The soft drink industry is a duopoly with differentiated products. Two firms, Coca-cola and Pepsi, compete through Cournot quantity-setting competition. Denote the quantity that Coca-cola and Pepsi produce by Q1 and Q2, respectively. The demand curve for the industry is P = 10 - Q1 - 2Q2. Each firm has the marginal cost is $1 per unit and both firms have no fixed cost.
a. Construct the profit functions for Coke and Pepsi, which should be a function of Q1 and Q2.
b. What is the reaction function for each firm?
c. What is the Cournot equilibrium quantity and profits for each firm? What is the resulting price?