1. [20p] A monopoly manufacturer of a good sells to a monopoly retailer. The consumers' demand for the good is q = 120-2P, where q is quantity sold and p is the final price. The retailer has zero cost and the manufacturer's cost function is C(q) = q/2. The timing is as follows: first the manufacturer chooses a tariff, and then the retailer chooses the final price. a) What is the aggregate profit under vertical integration? [2p] b) What are the manufacturer's and the retailer's profits under the optimal linear tariff, T(q) = pq? What is the joint profit? [5p] c) Suppose the manufacturer can impose a resale price maintenance agreement on retailer, fixing price at level p*. What p* and p, the manufacturer will impose in order to maximise his profit? What are the equilibrium profits? [5p] d) What are the equilibrium profits under the optimal two-part tariff, T(q) = A + pq? [5p] e) Compare manufacturer's profits and total surpluses in all points and provide intuition for the results. [3p]