1) Suppose that in a duopoly firms have constant marginal cost MC = 10 per unit. Firm 1 faces demand function q1 = 100 - 2p1 + p2, while firm 2 faces demand function q2 = 100 - 2p2 + p1. What is the Nash equilibrium of this game?
2) Suppose that in a duapoly the first compete in quantities, ala Cournot. What is the Nash equilibrium if the market demand function is Q=1000-1000P and each firm's marginal cost is $0.28 per unit?