Note: For 2c you'relooking for H*, p*H, *, and CS

2. Consider an upstream monopolist A that sells wool W to a downstream monopolist B, which in turn produces hats H. Suppose that the demand for hats is represented by the inverse demand curve ph(H) = 100 H. Monopolist A produces wool with the following cost structure C(W) = W2 + {w. Monopolist B produces hats according to the production technology H = jw (i.e. 4 units of wool yields 1 hat), and manufactures hats with the following cost structure C(H) = 10H (notice that monopolist B additionally faces a cost related to the purchase of wood). (a) Find the optimal quantities W and H, the price of wool pw, and the price of hats ph: (15 points) W* = H* PW PM (b) Derive the profits for both firms and the consumer surplus. (8 points) 5 (C) Suppose the two firms merge and vertically integrate. Find the optimal quantity of hats H, price of hats ph, the integrated monopolist's profits, and the consumer surplus. You might need to use a calculator for this part. (12 points) 2. Consider an upstream monopolist A that sells wool W to a downstream monopolist B, which in turn produces hats H. Suppose that the demand for hats is represented by the inverse demand curve ph(H) = 100 H. Monopolist A produces wool with the following cost structure C(W) = W2 + {w. Monopolist B produces hats according to the production technology H = jw (i.e. 4 units of wool yields 1 hat), and manufactures hats with the following cost structure C(H) = 10H (notice that monopolist B additionally faces a cost related to the purchase of wood). (a) Find the optimal quantities W and H, the price of wool pw, and the price of hats ph: (15 points) W* = H* PW PM (b) Derive the profits for both firms and the consumer surplus. (8 points) 5 (C) Suppose the two firms merge and vertically integrate. Find the optimal quantity of hats H, price of hats ph, the integrated monopolist's profits, and the consumer surplus. You might need to use a calculator for this part. (12 points)