Question: Two individuals i = {1, 2} have preferences over a private good, X, and a public good, G. Denote individual is purchase of the private
Two individuals i = {1, 2} have preferences over a private good, X, and a public good, G. Denote individual is purchase of the private good Xi and his purchase of the public good as Gi . The individuals preferences over the public and private good are:
Ui = 5 ln(Xi) + ln(G1 + G2)
While he benefits only from his own purchase of the private good, he benefits from is purchases of the public good as well as his own. The price of the private good and the public good is 1 and both individuals have an income of 60.
a. What will be the free-market provision of the public good? How much is paid for by individuals 1 and 2?
b. What is the socially optimal amount of the public good?
c. Suppose the government decides to provide 8 units of the public good. It taxes each individual 4 to pay for it. What is the total amount of the public good provided after the government intervention?
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