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Chapter 7Economic Growth

Questions

1. What is meant by economic growth? How has the U.S. economy grown over the past 200 years?

Answer: Economic growth refers to an increase in real GDP per capita in a country. Over the last 200 years, there has been a marked increase in real GDP per capita in the United States, though the increase is not entirely steady. One of the major economic fluctuations in the United States was the Great Depression, which started in 1929 and recorded a major contraction in real U.S. GDP per capita. However, this was a temporary event, and the sustained and steady growth of real GDP per capita characterizes the U.S. economy both before and after it.

2. What are catch-up growth and sustained growth? Explain with examples.

Answer: Catch-up growth refers to a growth process whereby relatively poorer nations increase their incomes by taking advantage of knowledge and technologies already invented in other, technologically more advanced countries. For example, South Korea, Spain, and China were poorer relative to the United States by 1970. But over the last 40 years, these countries grew faster than the United States, closing the gap that had opened up previously. Sustained growth refers to a growth process in which real GDP per capita grows at a positive and relatively steady rate for long periods. For example, the United States demonstrated sustained growth between 1820 and 2007. This means that there was a positive and relatively steady growth rate in every 50-year period, and the growth rate for the entire period was significantly positive.

3. According to the aggregate production function, how does GDP increase?

Answer: The aggregate production function Y = A × F(K,H) links aggregate output to physical capital (K), total efficiency units of labor (H), and technology (A). To increase GDP, a nation can increase its stock of physical capital, K; increase the human capital of its workers, H (so that it has greater efficiency units of labor for the same workforce); or improve its technology, A.

4. The chapter emphasizes the importance of saving in economic growth.

a. How is the saving rate in an economy defined?

b. What factors help households decide whether to consume or save their income?

c. How do household saving decisions impact investment in the economy?

Answer:

a. The saving rate is the fraction of total income that households save.

b. Saving is a way of allocating some of today’s resources for consumption tomorrow. So, in deciding how much to save, households are trading off consumption today for consumption tomorrow. These choices are affected by several factors:

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Chapter 7 | Economic Growth 70

The first one is the interest rate. The interest rate determines how much households will earn on their savings. Higher interest rates typically encourage more saving.

Second, expectations about future income will affect savings: Households that expect rapid income growth in the future will have less reason to save to finance future consumption (because future income growth will enable them to do this).

Third, expectations about taxes will also impact saving decisions: If households expect high taxes in the future, they may save more in order to be able to pay these taxes without reducing future consumption.

c. An increase in the saving in an economy facilitates an increase in investment. This, in turn, can lead to an increase in the economy’s stock of physical capital, which we have seen is a key to economic growth.

5. Holding all else equal, will increasing the efficiency units of labor lead to sustained growth? Why or why not?

Answer: Increasing the efficiency units of labor by itself is not likely to lead to sustained growth. Efficiency units of labor are calculated as the product of the number of workers and the level of human capital in the economy. Suppose the number of workers in the economy increases. Holding other factors constant, every additional worker will increase output by less and less because of the diminishing marginal product of labor.

Likewise, increasing only the level of human capital will not achieve sustained growth. Because each individual has a finite life, there is a limit to how many years of schooling he or she can obtain. Thus, achieving greater levels of efficiency units by continuously increasing the years of schooling of the workforce does not appear feasible.

6. What explains economic growth in the United States over the past few decades?

Answer: Data on the contribution of physical capital, human capital, and technology to the growth of output per hours worked shows that technology is the single most important contributor to economic growth in the United States. Although physical and human capital did contribute to growth, technology played a central role in U.S. economic growth.

7. Why was there no sustained economic growth before modern times, that is, before 1800?

Answer: The period before modern times was not stagnant, but it was not characterized by sustained growth. One of the possible explanations is the fact that the pace of technological change was much slower than in more recent times. Also, any increases in aggregate income were offset by increases in population, keeping per capita income low.

8. What did Malthus predict about economic growth? Did his predictions come true? Why or why not?

Answer: According to Thomas Malthus, the number of children per woman or per family would always adjust so that income remained close to a subsistence level. Whenever living standards were above this subsistence level, couples would increase their number of children, and this, in turn, would push incomes down toward the subsistence level. When population increases too much, income per capita falls below subsistence and induces famines and/or wars that kill a large fraction of the population. This cycle would then repeat to ensure that incomes always remained close to subsistence.

Malthus’ predictions failed to come true. Although the Malthusian model was a good representation of



how the world was before 1800, it failed to account for the demographic transition. In several countries, population growth rapidly increased due to increased life expectancy and migration. Around the same time, fertility declined, with families having fewer children. This process, which has both economic and social causes, is referred to as the demographic transition. The demographic transition, combined with the Industrial Revolution, enabled economies to break away from the Malthusian cycle. This led to relatively sustained growth in income per capita in many economies, particularly in the Western world.

9. How did the Industrial Revolution affect economic growth?

Answer: The Industrial Revolution is the term given to the series of innovations and their implementation in the production process that started to take place at the end of the eighteenth century in Britain. The Industrial Revolution is important both as an event in itself (because it was the first time technology and scientific methods were used in production in such a coordinated manner) and also as heralding the wave of industrialization that affected many other countries around the world. It was the Industrial Revolution that opened the way for steady and rapid technological changes that have underpinned modern economic growth.

10. Does an increase in GDP per capita of a nation imply a fall in the extent of inequality of the country? Explain.

Answer: GDP per capita is the aggregate amount of income for all households. Therefore, if only the poorest households experience an increase in income, than inequality will decrease. Alternatively, if the income of the richest households is growing by a larger proportion than the income of the poorer households, then once again inequality is increasing.

11. Based on your understanding of the chapter, how can poverty best be reduced?

Answer: Economic analysis suggests several potentially useful approaches to reducing poverty. For poor countries that have natural resources and agricultural sectors, international trade could help raise aggregate incomes. Trade does create certain distributional conflicts, but the overall benefit is positive. Improvements in knowledge and the technologies available in the world economy will also help in raising living standards around the world.

12. What factors explain the dramatic increases in life expectancy that we saw in most countries in the twentieth century?

Answer: Scientific advances in the United States and Western Europe were primarily responsible for the increase in life expectancy throughout the world in the last century. Three were highlighted in the chapter: (1) the development of new drugs, especially antibiotics; (2) the discovery of DDT, which was very effective in attempts to control malaria; and (3) the proliferation of basic but effective medical and public health practices, like boiling water, in poor countries.

Problems1. In the second half of the 20th century, post-war Japan experienced exceptional growth. According to

World Bank data, in 1985, Japan’s GDP was 3.67 trillion, and its annual growth rate was 6.33%. The GDP in this problem is in constant 2010 dollars.

a. Assuming an exponential annual growth rate of 6.33%, calculate Japan’s projected GDP in 2010.

b. In fact, Japan’s 2010 GDP was 5.7 trillion. What could explain any discrepancy between this number and your answer to part (a)?



Answer:

a. Every year between 1985 and 2010, Japan’s GDP grows by 6.33%. If we write down the equations for every year, we get:

Year 1 (1986) = 3.67 * 1.0633

Year 2 (1987) = 3.67 * 1.0633 * 1.0633

Year 3 (1988) = 3.67 * 1.0633 * 1.0633 * 1.0633

…. And so on. We see a pattern—every year, we multiply by an additional 1.0633. In year x, then, the GDP will be:

3.67∗(1.0633)x

In 2010 (or year 25 = 2010 – 1985), gdp will be equal to:

3.67∗1.063325=17.02b. This number is clearly substantially lower than what we calculated above. In fact, this makes

sense; as we discussed, countries experiencing catch-up growth often experience high, then declining growth rates. While the initial post-war growth may have been high, then, it clearly declined in later years.

2. Currently, some of the fastest growing countries in the world remain desperately poor. For example, of the top five fastest-growing economies in 2016, three—Iraq, Burma, and Nauru—had real per capita GDP that were 101th, 162nd and 112th in the world, respectively. (Source: CIA Factbook estimates for 2016, PPP basis)

This seems like something of a contradiction.

Using the equations for growth given in the chapter, explain why a country that has a very low real per capita GDP can also have a very high growth rate.

Answer: Recall that the equation for growth from year t to year t +1 is .

So a lower number in the denominator means that even a small figure in the numerator will result in a large growth rate. For example, in 2016, Burma had a GDP of only $311 B and a population of 56.9 M, resulting in a per capita GDP of around $5,466. However, an increase in per capita GDP of just $100 (which hardly makes Niger a rich country) would result in a GDP figure of $316.69 B, and a GDP growth

rate of By contrast, a $100 increase in U.S. GDP per capita (from $57,300 to $57,400) reflects a GDP growth rate of only 0.2 percent.

Mathematically, these results are due to the fact that we are starting from a much larger base in the United States and a much smaller one in Niger.



3. The following table lists GDP per capita from 1970 to 2010 for South Korea and the United States. As you can see, both grew substantially over that 40-year period.

Year South Korea GDP per Capita U.S. GDP per Capita

1970 317 5247

1980 1778 12598

1990 6642 23955

2000 11948 36467

2010 22151 48358

[Data from the World Bank, World Development Indicators]

a. Plot the five data points for each country on a graph using a nonproportional scale, as in Exhibit 7.3 in the chapter. Connect the points to create a line graph.

b. Plot the five data points for each country on a graph using a proportional scale, that is, a scale where equal distances represent equal percentage changes. Connect the points to create a line graph.

c. Interpret the differences you see in the two graphs.

Answer:

a.Nonproportional Scale



b. Proportional Scale

c. The graph using a nonproportional scale shows an upward-sloping line that gets steeper over time, especially for South Korea. The line in the graph using a proportional scale, on the other hand, is also upward sloping, but flattens out over time, especially for the United States.

This difference in the shape of the lines illustrates the difference between a proportional and a nonproportional scale. Recall that on a proportional scale, equal vertical distances represent equal percentage changes. In the graph from part b, this means that the distance from 300 to 3,000 (a ten-fold increase) is the same as the distance from 3,000 to 30,000. This in turn implies that the slope of the line indicates that rate at which a given quantity is growing. So, for both South Korea and the United States, the rate of growth slowed over the 40-year period, shown by the flatter slopes of the lines in the later years.

Note also that the line is steeper for South Korea than the United States, especially in earlier years. This shows that South Korea was growing more rapidly than the United States, that is, at a higher rate. And this explains why South Korean GDP per capita was only 6 percent of the U.S. level in 1970, but by 2010 had grown to be 46 percent of the U.S. level.

4. Economists Andrew McAfee and Erik Brynjolfsson have written about “The Great Decoupling”—the divergence between productivity growth and employment. Since the mid-1990’s, labor productivity and real GDP have continued to increase, while employment and wages have remained stagnant. Use the concepts from this chapter to explain how this “Decoupling” might work; how could productivity and real GDP continue to increase, even with the declining employment? Why might it be the case that employment has not increased while real GDP has continued to grow? How might this dynamic influence inequality?

Answer: As we saw in the chapter, technology can improve productivity at any level of employment (by increasing A in the production function); the rise in technology, then, is likely responsible for this phenomenon. Indeed, if labor allows for capital to substitute for labor, then we would expect unemployment to remain stable or even increase. Ultimately, this dynamic will likely increase inequality, particularly if the jobs lost to technology are lower skill jobs; the owners of capital will benefit of the substitution toward capital, and the employed will make more money while the unemployed rely on transfers.



5. The graph below shows an index of world GDP per capita from 1000 B.C. to the year 2000.

Source: Jeff Speakes, “Economic History of the World,” Center for Economic Research and Forecasting, California Lutheran University

As you can see, over most of that period, global economic growth was virtually nonexistent. While there were periods that experienced some increase in per capita income, sustained growth begins only in the mid-eighteenth century, and explodes after that—by the year 2000, income per capita is 12 times what it had been 250 years before.

Explain what accounts for such a dramatic change in economic growth beginning in the eighteenth century.

Answer: As detailed in the chapter, the development of technology is crucial for economic growth. For centuries, technology did not change much. The main source of power was human or animal muscle, which severely constrains the ability to build, transport, and manufacture. People in this era lived in much the same way as their ancestors had. However, beginning with the Industrial Revolution in England in the mid-eighteenth century, other sources of power were harnessed—first steam and then electricity. Humankind’s power was magnified many times over in a relatively brief time. Moreover, these changes affected almost every dimension of life and led to still more powerful technology and still faster growth.

6. Productivity (GDP per hour worked) in the United States increased significantly in the 1990s and 2000s. This can be clearly seen in Exhibits 7.10 and 7.11.

a. Based on Exhibit 7.10, is it physical capital, human capital, or technology that is responsible for the overall increase in the annual growth rate of GDP, per hour worked, in these two decades? Explain your answer with reference to the exhibit.



b. When focusing on productivity increase in the 2000s, what technologies may have contributed most to the increased productivity?

Answer:

a. Since 1950, growth that resulted from physical capital (column 4) has been relatively constant until 1999. In the 2000s, there was a 17 percent increase in growth from physical capital. Growth from human capital actually declined between the 1990s and 2000s. Whereas there seems to be a marked increase resulting from the use of technology: there has been a 93 percent increase in returns from technology in the 1990s and a further 48 percent increase in the 2000s. We can also see that 42 percent growth comes from technology in the 1990s and 52% growth in the 2000s. This is opposed to only 28 percent growth stemming from technological advancements in the 1980s.

b. We can safely assume that it is based on the spread of the usage of computer and Internet-based technologies.

7. The concept of diminishing returns to a factor of production applies not only to physical capital but to labor as well. Use the concept of diminishing returns to labor to explain and illustrate why there was no sustained growth in living standards prior to the Industrial Revolution. Draw a graph to illustrate the relationship between population and real GDP, where population is measured on the horizontal axis. Explain how your graph changes after the Industrial Revolution.

Answer: The relevant graph is below:

Note that real GDP increases at a decreasing rate, as is also the case with capital. Barring technological change, this does not allow for an increase in living standards, especially as the population continues to grow.

The Industrial Revolution led to the invention of capital and technology that shifted the production function upward in terms of both labor and capital.

8. In Question 8, we discussed the Malthusian cycle prediction. Under what conditions might the Malthusian cycle be a reality as it was in the preindustrial age?

Answer: As long as technological advancements in agriculture can keep up with population growth on the one hand and increased food consumption due to increased wealth in developing countries on the other



hand, the Malthusian cycle is unlikely to become a problem. However, should climate change destroy mass amounts of previously arable land or fresh water supplies run out or technological advancements slow down and population growth remain constant, the Malthusian cycle might very well be a problem in the future.

9. The “Letting the Data Speak” box on levels versus growth points out how one important index of health—life expectancy—has changed in various countries over time.

To see a dramatic animation of the data mentioned in the box, go to

http://www.gapminder.org/videos/200-years-that-changed-the-world-bbc/#.U8aTaJRdXTo

Hans Rosling is an expert in global health and is known for his creative presentation of statistics. Watch the brief video, and answer the following questions.

a. What was the upper limit on life expectancy in almost all countries in 1810? Which two countries were slightly better off?

b. Which countries failed to improve much in life expectancy and income as a result of the Industrial Revolution?

c. As of 1948, had disparities in life expectancy and income between countries narrowed or widened? Which were some of the countries that had not made much improvement in either measure by 1948?

d. As of 2009, what was the general situation regarding the distribution of countries in terms of health and income? What countries still lagged behind?

e. Based on the video, how can country averages disguise the wide variation in living standards within a country? Give an example from the video.

Answer:

a. The upper limit on life expectancy in almost all countries in 1810 was 40. Only Britain and the Netherlands were slightly better off.

b. Countries in Asia and Africa did not realize much improvement in either life expectancy or income during the Industrial Revolution. The benefits of that period were confined mostly to European nations.

c. By 1948, the differences in life expectancy and income between countries were higher than ever. Europe and North America, followed by Japan, had made great strides on both measures, while such countries as China, India, Indonesia, Bangladesh, and most of the African countries were still characterized by short life expectancies and poverty.

d. By 2009, most Asian and some African countries had made great improvements in life expectancy and income. Rosling comments that by then, most people in the world were “in the middle” between the richest countries with the highest life expectancy (Europe, North America, and Japan) and the poorest countries, like many in sub-Saharan Africa that had endured civil strife or the HIV epidemic (Congo and South Africa).

e. When the data are examined in more detail, significant differences emerge within countries. For example, life expectancy and income in China range all the way from the situation in Shanghai,



which has figures comparable to those of Italy, and the poor inland province of Guizhou, whose rural areas have the same health and wealth as Ghana, a very poor country. Hence, although taken as a whole, China has made great strides in living standards, there are still enormous regional disparities that are hidden in the countrywide data.

10. Increasingly, independent programmers are making their code “open-source.” The statistical programming language “R,” for example, is completely free and open; anyone can submit a new “package” of specialized functions. How might open source technology affect growth in developing countries? Imagine every technology company in the United States suddenly made their code open-source; would this increase growth in developing countries? Explain.

Answer: Open source technology likely has the potential to boost growth in developing countries—it makes productivity-enhancing tools available to a broader group of people, increasing A in countries around the world. Indeed, the chapter discussed the importance of infusing technology in stimulating growth. However, suddenly making all code open-sourced wouldn’t necessarily boost growth immediately in developing countries—software, in particular, needs the appropriate hardware. The technologies of foreign economies may not be immediately useful. In addition, any code that’s open-sourced and available off-the-shelf could go directly to consumers with technology—and wouldn’t be counted in GDP.

11. Suppose that a 10 percent increase in the physical capital stock increases GDP by 10 percent. Now consider an additional 8 percent increase in the physical capital stock. Will this increase GDP by less than 8 percent, 8 percent, or more than 8 percent? Explain.

Answer: The second, 8 percent increase in the physical capital stock will increase the capital stock by less than 8 percent. This is due to the diminishing marginal product of physical capital. Each additional increment in the stock of physical capital leads to smaller and smaller increases in GDP.

12. Challenge Problem: Refer to Exhibit 7.4. If the United States, Guatemala, Haiti, Rwanda, Ghana, Kenya, and India continue to grow at the rates given in the exhibit, how many years (starting from 2010) would it take for each to catch up to the United States in terms of per capita GDP? Why might these calculations be less reliable? (Hint: If a country’s GDP per capita is growing at a constant rate, g, then the natural log of GDP per capita t years into the future is: ln y(t) = ln y(0) + gt, where y(0) is GDP per capita in the initial year.)

Answer: Look carefully at the table (Exhibit 7.4). The U.S. per capita GDP is growing at 2 percent per year. Hence, any country that starts from a lower GDP per capita, and has a growth rate of 2 percent or less, will never catch up—it is simply a mathematical impossibility.

This means that, if the growth rates listed continue to prevail, Guatemala, Haiti, Rwanda, Ghana, and Kenya will never catch up to the United States in terms of per capita GDP.

Therefore, that leaves India, whose per capita GDP is growing at 3.20 percent.

To see how long it will take India to catch up to the United States, we can use the formula provided in the hint: ln y(t) = ln y(0) + gt, where y(0) is GDP per capita in 2010. Substituting in the 2010 value for y(0) and the value for g in the United States gives the following:

ln yUS(t) = ln 41,365 + 0.02t

The comparable equation for India is as follows:

ln yIndia(t) = ln 3,477 + 0.032t



We want to find how many years (t) it will take India to catch up to the United States in terms of per capita GDP. We must keep in mind that U.S. per capita GDP is continuing to grow, just not as fast as India’s.

To find how long it will take India to catch up, we simply set the above equation for the United States equal to the equation for India:

ln 41,365 + 0.02t = ln 3,477 + 0.032t

Solving this equation for t:

tIndia = (ln 41,365 – ln 3,477)/0.012 = approximately 206 years.

Therefore, if the rates of growth of GDP per capita listed in the table persist from 2010 on, India would catch up with the United States in around 206 years.

A problem with these calculations is that many factors can influence growth: this means that due to technological discoveries in India its growth might increase, whereas if the United States does not invest in technology its growth can decline. It is difficult to predict with certainty GDP growth for the next 5 years, but doing it for more than that is quite unreliable.



Appendix to Chapter 7 Problems

A1. Use a diagram to represent the Solow growth model using the aggregate production function and the relationship between the physical capital stock and aggregate saving.

a. Which point in the figure represents the steady-state equilibrium? Why?

b. Use the diagram to show the impact of an increase in human capital on GDP.

Answer: The following figure represents the Solow growth model. The straight line represents the value of depreciated capital, d × K. The curve labeled Y = A × F(K,H) represents the aggregate production function, or more specifically, the relationship between aggregate incomes and the (physical) capital stock, for a given level of efficiency units of labor (and for a given technology). The curve labeled s × A × F(K, H) shows the relationship between the level of investment and the capital stock given the saving rate of households, s. The distance between this curve and the horizontal axis at a given level of capital stock corresponds to aggregate saving or investment, while the distance between the curve labeled s × A × F(K, H) and the curve labeled Y = A × F(K, H) represents consumption.

a. In the figure, there is a unique point where the straight line labeled (d × k) intersects the curve labeled s × A × F(K,H), representing investment. This intersection gives the steady-state equilibrium capital level on the horizontal axis, marked as K*, and the steady-state equilibrium output level on the vertical axis is Y*. When the economy is in steady-state equilibrium, the level of investment (saving) and the value of depreciated capital are equal.



b. The following figure shows the effect of an increase in human capital on aggregate output.

When the human capital of workers increases, the total efficiency units of labor also increases. This implies that the economy can produce more with the same capital stock and technology, so the curve for the aggregate production function shifts up. This leads to a new steady-state equilibrium with higher capital stock and aggregate income. In particular, the capital stock increases from K* to K** and aggregate income from Y* to Y**.

A2. In the 1980s, the saving rate in Japan was extremely high. Gross saving as a percentage of GDP ranged between 30 percent and 32 percent. Can such a high saving rate lead to sustained economic growth? Use the Solow model to explain your answer.

Data source: http://data.worldbank.org/indicator/NY.GNS.ICTR.ZS/countries/JP?page=5&display=default



Answer: No, a high saving rate cannot sustain economic growth. With given levels of total efficiency units of labor and technology, there is a maximum amount of aggregate income that an economy can achieve by increasing saving because we can never go above a saving rate of 100 percent. This can be explained using the following figure.

In the figure, the Solow model shows that economies with higher saving rates have higher aggregate incomes, but increases in the saving rate cannot be the source of sustained growth. This is because there is a maximum to how much an economy can save and thus a limit to what aggregate income it can achieve by just saving more.

A3.

A4. The appendix details the important distinction between arithmetic and geometric averages in determining growth rates.

a. Using the procedure outlined in the Appendix for geometric average growth rates (in the section titled “Calculating Average (Compound) Growth Rates,” see if you can reproduce the “Implied (average) annual growth” figures given in the last column of Exhibit 7.4 for the following countries: France, Singapore, Botswana, India, and Kenya.

b. Using the procedure outlined in the Appendix for finding arithmetic average growth rates, calculate the arithmetic average growth rate for the five countries. Compare these with the rates you obtained in part a. Does the arithmetic average understate or overstate the actual growth rate? Explain.

Answer:

a. From the formula in the Appendix, we know that to find the geometric average growth rate (g) over the 50-year period listed in the table, we start by finding the ratio of GDP per capita in 2010 to GDP per capita in 1960. We then plug that ratio into the following equation:



Below are the calculations for the five countries given in the problem:

b. From the formula in the Appendix, we know that to find the arithmetic average growth rate over the 50-year period listed in the table is to use the following equation:

Using this formula yields the following arithmetic growth rates:

In each case, the calculated arithmetic average growth rate overstates the actual growth rate that is consistent with the observed data for per capita GDP in 2010. This is due to the fact that using the arithmetic average does not account for compounding and, therefore, ignores the cumulative effects of growth


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