[Vertical integration may reduce welfare] Consider a market with two types of consumers. Those with a high willingness to pay, h, do not care about extra e¤ort or services. Those with a low willingness to pay care about extra e¤ort or services and have a valuation l + e for the good, with h > l. Normalise the population of consumers to 1 and assume that the shares of high and low types are respectively and 1 . Assume that l c h c . On the market, one upstream rm sells to two retailers who then sell to the consumers. The upstream rm has a constant marginal cost of production equal to c. The two retailers compete by setting prices simultaneously. Assume that price discrimination is not possible, and the two retailers use linear prices (set one price each). Assume e = e1 + e2 and Ci(qi;ei) = wqi + e2 i 2 , i = 1;2. Assume also > 2 h l (which guarantees that the low types will never have the highest willingness to pay in the market).
(a) [Separation] In the wholesale stage, the upstream rm sets a wholesale price w. In the retail stage, the two retailers rst choose (e1;e2) simultaneously and then choose (p1;p2) simultaneously. Solve for the equilibrium w, e1, e2, p1, p2, and total surplus.