Question

Suppose that the natural rate of unemployment in a particular year is 5 percent and the actual unemployment rate is 9 percent. Use Okun’s law to determine the size of the GDP gap in percentage-point terms. If potential GDP is $500 billion in that year, how much output is forgone because of cyclical unemployment?

Short answer

GDP gap is negative 8%.

$40 billion of potential output is forgone due to cyclical unemployment.

Step-by-step solution

Size of GDP gap

According to Okun’s law, the GDP gap is inversely related to twice the difference between the actual unemployment rate and the natural rate of unemployment.

$$\begin{gathered} \mathrm{GDP}\mathrm{gap}=-2\times (\mathrm{actual}\mathrm{unemployment}\mathrm{rate}-\mathrm{natural}\mathrm{unemployment}\mathrm{rate}) \\ \mathrm{GDP}\mathrm{gap}=-2\times \left(9-5\right)\% \\ =-2\times 4\% \\ =-8\% \end{gathered}$$

Therefore, the economy has a negative GDP gap of 8%.

Forgone output due to cyclical unemployment

The GDP gap is the deviation in actual GDP from the potential GDP.When actual GDP is less than the potential GDP, some of the potential output is forgone from the economy due to the underutilization of resources. At this point, the actual unemployment rate is higher than the natural rate of unemployment (potential GDP level of unemployment), resulting in a negative GDP gap.

The condition given above is caused by the presence of cyclical unemployment. The GDP gap is -8%, as calculated in step 1. Thus, 8% of the potential GDP is foregone due to cyclical unemployment. The output foregone is 8% of $500 billion, which is equal to $40 billion.