Reproducible resources: open-access problems

Each reproducible and renewable resource has a specific character. Some are market­able, while others are not. Property rights are defined for some reproducible resources, but not for others.

Consider a static equilibrium analysis, following the pioneering work of Gordon (1954). Suppose that a fishing ground is a common property, so that any fisherman can have access to it. For simplicity, assume that there is only one input to fishery called fishing effort, which is denoted as e, and its unit cost is denoted as w. Marginal and average productivities are denoted as MP(e) and AP(e) respectively.

The total rent from this fishing ground at the fishing effort level e is expressed as p ∖0)MP (ε) dε — we, where p denotes the price of fish. Consequently, the rent is maxi­mized at the fishing effort level e* such that pMP(e*) = w holds. This is formally the same as profit maximization of production, apart from the fact that the fishing ground is in fixed supply and not variable as input.

Yet, notice that the fishing ground is a common property, so that open-access prevails. When the average rent is positive, it is likely that there will be an additional gain for a fisherman if he increases the fishing effort. Since every fisherman thinks in the same way, fishing effort is increased until the average rent (thus the total rent) disappears. Consequently, in an open-access equilibrium, pAP(e**) = w holds. Since as the “first come, first served” principle is applicable to the fishing ground, there should be new entry as far as there is positive rent.

This type of inefficiency more or less occurs in almost all common properties unless carrying capacities are so large that marginal productivity does not decline. There may be an exception: population explosion does not affect production of oxygen in the atmosphere, which is an indispensable input in human activity, since the carrying capac­ity of the atmosphere is large enough. This is, however, a mere exception, which is not applicable to other natural or environmental resources.

Although a static equilibrium explains the aforementioned interesting characteristics of a common property, it does not tell about stocks of reproducible resources, which is sometimes essential, particularly from the viewpoint of sustainable resource use. This can be shown with reference to Gould (1972).

In addition to the variables defined above, define the stock of fish in a fishing ground as S. It is usual to assume that the natural growth rate of the stock depends upon itself, and is expressed by f(S), where there exist S* and S(0 < S* < S) such that f(S) = 0, f(S) > 0 for S ∈ [0, S’), and f (S) < 0 for S ∈ (S*, S] holds. Obviously,f(S) is maximized at the stock level S*. It is the maximum yield of fish which can make the fishery stock

Note: The highest point of the curve is MSY. The equilibrium catches are given by A and B, the former being unstable and the latter stable.

Figure 8 The relationship between fish stock and its growth

constant, so that f(S*') is called the maximum sustainable yield (MSY) (see Figure 8). A simple example of the function is:

must hold, where p denotes the market price of fish. Substituting (4) into y = g(e, S), and solving the equation with respect to y, we obtain y = h(S), where h is an increasing func­tion of S.

It can easily be seen that, by construction, location and shape of the curve obtained by h(∙) depend upon the market price of fish (p) and the real wage rate (or the fishing­effort price) (w). As the market price increases (decreases) and/or the fishing effort price decreases (increases), the curve shifts upward (downward).

How the dynamic system works and an equilibrium obtains is explained by Figure 8. Two h curves are drawn in it. Consider h₁ first. There are two equilibria shown as A and B. In the intervals of [0, S_a) and (SB, S], clearly f(S) < h(S) holds, so that the fishery stock decreases due to (5). On the other hand, in the interval of (S_a, Sb), it increases, since f(S) > h(S) holds. Consequently, SB is a stable equilibrium, while S_a is an unstable equilib­rium. If the initial fishery stock is smaller than S_A, it decreases continually and converges to zero. Hence, in the long run, the fishery stock vanishes.

Next, look at the curve h₂. For all the stock levels S, an inequality f(S) < h(S) holds. This implies that the fishery stock decreases, starting from any stock level. The final state is that of the extinction of the fish. As the price of fish is sufficiently high and/or the wage rate is sufficiently low, the curve h may possibly be located in a rather high position, and thus, the possibility of extinction becomes high in such a situation. This partly explains how the rising price of caviar has accelerated the crisis of extinction of sturgeon in the Caspian Sea. Yet it must be noted that extinction is not a problem peculiar to open­access resources, and could occur in non-open-access resources as well (Peterson and Fisher 1977).