Shown in figure 14 1 in the long run expected

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shown in Figure 14-1. In the long run, expected inflation equals actual inflation, so that π = π –1 , and output and unemployment equal their natural rates. The long- run Phillips curve thus is vertical at an unemployment rate of 6 percent. LRPC SRPC u 0.06 Unemployment Inflation 0.5 π 1 π Figure 14-1
150 Answers to Textbook Questions and Problems c. To reduce inflation, the Phillips curve tells us that unemployment must be above its natural rate of 6 percent for some period of time. We can write the Phillips curve in the form π π –1 = 0.5( u – 0.06). Since we want inflation to fall by 5 percentage points, we want π π –1 = –0.05. Plugging this into the left-hand side of the above equation, we find –0.05 = –0.5( u – 0.06). We can now solve this for u : u = 0.16. Hence, we need 10 percentage points of cyclical unemployment above the natural rate of 6 percent. Okun’s law says that a change of 1 percentage point in unemployment trans- lates into a change of 2 percentage points in GDP. Hence, an increase in unem- ployment of 10 percentage points corresponds to a fall in output of 20 percentage points. The sacrifice ratio is the percentage of a year’s GDP that must be forgone to reduce inflation by 1 percentage point. Dividing the 20 percentage-point decrease in GDP by the 5 percentage-point decrease in inflation, we find that the sacrifice ratio is 20/5 = 4. d. One scenario is to have very high unemployment for a short period of time. For example, we could have 16 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 8 percent unemployment for 5 years. Both of these plans would bring the inflation rate down from 10 percent to 5 per- cent, although at different speeds. 3. The cost of reducing inflation comes from the cost of changing people’s expectations about inflation. If expectations can be changed costlessly, then reducing inflation is also costless. Algebraically, the Phillips curve tells us that π = E π β ( u u n ) + v . If the government can lower expected inflation E π to the desired level of inflation, then there is no need for unemployment to rise above its natural rate. According to the rational-expectations approach, people form expectations about inflation using all of the information that is available to them. This includes informa- tion about current policies in effect. If everyone believes that the government is commit- ted to reducing inflation, then expected inflation will immediately fall. In terms of the Phillips curve, E π falls immediately with little or no cost to the economy. That is, the sacrifice ratio will be very small. On the other hand, if people do not believe that the government will carry out its intentions, then E π remains high. Expectations will not adjust because people are skep- tical that the government will follow through on its plans.

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