An economy has the following equation for the Phillips curve: = E 0.5(u 6) Peopl

Question

An economy has the following equation for the Phillips curve:
= E 0.5(u 6)
People form expectations of inflation by taking a weighted average of the previous two
years of inflation:
E = 0.7 1 + 0.3 2
Okuns law for this economy is:
(Y Y 1 )/Y 1 = 3.0 2.0(u u 1 )
The economy begins at its natural rate of unemployment with a stable inflation rate of 5
percent.
1. What is the natural rate of unemployment for this economy?

2. Graph the short-run trade-off between inflation and unemployment that this econ-
omy faces. Label the point where the economy begins as point A. (Be sure to give
numerical values for point A.)

3. A fall in aggregate demand leads to a recession, causing the unemployment rate to
rise 4 percentage points above its natural rate. On your graph in part (1), label the
point the economy experiences that year as point B. (Once again, be sure to give
numerical values.)

4. Unemployment remains at this high level for two years (the initial year described in
part (3) and one more), after which it returns to its natural rate. Create a table show-
ing unemployment, inflation, expected inflation, and output growth for 10 years
beginning two years before the recession. (These calculations are best done on a
computer spreadsheet.)

5. On the same graph you used in part (2), graph the short-run trade-off the economy
facesattheendofthis10-yearperiod. Labelthepointwheretheeconomyfindsitself
as point C. (Again, use numerical values.)

6. Compare the equilibrium before the recession with the new long-run (period ten)
equilibrium. How much does inflation change? How many percentage points of
out- put are lost during the transition? What is this economys sacrifice ratio?d.

Explanation / Answer

1) The philips curve is given by: pi=E(pi)-0.5(u-6); E(pi)=0.7(pi)-1+0.3(pi)-2 and Okun's law is given by (Y-Y-1)/Y-1=3-2(u-u-1)

Stable inflation rate =5%, Substiuting this 5% figure in the expected inflation equation we get E(pi)=0.7(5)+0.3(5)

i.e. E(pi)=3.5+1.5, E(pi)=5. Now substituting this E(pi) into the philips curve equation we get 5=5-0.5(u-6) i.e.0.5u=3, i.e.u=(30/5) i.e. u =6

The natural rate of unemployment is 6%.

2) The short run trade off between inflation and unemployment is given by the philips curve. So here we have, (pi)=E(pi)-0.5(u-6) The Unemployment is mapped on the X-axis and Inflation is mapped on the Y-axis. The philips curve is a downward sloping curve with slope=-0.5 and y-intercept=E(pi)+3. Economy begins at the natural rate of unemployment as given in the question above where x-intercept =6.(point A)

3) With a fall in aggregate demand the philips curve shifts out and to the right with x-intercept=10. This is point B.

4)

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