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Question 1 Consider the wage setting relation to be W = P F(u,z) (for the case when P=P) and the price setting relation to be W/P = 1/(l+ m). a) Graph the equilibrium unemployment level. 12) Corporations decide to increase the mark up from m to m'. Graph the new wage setting relation and describe what will happen to the unemployment level. c) If F(u,z) = 15 2n and m = 0.5, what is the value of the unemployment level. d) What would happen if the unemployment benets indicator decreases from 15 to 10. Graph and explain. Consider the market for used cars. The overall population of used cars is a fraction p plums and a fraction 1 - p lemons. Used car sellers value plums at $2,000 and lemons at $1,000. Used car buyers value plums at $2,400 and lemons at $1,200. There is asymmetric information. The seller of a car knows the type of the car and the potential buyer does not. Market equilibrium is defined as a Nash equilibrium. 1. Suppose p = 0.5. What is the market equilibrium price. What kinds of cars are traded in the equilibrium? (Nash equilibrium) 2. Suppose p = 0.8. What are the possible market equilibria (Nash equilibria)? What kinds of cars are traded in the equilibria? (hint: it is on purpose that the question uses the plural for possible equilibria).Question 2 Consider the wage setting relation to be W = P(1-autz) and the price setting relation to be P = (1+m)W, such that P = P (1 + m)(1 - au + z). The inflation growth rate is nutt1 = (Put-P.)/Pt. a) Show how using both equations and rearranging, inflation can be expressed as: n=n'+(m+z)-au b) If expectations are anchored such that = II, graph the Phillips Curve. The Fed did not control inflation and expectations de-anchored, such that: at=(1-0)n+0ntt-1+(m+z)-out c) What would happen if 0=2? d) What would happen if 0=0? e) What is the natural rate of unemployment and how can it be calculated using the Phillips Curve equation =n'+(m+z)-au?2. Consider a closed economy in which the central bank follows an interest rate rule. The [S relation is given by Y = C(YT) +I[Y,r) +G, where r is the real interest rate. The central bank sets the nominal interest rate according to =i*+a(7re7r*)+b[YYn), (l) where We is expected ination, if\" is the ination target, and Y. is the natural level of output, a. > 1, and b > U. The symbol 2"\" is the target interest rate the central bank chooses when expected ination equals the target rate and output equals the natural level. The central bank will increase the nominal interest rate when expected ination rises above target, or when output rises above the natural level. Note that this is a modied Taylor rule from the one 8 shown in class. Real and nominal interest rates are related by the Fisher relation, r : i 1r . (a) Dene the variable 2!\" as r'\" = 2"\" 7r*. Use the denition of the real interest rate to express the interest rate rule as r=r*+(a \"(We W*)+5(Y_Y) (b) Graph the IS relation in a diagram, with r on the vertical axis and Y on the horizontal axis. In the same diagram, graph the interest rate rule you derived in part (a) for given values of ire", 7T" and Y\". Call the interest rate rule the MP relation. (c) Using the diagram you drew in part (b), show that an increase in government spending leads to an increase in output and the real interest rate in the short-run. ((1) Now consider a change in the monetary policy rule. Suppose the central bank reduces its target ination rate, 1v". How does the fall in av\" affect the MP relation? What happens to output and the real interest rate in the short-run\"?I