Chapter 14, Problem 2PA

(a)

To determine

The natural rate of unemployment in the economy.

Explanation of Solution

The IS LM framework of the economy deals with the closed economy and does not consider the international trade and Balance of Payments into consideration. This leads to the generation of the new model that incorporated the Balance of Payment into the calculations which is known as the Mundell - Fleming model. The Phillips curve of the economy is given to be $\text{π}={\text{π}}_{-\text{1}}-\text{0}\text{.5}\left(\text{u}-\text{5}\right)$.

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.

Thus, the expected inflation in this case will be equal to the last period's inflation in the economy. Thus, setting the inflation to the last period's inflation, $\pi ={\pi }_{-1}$ and thus, the remaining $\left(\text{u}-5\right)$ will help to identify that the natural rate of unemployment in the economy is 5 percent.

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 and long run relationship between the inflation and unemployment.

Explanation of Solution

The inflation and the unemployment are the two important aspects that an economy has to handle very carefully. When the measure to tackle and reduce the inflation is taken, it will increase the unemployment and vice versa in the economy. This happens in the short run and thus, they both are inversely related with each other. This short run or single period relation between the inflation and the unemployment is explained using the Phillips curve for the economy. Here, the expected inflation rate is equal to the last period's inflation rate and the slope of the Phillips curve will be 0.5. The short run Phillips curve will pass through the point where the $\pi ={\pi }_{-1}$.

The long run period or the multi period relation is different from the short run relation. The expected inflation of the economy will be equal to the actual level of inflation in the economy. Thus, $\pi ={\pi }_{-1}$ will be the case of inflation in the economy. The unemployment rate will be at its natural rate of 5 percent so as the output level of the economy. Thus, whatever be the change in the inflation, the output and the unemployment would remain unchanged. This relation between the two is indicated with the help of a vertical Phillips curve. Thus, the short run and long run relations between the inflation and unemployment can be indicated with the help of the short run Phillips curve and Long run Phillips curve as follows:

(c)

To determine

The cyclical unemployment required to reduce the inflation by 4 percentage points.

Explanation of Solution

The Phillips curve of the economy is given to be $\text{π}={\text{π}}_{-\text{1}}-\text{0}\text{.5}\left(\text{u}-\text{5}\right)$. 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. It is identified that the natural rate of unemployment of the economy is 5 percent.

When the inflation has to be reduced, the unemployment in the economy should be above its natural level of unemployment according to the Phillips curve. Thus, the required fall in the inflation rate should be plugged into the left side of the Phillips curve equation as follows:

$\begin{array}{c}\text{π}={\text{π}}_{-\text{1}}-\text{0}\text{.5}\left(\text{u}-\text{5}\right)\\ \text{π}-{\text{π}}_{-\text{1}}=-0.5\left(\text{u}-\text{5}\right)\\ -4=-0.5\left(\text{u}-\text{5}\right)\\ -4\times -0.5=\text{u}-5\\ 8=\text{u}-5\\ 8+5=\text{u}\\ \text{u}=13\end{array}$

Thus, it indicates that there should be 8 percent more cyclical unemployment in the economy in order to bring the inflation by 4 percentage. The Okun's law states that an increase in the unemployment by 1 percent will correspond to the 2 percent fall in the total GDP of the economy. Thus, when the unemployment increases by 8 points, there will be 16 percent point fall in the GDP of the economy according to the Okun's law.

The sacrifice ratio is the ratio of the percentage of GDP that the economy must foregoin order to reduce the inflation by 1 percentage point. Here, the total GDP foregone is 16 percentage points and the total inflation reduced is 4 percentage points. Thus, the sacrifice ratio can be calculated by dividing the total GDP foregone with the inflation reduced as follows:

$\begin{array}{c}\text{Sacrifice ratio}=\frac{\text{Total GDP foregone}}{\text{Inflation reduced}}\\ =\frac{16}{4}\\ =4\end{array}$

Thus, the sacrifice ratio of the economy is 4.

(d)

To determine

The scenarios to reduce the inflation by 4 percentage points.

Explanation of Solution

The Phillips curve of the economy is given to be $\text{π}={\text{π}}_{-\text{1}}-\text{0}\text{.5}\left(\text{u}-\text{5}\right)$. It is identified that the natural rate of unemployment of the economy is 5 percent. It is given that the present rate of inflation is 6 percentage points and the government needs to reduce the inflation by 4 point to make it 2 percentage points.

In order to reduce the inflation by 4 percentage points, the economy should have to face the higher unemployment rate of 13 percent for the short run as calculated above. Thus, the first measure that the government can relay is to make the unemployment rate very high at 13 percent in order to reduce the inflation by 4 percentage points.

The second measure that the government can relay is to fix the level of unemployment at 7 percent for 4 years which would slowly reduce the level of inflation in the economy by 4 percentage points. These are the two different measures that the government can relay up on in order to reduce the inflation by 4 percentage points.