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PS#4solutions3140

# PS#4solutions3140 - Economics 3140-1 Fall 2011 Problem Set...

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Economics 3140-1 Fall 2011 Problem Set 4 Suggested Solutions Questions 1: 1. The economy has the Phillips curve: π = π -1 – 0.4(u – 0.05). 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 inflation rate, that is, π = π -1 , we find that u = 0.05. Thus, the natural rate of unemployment is 5 percent. b. In the short run (that is, in a single period) the expected inflation rate is fixed at the level of inflation in the previous period, π -1 . Hence, the short-run relationship between inflation and unemployment is just the graph of the Phillips curve: it has a slope of -0.04, and it passes through the point where π = π -1 and u = 0.05. In the long-run, expected inflation equals actual inflation, and so π = π -1 , and output and unemployment equal their natural rates. The long-run Phillips curve thus is vertical at an unemployment rate of 5 percent. The curves are graphed below. π LRPC -0.4 π -1 SRPC 0.05 u

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c. To reduce inflation, the Phillips curve tells us that unemployment must be above it natural rate of 5 percent for some period of time. We can write the Phillips curve in the form π - π -1 = 0.4(u – 0.05). Since we want inflation to fall by 2 percentage points, we want π π -1 = - 0.02. Plugging this into the left-hand side of the above equations, we find -0.02 = -0.4(u – 0.05). We now solve the above equation for u: u = 0.10. Hence, we need 5 percentage points of cyclical unemployment above the natural rate of 5 percent. Okun’s law says that a change of 1 percentage point in unemployment translates into a change of 2 percentage points in GDP. Hence, an increase in unemployment of 5 percentage points corresponds to a fall in output of 10 percentage points. The sacrifice ratio is the percentage of a year’s GDP that must be foregone to reduce inflation by 1 percentage point. Dividing the 10 percentage-point decrease in GDP by the 2 percentage-point decrease in inflation, we find that the sacrifice ration is 10/2 = 5. d. One scenario is to have very high unemployment for a short period of time. For example, we could have 10 have percent unemployment for a single year. Alternatively, we could have a small amount of cyclical unemployment spread out over a long period of time. For example, we could have 6 percent unemployment for 5 years. Both of these plans would bring the inflation rate down from 4 percent to2 percent, although at different speeds.
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PS#4solutions3140 - Economics 3140-1 Fall 2011 Problem Set...

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