I really need a help solving this problem. Suppose that an economy has the follo

Question

I really need a help solving this problem.

Suppose that an economy has the following Phillips curve: ? = ?-1 - 0.6 (u - 0.04) What is the natural rate of unemployment? Graph the short-run and long-run relationship between inflation and unemployment. Clearly label the horizontal axis, the vertical axis, the slope of the short-run relationship and the intersection point between the two. How much cyclical unemployment is it necessary to reduce inflation by 5 percentage points? Using Okun's law, compute the sacrifice ratio. Suppose that the economy is initially at a long-run equilibrium. Then the Fed increases the money supply. Assuming any resulting inflation is unexpected, explain any changes in GDP, unemployment, and inflation that are caused by the monetary expansion. Explain your conclusions using three diagrams: one for the IS-LM model, one for the AD-AS model and one for the Phillips curve.

Explanation / Answer

1.

a) The natural rate of unemployment is the rate at which the inflation rate does not deviate from the expected inflation rate.

Here, the expected inflation rate is just last period's actual inflation rate. Setting the inflation rate equal to last period's rate, that is, ? = ? -1, we find that u = 0.06. Thus the natural rate of unemployment is 6 percent.

b) With inflation on the vertical axis and unemployment on the horizontal axis, the short run PC is negatively sloped. The long run PC is vertical at the natural rate of unemployment.

c) To reduce inflation, the Phillips Curve (PC) tells us that unemployment must be above its natural rate of 6 percent for some period of time. We can write the PC in the form: ? - ? -1 = 0.5(u-0.06). Since we want inflation to fall by 5 percentage points, we want ? - ? -1 = -0.05. Plugging this into the above equation gives us u = 0.16. Hence, we need 10 percentage point-years of cyclical unemployment above the natural rate of 6 percent. According to Okun's law, a 1% increase in unemployment requires a 2% drop in GDP. Thus, a 10 percentage point increase in unemployment requires a 20 percentage point drop in GDP. This makes the sacrifice ratio = 20/5 = 4.

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