Question

consider market with demand function q = 200 - 2p. In this market there is a dominant firm and a competitive fringe of small firms. The competitive fringe takes the price of the dominant firm as given and offer an aggregate output S = p - 70; (p > 70), where p is the price quoted by the dominant firm. The residual demand is covered by the dominant firm. Determine the optimal solution for the dominant firm assuming that its marginal cost is constant and equal to (i) c = 70, (ii) c = 45, (iii) c = 20.

Answer 1

Residual demand RD = 200 - 2p - p + 70 or q = 270 - 3p. Inverse demand function is 3p = 270 - q or p = 90 - q/3. Marginal revenue MR = 90 - 2q/3

i) When c = 70

MR = MC

90 - 2q/3 = 70

20 = 2q/3

q(dominant firm) = 30 units

p(dominant firm) = 90 - 30/3 = $80

ii) c = 45

MR = MC

90 - 2q/3 = 45

45 = 2q/3

q(dominant firm) = 67.5 units

p(dominant firm) = 90 - 67.5/3 = $67.5

iii) c = 20

MR = MC

90 - 2q/3 = 20

70 = 2q/3

q(dominant firm) = 105 units

p(dominant firm) = 90 - 105/3 = $55