Two firms compete in a market by selling imperfect substitutes. The demand equations are given by the following equations:
Q1 = 50 - p1 + p2
Q2 = 50 - p2 + p1
For now, assume that each firm has a marginal cost and average cost of 0.
a. From the equations, how can you tell these goods are substitutes? How can you tell they are imperfect substitutes?
b. Suppose the firms compete by simultaneously choosing price. Find the best response function of each firm as a function of the other firm's price.
c. Compute the equilibrium price and quantity for each firm.
d. Suppose firm 1 (and only firm 1 ) had a marginal and average cost of $10. How would the equilibrium change? How does this compare to the Bertrand result when the firms sell perfect substitutes?
a. The price of the other good increases the firm's own demand.
b. pi = (pj +50)/2
c. p = 50 = Q
d. It would shift out that firm's BR function, but it would still be able to compete.
Demand curves are downward sloping—not horizontal. The firm with the higher marginal cost is not forced out of the market necessarily.
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