Question

The market demand for coins is Q=800-3P. Assume there is a dominant firm and a set of fringe firms. The dominant firm’s total costs are TC=80Qd and the fringe supply is

Qf= -200 + 2P.

1. Find the dominant firm’s residual demand curve.

2.Find the dominant firm’s profit-maximizing output and price.

3.Find dominant firm profits.

4.Find fringe firm output and profits.

Answer 1

The market demand for coins is Q=800-3P. Assume there is a dominant firm and a set of fringe firms. The dominant firm’s total costs are TC=80Qd which implies that the marginal cost of dominant firm is 80. And the fringe supply is Qf= -200 + 2P.

Residual demand RD = Q - Qf = 800 - 3P - (-200 + 2P)

RD = 1000 - 5P

Inverse residual demand is 5P = 1000 - Q or P = 1000/5 - Q/5 or P = 200 - 0.2Q

MR = 200 - 0.4Q

MC = 80

Use MR = MC

200 - 0.4Q = 80

Q (dominant firm) = 120/0.4 = 300 units

Price = 200 - 0.2*300 = $140 per unit

Profits = TR - TC = 140*300 - 80*300 = $18000

Fringe supply is Q = 2*140 - 200 = 80 units. Profit = 0 because fringe has P = MC