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21.6 End-of-Chapter Material

In Conclusion

We live in a world today that would be unrecognizable and unimaginable to those born two centuries ago. Things we take for granted—jet travel, antibiotics, electricity, the Internet, dentistry—are all products of the extraordinary growth of the last 200 years. Yet despite all our technological advances, billions of people in the world still live in poverty. Although some countries continue to grow rapidly, others stagnate or even go backward. If we could unlock the secrets of economic growth, we would have the means to help people to permanently better lives.

Even as economists emphasize economic growth as a way to combat poverty, noneconomists are often critical of economic growth, pointing out that it comes with costs as well as benefits. For example, as countries become richer, they use more energy and more of the world’s natural resources. Oil reserves are being depleted, and rainforests are disappearing. Growth may lead to increased pollution, such as greenhouse gas emissions that in turn contribute to climate change. These are serious and legitimate concerns. In brief, economists have four main responses.

  1. The framework we presented in this chapter does, in fact, capture the effect of declining natural resources. They lead to a slower rate of growth in technology. Indeed, it is possible that declining natural resources could more than offset growth in knowledge and social infrastructure so that the technology growth rate becomes negative. As yet, there is no evidence that this is a significant concern, but—at least until we have a better understanding of the drivers of knowledge and social infrastructure growth—it certainly might become relevant in the future.
  2. There are indeed uncompensated side effects of economic growth, such as increased pollution. Economists agree that such effects can be very important. However, they can and should be corrected directly. Curtailing growth is an extremely indirect and inefficient response to its adverse side effects. As Nobel Prize–winner Robert Solow put it, “What no-growth would accomplish, it would do by cutting off your face to spite your nose.”Robert M. Solow, “Is the End of the World at Hand?” Challenge 16, no. 1 (March/April 1973): 39–50. Also available at
  3. The evidence reveals that some environmental problems are solved rather than exacerbated by growth. Air pollution is a much more serious problem in the developing countries of the world than in the rich countries of the world. In part this is because a clean environment is a luxury good; people only worry about the state of the environment once their basic needs of food and shelter are addressed.
  4. The most serious problems are those where we cannot rely on market mechanisms. If oil becomes scarce, then increases in the price of oil will provide incentives for people to economize on their use of fuel and look for alternative sources of energy. These incentives will at least ease the adjustment of the world economy. But there are no functioning market mechanisms to deal with climate change, for example.

Decades of research by economists have told us that there is no magic bullet, no simple and painless way to encourage economic growth. At the same time, we have learned a great deal about how and why countries grow. We have learned that growth depends on the accumulation of both physical and human capital. We have learned that growth ultimately hinges on the growth of knowledge, highlighting the importance of education, training, and research and development (R&D). And we have learned that good institutions are critical for countries that want to promote economic growth.

We have made progress, but the study of economic growth remains one of the most fascinating and challenging problems in all economics. There is no doubt that economists will continue their search for the elusive secrets of prosperity. As the Nobel Prize–winning economist Robert Lucas observed, “Once one starts to think about [economic growth], it is hard to think about anything else.”


  1. Think about your last visit to a shopping center or a large food store in the United States or other developed economy. Which of these goods and services do you think are available in a typical market in Niger? Which were available in the United States 50 years ago? 100 years ago?
  2. (Advanced) In the late 1990s, the US government was running a surplus of about 1 percent of gross domestic product (GDP). Current projections show that the government is going to run deficits in excess of 5 percent of GDP in the future. Let us imagine that there are no changes in private saving or in foreign borrowing/lending.The condition that private savings do not change is important. For example, if the government cuts taxes, it is possible that people will predict that taxes will be higher in the future and will increase their savings in anticipation. We will say more about this in Chapter 29 "Balancing the Budget". In this case, the increased deficit translates directly into a decrease in the investment rate. To investigate the implications of such a decrease, suppose that, in the year 2000

    investment rate = 0.24, depreciation rate = 0.085, and output growth rate = 0.035.
    1. On a balanced-growth path, the ratio of capital stock to output is given by the following formula:

      capitaloutput=investment ratedepreciation rate+output growth rate.

      Suppose that the economy was on a balanced-growth path in 2000. Calculate the balanced-growth ratio of the capital stock to GDP.

    2. Suppose the production function for this economy is output per worker = 15,000 × capital/output. What is output per worker in 2000?
    3. Now suppose that the increase in the government deficit means that the investment rate decreases to 0.18. What is the new balanced-growth ratio of the capital stock to GDP?
    4. Suppose that by 2040, improvements in technology and human capital mean that the production function is given by output per worker = 30,000 × capital/output. Suppose also that the economy has reached its new balanced-growth path. What is output per worker in 2040?
    5. What would output per worker equal in 2040 if there had been no change in the investment rate?
  3. Try to estimate approximately how much you spend every day. Be sure to include an amount for rent, utilities, and food. Do you think it would be possible for you to live on $2 per day?
  4. Suppose there are two economies. The first has a current level of real GDP of 100, and the second has a current level of real GDP of 200. The poorer country is forecasted to grow at 10 percent in the coming year, while the richer country is forecasted to grow at 15 percent. If these forecasts are true, what will their levels of real GDP be next year? Is this a case of divergence or convergence?
  5. When capital’s share of output (a) is larger, does an economy move to its balanced-growth path more quickly or more slowly? Explain.
  6. Suppose that capital’s share of output is 0.5, the human capital growth rate is 2 percent, the technology growth rate is 1 percent, and the workforce is not growing. What is the balanced-growth growth rate of output?
  7. Look at Table 21.6 "Approaching the Balanced-Growth Path". Explain why the output growth rate decreases over time.
  8. (Advanced) Think about Juan in Solovenia. Consider two cases. In the first case, he experiences an increase in his productivity that he knows will last for only one month. In the second, he experiences a permanent increase in his productivity. How do you think his decisions about how hard to work will be different in the two cases?
  9. On a balanced-growth path, the ratio of capital stock to output is given by the following formula:

    capitaloutput=investment ratedepreciation rate+output growth rate.

    Use the formula for the balanced-growth rate of output to determine how the ratio of capital stock to output depends on the growth rate of the workforce. Does an increase in the growth rate of the workforce lead to an increase or a decrease in the ratio of capital stock to output?

Economics Detective

  1. Find savings rates for the United States, India, and Niger and compare these to the investment rates for these countries. What can you say about capital inflows from other countries?
  2. Go to the Penn World Tables ( Click on “Alphabetical List of Countries.” Select the United States and two other countries of your choice. Look at the data for real GDP per capita and real GDP per worker. Briefly describe in words what has happened to these two variables over the period for which data are available.

Spreadsheet Exercises

  1. Using a spreadsheet, reproduce Figure 21.13 "Output and Capital Stock in a Balanced-Growth Economy". Specifically, suppose that GDP starts with the value 10 in the year 2000, and capital stock in the same year has the value 20. Now set the growth rate of each series equal to 3 percent (0.03). What is the capital stock in 2050? What is GDP? Has the ratio of capital stock to GDP stayed constant?
  2. Using the same spreadsheet and keeping the growth rate of GDP equal to 3 percent, examine what happens if the growth rate of capital is (a) 1 percent; (b) 5 percent.
  3. Suppose that an economy has the following production function:

    output per worker=the ratio of capital to GDP×human capital.

    Suppose that the workforce is growing at 1 percent per year, and human capital is growing at 2 percent per year. (We are assuming technology is constant in this example.) Suppose that we find that the ratio of capital stock to GDP is 4 on all dates and, initially, human capital is 15,000. What are the values for the growth rate of output per worker, the growth rate of output, and the growth rate of capital?

  4. By experimenting with a spreadsheet, find out how long it will take for output per worker to double in this example.