ECOS3005 Problem set 4 1
Problem set 4
1. Suppose that a monopoly manufacturer (the “Upstream firm”) of a product relies on a monopoly
distributor (the “Downstream firm”) to sell the product. The demand for the final product is
given by Q = D(P) = 100?P. The upstream firm has a constant marginal cost of 20. The
downstream firm faces constant marginal costs of storage and distribution of 10. The firms
face no fixed costs. The two firms play a two stage game. First, the upstream firm chooses
a price for the wholesale product, PU . Then, the downstream firm chooses a price for the
final product, PD. The downstream firm must pay the upstream firm PU for every unit of the
product sold. Total sales to final consumers depend on the downstream price, Q= D(PD).
(a) Find the downstream monopolist’s reaction function as a function of the price of the
upstream monopolist, PD = RD(PU).
(Hint: Think of the monopoly problem where the monopolist has marginal cost of 10+
PU ).
(b) The upstream monopolist considers the reaction of the downstream monopolist when
setting its price.
i. Solve for the upstream monopolist’s price, PU .
ii. Use PU to solve for the price of the downstream firm, PD, and the sales of the final
product, Q.
iii. Find the profits of each firm.
(c) Suppose the upstream firm buys out the downstream firm.
i. Solve for the integrated monopolist’s optimal price. What are the sales of the final
product, Q?
ii. Find the profits of the integrated firm.
(d) Define total welfare to be the consumer surplus plus the total producer surplus (profits)
of all firms.
i. What is the change in total welfare that results from the integration of the two
firms?
ii. If it were costly to integrate (for example, due to legal fees), how much would
consumers be willing to compensate the firms to encourage them to integrate?