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

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Question:

An economy has the following equation for the Phillips curve: π = Eπ − 0.5(u − 6)

(1) People form expectations f inflation by taking a weighted average of the previous two years of inflation: Eπ = 0.7π−1 + 0.3π−2.

(2) Okun's law for this economy is Y − Y−1 Y−1 = 3.0 − 2.0(u − u−1).

(3) 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 in this economy?

2. Graph the short-run tradeoff between inflation and unemployment that this economy 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 percent points above its natural level. On you graph in part 2, label the point the economy experienced that year as point B.

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 showing 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 used in part 2, graph the short-run tradeoff the economy faces at the end of the 10-year period. Label the point where the economy finds itself as point C, again using numerical values. 2

6. Compare the equilibrium before the recession with the new long-run equilibrium (period 10) equilibrium. How much does inflation change? How many percentage points of output are lost during the transition? What is this economy's sacrifice ratio?