The town of Cinecity has two residents: Spielberg and Lucas. The town currently funds its free outdoor movie projections solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total movie projections (M), of the form:
U = 3*ln(x)+ln(M).
The total number of movie projections, M, is the sum of the number paid for by each of the two persons: M = MS + ML. Spielberg and Lucas both have income of 70, and the price of both the private good and a movie projection is 1. They are limited, for the purposes of this problem, to providing between 0 and 70 projections.
a) How many movie projections are given if the government does not intervene (each individual take the number of movie projections given by the other as given)? How many are paid for by Spielberg? By Lucas?
b) What is the socially optimal number of movie projections ? If your answer differs from (a), why?
c) Suppose the government is not happy with the private equilibrium and decides to provide 10 movie projections (at a production cost of 1 per projection) in addition to what Spielberg and Lucas may choose to provide on their own. It taxes Spielberg and Lucas equally to pay for the new movie projections. What is the new total number of movie projections? How does your answer compare to (a)? Have we achieved the social optimum? Why or why not?
d) Suppose that the government is still not happy and it decides to provide 30 movie projections instead. It taxes Spielberg 15 to pay for them and taxes Lucas 15. What is the new total number of movie projections? How many are provided by Spielberg? by Lucas? How does this compare to the level of provision in (c)? Why?
e) Suppose that, starting from the situation in part (a), an anonymous benefactor pays for 10 movie projections. What is the new total number of movie projections? How many are provided by Spielberg? by Lucas? Is this the same level of provision as in (c)? Why or why not?