Managerial Economics 13th Edition by James McGuigan,Charles Moyer,Frederick Harris

Exercise 4

Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function:
p = 200 Q A Q B
where Q A and Q B are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are
TCA = 1,500 + 55Q A +Q 2 A
TCB = 1,200 + 20Q B + 2Q 2 B
Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm's output will not change).
a. Determine the long-run equilibrium output and selling price for each firm.
b. Determine Firm A, Firm B, and total industry profits at the equilibrium solution found in Part (a).