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?

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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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?
Transcribed Image Text: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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