Answered: (a) Assuming that each fishery chooses…

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter3: Interdependence And The Gains From Trade

Section: Chapter Questions

Problem 3CQQ

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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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