Question 1. [50 points] Consider a duopoly operating in a market with the inverse market demand function given by P = 300 3Q, where P is the price and Q is the total quantity of the good per year demanded at price P. For parts (a) (c) assume that both firms have the same constant marginal cost, MC = 100, and zero fixed cost. (a) What is Firm 1's profit-maximising quantity if Firm 2 produces 50 units per year? [5 points] (b) Assuming that the firms compete in quantities, derive the best-response function for each firm. What is the Cournot equilibrium quantity for each firm? What is the market price? Illustrate your answer on an appropriate diagram. [15 points] (c) Compare the Cournot equilibrium price and quantity with the perfectly competitive equilibrium (i.e. when the two firms are price-takers) and the collusive outcome (i.e. when the two firms act as a monopoly). Can the collusion be sustained? Why or why not? [15 points] Now assume that Firm 1 has a marginal cost of 100 and Firm 2 has a marginal cost of 90. (d) What will the equilibrium price and quantity be in this market if the firms compete in prices? Illustrate your answer on a separate diagram. [15 points]