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^1.

1) Derive the inverse residual demand function for a new firm in terms of q^1 and q^E?

2)Given that the incumbent firm is currently producing q^1, if a potential entrant was to enter, how much would it produce?

3) Find the limit price. Suppose instead of assuming Bain-Sylos,

4) we now assume active firms expect to achieve a Cournot solution. Does entry depend on q^1? Will there be entry?