Problem:

Consider the following data for a hypothetical economy:

1. Calculate the growth rate of real GDP.
2. At this rate of growth, approximately how many years will pass before real GDP doubles?
3. Find real GDP per capita in each of the two years. Calculate the growth rate of real GDP per capita.
4. At this rate of growth, approximately how many years will pass before real GDP per capita doubles?

Answer:

1. The rate of growth is [($51,400 - $50,000)/$50,000] x 100 = 2.8%.
2. The rule of 70 tells us that real GDP will double in approximately 70/2.8 = 25 years.
3. Real GDP per capita in year 1 is $50,000/200 = $250, while in year 2 it is $51,400/202 = $254.46. The growth rate of real GDP per capita is then found as [($254.46 - 250)/250] x 100 = 1.78%.
4. The rule of 70 suggests that real GDP per capita will double in approximately 70/1.78 = 39.3 years.

Problem:

Recent data for the U.S. reveal the following (all figures in millions).

Use the data to find the following:

1. The size of the labor force.
2. The number classified as "not in the labor force."
3. The unemployment rate.

 

Answer:

1. The labor force consists of all those either employed or unemployed. The labor force in this period was 142.0 + 7.7 = 149.7 million people.
2. Those classified as "not in the labor force" are those individuals age 16 or older and not institutionalized who are neither employed nor unemployed. For the period given, this amounts to 330.0 - 102.3 - 142.0 - 7.7 = 78.0 million people.
3. The unemployment rate is found as the proportion of the labor force that is classified as unemployed. For this period, the unemployment rate is 7.7/149.7 = .051, or 5.1%.

Problem:

Suppose the natural rate of unemployment is 4.5% and the current unemployment rate is 6%.

1. According to Okun's Law, what is the size of the GDP gap?
2. If potential GDP is $1,000 billion, how much output is being lost as a result of the economy being below its potential?
3. Recent data for the U.S. show an unemployment rate of 5.1%. Suppose the natural rate at the time was 4.5%. What was the size of the GDP gap?
4. At that time, GDP was $12,735 billion. What was potential GDP?

 

Answer:

1. Okun's Law suggests a GDP gap of 2% for every 1% that the unemployment rate exceeds its natural rate. In this case, the GDP gap is (6.0 - 4.5) x 2 = 3%.
2. A GDP gap of 3% implies that $1,000 x .03 = $30 billion of output is being foregone.
3. The GDP gap is (5.1 - 4.5) x 2 = 1.2%.
4. By Okun's Law, actual GDP of $12,735 billion was 1.2 percent below its potential. Equivalently, actual GDP is 98.8% of potential GDP. Potential GDP is then found as $12,735/.988 = $12,890 billion.

Problem:

Suppose the CPI stands currently at 198, while last year it was 191.3.

1. What was the rate of inflation over the past year?
2. At this rate of inflation, approximately how long will it take for the price level to double?
3. Suppose Janice's nominal income rose by 5% last year while Jeff's increased by only 3%. By what percentage did each of their real incomes change?

 

Answer:

1. The rate of inflation is measured by the percentage increase in the value of the CPI. In this case, the rate of inflation is [(198 - 191.3)/191.3] x 100 = 3.5%
2. Using the rule of 70, the price level will double in 70/3.5 = 20 years.
3. The percentage change in real income can be approximated as the difference in the percentage change in nominal income and the percentage change in the price level. For Janice, this is 5% - 3.5% = 1.5%, while Jeff's real income fell by one half a percent: 3.0% - 3.5% = -.5%.