fixed at one (q= 1). Using Monte Carlo simulation results, he concluded that the estimated population size, harvest rate, and fishing effort showed as much as 40–50% error depending on the simulation models adopted. However, Uhler [1980] admitted that until better techniques are developed that can provide accurate estimates of the actual population biomass, management decisions will continue to rely on the catch and effort data. In economics, so long as the estimated catch–effort equation meets the theoretical specifications and statistical requirements, it can be used to predict those policy variables. The Schaefer's model will continue to be useful because it provides insight into the approximations of essential economic concepts. The issue of fishery management, particularly on depletion due to over-fishing, and the nature of fishery resources being common property shared by many players will continue to be addressed and investigated by fisheries economists (McWhinnie [2004], Torrieiro and Regueiro [2004]). The current study utilizes quite a similar form of fishery model, the quadratic function for analyzing the management issues in the Malaysian fishing industry. The methodology is applicable to any other fishery economy with similar management problem.

4. Extension of steady state model in economic studies

Fishing industries of the developing countries are being gradually modernized with new and more advanced technology—in particular with fishing gears and fishing techniques being introduced and adopted widely. The change in the industry's infrastructure may be seen as a result of the fishing operators' attempt to expand their fishing activities such that higher economic rents can be obtained from their operations. The modernization of the fishing industry over time can be related to the government policy, which attempts to exploit the potential of the offshore fisheries that have been either untapped or are being exploited by the encroaching neighbors that have better fishing equipment.

With the enlargement of fishing jurisdiction through the establishment of the EEZ the fisheries policy of a country would tend to be shifted to deep-sea fishing from originally tradition-based or inshore fishing. This policy option (to extend fishing from inshore to offshore/deep sea fishing) is happening because to enforce laws and regulation of the EEZ (to watch guard/police the sea) effectively is costly to the government, as such encroachment from foreign vessels is common. In view of the probable development occurring within the fishing industry, it is not uncommon to expect the influx of the modern vessels into the industry that may inflict negative impact on the traditional fishing methods. Under this condition of fishing activity two problem issues of economic significance in fishing may arise. First, the researcher would like to know the extent to which labor is being substituted for capital so that comparison can be made between regions. Second, the direct problem arising from multiple-fleet fishing operation relates to the possible externalities of modern gears on the traditional fishing methods. The operation of trawlers is expected to reduce the potential for line fishing, which can be shown by the interaction term between these fishing gears.

Replacing effort by vessels of types 1 and 2 (Et=V1t+ V2t) expressing catch as the function of newly defined effort, the catch–effort function now becomes the quadratic function with two vessel inputs. This fishery catch function is the normal quadratic production function found in agriculture but with the constant term forced to emanate from the origin. The two-input catch function provides the possibility for deriving the maximum sustainable catch associated with the biological equilibrium of the fisheries population and the ESC related to the economic rent maximization.

One of the usefulness of the two-input catch function is its ability to locate the composition-mix between labor- and capital-intensive vessels, which enable the researcher to identify the intensity of factor use in fishing industry. In multiple-fleet fishing industry an extended model can be used to identify the impact of externalities inflicted by bigger vessels on smaller ones via analyzing the interaction terms (Nik Hashim [1990]). Hence, specific management measures can be recommended for the management of the fisheries.

5. Intertemporal fisheries models

In solving the dynamic fisheries management problem involving time, the modern optimal control theory formally known as the calculus of variations is used. The objective of the intertemporal analysis is to arrive at the optimal time path that will maximize the economic rent of the fishing industry managed by the fishermen as the operating firms. In economics, information on fisheries population is rarely available, as such the optimal time path for the management of the stock is therefore inaccurate. In view of this shortcoming, fisheries economic studies tend to divert attention to alternatively predict the future trend in the utilization of essential policy variables like the rate of harvest, level of effort application, and the pressure on the fisheries population arising from the current level of resource utilization. From current information the future direction is deduced and a sound management policy is recommended to the fisheries authority. One of these fisheries management policies in economics relates to the issue of sustaining the resource for the future.

In the next section, we will review the basic but useful intertemporal fisheries model developed by Clark [1977], and the theoretical aspects of this intertemporal model will be subsequently highlighted. The application of steady state and intertemporal fisheries models will follow in the light of sustainable resource management if the given fisheries were to be managed under open access, steady state, and the intertemporal limited entry.

5.1 Intertemporal fisheries model The widely discussed intertemporal fisheries model is the one developed by the mathematician Clark [1976]. In this theoretical development, fisheries stock is treated as synonymous with capital. Clark utilizes the normal catch effort and stock equation in the form of a Cobb–Douglas production function


where γ is a constant term, and a and b are parameters of the variable factors for fishing efforts and fish stock, respectively. The rest of the notations are defined as before. Assuming that a= 1, the economic rent equation becomes


where π is the economic rent in terms of monetary value per season, p is the per unit price of fisheries harvest, and c(x(t)) =c/F(x(t)) is the cost per unit of fishing operation, which is a decreasing function of the fish stock. Whenever time is noted in the variable it means that it is a function of time. The objective of the intertemporal problem is to maximize the present value of the stream of the future economic rents within the range of time denoted by the integral that is from the initial time 0 to the terminal time ∞. This optimization objective is constrained by the per time stock-growth equation. Presented in mathematical expression the intertemporal fisheries objective is to


subject to


where, δ is the discount rate and e−δt is the discounting factor for a continuous problem for t number of years time horizon. The stock-growth equation is often referred to the equation of motion and x(t) is the control variable without which there is no need for intertemporal optimization. The objective is to find the optimal time path for the control variable fish stock that will maximize economic rent overtime and conforms to the aim of sustaining resource utilization into the future. The intertemporal maximization result proven by Clark [1976, 1977] is similar to that of golden rule basic equilibrium condition of the capital theory:


F′(x) is the marginal growth rate of the fishery population and c′(x) is the marginal cost of harvesting the stock. When the marginal cost of harvesting fisheries stock is zero the discount rate equation would reduce to δ=F′(x), identical to short run demand for and supply of investment funds under the capital theory. The case of fisheries is somewhat different from the capital theory because of the stock effect represented by the second term of the right-hand side of the equation. Clark assures that this stock effect is negative because as the fisheries stocks decline due to the fishing harvest the extraction cost eventually raises. In other words, it needs higher operation cost to capture a smaller stock of fisheries.

In our intertemporal fisheries formulation we stick to the original economic rent equation represented by the difference between the normal definition of total revenue and the total cost of the fishing undertaking. We further assume that this fishing undertaking is operational under the government-managed firm like its authorized fisheries agency, with the objective of maximizing the economic rent function of the firm under a given simplified market condition of perfect competition. Under this last assumption the firm's output price and cost of harvesting the stock are held as constants. The objective function written in the Hamiltonian expression is given in equation (13) and solutions to this intertemporal fisheries problem can be found using the maximum conditions of optimum control theory.


The partial differentiation of the Hamiltonian equation with respect to effort yields the simplified result of the optimum utilization of fishing effort in equation (12).


The result in equation (12.2) shows that the marginal user cost, μ(t) =e−δtλ(t), is defined as the difference between price and the marginal cost of fishing effort. The concept of marginal user cost coined by J. M. Keynes (see Clark[1976, p. 103]) is used interchangeable with the scarcity rent concept used to explain λ(t) in resource economics. In our fisheries intertemporal problem the marginal user cost is the current scarcity rent value (marginal user cost multiplied by the quantity of catch) of the fisheries resource after discounting.

On the other hand, the same result when translated into the marginal physical product concept as often used by agricultural production economist reduces to the ratio of per unit effort to the difference of catch price and marginal user cost. Without time dimension, μ(t) is absent and the optimum result for effort would be reduced to the familiar steady-state condition.

Because the value of marginal user cost of the in situ fisheries is positive, the input–output price ratio for the intertemporal optimization should be higher than the steady-state optimization case, that is c/(p–μ(t)) > c/p. Evidently this outcome tends to support the fact that effort application under the intertemporal optimization would be smaller compared to the steady-state optimization. Therefore, the pressure on resource utilization is relatively milder under the intertemporal case and thus more appealing to resource sustainability. With a lower fishing effort applied to the fisheries, it is likely that the impact in terms of damage inflicted on the environment and fisheries habitat is also minimal. As a result fisheries population tends to breed favorably under the intertemporal management condition.

For this to be really achievable it must be conditioned such that the assignment of the property right in fishing jurisdiction is made possible and that enforcement to refrain unauthorized users is effectively implemented. Private and social cost involved in the assignment of property rights and policing of laws and regulations should fall short of the potential benefits generated from fishing operation.

Partial differentiation of the Hamiltonian expression with respect to stock requires the use of the Pontaryagin maximum principle, that is dλ/dt=−∂H/∂x(t) (see Nagatani [1981, pp. 15–17]). This condition can be derived and simplified further based on our earlier reference to the definition of the discounted marginal user cost λ(t) =eδtμ(t), which reduces to the equilibrium condition for fisheries stock as:


Using the above equilibrium intertemporal condition yields the following desired optimal time path for fisheries stock:


Expressed in terms of the rate of change of the marginal user cost over time equation (13.1) becomes


When price equals the marginal user cost (p=μ), the growth rate of marginal user cost over time should be equal to the discount rate minus the rate of growth of stock effect. For the case in which price is greater or smaller than the marginal user cost, the growth rate of marginal user cost is greater or smaller than the discount rate depending on the magnitudes of catch- and growth-stock effects. The above intertemporal optimum time path result also shows that the growth rate of marginal user cost would be equivalent to the discount rate in the absence of catch- and growth-stock effects on the fisheries. In the case of the undisturbed fisheries whereby the impact of fishing mortality on stock is minimal, the change in the marginal user cost over time should be equal to the discount rate minus the rate of growth of the fisheries stock.

Letting ∂μ/∂t= 0 and μ= 1, an equilibrium steady state condition in output space representing per unit cost and price on the y-axis and quantity of harvest on the x-axis could be derived from equation (13.2), which is equal to


where MCx=δ/h(x), the marginal cost of stock extraction, g(x) is the stock growth rate, and h(x) is the stock harvest rate. An interpretation of the above equality is that when g(x) =h(x) the equilibrium is achieved as in the case of the perfect competition steady-state fisheries management. For h(x) > 0 and g(x) > h(x), the marginal cost curve or the supply function for the fishing industry shifts to the right, which means that at the same existing price more quantity of fisheries can be caught. On the other hand, when g(x) < h(x) the equilibrium condition requires that price be equated to marginal cost of stock extraction plus some percentage of marginal user cost represented by 1. This scenario seems to support a smaller level of catch because the marginal cost curve with the marginal user cost for the dynamic equilibrium is higher (above) the marginal cost under the static optimization.

In fact we may incorporate the effect of the environmental degradation as the result of resource extraction, which requires a higher marginal cost curve by the magnitude of the marginal environmental cost and a much lower quantity of harvest for an equilibrium condition. By this reasoning, fish population and fish habitat exposed to constant exploitation is most likely to exhibit higher probability of environmental and ecosystem damages.

6. Fisheries modeling for the current studies

In this section, we will develop some practical fisheries management models that can be applied to analyze any fishery resource believed to be under the pressure of over-fishing because of extensive application of fishing effort. We intend to prove which of these management policies will ensure better results of marine fisheries sustainability in terms of the least impact on resource depletion and exhaustion. The three fisheries models refer to the open-access management that allows fisheries to be utilized according to the condition whoever has the capacity to exploit the resource is allowed to do so without regulatory restrictions. The limited-entry management refers to the fisheries production policy that works to recommend fishing activities in accordance with the steady state optimal conditions whereas the intertemporal management policy refers to an ideal fishing activity that conforms with the dynamic optimization principles. The objective of these steady state and intertemporal management policies is to have a comparative study that will help decision makers in their choice of the best method for marine fisheries conservation. The last two management policies of limited entry require some forms of government intervention in terms of fishing restrictions and enforcement of the laws.

6.1 Open-access management Open-access management is a policy of no restriction, that is, free entry for all who wish to derive benefit from the resource. Restriction is not imposed by the controlling agency empowered to be responsible for the utilization of the resource. This is particularly true in the initial stage of resource use when its availability is plentiful and the technology to extract this particular resource is essentially traditional. However, as the economy of a country is gradually developed and the market begins to expand domestically and internationally, returns from this resource start to rise accordingly with the increased demand. The open-access management policy of the marine fisheries is stipulated to result in overexploitation of the resource, which finally reduces average revenue from fishing operation to be equal to its average cost. We begin the construction of the open-access management of the marine fisheries with the economic rent equation as


In reality the economic rent equation (14.1) could be more accurately presented to internalize any quantifiable cost incurred by the society in terms of ecological degradation and/or negative externalities that might be measured as a function of catch or effort. Equation (14.2) shows that under the assumption of perfect competition, the open-access average price, which also represents the average revenue from fishing, is equated to the average cost of fishing effort. Thus if fisheries catch–effort function is known, one can express fishing effort in terms of the remaining constants and variable, that is, average price, average cost of fishing effort, and population stock of the studied fisheries.

The open-access fishing effort that may be measured in terms of boat capacity like horse power or tonnage, p and c are constants representing average price of catch and average cost of fishing effort, respectively, and xt is the estimated fisheries stock population, say measured in metric tons. Having obtained the level of open-access fishing effort one can proceed to estimate the level of open-access catch or landing for that particular year or time. Assuming that we are provided with the initial level of fisheries stock as in equation (18) the estimated open-access volume of catch is computable from the catch–effort-stock function or simply the fisheries production function as shown below.

6.2 Limited-entry optimal management The limited-entry fisheries resource is supposed to be managed by a sole ownership in which the property right to its use is established and it is actually a steady state optimal management. The limited-entry management policy for the marine fisheries adopts the same methodology as that of the open access. It only differs in the initial level of fishing effort applied to the existing fisheries whereas the initial fisheries stock is presumed to be given and fixed at some base year level as in the case of the open access. Because the formulation of an optimal steady state fishing effort application differs from that of the open-access management, the subsequent catch, fisheries stock, and economic rent obtained from the industry are expected to differ significantly. Depending on the strength of the initial fisheries population and the direction in which the current fisheries are being exploited, either depleting or otherwise, one is able to compare the influence of efforts on catch and then stocks. Given the economic rent equation, the objective of economic rent maximizing is achieved when the average price, which is also the marginal revenue under perfect competition, is equated to the marginal cost of fishing effort as


Solving equation (15) yields the limited-entry optimal result of fishing effort expressed in terms of the average price and cost of effort as constants and fisheries stock at a specified time period as a variable (for Cobb–Douglas and quadratic function with interaction).

The limited-entry fishing effort in reality exists in several forms such as the seasonal closure, zoning of the fishing areas according to the vessel's capacity, restriction of fishing techniques known to cause damage to small fisheries, and so forth. In some states like those facing the South China Sea, seasonal closure coincides with the monsoon time whereby rough sea deters fishing operation during this period. The limited-entry optimal fishing effort applied to the country's fisheries resource should be smaller than the open-access fishing effort defined above and similarly the expected limited-entry catch derived from the current application.

6.3 Intertemporal optimal management Intertemporal management policy results from the management of the fisheries under an optimal dynamic optimization. Optimal management of the fisheries resource involving time in this case specifically refers to a partial intertemporal optimal application of fishing effort to a specific fisheries resource. The methodology is again similar to the above open access and the limited-entry management. Under dynamic optimization, the owner of an assigned property right resource or the trustee like the government agency would consider, besides price and cost of production, its in situ scarcity rent value when utilizing the resource overtime. Any resource left in its natural environment will normally fetch a higher price in the future compared to its present utilization, assuming that demand for the resource persists. This fact is seen from the viewpoint of a supplier who is taking advantage of a global supply that is diminishing due to constant usage of the resource overtime.

From intergeneration equity consideration the preserved resource will be available to the future users and also resource left in its natural environment will not pose as a threat to the ecological damage. Thus when time is neglected in the dynamic optimization, that is, when production and consumption are totally geared to the present usage, the value of the in situ resource reduces to nothingness. For simplicity the corresponding equations required for the formulating and generating simulation results of the intertemporal optimal fisheries management are presented below as


Before the intertemporal optimal fishing effort can be calculated the estimate of marginal user cost must first be obtained. From equation (16) marginal user cost should be equal to the difference between the price and marginal cost of resource extraction. In the environmental economics the socially optimum level of environmental management is given by the difference between the private and the social marginal cost curve. Although the intertemporal and socially optimum objectives may differ, the underlying principal is that both resources—fisheries and the environment under optimum conditions should be reasonably reduced to a manageable level.

The estimate of catch is obtained by substituting the initial stock and the level of fishing effort for the above fishing management alternatives. Specifically the production function would be applicable for all conditions of management alternatives.


We may be interested in investigating further to understand what will happen to the left over fisheries stock in the succeeding year following the impact of open-access fishing activities. For this purpose it is necessary to develop a time-related equation explaining the relationship between the future fisheries stock and the current fish population after it has been exploited. The future fisheries stock, say at time t+ 1, is depending on the current time t fisheries stock less the proportion of body weight loss caused by natural mortality and plus the proportion that contributes to body weight gain due to recruitment and growth. The remaining fisheries stock at time t+ 1 is also governed by the current open-access rate of harvest. Presenting this in mathematical expression the above equality can be written as


where ϕ is a constant denoting that without the current reproductive fisheries stock there is already some fixed level of fisheries, and φ represents the magnitude of the fisheries stock growth over the period investigated. It can be greater than 1 if the gains in population body weight through recruitment and growth is higher than the loss in body weight owing to the natural mortality and vice versa. Without the last variable, one is able to identify the direction of fisheries stock, it increases when φ > 1 and reduces when φ < 1. Relying on the information generated in equations (23) and (24), again we are able to predict the succeeding level of fisheries stock relating to the limited-entry optimal fishing activities for a particular fisheries resource under investigation.

In summary, the system of equations required for the simulation for the desired management alternatives of the Malaysian fisheries of open access, limited-entry steady state, and limited-entry intertemporal optimizations are presented as follows:


where Ω=a0+ a3xt− a4xt2 and Et* is the optimal fishing effort applied to the steady-state limited-entry fisheries at time t and a1, a2 are coefficients for effort (Et and Et2), respectively, c is the cost per unit of vessel in ringgits, and p is the price per metric ton of catch in ringgits. This optimal steady state and intertemporal effort are constants because interaction effect between inputs is not considered.

Simulation of the open access, steady state, and intertemporal limited-entry policy variables including fishing effort, the rate of harvest, and the fisheries stock can be subsequently generated from equations (19) to (24). The scenario underlying the open-access fisheries management is governed by the fact that the industry economic rent is fixed at the zero level. Simulation results of open-access management are stipulated to be in disagreement with resource conservation, and as such contravene to the idea of resource sustainability. The steady-state optimal management depicts an optimal level of economic activities that conforms to the theoretical static, whereas the intertemporal condition represents the dynamic economic rent maximization.

Under the limited-entry management the economic rent is assured to be positive so long as there is fisheries stock left to be caught. A series of expected economic rent for the duration of the projected time horizon of a limited-entry management ownership is computable from the economic rent equation. One is able to stipulate that the fisheries resource under limited entry is more favorable to the need of sustainable fisheries management compared to the open-access case. The extent of resource depletion or conservation can only be shown with certainty when actual fisheries data are translated to empirical investigation results using the suggested methodology.

The simulation results of intertemporal optimal fishing effort and catch will be much lower compared to the steady state management of effort and catch. This means the rate at which the fisheries stock is being exploited is slower and favorable from the viewpoint of this resource management, which is particularly essential for the overexploited fisheries or nonrenewable and renewable resources. Consequently the fisheries stock population will be better preserved and sustained under the intertemporal optimal management compared to the previous two management policies of open access and limited entry.

The question is whether or not the intertemporal management serves the desired goal of a particular national fishery policy when other economic problems such as that of society's need for food and poverty eradication programs are socially more demanding to be fulfilled. The current global viewpoint seems to come to consensus that the former sustainable development policy would be needed because the major resources of the world have been under use for a long period of time. Moreover, the utilization of major resources of the world appears to be utilized for the purpose of well-advanced bigger and richer nations but the economic benefits have not been fairly distributed or passed back to the poorer nations both in terms of current and the future generation.

7. Results and discussion

Before the set of equations on economic rent, fishing effort, catch, and fisheries stock can be used to simulate results of the three categories of management alternatives, some of them need to be empirically estimated and tested for validity from statistical standpoints. First is the stock equation model where the methodology of approximation stock was already explained above. Official data published in the Annual Fisheries Statistics 2003 on number of vessels and landings for 1979–2003 collected by the Department of Fisheries Malaysia were used. Results of regression analysis for t+ 1 fisheries stock and fisheries production function using Shazam econometric package are shown in equations (25) and (26), respectively.


Note: figures in parentheses denote the value of Student's t-test, **: significant at 0.01 probability level, and ***: significant at 1.00 probability level.

Simulation results of open-access management for effort, catch, and economic rent are shown in Table 1. As noted, this policy of allowing fisheries to be freely utilized to the potential investors would ultimately bring resource closer to the risk of being overexploited. Any fisheries policy that works toward diminishing the economic rent to zero level is economically inefficient. The open-access effort and catch are generally higher than the alternative management options and the remaining stocks more depressed (Figures 1 & 2). Overexploitation and depletion of the resource would lead to quicker exhaustion as evident from higher rates of decline in all economic variables. In reality, open access management is a rather effort intensive, effective use of technology but it is economically inefficient. As depicted by economic rent actually procured, it could either be insufficient to cover the cost or, in extreme cases, reflecting losses. Exhaustion of fisheries resource could only take place after a continuous application over time of the intensive fishing effort to the depressed fish stock. Open-access management is considered contrary to the idea of resource sustainability.

Table 1.  Simulation of effort, catch, stock (in 1000 metric tons), and economic rent (in 1000 ringgits) for open-access management.
YearEffort (Et)Catch/landings (ht)Stock (xt+1)Economic rent (Πt)
  1. Note: The exchange rate for the United State dollar to the Malaysian ringgit is US$1.00 = MR3.80.

Rate of change 2004–2014 (%)−0.550−0.550−0.9550
Figure 1.

Simulation of annual fishing effort.

Figure 2.

Simulation of annual fish harvest.

As evident from the open-access management in Table 1, the Malaysian marine fisheries exhibit trends of a gradual decline in fishing effort, landing, and the remaining stock. If a constant optimal effort level were to be adopted as in the limited-entry management of Table 2 or Table 3, the remaining stocks are expected to be more resilient and sustained. With a reduction in the optimal fishing effort, we believe the remaining stocks would be better sustained and perhaps fisheries prices can be raised to the desired level.

Table 2.  Simulation of effort, catch, stock, and economic rent for limited-entry steady-state management.
YearEffort (Et)Catch/landings (ht)Stock (xt+1)Economic rent (ΠI)
  1. Note: The exchange rate for the United State dollar to the Malaysian ringgit is US$1.00 = MR3.80.

Rate of change 2004–2014 (%)0−0.460−0.473−1.527
Table 3.  Simulation of effort, catch, stock, and economic rent for limited-entry intertemporal management.
YearEffort (Et)Catch/landings (ht)Stock (xt+1)Economic rent (Πt)
  1. Note: The exchange rate for the United State dollar to the Malaysian ringgit is US$1.00 = RM3.80.

Rate of change 2004–2014 (%)0−0.331−0.332−1.059

Limited-entry management either steady state or intertemporal is certainly preferred to the open-access management for the reason that these management alternatives are economically efficient. By limiting fishing effort to some 17.9 thousand vessels annually, the contribution to the gross national income is approximated around 1 billion ringgit. Besides the national income contribution, the fishing industry will also generate further income through multiplier effects on the economy and employment to the country so long as it is sustained.

Comparing the benefits and costs of letting fisheries be managed either by steady state or intertemporal limited entry of Tables 2 and 3, the intertemporal management seems to apply smaller fishing effort and extracts lower volume of catch per time. Between these management alternatives intertemporal appears to exert lesser pressure on the fish stock as the resource will be sustained for a longer period of time relative to the steady state. As noted, the intertemporal economic rent is higher than the steady state, especially toward the end of the simulation period and vice versa. Higher attainment of economic rent is likely due to a milder declining rate of 1.06% per annum for the intertemporal compared to the steady state, which is estimated at 1.53% per annum. If we consider the value of fish stock (shadow price multiplied by the quantity of fish stock) as capital cost then the economic rent for intertemporal management regime is probably lower than the steady state.

Comparison between intertemporal and steady state management can be further evaluated on the basis of social versus the private net benefits and costs. If the private firm was given the property right to manage the fisheries and the government is interested in preserving the welfare of the society, then any social cost inflicted on the environment and any form externalities or ecological damage in resource extraction should be internalized by the firm. The net return of fisheries undertaking of the private firm would be further reduced, and the extraction of fisheries resource intertemporally would be optimized to a desired consumption level that is in agreement with the sustainability development goal.

8. Conclusion

One of the constraints encountered in the empirical application of the theory of marine fisheries, in particular, for economic analysis is the difficulty of getting the true estimate of the policy variables. For instance, researchers in social sciences normally rely heavily on the methods of estimating fisheries stock and to some extent also on the fisheries production functions developed by fisheries biologists. There are obviously practical problems involved in the utilization of these techniques. One of the problems in question refers to the tradeoff between getting accurate estimation of these variables and the extent of their usefulness in application. We may be able to accurately approximate the biological fisheries function that has limited applications to the fisheries economists.

Possible complications may be in the forms of the technicality in which fisheries data are collected that is not familiar to the social sciences and the application beyond mere estimation is again simply not quite possible. Economists usually require the estimation of the fisheries function to serve more useful purposes of estimating the ESY and to identify the causes and extent of externalities between different fishing efforts that compete in the same fishing ground. In scientific investigation, fisheries biologists and economists obviously differ in their ultimate goals so it is therefore not surprising to expect differences in the emphasis. It would be better if fisheries and economists could sit together to find solutions to their differences such that this disciplinary segregation can be minimized for the betterment of marine fisheries research.

Another possible issue that may arise in applying the fisheries theory developed in the last sections is the oversimplification of the fisheries dynamics into a simple and manageable analysis. This is especially apparent from the assumptions adopted in the analysis of a steady-state fishery whereby time is held constant for the duration of the study. To an economist the assumptions are necessary to make the real and complicated world more meaningful for the analysis. It would not be practical to include all variables that contributed to the dynamism of fisheries production. However, the results obtained from a simplified production function analysis may be more practical in terms of formulating fisheries management policy because a complicated production model may not necessarily yield results that are easy to interpret and useful for fisheries management.

It is true that we never come close enough in our attempt to estimate the marine fisheries populations in our studies because the fisheries are constantly on the move and it is almost inaccurate to count the moving target. Tagging method may be technically reliable but it is still based on the probability estimate. Economists prefer to use the econometric method by fitting fisheries data on productivity that is catch per effort, against the cumulative landings of fish for a period of time. The variation in average catch represents the growth rate of the fisheries and the summation of landing represents the stock-growth equation. Because this relationship is assumed to be linear, the coefficient of the stock-growth equation provides a measure of catchability coefficient that can be used in the estimation of the fisheries stock of a particular fishing ground. Nevertheless, because economics is not an exact science it only needs to show the direction of resource utilization. Accuracy in stock estimation is necessary because the policy makers need to project the direction of resource use—depleting or otherwise. Obviously fisheries management policy could be efficiently formulated and implemented with accurate information.