Consider an upstream monopolist A which sells woolWto a downstream monopolist B which produces Texas A&M University hatsH.Suppose that the demand for Texas A&M hats is represented by the inverse demand curve P(H) = 200 H.Monopolist B produces tables according to the following production technology H = 2W (i.e 1 unit of wool yields two Texas A&M hat). Suppose that both firms are monopolists in their respective markets. Further-more, monopolist A harvests wool with the following cost structure C(W) = W²while monopolist B manufacturers Texas A&M hats with the following cost structure C(H) = 5H.

1. (10 points) Find the price of wool P_W, the price of Texas A&M hats P_H, the consumer surplus and the profits for both firms.

2. (10 points) Suppose both firms vertically integrate.Find the price of Texas A&M hats P_Hand discuss the efficiency gains associated with the integration. Why would there (or would there not) be efficiency gains?

3.BONUS(5 points): Consider the following event when the firms are not integrated: Suppose that there is a drought that kills much of the wool crop . What do you expect to happen to the price of hats? Explain why the price of hats changes (or doesn't change).