Question

Suppose a manufacturer (upstream monopolist labeled u) sells a product to a retailer (downstream monopolist labeled d). Assume the manufacturer’s marginal cost of production is c = 20, while the retailer’s marginal cost is simply the wholesale price w set by the manufacturer. (i.e. w is just a transfer price across sectors). Moreover, denote the quantity produced by upstream firm u by X and the quantity sold by the downstream retailer d to consumers by Q. Consumer’s demand for the good is p = 75−3Q and the market-clearing condition is X = Q. (Hint: Use backward Induction)

(a) Suppose that firms u and d are vertically separated. Set up and solve the downstream profit maximization problem, taking as given w.

(b) Set up and solve the upstream profit maximization problem, taking as given the best response function of the retailer and the Market Clearing condition. 6

(c) Report the equilibrium of this economy (X∗, Q∗, p∗, w∗).

(d) Compute the equilibrium profits (πu ∗ , πd ∗ ).

Answer 1