Let: U1 = x1 + z^.5, Y1 = x1 + pz1 U2 = x2 - .5z^.5, Y2 = x2 + pz2 z = z1 + z2, Y is the income of the agent, and p is the price of z1 and z2. What is the social-optimal amount of z1 and z2? What is the optimal amount of z1 agent 1 would choose given z2, and vice versa? What can the social planner do so that the agents choose the socially optimal level of z1 and z2? How much is needed to achieve the social-optimal amount?

Let: U1 = x1 + z^.5, Y1 = x1 + pz1 U2 = x2 - .5z^.5, Y2 = x2 + pz2 z = z1 + z2, Y is the income of the agent, and p is the price of z1 and z2. What is the social-optimal amount of z1 and z2? What is the optimal amount of z1 agent 1 would choose given z2, and vice versa? What can the social planner do so that the agents choose the socially optimal level of z1 and z2? How much is needed to achieve the social-optimal amount?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.1P

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Question

Let:
U1 = x1 + z^.5, Y1 = x1 + pz1
%3D
%3D
U2 = x2 - .5z^.5, Y2 = x2 + pz2
%3D
%3D
z = z1 + z2, Y is the income of the agent,
and p is the price of z1 and z2.
What is the social-optimal amount of z1 and
z2?
What is the optimal amount of z1 agent 1
would choose given z2, and vice versa?
What can the social planner do so that the
agents choose the socially optimal level of
z1 and z2? How much is needed to achieve
the social-optimal amount?

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