Answered: (a) Assuming that each fishery chooses…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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(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?

云2
There are two fisheries who catch fish in the
same pond. The total amount of fish in the pond is F> 0. If fishery
ie{1,2} catches the quantity of fish fi, the remaining amount of fish
is F- fi-f2. Each player derives utility from catching f; and from
the remaining fish in the pond.
To be more specific, the payoff of fishery i is given by
1.
4(fis f;) = 2 In(ft)+In(F – f; – f;), j#i€{1,2}.
(a) Assuming that each fishery chooses fi E (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 equi-
librium payoffs?
F10
F11

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