Microeconomic Theory 11th Edition by Walter Nicholson,Christopher Snyder

Exercise 4

Suppose that firms 1 and 2 operate under conditions of constant average and marginal cost but that firm 1's marginal cost is c 1 = 10 and firm 2's is c 2 = 8. Market demand is Q = 500 - 20P.
a. Suppose firms practice Bertrand competition, that is, setting prices for their identical products simultaneously. Compute the Nash equilibrium prices. (To avoid technical problems in this question, assume that if firms charge equal prices, then the low-cost firm makes all the sales.)
b. Compute firm output, firm profit, and market output.
c. Is total welfare maximized in the Nash equilibrium? If not, suggest an outcome that would maximize total welfare, and compute the deadweight loss in the Nash equilibrium compared with your outcome.