Consider an oligopoly market where the competitors compete through Cournot quantity setting competition. There are only two competitors in this market; Firm X and Firm Y. Each firm produces the same product, Widgets. The demand curve for the Widget industry is:

P = 100 - Q

where P is the price of Widgets and Q is the total quantity produced by Firm X and Firm Y. Both firms use the same production process and technologies which has a constant marginal cost (MC) of MC = $40. There are no fixed costs. The best response functions for each firm is the following,

Qx = 30 - Qy

Qy = 30 - Qx

Show that the equilibrium price is P = $60, with each firm producing 20 Widgets

(i.e., QX = QY = 20) and earning profits of x = y = $400.