1- [14 points] Consider a three-firm oligopoly in which the market demand for the homogeneous good is given by q = 24 – p, and costs are zero. Suppose firm 1 and 2 simultaneously pick their output, and then firm 3, observing these choices, picks its output (i.e. two “leaders”, one “follower”). Find the subgame perfect equilibrium quantities produced by these forms.   2- [20 points] Firms A and B can choose to adopt a new technology (N) or to adhere to their old technology (O). The table below exhibits the profit made by each firm under different technology choices. Firm B NEW OLD Firm A NEW 200, 0 0, 200 OLD 50, 100 100, 50   [4 points] Find the Nash equilibrium(s) of the simultaneous game if they exist? [4 points] Draw the tree of a two-stage extensive-form game in which firm A chooses its technology in stage I, and firm B choses its technology in stage II (after observing the choice made by firm A). Make sure you indicate firm’s profits at the termination points on the tree. [8 points] Write down the normal form of the above sequential game and find the Nash Equilibrium(s), if they exist? [ [4 points] Solve for the subgame perfect equilibrium of the sequential game? Provide an explanation justifying our answer.     3- [16 points] consider the following variant to the Hotelling’s model. Two stores are located at points zero (store 0) and one (store 1) along a linear street of length one. Due to heavy winds, it costs more to travel towards store 1. Suppose the marginal travelling cost is 1 towards store 0, but is 3 towards store 1 per unit of distance. Let the consumer’s valuation of the commodity be 10. Each consumer buys only 1 unit. Let P0 and P1 be the prices of the commodity at store 0 and store 1, respectively. [4 points] Derive the utility of consumer located at point 0 < x < 1 if she buys from firm 0. Derive the utility if she buys from firm 1.               [6 points] Suppose there are 100 consumers who are uniformly located on the line. Derive the demand for store 0, which is the number of people who want to buy at store 0. Derive the demand for store 1 as well. Show your work:             [6 points] Assume no production cost. Suppose the firms compete over prices. Solve for the Nash-Bertrand equilibrium price and quantity for each firm.     4- [30 points] Suppose that you are the managing director of a pharmaceutical company that sells a unique patented drug to hospitals and drug stores. You are free to charge different per-unit prices at these two markets. Let p be the price per unit of drug and q be the quantity demanded. The hospitals demand curve is described by p = 12 – q and the drug stores demand curve is given by p = 8− q. The marginal cost of producing the drug is constant and equal to c = 2 per unit. [10 points] What is the price that you will charge to hospitals (H)? To drug stores (D)?   [10 points] If you were to charge a uniform price to all the buyers, what would it be? [10 points] [10 points] If the Antitrust Division cares about the sum of your company’s profits plus the total consumer surplus of all the buyers, do you think it should ban price discrimination? (Computation required for full credit. Hint: compute the consumer surplus separately for drug stores and hospitals, even if they buy at the same price, and then add them up.)