(a) Assuming that each fishery chooses fi ∈ (0,F), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs? (c) Suppose that a benevolent social planner wants maximize the util- ity of both fisheries. In other words, the social planner solves the following problem: max w(f1, f2) = u1(f1, f2) + u2(f1, f2) (f1 ,f2 )= 2ln(f1)+2ln(f2)+2ln(F −f1 −f2). Find the social planner’s solution. (d) What are the fisheries’ payoffs if the quantities of fish they catch are solutions to the social planner’s problem? What can you say about the Nash equilibrium quantities of fish being caught as compared to the social planner’s solution? (e) If fishery j decides to follow the recommendation of the social planner, how much fish will firm i catch?
(a) Assuming that each fishery chooses fi ∈ (0,F), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium.
(b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs?
(c) Suppose that a benevolent social planner wants maximize the util- ity of both fisheries. In other words, the social planner solves the following problem:
max w(f1, f2) = u1(f1, f2) + u2(f1, f2) (f1 ,f2 )= 2ln(f1)+2ln(f2)+2ln(F −f1 −f2). Find the social planner’s solution.
(d) What are the fisheries’ payoffs if the quantities of fish they catch are solutions to the social planner’s problem? What can you say about the Nash
(e) If fishery j decides to follow the recommendation of the social planner, how much fish will firm i catch?
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