<p>Suppose that an economy has the Phillips curve <br /> π=π<sub>-1</s
ID: 1254844 • Letter: #
Question
<p>Suppose that an economy has the Phillips curve <br /> π=π<sub>-1</sub>-0.5(u-0.06)<br />a. What is the natural rate of unemployment? <br />b. Graph the short- run and long-run relationships between inflation and unemployment. (Hint: <br />In the long-run, output and unemployment equal their natural rates.)<br />c. How much cyclical unemployment is necessary to reduce inflation by 5 percentage points? <br />Using Okun’s law, compute the sacrifice ratio.</p>Explanation / Answer
Suppose that an economy has the Phillips curve p = p-1 - 0.5(u - u^n),
and that the natural rate of unemployment is given by an average of the past two years’ unemployment:
u^n = 0.5(u-1 + u-2).
1) Why might might the natural rate of unemployment depend on recent unemployment (as is assumed in the preceding equation)?
Because an economy cannot "snap back" to some arbitrary rate of natural unemployment - natural unemployment is what people are used to. If they've been out of work for too long, the natural rate increases.
2) Suppose that the Fed follows a policy to permanently reduce the inflation rate by 1 percentage point. What effect will that policy have one the unemployment rate over time?
First, let P = 1
p = p-1 - 0.5(u - u^n)
1 = (1-1) - 0.5(u - u^n)
2 = u - u^n
P = 0.99 of current rate
0.99p = (0.99)p-1 - 0.5(u - u^n)
0.5(u - u^n) = 0.99
1.98 = u - u^n
Deceases employment by 2 - 1.98 = 2% (increases unemployment by 2%)
3) What is the sacrifice ratio in this economy? Explain. Two - for every 1% inflation, 2% employment and ice-versa.
4) What do these equations imply about the short-run and long-run tradeoffs between inflation and unemployment? Small changes in inflation bring greater changes to unemployment.
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