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Exercise 2. Firm 1 and firm 2 are in a duopoly market. They are faced with an inverse demand of P(Q1, Q2) = 4 -2(Q1 + Q2) and total costs of TC(Q.) = 2Q? for i = 1, 2. Note that the marginal cost is not constant! (a) Derive the Cournot equilibrium quantities and profits. (b) Derive the Stackelberg equilibrium in which firm 1 moves first. Compare with the Cournot equilibrium. (c) Derive the Cartel solution. Compare with Stackelberg and Cournot