a. Find the Bertrand equilibrium prices and quantities for these two competitors — Consider market brie Francois Babette cheeses are differentiated with demand Francois' cheese

Consider two Bertrand competitors in the market for brie, Francois and Babette. The cheeses of Francois and Babette are differentiated, with the demand for Francois' cheese given by qF = 30 - pF + pB, where qF is the quantity Francois sells, pF is the price Francois charges, and pB is the price charged by Babette. The demand for Babette's cheese is similarly given as qB = 30 - pB + pF.

a. Find the Bertrand equilibrium prices and quantities for these two competitors.

b. Now consider a situation in which Francois sets his price first, and Babette responds. Follow procedures similar to those you used for Stackelberg quantity competition to solve for Francois' profit-maximizing price, quantity, and profit.

c. Solve for Babette's profit-maximizing price, quantity, and profit.

d. Was Francois' attempt to seize the first-mover advantage worthwhile?

SOLUTION

a. Francois's marginal revenue is

MRF = 30 - 2pF + pB

Babette's marginal revenue is

MRB = 30 - 2pB + pF

Assuming that the marginal cost is zero, we can find the firm's reaction curve:

MRF = 30 - 2pF + pB = 0 = MC

pF = 15 + 0.5pB

pB = 15 + 0.5pF

The equilibrium prices are

The equilibrium quantities are

qF = 30 - pF + pB = 30