The town of Musicville has two residents: Bach and Mozart. The town currently funds its free outdoor concert series solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total concerts (C), of the form U = 3 x log(X) + 2 × log(C). The total number of concerts given, C, is the sum of the number paid for by each of the two persons: C = CB + CM. Bach and Mozart both have income of 80, and the price of both the private good and a concert is 1. Thus, they are limited to providing between O and 50 concerts. a. How many concerts are given if the government does not intervene?

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Chapter1: Making Economics Decisions
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The town of Musicville has two residents: Bach and Mozart. The town currently funds its free outdoor
concert series solely from the individual contributions of these residents. Each of the two residents has a
utility function over private goods (X) and total concerts (C), of the form U = 3 x log(X) + 2 × log(C). The
total number of concerts given, C, is the sum of the number paid for by each of the two persons: C = CB +
CM. Bach and Mozart both have income of 80, and the price of both the private good and a concert is 1.
Thus, they are limited to providing between 0 and 50 concerts.
a. How many concerts are given if the government does not intervene?
Transcribed Image Text:The town of Musicville has two residents: Bach and Mozart. The town currently funds its free outdoor concert series solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total concerts (C), of the form U = 3 x log(X) + 2 × log(C). The total number of concerts given, C, is the sum of the number paid for by each of the two persons: C = CB + CM. Bach and Mozart both have income of 80, and the price of both the private good and a concert is 1. Thus, they are limited to providing between 0 and 50 concerts. a. How many concerts are given if the government does not intervene?
b. Suppose the government is not happy with the private equilibrium and decides to provide 8 concerts in
addition to what Bach and Mozart may choose to provide on their own. It taxes Bach and Mozart equally to
pay for the new concerts. What is the new total number of concerts? How does your answer compare to
your answer to (a)? Have we achieved the social optimum? Why or why not?
Transcribed Image Text:b. Suppose the government is not happy with the private equilibrium and decides to provide 8 concerts in addition to what Bach and Mozart may choose to provide on their own. It taxes Bach and Mozart equally to pay for the new concerts. What is the new total number of concerts? How does your answer compare to your answer to (a)? Have we achieved the social optimum? Why or why not?
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