1. In an industry with demand P = 160 - Q, there are two companies with marginal production costs $ 0 each. Suppose that if a company chooses to compete, it produces 53 units, while if he chooses to collude he will produce 40 units. Show on a matrix what is the Nash equilibrium in this simultaneous game, where the strategies available for each company are to compete or collude. Suppose each company seeks to maximize your profits Since then, consider the interdependence between them. 2. What will be the Nash equilibrium when companies compete by choosing the prices they must charge, the product they sell is homogeneous, there are no relevant capacity restrictions and a company has a higher marginal cost than the other (let's say that the marginal cost of firm 1 is higher than the company 2)? 3. Suppose two firms compete by choosing the price of their differentiated products. Assume that the marginal production costs are zero and the demands for products 1 and 2 are: Ql = 20 - 2P1 + P2 Q2 = 20 - 2P2 + P1 0) Calculate equilibrium prices and profits from each firm assuming that firm 1 chooses its price first and, once this is observed, firm 2 chooses its price. b) Compare the results obtained in a) with those that would have been obtained if the two companies had selected your prices simultaneously. c) If you could choose, what would you prefer between: i. Is the game simultaneous? ii. Is the game sequential and you move first? iii. Is the game sequential and you move second? d) How much is the "move first" advantage worth here, compared to moving second? Based on your intuition, from an explanation about the result of moving first in this case. 4. Suppose a market where there is a duopoly with identical producers, each one with zero cost of production, and that they face a total demand for the product that is represented by p = 120 - q. Suppose that the "do not cooperate" strategy implies that the company produces Cournot output and the "cooperate" strategy involves producing half of the collusion output (since there are two companies, each one produces half). Fill in the following matrix and find the balance from it. Company 2 Cooperate Do not cooperate Company 1 Cooperate Not cooperate