1. Suppose there are two firms with constant marginal cost MC = 3 and the market demand is P = 63 ? 5Q.

(a) Calculate the market price and profits for each firm in each of the following settings:

• Cartel

• Cournot duopoly

• Bertrand duopoly (firms can set any price)

(b) Using part a), construct a 3×3 payoff matrix where the firms are choosing prices. The actions available to each of two players are to charge the price from the three settings above. If there is a tie, they split the demand. If one has a lower price, the firm with the lower price gets all of the demand.

(c) What are the Nash equilibria of this 3 × 3 game?