Chapter 14, Problem 3PA

(a)

To determine

The natural rate of unemployment of the economy.

Explanation of Solution

The Phillips curve of the economy is given to be $\text{π}=\text{Eπ}-\text{0}\text{.5}\left(\text{u}-\text{6}\right)$. The natural rate of unemployment is the unemployment rate in the economy at the time when the labor market is in equilibrium. Thus, it consists of the structural and frictional unemployment in the economy when the economy is operating efficiently. This natural rate of unemployment is a case where the inflation in the economy will be equivalent to the expected rate of inflation. Thus, there will be no deviation to the actual level of inflation from the expected.

Here, the people make their expectations about inflation on the basis of the weighted average of the past two year's inflations. When the inflation rate is stable at 5 percent, it means that the actual inflation is same as the expected inflation and so, $\pi =\text{E}\pi$ which means that the remaining (u-6) gives the natural rate of unemployment equal to 6.

Economics Concept Introduction

Natural Rate of Unemployment: The natural rate of unemployment is the rate of unemployment that is persisting in the economy when the labor market of the economy is in its equilibrium.

(b)

To determine

The short run trade-off between the inflation and unemployment.

Explanation of Solution

The Phillips curve of the economy is given to be $\text{π}=\text{Eπ}-\text{0}\text{.5}\left(\text{u}-\text{6}\right)$. The natural rate of unemployment is equal to 6. The stable rate of inflation in the economy is given to be 5 percent. Thus, the short run trade-off between the two can be illustrated as follows:

Thus, the short run trade-off between the inflation which is stable at 5 percentage point and the unemployment which is at its natural rate of 6 percentage point is indicated at point A.

(c)

To determine

The impact of fall in aggregate demand short run trade-off between the inflation and unemployment.

Explanation of Solution

The Phillips curve of the economy is given to be $\text{π}=\text{Eπ}-\text{0}\text{.5}\left(\text{u}-\text{6}\right)$. The natural rate of unemployment is equal to 6. The stable rate of inflation in the economy is given to be 5 percent. Thus, the short run trade-off between the inflation which is stable at 5 percentage point and the unemployment which is at its natural rate of 6 percentage point is indicated at point A.

When the unemployment in the economy rises by 4 percentage points and becomes 10 percentage, the impact on the Phillips curve will be different  because the expected inflation in the economy does not change. Thus, the Phillips curve determined the inflation rate and this can be calculated as follows:

$\begin{array}{c}\text{π}=\text{Eπ}-\text{0}\text{.5}\left(\text{u}-\text{6}\right)\\ =5-0.5\left(10-6\right)\\ =5-\left(0.5\times 4\right)\\ =5-2\\ =3\end{array}$

Thus, the point B that indicates the change in the trade-off between the unemployment and inflation in the economy which will be on the same short run Phillips curve and can be illustrated as follows:

(d)

To determine

The economy during higher unemployment and after 2 years at natural rate for 10 years.

Explanation of Solution

The Phillips curve of the economy is given to be $\text{π}=\text{Eπ}-\text{0}\text{.5}\left(\text{u}-\text{6}\right)$. The natural rate of unemployment is equal to 6. The stable rate of inflation in the economy is given to be 5 percent. Thus, the short run trade-off between the inflation which is stable at 5 percentage point and the unemployment which is at its natural rate of 6 percentage point is indicated at point A.

When the unemployment in the economy rises by 4 percentage points and becomes 10 percentage, the impact on the Phillips curve will be different  because the expected inflation in the economy does not change. Thus, the economy's inflation rate will be 3%. The unemployment rate, inflation rate, expected inflation rate, and the rate of output growth for the 10 years can be calculated in the following table:

Year	Unemployment Rate	Inflation Rate	Expected Inflation Rate	Rate of Output Growth
1	6	5	5	3
2	6	5	5	3
3	10	3	5	−5
4	10	1.6	3.6	3
5	6	2.02	2.02	11
6	6	1.89	1.89	3
7	6	1.93	1.93	3
8	6	1.92	1.92	3
9	6	1.92	1.92	3
10	6	1.92	1.92	3

(e)

To determine

The impact of fall in aggregate demand short run trade-off between the inflation and unemployment.

Explanation of Solution

The Phillips curve of the economy is given to be $\text{π}=\text{Eπ}-\text{0}\text{.5}\left(\text{u}-\text{6}\right)$. The natural rate of unemployment is equal to 6. The stable rate of inflation in the economy is given to be 5 percent. Thus, the short run trade-off between the inflation which is stable at 5 percentage point and the unemployment which is at its natural rate of 6 percentage point is indicated at point A.

When the unemployment in the economy rises by 4 percentage points and becomes 10 percentage, the impact on the Phillips curve will be different  because the expected inflation in the economy does not change. Thus, the Phillips curve determined the inflation rate and this can be calculated as follows:

$\begin{array}{c}\text{π}=\text{Eπ}-\text{0}\text{.5}\left(\text{u}-\text{6}\right)\\ =5-0.5\left(10-6\right)\\ =5-\left(0.5\times 4\right)\\ =5-2\\ =3\end{array}$

Thus, the point B that indicates the change in the trade-off between the unemployment and inflation in the economy will be on the same short run Phillips curve. When the unemployment rate falls, the expected inflation rate would fall in the economy. This leads to the downward shift in the short run Phillips curve in the economy. From the table above, it is identified that the expected inflation rate in the economy at the end of the 10th year is 1.92 percent but the unemployment rate is 6 percent. This combination is illustrated at the point C as follows:

(f)

To determine

Before recession and after recession equilibrium.

Explanation of Solution

The Phillips curve of the economy is given to be $\text{π}=\text{Eπ}-\text{0}\text{.5}\left(\text{u}-\text{6}\right)$. The natural rate of unemployment is equal to 6. The stable rate of inflation in the economy is given to be 5 percent. Thus, the short run trade-off between the inflation which is stable at 5 percentage point and the unemployment which is at its natural rate of 6 percentage point is indicated at point A.

After recession, equilibrium is indicated at point C where the inflation rate is 1.92 and the unemployment rate is 6 percentage points. This indicates that the inflation in the economy has been decreased by 3.08 percent points in the economy. While looking at the table for the rate of growth of output, it is identified that there were a loss of 8 percent during from year 2 to year 3, whereas there were a gain of 8 percent from year 3 to year 4. From year 5 to 10, the rate of output growth remained the same which means that there is no long run sacrifice in reducing the inflation rate by the economy.