6. Suppose that there are two firms in a supply chain: a manufacturer who sells to a retailer. The timing is as follows: 1. Manufacturer has a constant marginal cost c = 1 and sets input price w to maximize profit. 2. Retailer buys input from manufacturer for price w. Retailer sets price p to maximize profit with demand D(p) 8 p. (a) (20 points) What are the joint profits of the firms (i.e. the sum of the profit of the manufacturer and the retailer) under vertical separation? (b) (10 points) Explain in one to two sentences why the joint profits will be higher under vertical integration than under vertical separation