Question One (1) Suppose there are 2 firms in the Cournot duopoly model. The market demand function for the two firms is 1 + 2 = 100 0.5. Where, 1 is the output produced by firm 1 and 2 is the output produced by firm 2. These two firms are equal and face the following total costs: 1 = 201, 2 = 202. Firms choose their quantities simultaneously. i. Derive firm 1 and firm 2's best response functions [3 Marks] ii. Find the Nash equilibrium strategy for each firm [3 Marks] iii. Find the payoff for each firm at the Nash equilibrium [2 Marks] iv. Assume that the firms form a cartel to maximize their payoff. Find the Nash equilibrium strategy for each firm. [3 Marks] v. What is the problem with the arrangement under (iv)? [2 marks] vi. Comparing your answer in (ii) to that for (v), what conclusion can you make regarding how the firms should behave and why? [2 Marks] vii. If firm 1 must decide its output first and subsequently firm two decides on its output after observing firm 1's output. What will be the new Nash equilibrium? [3 Marks] viii. Under what condition(s) will this game be equivalent to the prisoners' Dilemma? [2 Marks]