1.

Seven people live in Sejong city. 4 A type residents, 2 B type residents, and 1 C type resident. A's demand for bike paths, a public good, is given by Q = 12 - 2P. B's demand is Q = 18 - P, and C's is Q = 8 - P/3. The marginal cost of building a bike path is MC =49.

a. Write down an equation for the social marginal benefit of consumption of the private good. b. Show that the government can achieve the social optimum by setting the correct tax prices to each resident. What prices should it set?

2.

Sejong city has two residents: H and B. The town currently funds its fire department solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total firefighters (M) of the form U = 4 log(Xi) + 2 log(M), for i = H and B. The total provision of firefighters hired, M, is the sum of the number hired by each of the two persons:M = MH + MB. H and B both have income of $100, and the price of both the private good and a firefighter is $1. Thus, they are limited to providing between 0 and 100 firefighters.

a. Suppose the government is not happy with the private equilibrium and decides to provide 10 firefighters in addition to what H and B may choose to provide on their own. It taxes H and B equally to pay for the new firefighters. What is the new total number of firefighters?

b. What is the socially optimal number of firefighters? If your answer differs from a, why?