There are 9 firms in an industry. The demand curve is given by Q = 55 - p.

a. Assume each firm has cost function C(qi) = 5qi. (That is, MCi = 5, for all i = 1...9). Find each firm's output, total industry output Q, the price, each firm's profits and the Herfindahl index.

b. Assume instead each firm i has cost function C(qi) = iqi, i = 1..9 (That is, MC1 = 1, MC2 = 2, MC3 = 3,..., MC9 = 9.) Find the total industry output and the industry price.

c. Is the Herfindahl index higher in part a. or part b.? Is welfare higher in part a. or part b.? You can infer it from your answer- use your answers for Q and P to infer which outcome is more efficient. Ask yourself what the asymmetry in costs reveals about the Herfindahl?

d. Let C(qi) = iqi as in part b. but assume that demand has fallen to Q = 10 - P. Find total industry output and industry price. Hint: sum up the first order conditions. This is tricky -- look carefully at your answer...are you violating any implicit constraints? If you are (and you probably are), impose the constraints and solve again.