1. Consider two consumers who each choose how to split their income, m, between a private good, x, and a public good. The amount of public good consumer į buys is denoted by g, and the total amount of public good is G. The price of each good is 1 and the consumer's utility functions are as below: u, = 2log(x) + log(G) u₂ log(x₂)+log(G) a) By referring to the utility functions, explain why good G satisfies the definition of a public good.
1. Consider two consumers who each choose how to split their income, m, between a private good, x, and a public good. The amount of public good consumer į buys is denoted by g, and the total amount of public good is G. The price of each good is 1 and the consumer's utility functions are as below: u, = 2log(x) + log(G) u₂ log(x₂)+log(G) a) By referring to the utility functions, explain why good G satisfies the definition of a public good.
Principles of Economics, 7th Edition (MindTap Course List)
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Author:N. Gregory Mankiw
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Chapter22: Frontiers Of Microeconomics
Section: Chapter Questions
Problem 8PA
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![1. Consider two consumers who each choose how to split their income, m, between
a private good, x, and a public good. The amount of public good consumer į buys
is denoted by g, and the total amount of public good is G. The price of each
good is 1 and the consumer's utility functions are as below:
u, = 2 log(x,)+log(G)
uz = log(x,)+ log(G)
a) By referring to the utility functions, explain why goodG satisfies the definition
of a public good.
b) Find each individual's best-response function.
c) Find the Nash Equilibrium amount of public goods purchased.
d) Use the Samuelson rule to show that the level of public goods purchased in
the Nash Equilibrium is inefficient. Explain your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2656c93c-2b7a-40b9-9155-b9217bbdb35f%2F94589e3c-98ae-46f9-9133-2e54fe3b417b%2Fwnk9p0w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider two consumers who each choose how to split their income, m, between
a private good, x, and a public good. The amount of public good consumer į buys
is denoted by g, and the total amount of public good is G. The price of each
good is 1 and the consumer's utility functions are as below:
u, = 2 log(x,)+log(G)
uz = log(x,)+ log(G)
a) By referring to the utility functions, explain why goodG satisfies the definition
of a public good.
b) Find each individual's best-response function.
c) Find the Nash Equilibrium amount of public goods purchased.
d) Use the Samuelson rule to show that the level of public goods purchased in
the Nash Equilibrium is inefficient. Explain your answer.
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