1. (Ch. 7, Q3) The natural rate of unemployment Suppose that the markup of goods prices over marginal cost is 5%, and that the wage setting equation is: W=P(1-u) where u is the unemployment rate. a. What is the real wage, as determined by the price-setting equation? b. What is the natural rate of unemployment? c. Suppose the markup of prices over costs increases to 10%. What happens to the natural rate of unemployment? Explain the logic behind your answer. d. Provide one graph illustrating your answers to (a), (b), and (c). 2. (Ch. 8, Q5) Mutations of the Phillips Curve Suppose that the Phillips Curve is given by m, =nf +01u, and expected inflation is given by Tl'f = (1 Q)' + 9Trt_1 and suppose that 6 is initially equal to zero and 7 is given and equal to 2%. Suppose that the rate of unemployment is initially equal to the natural rate. In year , the authorities decide to bring the unemployment rate down to 3% and hold it there forever. a. Determine the rate of inflation in periods t+1, t+2, t+3, t+4, and t+35. b. Do you believe the answer given in part (a)? Why or why not? (Hint: Think about how people are more likely to form expectations of inflation.) Now suppose that in year +6, 8 increases from 0 to 1. Suppose that the government is still determined to keep u at 3% forever. c. Why might 8 increase in this way? d. What will the inflation rate be in years 7+6, t+7, and t+8? a - e. What happens to inflation when 6=1 and unemployment is kept below the natural rate of unemployment? f. What happens to inflation when 8=1 and unemployment is kept at the natural rate? 3. (Ch. 9, Q2) The medium-run equilibrium is characterized by four conditions: Output is equal to potential output, = a. The unemployment rate is equal to the natural rate, u=un. The real policy interest rate is equal to the natural rate of interest, r, where aggregate demand equals Y. The expected rate of inflation m is equal to the actual rate of inflation . a. Ifthe level of expected inflation is formed so that equals 1(-1), characterize the behavior of inflation in the medium-run equilibrium. b. Ifthe level of expected inflation is 77, what is the level of actual inflation in the medium run equilibrium? c. Write the IS relation as = C(Y-T)+1(Y,r+x)+G. Suppose that r is 2%. If x increases from 3% to 5%, how must the central bank change the policy rate to maintain the existing medium-run equilibrium? d. Suppose G increases. How must the central bank change the policy rate to maintain the existing medium-run equilibrium? Explain in words. e. Suppose T decreases. How must the central bank change the policy rate to maintain the existing medium-run equilibrium? Explain in words. f. Discuss: In the medium-run, a fiscal expansion leads to an increase in the natural rate of interest