Question

2. There is a monopolistic incumbent in a market. Its cost function is C(q) =49 + 2q, and the market demand function is D(P) = 100 − P. There is a potential entrant who has the same cost function as the incumbent. Assume the Bain-Sylos postulate. Let the I incumbent firm’s output be denoted by q .

a. Derive the residual demand function for the potential entrant. I

b. Given that the incumbent firm is currently producing q , if a potential entrant were to enter, how much would it produce?

c. Find the limit price. Hint: Find the output for the incumbent that would make the potential entrant’s profit would be zero when the potential entrant produces according to the answer in part b. Alternatively, find the output for the incumbent such that the slope of the entrant’s average cost curve equals the slope of the potential entrant’s residual demand curve.

d. Instead of the assuming the Bain-Sylos postulate, assume that active firms expect to achieve a Cournot solution. Does entry depend on the preentry output by the incumbent qI? Explain.

e. Making the assumption in part d, will there be entry?

Answer 1

e.

Considering the assumption where the entrant expects to achieve a Cournot solution once enter the market, it is possible for the entrant to achieve positive profit even with limit-pricing. Because the entry will make each firm to make its decision with mutual interdependence and competition and the same cost of both the firm makes it possible to have a Cournot solution.