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Problem 1. Dynamic Games (48 points) Two companies produce the same good. In the first period, firm1 sells its product as a monopolist on the West Coast. In the second period, firm 1 competes with firm 2 on the East Coast as a Cournot duopolist. There is no discounting between the two periods. Firm 1 produces quantity xW c/ at the West at cost cxW . On the East Coast, and that's what makes this problem interesting, firm 1 produces quantity xE at cost (c xW ) xE, where 0 <

Consider first the case of simultaneous choice. Assume that firm 2 does not observe xW before making its production decision. This means that, although formally firm 1 chooses output xW first, that you should analyze the game as a simultaneous game between firm 1 and firm 2. Use Nash Equilibrium. Write down the profit function that firm 1 maximizes (careful here) and the profit function that firm 2 maximizes (5 points) 2. Write down the first order conditions of firm 1 with respect to xW and xE, and the first order condition of firm 2 with respect to x2. Solve for x W , x E, and x 2. (4 points)

3. Check the second order conditions for firm 1 and for firm 2. (3 points) 4. What is the comparative statics of x W and x E with respect to ? Does it make sense? How about the comparative statics of x 2 with respect to ? (4 points) 5. Compute the profits of firm 2 in equilibrium. How do they vary as varies? (compute the comparative statics) Why are firm 2's profits affected by even though the parameter does not directly affect the costs of firm 2? (5 points) 6. Now consider the case of sequential choice. Assume that firm 2 observes xW before making its production decision x2. This means that you should analyze the game as a dynamic game between firm 1 and firm 2, and use the concept of subgame-perfect equilibrium. Remember, we start from the last period. Write down the profit functions that firm 1 and firm 2 maximize on the East Coast (4 points) 7. Write down the first order conditions of firm 1 with respect to xE, and the first order condition of firm 2 with respect to x2. Solve for x E and x 2 as a function of x W (4 points) 8. Compute the comparative statics of x E and x 2 with respect to x W . Do these results make sense? (3 points) 9. Compute the profits of firm 1 on the East Coast as a function of x W . (2 points) 10. Using the answer to point 9, write down the maximization problem of firm 1 in the first period, that it, when it decides the production on the West Coast. (3 points) 11. Write down the first order conditions of firm 1 with respect to xW . Solve for x W and then, using the solution for x W , find the solution for x E and x 2. (5 points)

12. Compare the solutions for x W under simultaneous and under sequential choice. What can you conclude? Under which conditions the firm does more preemption, that is, produces more on the West Coast in order to reduce the production in equilibrium of firm 2? (6 points)

The purpose of this recitation is to familiarize students with a variety of integer programming modeling techniques as described in the IP Formulation Guide and in the powerpoint tutorial on IP formulations. We start with an integer program IP1 defined as follows: max 21x1 + 32x2 + 40x3 + 49x4 + 57x5 + +71x6 + 82x7 + 91x8 + 100x9 + 109x10 s.t.: 2x1 + 3x2 + 4x3 + 5x4 + 6x5 + +7x6 + 8x7 + 9x8 + 10x9 + 11x10 900 i = 1, . . . , 3 xi {0, 1} i = 4, . . . , 10 0 xi 100. (IP1) For each of the parts below, you are to add constraint(s) and possibly variables to ensure that the logical condition is satisfied by the integer program. Each part is independent; that is, no part depends on the parts preceding it. You do not need to repeat the integer programming objective or constraints given above. You may use the big M method for formulating constraint when it is appropriate. (a) (4 points) Write a single linear constraint that is equivalent to the statement "If x1 = 1, then x2 = 0."

The 'Law of Comparative Advantage' suggests that specialisation and trade increases world output. (i) Explain the meaning of the underlined term in the context of international trade. (ii) Identify the main assumptions underlying this law. (iii) Identify two sources of comparative advantage for the Irish economy. (30 marks) (b) Ireland is a small open economy which relies very heavily on international trade. (i) Discuss the importance of international trade to the Irish economy. (ii) Are there any economic justifications for a government intervening in order to restrict international trade? Outline reasons for your answer. (30 marks) (c) Write a brief note on David Ricardo's contributions to economic thought. (15 marks) [75 marks] 8. (a) Discuss the factors that influence the size of the Irish labour force. (20 marks) (b) 'According to the Quarterly National Household Survey (QNHS) the rate of unemployment was 7.7% in December 2008'. (i) Name a source, other than QNHS, for unemployment statistics in Ireland. (ii) State, with reasons, which of the measurements of unemployment used by each of these sources gives the most accurate estimate of Irish unemployment. (15 marks) (c) (i) Outline the major causes of the recent increases in unemployment in the Irish economy. (ii) Discuss economic policies which the Irish government might pursue in order to reduce the level of unemployment. (40 marks) [75 marks] Remember to return this question paper with the answer book(s) used to answer the questions in