Problem:

Suppose an economy produces only one good. In the base year, production was 8 units at a price of $10 each. The next year, production increased to 9 units and the price of the good increased to $12.

1. Find nominal GDP in years 1 and 2.
2. If the price index is 100 in the base year, what is the value of the price index in year 2?
3. Find real GDP in year 2.
   Suppose a hypothetical national economy can be represented by the following data:

   Year	Nominal GDP	Price Index (2000 = 100)	Real GDP
   2007	$1536	128
   2008	$1663	132
   2009		135	$1274
   2010	$1792	140

4. Find real GDP in years 2007, 2008, and 2010.
5. Find nominal GDP in year 2009.

Answer:

1. In this simple economy, nominal GDP is simply the total output for the year times the price in that year. Year 1 nominal GDP is $10x8 = $80, while year 2 nominal GDP is $12x9 = $108.
2. The price index is found as the ratio of the value of year 1's "market basket" evaluated at year 2 prices relative to the same market basket evaluated at year 1 prices (multiplied by 100.) In this example, the year 2 price index is ($12x8)/($10x8) times 100 = 120.
3. Real GDP is equal to nominal GDP divided by (one one-hundredth of) the price index. Year 2 real GDP in this example is $108/1.2 = $90.
4. 2007 real GDP is $1536/1.28 = $1200. 2008 real GDP is $1663/1.32 = $1260. In 2010, real GDP is $1792/1.40 = $1280.
5. Nominal GDP for 2009 is found by multiplying that year's real GDP by (one one-hundredth of) the price index for that year. 2007 nominal GDP = $1274 x 1.35 = $1720.

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:

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 the 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. Use the formula: labor productivity = real GDP / 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 approximately 6% [= 100 x (5,302.5 – 5,000) / 5,000].