# 8.4: Review and Practice

### Summary

We saw that economic growth can be measured by the rate of increase in potential output. Measuring the rate of increase in actual real GDP can confuse growth statistics by introducing elements of cyclical variation.

Growth is an exponential process. A variable increasing at a fixed percentage rate doubles over fixed intervals. The doubling time is approximated by the rule of 72. The exponential nature of growth means that small differences in growth rates have large effects over long periods of time. Per capita rates of increase in real GDP are found by subtracting the growth rate of the population from the growth rate of GDP.

Growth can be shown in the model of aggregate demand and aggregate supply as a series of rightward shifts in the long-run aggregate supply curve. The position of the LRAS is determined by the aggregate production function and by the demand and supply curves for labor. A rightward shift in LRAS results either from an upward shift in the production function, due to increases in factors of production other than labor or to improvements in technology, or from an increase in the demand for or the supply of labor.

Saving plays an important role in economic growth, because it allows for more capital to be available for future production, so the rate of economic growth can rise. Saving thus promotes growth.

In recent years, rates of growth among the world’s industrialized countries have grown more disparate. Recent research suggests this may be related to differing labor and product market conditions, differences in the diffusion of information and communications technologies, as well as differences in macroeconomic and trade policies. Evidence on the role that government plays in economic growth was less conclusive.

## Concept Problems

1. Suppose the people in a certain economy decide to stop saving and instead use all their income for consumption. They do nothing to add to their stock of human or physical capital. Discuss the prospects for growth of such an economy.
2. Singapore has a saving rate that is roughly three times greater than that of the United States. Its greater saving rate has been one reason why the Singapore economy has grown faster than the U.S. economy. Suppose that if the United States increased its saving rate to, say, twice the Singapore level, U.S. growth would surpass the Singapore rate. Would that be a good idea?
3. Suppose an increase in air pollution causes capital to wear out more rapidly, doubling the rate of depreciation. How would this affect economic growth?
4. Some people worry that increases in the capital stock will bring about an economy in which everything is done by machines, with no jobs left for people. What does the model of economic growth presented in this chapter predict?
5. China’s annual rate of population growth was 1.2% from 1975 to 2003 and is expected to be 0.6% from 2003 through 2015. How do you think this will affect the rate of increase in real GDP? How will this affect the rate of increase in per capita real GDP?
6. Suppose technology stops changing. Explain the impact on economic growth.
7. Suppose a series of terrorist attacks destroys half the capital in the United States but does not affect the population. What will happen to potential output and to the real wage?
8. “Given the rate at which scientists are making new discoveries, we will soon reach the point that no further discoveries can be made. Economic growth will come to a stop.” Discuss.
9. Suppose real GDP increases during President Obama’s term in office at a 5% rate. Would that imply that his policies were successful in “growing the economy”?
10. Suppose that for some country it was found that its economic growth was based almost entirely on increases in quantities of factors of production. Why might such growth be difficult to sustain?

## Numerical Problems

1. The population of the world in 2003 was 6.314 billion. It grew between 1975 and 2003 at an annual rate of 1.6%. Assume that it continues to grow at this rate.
1. Compute the doubling time.
2. Estimate the world population in 2048 and 2093 (assuming all other things remain unchanged).
2. With a world population in 2003 of 6.314 billion and a projected population growth rate of 1.1% instead (which is the United Nations’ projection for the period 2003 to 2015).
1. Compute the doubling time.
2. State the year in which the world’s population would be 12.628 billion.
3. Suppose a country’s population grows at the rate of 2% per year and its output grows at the rate of 3% per year.
1. Calculate its rate of growth of per capita output.
2. If instead its population grows at 3% per year and its output grows at 2% per year, calculate its rate of growth of per capita output.
4. The rate of economic growth per capita in France from 1996 to 2000 was 1.9% per year, while in Korea over the same period it was 4.2%. Per capita real GDP was $28,900 in France in 2003, and$12,700 in Korea. Assume the growth rates for each country remain the same.
1. Compute the doubling time for France’s per capita real GDP.
2. Compute the doubling time for Korea’s per capita real GDP.
3. What will France’s per capita real GDP be in 2045?
4. What will Korea’s per capita real GDP be in 2045?
5. Suppose real GDPs in country A and country B are identical at $10 trillion dollars in 2005. Suppose country A’s economic growth rate is 2% and country B’s is 4% and both growth rates remain constant over time. 1. On a graph, show country A’s potential output until 2025. 2. On the same graph, show country B’s potential output. 3. Calculate the percentage difference in their levels of potential output in 2025. Suppose country A’s population grows 1% per year and country B’s population grows 3% per year. 1. On a graph, show country A’s potential output per capita in 2025. 2. On the same graph, show country B’s potential output per capita in 2025. 3. Calculate the percentage difference in their levels of potential output per capita in 2025. 6. Two countries, A and B, have identical levels of real GDP per capita. In Country A, an increase in the capital stock increases the potential output by 10%. Country B also experiences a 10% increase in its potential output, but this increase is the result of an increase in its labor force. Using aggregate production functions and labor-market analyses for the two countries, illustrate and explain how these events are likely to affect living standards in the two economies. 7. Suppose the information below characterizes an economy: Employment (in millions) Real GDP (in billions) 1 200 2 700 3 1,100 4 1,400 5 1,650 6 1,850 7 2,000 8 2,100 9 2,170 10 2,200 1. Construct the aggregate production function for this economy. 2. What kind of returns does this economy experience? How do you know? 3. Assuming that total available employment is 7 million, draw the economy’s long-run aggregate supply curve. Suppose that improvement in technology means that real GDP at each level of employment rises by$200 billion.

1. Construct the new aggregate production function for this economy.
2. Construct the new long-run aggregate supply curve for the economy.
8. In Table 8.1 “Growing Disparities in Rates of Economic Growth”, we can see that Japan’s growth rate of per capita real GDP fell from 3.3% per year in the 1980s to 1.4% per year in the 1990s.
1. Compare the percent increase in its per capita real GDP over the 20-year period to what it would have been if it had maintained the 3.3% per capita growth rate of the 1980s.
2. Japan’s per capita GDP in 1980 was about $24,000 (in U.S. 2000 dollars) in 1980. Calculate what it would have been if the growth rate of the 1980s had been maintained Calculate about how much it is, given the actual growth rates over the two decades. 3. In Table 8.1 “Growing Disparities in Rates of Economic Growth”, we can see that Ireland’s growth rate of per capita real GDP grew from 3.0% per year in the 1980s to 6.4% per year in the 1990s. 4. Compare the percent increase in its per capita real GDP over the 20-year period to what it would have been if it had maintained the 3.0% per capita growth rate of the 1980s. 5. Ireland’s per capita GDP in 1980 was about$10,000 (in U.S. 2000 dollars). Calculate what it would have been if the growth rate of the 1980s had been maintained. Calculate about how much it is, given the actual growth rates over the two decades.