Its macro economics solve the following

1. Question 1 (20 points) Suppose I prefer $20 for sure to a lottery that pays $100 with probability 1/4 and $0 with probability 3/4. Also suppose that I prefer lottery A to lottery B, where lottery A pays $100 with probability 1/8, $0 with probability 7/8, and lottery B pays $20 with probability 1/2, $0 with probability 1/2. Is there a vN-M utility function that is consistent with my preferences? If so, describe such a utility function. If not, explain why. 2. Question 2 (40 points) You have initial wealth Wo dollars. With probability p you will suffer a loss that will reduce your wealth by L 0 and b > 0. (a) First suppose that there are n firms in the industry who have paid the fixed cost. Suppose that they compete as Cournot quantity setting oligopolists. How must will each firm produce? What will be the market price and the total quantity produced? (b) Now suppose that firms will exit the industry if their profit (net of fixed cost) is negative and that identical firms may enter if there are profits to be made. How many firms will enter? [Remember that your answer must be an integer]. (c) What happen to the number of firms in the industry and prices as f becomes small? Give some economic intuition for your answer. 3. Question 3 (30 points) Two firms produce an identical good. The inverse demand curve for the good is P = 101 - X, where X is the total quantity produced by the two firms. Firm 1 has a constant marginal cost 1 of producing the good. Firm 2 has a constant marginal cost 1 + c of producing the good, with 0