Consider two firms, 1 and 2, who produce in a oligopoly market. Firm 1 chooses its quantity of output q1 and firm 2 chooses q2. Given these outputs, the market price is given by p = 100 (q1 + q2). The marginal cost of production is 10 for each firm. (a) Write the profit functions for firms 1 and 2. Find the optimal quantity of output q2 for firm 2, as a function of q1. (b) Define the notion of Cournot equilibrium for this situation (i.e., which conditions in terms of the choices q1 and q2 and the profit functions have to be satisfied). (c) Find the Cournot equilibrium outputs for firm 1 and firm 2 and the resulting profits for each firm. (d) Find the symmetric level of output (q1; q2) = (q; q) that would maximize the sum of firm 1 and firm 2s profits if they each produce q. How does this compare to your answer from part c, and why? In addition, explain why producing q does not constitute a best response for either firm. (e) Suppose now that the marginal costs for firm 1 are equal to zero, while marginal costs remain 10 for firm 2. Find the Cournot equilibrium outputs for firm 1 and firm 2 and the resulting profits for each firm.