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? 4

(c) Suppose that a benevolent social planner wants maximize the utility of both fisheries. In other words, the social planner solves the following problem:

max w(f₁,f₂) w(f₁, f₂) = u1(f₁, f₂) + u2(f₁, f₂)

=2 ln(f₁) + 2 ln(f₂) + 2 ln(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?

There are two firms, whose production activity
consumes some of the clean air that surrounds our planet. The total
amount of clean air is K> 0, and any consumption of clean air comes
out of this common resource. If firm i E{1,2} uses k, of clean air
for its production, the remaining amount of clean air is K - k - k2.
Each player derives utility from using k, for production and from the
remainder of clean air.
To be more specific, the payoff of firm i is given by
4;(ki, k;) = In(k;) + In(K – k; – k;), j#iE {1,2}.

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