Consider a discrete-time fishery model where the stock is fished down from an initial level R...

 

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Consider a discrete-time fishery model where the stock is fished down from an initial level R to a level S over a period. Then the stock grows until the end of the period. a) Suppose the price of fish is constant but the cost per unit of fish is inversely proportional to the stock exploited at any moment. Formulate the net revenue from fishing in one period. b) Suppose that identical countries fish the stock in a common pool. They have agreed to a cooperative solution where they leave behind an optimal stock of Sº after fishing in every period. Formulate the present value of the fishery for one country over an infinite time horizon. c) Now suppose that one of the countries abandons cooperation, but is found out when the period is over and is punished by the other countries doing likewise. Formulate the payoff function over an infinite time horizon for the deviating country. d) What is the condition for deviation not being profitable? What are the critical factors for this? Explain carefully. Consider a discrete-time fishery model where the stock is fished down from an initial level R to a level S over a period. Then the stock grows until the end of the period. a) Suppose the price of fish is constant but the cost per unit of fish is inversely proportional to the stock exploited at any moment. Formulate the net revenue from fishing in one period. b) Suppose that identical countries fish the stock in a common pool. They have agreed to a cooperative solution where they leave behind an optimal stock of Sº after fishing in every period. Formulate the present value of the fishery for one country over an infinite time horizon. c) Now suppose that one of the countries abandons cooperation, but is found out when the period is over and is punished by the other countries doing likewise. Formulate the payoff function over an infinite time horizon for the deviating country. d) What is the condition for deviation not being profitable? What are the critical factors for this? Explain carefully.

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a Net revenue from fishing in one period The net revenue from fishing in one period can be calculated as the total revenue minus the total cost The total revenue is equal to the price of fish multipli... View the full answer