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

Exercise 8

Compare the optimal solutions obtained in Exercises 1 and 2 Specifically:
a. How much higher (lower) is the optimal selling price when the two firms form a cartel to maximize industry profits, compared to when they act independently
b. How much higher (lower) is total industry output
c. How much higher (lower) are total industry profits
Exercise 1
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).
Exercise 2
Consider Exercise 2 again. Assume that the firms form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits).
a. Determine the optimum output and selling price for each firm.
b. Determine Firm A, Firm B, and total industry profits at the optimal solution found in Part (a).
c. Show that the marginal costs of the two firms are equal at the optimal solution found in Part (a).