Question

15. Suppose that the natural rate of unemployment equals 6%, and the public expect inflation to equal 4 %, and the coefficient a in PC equation = 0.4.

1. What is the unemployment rate when the actual inflation equals 2%? What if the actual inflation rate equals 10%?

2. During the 1990s, we observed the co-existence of low inflation and low unemployment. One of the arguments given by macroeconomists is that the expected inflation was lower than usual during the 1990s. Suppose now the public expect inflation rate to be 2%, do question (a) again.

Answer 1

We have the following information

Natural rate of unemployment = 6%

Expected rate of inflation = 4%

Phillips curve is given by the following equation

π = πe – ϵ(u – u*)

In the above

π = Actual inflation

πe = Expected inflation

u = Actual unemployment rate

u* = Natural rate of unemployment rate

ϵ = Measures the responsiveness of inflation to unemployment = 0.4

π = 0.04 – 0.4(u – 0.06)

Part a) It is given that the actual inflation is 2%

0.02 = 0.04 – 0.4(u – 0.06)

0.02 = 0.04 –0.4u + 0.024

0.02 = 0.064 –0.4u

0.4u = 0.044

Actual unemployment rate = 0.11 or 11%

Now it is given that the actual inflation rate is 10%

0.1 = 0.04 – 0.4(u – 0.06)

0.1 = 0.04 –0.4u + 0.024

0.1 = 0.064 –0.4u

–0.4u = 0.036

Actual unemployment rate = – 9%

Part b) Now it is given that the expected inflation rate is 2%. The Phillips curve equation will now become

π = 0.02 – 0.4(u – 0.06)

It is given that the actual inflation is 2%

0.02 = 0.02 – 0.4(u – 0.06)

0.02 = 0.02 – 0.4u + 0.024

0.02 = 0.044 – 0.4u

0.4u = 0.024

Actual unemployment rate = 0.06 or 6%

It is given that the actual inflation is 10%

0.1 = 0.02 – 0.4(u – 0.06)

0.1 = 0.02 – 0.4u + 0.024

0.1 = 0.044 – 0.4u

– 0.4u = 0.056

Actual unemployment rate = – 14%