3. Dominant Firm. The average avoidable cost for a fringe firm is AAC(q) =

_q. The marginal cost function for a fringe firm is MC = 2_q. There are

N fringe firms. The marginal cost of the dominant firm is 0 but it has a

capacity constraint equal to k. The demand function is Q = A - P.

(a) What is the supply function of the fringe? What is p0?

(b) What is the residual demand function for the dominant firm? [HINT:

Write it as P = (A QD)=X where X = 1 + N=(2_).]

(c) What is the profit-maximizing price of the dominant firm? [HINT: Set

marginal revenue equal to marginal cost.]

(d) Find market output, market price, dominant firm output, and fringe

output when A = 40, _ = 1, k = 30 and N = 6.

(e) Find market output, market price, dominant firm output, and fringe

output when A = 40, _ = 1, k = 30 and N = 18.

(f) Explain why the equilibrium price in (d) is bigger than in (c). [HINT:

Explain by demonstrating the effect on price by reducing the output of

the dominant firm to 25 in both cases.]