Question

The short-run Phillips curve is the negative short-run relationship between the unemployment rate and the inflation rate.  Suppose the Phillips curve is given by ?t = ?e + 0.2 – 5ut  where ?e= ? ?t-1. In this context ? is the actual inflation rate, ?e is the expected inflation rate and ? is a parameter indicating the relative speed of adjustment of expected inflation to actual inflation. Explain to the best of your abilities, the following questions.

a) Explain the difference between the short-run and long-run Philips curve and its implication on prices and inflation relative to potential output.

b) What is the natural rate of unemployment in this economy?

c) For now, assume that ?=0 (What does that mean?). Suppose that the government decides to lower unemployment to 3% and keep it there forever. What is the rate of inflation for the long term? Is this realistic? Why?

d) Assume that only for the first three periods (t=1, t=2, and t=3) people form their expectations using ?=0. After the third period, from t=4 on, they start using ?=1 forever. Also, the government still wants to keep unemployment at 3%. What is the rate of inflation for t = 4, 5, and 6? What is the expected rate of inflation for t=4, 5, and 6? Is this setup more realistic? Why?

Answer 1

A). In the short run, there is an inverse relationship between unemployment and inflation. This is because higher unemployment leads to lower inflation because high unemployment also means lower demand of goods and since lower amount of goods are demanded, lower will be the rate of inflation. This the Phillips curve is downward sloping in this case. However in the long run, the Phillips curve is vertical indicating the same amount of inflation at every level of unemployment.

B). In natural rate of unemployment, actual inflation = expected inflation. Taking this the case =? e =? t, then (0.2/5)= natural rate of unemployment. Thus, the natural rate of unemployment is 4%

C. This means that the coefficient of inflation and expected inflation is 0. Thus both inflation and expected inflation will automatically be zero. This shows that the level of unemployment will he equal to natural level of unemployment.

If the unemployment is reduced to 3, then rate of inflation will change to (0.2 - 0.03*5)=0.05. Thus the rate of inflation is 5%. It is not possible to keep this rate of inflation forever because in the long run, the rate unemployment because at a given level of unemployment the rate of inflation increases indefinitely as depicted by a vertical Phillips curve.