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Ace Washtub Company is currently the sole producer of washtubs. Its cost function is C(q)=49+2q, and...

Ace Washtub Company is currently the sole producer of washtubs. Its cost function is C(q)=49+2q, and the market demand function is D(P)=100-P. There is a large pool of potential entrants, each of which has the same cost function as Ace. Assume the Bain-Sylos postulate. Let the incumbent firm’s output be denoted q^I.

a. Derive the inverse residual demand function for a new firm in terms of q^I and q^E?

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

c. Find the limit price. Hint: Find the output for Ace such that the slope of a new firm’s average cost curve equals the slope of a new firm’s residual demand curve.

d. Suppose instead of assuming Bain-Sylos, we now assume active firms expect to achieve a Cournot solution. Does entry depend on q^I? Will there be entry?

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