Problem:

Consider the following data for a hypothetical economy:

1. Calculate the growth rate of real GDP over the year.
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. Using these two values, calculate the growth rate of real GDP per capita over the year.
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:

Suppose an economy's real GDP is $5,000 billion. There are 125 million workers, each working an average of 2,000 hours per year.

1. What is labor productivity per hour in this economy?
2. Suppose worker productivity rises by 5% over the following year and the labor force grows by 1%. What is the projected value of real GDP?
3. Based on your previous answer, what is this economy's rate of growth?

Answer:

1. Labor productivity can be found as real GDP divided by hours of work. There are 2,000 x 125 million = 250 billion worker hours available in the economy, producing a real GDP of $5,000 billion. Labor productivity is then $5,000/250 = $20 per worker-hour.
2. Productivity will rise by 5% to $21 (20 + .05 x 20 = 21) and work hours will rise by 1% to 252.5 billion (250 + .01 x 250 = 252.5). Since real GDP equals work hours times productivity, real GDP will rise to 252.5 billion x $21 = $5302.5 billion.
3. The rate of growth is just over 6% [100 x (5,302.5 – 5,000) / 5,000 = 6.05].