B. Consider in this part of the exercise only crowding on the cost side, with the cost of providing some discrete public good given by the function c1N2 5 FC 1 aN b

with a . 0 and b $ 0. Assume throughout that there is no crowding in consumption of the public good.

a. Derive the marginal cost of admitting additional customers. In order for there to be crowding in production, how large must b be?

b. Find the group membership at the lowest point of the average cost function. How does this relate to optimal group size when group size is sufficiently small for multiple providers to be in the market?

c. What is the relationship between

a, b, and FC for purely private goods?

d. Suppose that the good is a purely public good. What value of a could make this so? If a . 0, what value of b might make this so?

e. How does a affect optimal group size? What about FC and b? Interpret your answer.