Exercise 1. Consider two duopolists who each have a constant marginal cost c = c = 1 and face inverse demand P = 2- Q, where Q = Q1 + Q2 is the total output of both firms. (a) Derive the Cournot equilibrium quantity for each firm, the resulting market price and the profits for each firm. (b) Derive the Stackelberg equilibrium quantities, the prices, and the profits for each firm supposing that firm 1 is the industry leader.. (c) Suppose that firm 2 figures out a way to lower its marginal cost to c = 0 while firm 1 still has a marginal cost equal to 1: c = 1. How does this affect the Cournot equilibrium quantities, prices, and profits? (d) How does this affect the Stackelberg equilibrium (with firm 1 still as the leader) quan- tities, prices, and profits?