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Question 1
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 · ln(X)
+ 2 · ln(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 60, and the price of both the private
good and a concert is 1. Thus, they are limited to providing between 0 and 60 concerts
1. How many concerts are given if the government does not intervene?
2. 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?
3. Suppose that instead an anonymous out-of-town benefactor pays for 8 concerts. What is the
new total number of concerts? Is this the same level of provision as in (b)? Why or why not?
Question 2
Firms A and B each produce 80 units of pollution. The federal government wants to reduce
pollution levels. The marginal costs associated with pollution reduction are MCA = 50 + 3QA for firm
A and MCB = 20 + 6QB for firm B, where QA and QB are the quantities of pollution reduced by each
firm. Society’s marginal benefit from pollution reduction is given by MB = 620 − 3QT, where QT = QA
+ QB is the total reduction in pollution.
1. What is the socially optimal level of each firm’s pollution reduction? (Hint: At the optimal
amount of pollution reduction, MCA = MCB = MB.)
2. How much total pollution is there in the social optimum?
3. Can the social optimum be achieved using a tax on pollution? If so, what is the amount of the
tax?
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