Consider a cod fishery. Suppose the growth function for cod is g(S) = 0.4 S (1 – S/1000), where S is the stock of cod in the fishery (measured in metric tons). Marginal growth of the fishery is given by change in g/change in S = 0.4(1 – S/500). The price of a unit of cod harvests is constant: p = 3000. Suppose the fishery is a “schooling” fishery. In this case harvesting costs are independent of the stock, so that there are no marginal cost savings arising from a larger stock. Let harvest costs be given by TC = 200h, where h is the harvest. Marginal harvesting costs are constant and equal to MC = 200. The discount rate is r = 0.1.
A. Determine the marginal resource rents associated with the resource. Will this value change over time?
B. What is the steady state golden rule equation for this problem? Explain this equation, and use it to determine the steady state stock and harvest levels and the steady state level of economic net benefits.
C. What would happen to the steady state stock level if the intrinsic growth rate was reduced? Explain the economic intuition behind this result. What does this mean for slow growing populations like whales?
D. Do prices or costs play any role in determining the outcome?