1. [14 points] We consider a Quantity-Setting Duopoly operating in a market with demand curve Q=12 -Pif0 12. Here Q is the quantity demanded and P is the market price. Firm I has marginal cost 4 (and no fixed cost); so that if its output is q1 and the market price is P, its profit is II1 = P q1-4 q1; Firm 2 has marginal cost 2 (and no fixed cost); so that if its output is q2 and the market price is P, its profit is I12 = P q2-2 q2. As usual, we assume firms want to maximize their own profits; and all aspects of the model are common knowledge. (a) First we consider the Cournot Model. Each firm must decide on its own output level, simultaneously and independently of one another. Thus we can model this situation as a game in strategic form and determine its Nash Equilibrium. Find the equilibrium outputs (q1, q2) of the two firms and their profits. Show your reasoning. (b) Next we consider the Stackelberg Model. In this model, firm 1 produces its output q1 first. Then firm 2 decides on q2 after it has observed the output of firm 1. We model this situation as a game in extensive form with perfect information, and solve it by Backward Induction. Find the outputs (q1, q2) of the two firms and their profits in this solution. Show your reasoning. (c) Which duopoly structure, (a) or (b), is better for consumers? (d) Which duopoly structure, (a) or (b), does Form 1 prefer? Which one does Firm 2 prefer