Chapter 9

1. In Gelate, Pennsylvania, the market for compact discs has evolved as follows. There

are 2 firms that each use a marquee to post the price they charge for compact discs.

Each firm buys CDs from the same supplier at a cost of $5.00 per disc. The inverse

market demand in their area is given by P = 10 – 2Q, where Q is the total output

produced by the two firms.

a. Solve for the Bertrand equilibrium price and market output.

b. Would your answer differ if the products were not perfect substitutes? Explain.

2. The market for widgets consists of two firms that produce identical products. Competition in the market is such that each of the firms independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 is known to have a cost advantage over firm 1. A recent study found that the (inverse) market demand curve faced by the two firms is

P = 280 – 2(Q1 + Q₂)

and costs are

C₁ (Q₁) = 3Q₁

C₂ (Q₂) = 2Q₂.

a. Determine the marginal revenue for each firm.

b. Determine the reaction function for each firm.

c. How much output will each firm produce in equilibrium?

d. What are the equilibrium profits for each firm?