Utility = (x,y)² the individual's share of private good production (=x/100). Notice that the exclusive and that everyone benefits equally from its level of production. e market for x and y were perfectly competitive, what levels of those good ld be produced? What would the typical individual's utility be in this situa at are the optimal production levels for x and y? What would the typical vidual's utility level be? (Hint: The numbers in this problem do not come aly, and some approximations should suffice.)

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter19: Externalities And Public Goods
Section: Chapter Questions
Problem 19.7P
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3. Suppose the production possibility frontier for an economy that produces one public
good (y) and one private good (x) is given by
x*+100y =5,000
This economy is populated by 100 identical individuals, each with a utility function of
the form
Utility = (x,y)2
where x,is the individual's share of private good production (=x/100). Notice that the public
good is nonexclusive and that everyone benefits equally from its level of production.
a. If the market for x and y were perfectly competitive, what levels of those goods
would be produced? What would the typical individual's utility be in this situation?
b. What are the optimal production levels for x and y? What would the typical
individual's utility level be? (Hint: The numbers in this problem do not come out
evenly, and some approximations should suffice.)
Transcribed Image Text:3. Suppose the production possibility frontier for an economy that produces one public good (y) and one private good (x) is given by x*+100y =5,000 This economy is populated by 100 identical individuals, each with a utility function of the form Utility = (x,y)2 where x,is the individual's share of private good production (=x/100). Notice that the public good is nonexclusive and that everyone benefits equally from its level of production. a. If the market for x and y were perfectly competitive, what levels of those goods would be produced? What would the typical individual's utility be in this situation? b. What are the optimal production levels for x and y? What would the typical individual's utility level be? (Hint: The numbers in this problem do not come out evenly, and some approximations should suffice.)
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