# Ghana South Korea United States. Real GDP per capita (2005 dollars) Per centage of 1960 real GDP per capita real GDP per capita

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1 Long-Run Economic Growth chapter: 24 9 ECONOMICS MACROECONOMICS 1. The accompanying table shows data from the Penn World Table, Version 7.0, for real GDP in 2005 U.S. dollars for Argentina, Ghana, South Korea, and the United States for, 1970, 1980, 1990, 2000, and. Year \$6,243?? \$603?? \$1,782?? \$15,438?? 1970 \$7,810?? \$939?? \$3,018?? \$20,480?? 1980 \$8,638?? \$807?? \$5,339?? \$25,090?? 1990 \$6,823?? \$844?? \$11,437?? \$31,637?? 2000 \$9,172?? \$887?? \$18,926?? \$39,175?? \$11,961?? \$1,239?? \$25,029?? \$41,102?? a. Complete the table by expressing each year s as a percentage of its and levels. b. How does the growth in living standards from to compare across these four nations? What might account for these differences? 1. a. The accompanying table shows each nation s in terms of its and levels. Year Argentina Argentina Ghana South Korea United States Ghana South Korea United States \$6, % 52% \$ % 49% \$1, % 7% \$15, % 38% 1970 \$7, % 65% \$ % 76% \$3, % 12% \$20, % 50% 1980 \$8, % 72% \$ % 65% \$5, % 21% \$25, % 61% 1990 \$6, % 57% \$ % 68% \$11, % 46% \$31, % 77% 2000 \$9, % 77% \$ % 72% \$18,926 1,062% 76% \$39, % 95% \$11, % 100% \$1, % 100% \$25,029 1,405% 100% \$41, % 100% S-121 KrugWellsECPS3e_Macro_CH09.indd S-121

2 S-122 MACROECONOMICS, CHAPTER 9 ECONOMICS, CHAPTER 24 b. South Korea experienced the greatest increase in living standards from to ; in it produced 1,405% (\$125,029/\$1, ) of what it produced in. Argentina experienced only a modest growth in living standards over the same period, and Argentina s path was less consistent than that of Ghana. Compared with in, the United States in produced 266% (\$41,102/\$15, ) of what it produced in. The growth in living standards in Argentina, Ghana, and South Korea reflects the pattern for their different regions of the world. South Korea, like many other East Asian countries, had high productivity growth because of high savings and investment rates, a good education system, and substantial technological progress. Living standards grew more modestly in Argentina, as in other Latin American countries, because of low savings and investment spending rates, underinvestment in education, political instability, and irresponsible government policies. Ghana, in particular recently, has made some progress. Living standards in Africa suffered because of major political instabilities, poor education and infrastructure, and disease. 2. The accompanying table shows the average annual growth rate in for Argentina, Ghana, and South Korea using data from the Penn World Table, Version 6.2, for the past few decades. a. For each decade and for each country, use the Rule of 70 where possible to calculate how long it would take for that country s to double. b. Suppose that the average annual growth rate that each country achieved over the period continues indefinitely into the future. Starting from 2000, use the Rule of 70 to calculate, where possible, the year in which a country will have doubled its. Average annual growth rate of Years Argentina Ghana South Korea % 15.54% 7.50% a. The accompanying table shows the number of years it would take for per capita to double according to the Rule of 70 using the average annual growth rate in per decade in each country. Values corresponding to years with negative growth rates are left uncalculated because we cannot apply the Rule of 70 to a negative growth rate. Years for to double according to the Rule of 70 Years Argentina Ghana South Korea KrugWellsECPS3e_Macro_CH09.indd S-122

3 LONG-RUN ECONOMIC GROWTH S-123 b. If each nation continues to grow as it did from 1990 to 2000, per capita will have doubled in Argentina by 2018, in Ghana by 2033, and in South Korea by The accompanying table provides approximate statistics on income levels and growth rates for regions defined by income levels. According to the Rule of 70, starting in 2010 the high-income countries are projected to double their GDP in approximately 78 years, in Throughout this question, assume constant growth rates for each of the regions that are equal to their average value between 2000 and Average annual growth rate of real GDP per GDP Region capita (2010) ( ) High-income countries \$38, % Middle-income countries 3, Low-income countries Source: World Bank. a. Calculate the ratio of GDP in 2010 of the following: i. Middle-income to high-income countries ii. Low-income to high-income countries iii. Low-income to middle-income countries b. Calculate the number of years it will take the low-income and middle-income countries to double their GDP. c. Calculate the GDP of each of the regions in (Hint: How many times does their GDP double in 78 years, the number of years from 2010 to 2088?) d. Repeat part a with the projected GDP in e. Compare your answers to parts a and d. Comment on the change in economic inequality between the regions. 3. a. i. The ratio of GDP in 2010 of middle-income to high-income countries is or 10.4%. ii. The ratio of GDP in 2010 of low-income to high-income countries is or 1.3%. iii. The ratio of GDP in 2010 of low-income to middle-income countries is or 12.7%. b. Middle-income countries are projected to take 70/4.8 = 14.6 years to double their GDP, and low-income countries are projected to take 23.3 years. c. With a growth rate of 0.9%, it will take 70/0.9 = 78 years for GDP to double. Therefore high-income countries are projected to double their GDP in 78 years to \$76,586. During the same period, middle-income countries are projected to double their GDP approximately 78/14.6 = 5 times. So the projected GDP for middle-income countries is \$3, = \$127,360. In 2088, low-income countries are expected to increase their GDP by approximately 78/23.3 = 3 times. Hence, projected GDP for low-income countries is \$ = \$4,056. KrugWellsECPS3e_Macro_CH09.indd S-123

4 S-124 MACROECONOMICS, CHAPTER 9 ECONOMICS, CHAPTER 24 d. Using the projected GDP figures in 2088, the percentages are as follows: i. Middle-income to high-income countries: or 166.3% ii. Low-income to high-income countries: or 5.3% iii. Low-income to middle-income countries: or 3.2% e. Both the low-income countries and the middle-income countries (as defined in 2010) have improved their GDP relative to high-income countries due to their higher growth rates. In fact, growth in the middle-income countries is so strong that by 2088 living standards in today s middle-income countries will have overtaken living standards in today s high-income countries. The result is that inequality will be lower. However, since middle-income countries are growing faster than low-income countries, the inequality between those two regions will have widened. 4. You are hired as an economic consultant to the countries of Albernia and Brittania. Each country s current relationship between physical capital and output is given by the curve labeled Productivity 1 in the accompanying diagram. Albernia is at point A and Brittania is at point B. \$40,000 B Productivity 1 20,000 A \$10,000 30,000 Physical capital a. In the relationship depicted by the curve Productivity 1, what factors are held fixed? Do these countries experience diminishing returns to physical capital? b. Assuming that the amount of human capital and the technology are held fixed in each country, can you recommend a policy to generate a doubling of in Albernia? c. How would your policy recommendation change if the amount of human capital could be changed? Assume that an increase in human capital doubles the output when physical capital equals \$10,000. Draw a curve on the diagram that represents this policy for Albernia. 4. a. The curve reflecting the relationship between physical capital and output is drawn holding human capital and technology fixed. Both Albernia and Brittania experience diminishing returns to physical capital since in both countries equal successive increases in physical capital holding human capital and technology constant will result in smaller and smaller increases in. b. Albernia should increase its physical capital to \$30,000. KrugWellsECPS3e_Macro_CH09.indd S-124

5 LONG-RUN ECONOMIC GROWTH S-125 c. An increase in human capital shifts the curve Productivity 1 to Productivity 2 and Albernia doubles without a change in the physical capital. On the accompanying diagram, Albernia would move from point A to point C. So your policy recommendation should be to increase the amount of human capital. Productivity 2 \$40,000 C B Productivity 1 20,000 A \$10,000 30,000 Physical capital 5. The country of Androde is currently using Method 1 for its production function. By chance, scientists stumble onto a technological breakthrough that will enhance Androde s productivity. This technological breakthrough is reflected in another production function, Method 2. The accompanying table shows combinations of physical capital and output for both methods, assuming that human capital is fixed. Physical capital Method 1 Method 2 Physical capital a. Using the data in the accompanying table, draw the two production functions in one diagram. Androde s current amount of physical capital is 100. In your figure, label that point A. KrugWellsECPS3e_Macro_CH09.indd S-125

6 S-126 MACROECONOMICS, CHAPTER 9 ECONOMICS, CHAPTER 24 b. Starting from point A, over a period of 70 years, the amount of physical capital in Androde rises to 400. Assuming Androde still uses Method 1, in your diagram, label the resulting point of production B. Using the Rule of 70, calculate by how many percent per year output has grown. c. Now assume that, starting from point A, over the same period of 70 years, the amount of physical capital in Androde rises to 400, but that during that time period, Androde switches to Method 2. In your diagram, label the resulting point of production C. Using the Rule of 70, calculate by how many percent per year output has grown now. d. As the economy of Androde moves from point A to point C, what share of the annual productivity growth is due to higher total factor productivity? 5. a. The accompanying diagram, the line labeled Productivity 1 shows the production function using Method 1, and the line labeled Productivity 2 shows the production function using Method 2. Point A is the point, using Method 1, at which Androde produces output using 100 units of physical capital Productivity C Productivity A B Physical capital b. In the accompanying diagram, Point B is the point, using Method 1, at which Androde produces output using 400 units of physical capital. Output has grown from 50 units to 100 units. Since over a period of 70 years, output has doubled, output must have grown by 1% per year. c. In the accompanying diagram, Point C is the point, using Method 2, at which Androde produces output using 400 units of physical capital. From point A to point C, output has grown from 50 units to 200 units. Since over a period of 70 years, output has quadrupled, output must have grown on average by 2% per year. (Taking 70/2 = 35 years to double from 50 to 1000, and then another 35 years to double again from 100 to 200). d. Since, without the increase in technological progress, output would have grown at an annual rate of only 1%, but with the increase in technological progress, output has grown by 2%, half of that growth rate has to be due to an increase in total factor productivity. 6. The Bureau of Labor Statistics regularly releases the Productivity and Costs report for the previous month. Go to and find the latest report. (On the Bureau of Labor Statistics home page, from the tab Subject Areas, select the link to Labor Productivity & Costs ; then, from the heading LPC News Releases, find the most recent Productivity and Costs report.) What were the percent changes in business and nonfarm business productivity for the previous quarter? How does the percent change in that quarter s productivity compare to data from the previous quarter? KrugWellsECPS3e_Macro_CH09.indd S-126

7 6. Answers will vary with the latest data. For the second quarter of 2011, business productivity did not change (it grew by 0.0%) and nonfarm business productivity decreased by 0.3%. These were better than the productivity growth figures for the first quarter of 2011, which showed a decrease of 1.4% in business productivity and a decrease of 0.6% in nonfarm business productivity. 7. What roles do physical capital, human capital, technology, and natural resources play in influencing long - run economic growth of aggregate output? 7. Physical capital, human capital, technology, and natural resources play important roles in influencing long - run growth in. Increases in both physical capital and human capital help a given labor force to produce more over time. Although economic studies have suggested that increases in human capital may explain increases in productivity better than do increases in physical capital per worker, technological progress is probably the most important driver of productivity growth. Although natural resources played a prominent role historically in determining productivity, today they play a less important role in increasing productivity than do increases in human or physical capital in most countries. 8. How have U.S. policies and institutions influenced the country s long - run economic growth? 8. U.S. institutions and policies have greatly aided the country s economic growth. The United States has been politically stable, and its laws and institutions protect private property. The economy has attracted significant savings, both domestic and foreign, that have allowed investment spending to spur the growth of the capital stock and fund research and development. The government has directly supported economic growth through its support of public education as well as research and development. 9. Over the next 100 years, in Groland is expected to grow at an average annual rate of 2.0%. In Sloland, however, growth is expected to be somewhat slower, at an average annual growth rate of 1.5%. If both countries have a today of \$20,000, how will their differ in 100 years? [Hint: A country that has a today of \$x and grows at y% per year will achieve a of \$x (1 + (y/100)) z in z years. We assume that 0 y < 10.] 9. If in Groland grows at an average annual rate of 2.0%, in 100 years will be \$144,893 [\$20,000 ( ) 100 ]. At an average annual rate of growth of 1.5%, in Sloland in 100 years will be \$88,641 [\$20,000 ( ) 100 ]. Although both nations start with the same real GDP today, the differential growth rates will result in living standards in Sloland that are 61.2% (\$88,641/\$144, ) of those in Groland. LONG-RUN ECONOMIC GROWTH S-127 KrugWellsECPS3e_Macro_CH09.indd S-127

8 S-128 MACROECONOMICS, CHAPTER 9 ECONOMICS, CHAPTER The accompanying table shows data from the Penn World Table, Version 7.0, for real GDP U.S. in France, Japan, the United Kingdom, and the United States in 1950 and. Complete the table. Have these countries converged economically? 1950 Percentage Percentage of U.S. of U.S. France \$7,112? \$30,821? Japan 3,118? 31,958? United Kingdom 10,401? 33,386? United States 13,183? 41,102? 10. The accompanying table shows U.S. in France, Japan, and the United Kingdom as a percentage of in the United States Percentage of U.S. Percentage of U.S. France \$7, % \$30, % Japan 3, , United Kingdom 10, , United States 13, , Growth of in France, Japan, and the United Kingdom closed some of the gap in living standards with the United States between 1950 and. Japan s real GDP grew from only 23.7% of that in the United States to 77.8%, and France s rose from 53.9% to 75.0%. Living standards in the United Kingdom relative to those in the United States rose relatively little; grew from 78.9% of that in the United States to 81.2%. The in these countries has converged. 11. The accompanying table shows data from the Penn World Table, Version 7.0, for U.S. for Argentina, Ghana, South Korea, and the United States in and. Complete the table. Have these countries converged economically? Percentage Percentage of U.S. of U.S. Argentina \$6,243? \$11,961? Ghana 603? 1,239? South Korea 1,782? 25,029? United States 15,438? 41,102? KrugWellsECPS3e_Macro_CH09.indd S-128

9 11. The accompanying table shows U.S. in Argentina, Ghana, and South Korea as a percentage of in the United States. Percentage of U.S. Percentage of U.S. Argentina \$6, % \$11, % Ghana , South Korea 1, , United States 15, , LONG-RUN ECONOMIC GROWTH S-129 There is little evidence of convergence for Argentina. Living standards actually declined relative to those in the United States. In Argentina, fell from 40.4% of that of the United States to 29.1%. There is also no evidence of convergence for Ghana; Ghana s declined from 3.9% of that of the United States to 3.0%. South Korea s showed strong signs of convergence; rose from 11.5% of that in the United States to 60.9%. 12. Why would you expect in California and Pennsylvania to exhibit convergence but not in California and Baja California, a state of Mexico that borders the United States? What changes would allow California and Baja California to converge? 12. According to the conditional convergence hypothesis, other things equal, countries with relatively low tend to have higher rates of growth than countries with relatively high. We can apply this hypothesis to regions as well. It is more likely that the factors that affect growth will be equal in California and Pennsylvania: both states have similar educational systems, infrastructure, rule of law, and so on. But that is not true of California and Baja California: in comparing them, the factors that affect growth are not likely to be equal. California and Baja California have very different educational systems, different infrastructures, and differences in how the rule of law is applied. So it is less likely that they will converge. For California and Baja California to converge in, they would have to become more similar in the factors that affect growth. 13. According to the Oil & Gas Journal, the proven oil reserves existing in the world in consisted of 1,342 billion barrels. In that year, the U.S. Energy Information Administration reported that the world daily oil production was million barrels a day. a. At this rate, for how many years will the proven oil reserves last? Discuss the Malthusian view in the context of the number you just calculated. b. In order to do the calculations in part a, what did you assume about the total quantity of oil reserves over time? About oil prices over time? Are these assumptions consistent with the Malthusian view on resource limits? c. Discuss how market forces may affect the amount of time the proven oil reserves will last, assuming that no new oil reserves are discovered and that the demand curve for oil remains unchanged. 13. a. In one year, approximately million 365 = 26.4 billion barrels of oil are produced. At this rate, 1,342 billion barrels of oil will last for approximately 51 years. The numbers support the Malthusian view that there is a limit to the standard of living. Because population growth also results in a growing need for natural resources to continually raise the standard of living, the limited supply of resources like oil results in a limit on the standard of living. KrugWellsECPS3e_Macro_CH09.indd S-129

10 S-130 MACROECONOMICS, CHAPTER 9 ECONOMICS, CHAPTER 24 b. The calculation assumes that the reserves of oil cannot increase and that the search for alternative fuels would not affect the annual production of oil. More importantly, it assumes that the possibility of rising oil prices as reserves drain out will neither create incentives for alternative fuels nor affect total consumption. These assumptions are consistent with the Malthusian view on the on resource limits. c. Assuming that the demand curve for oil does not change, with decreasing supply as some oil reserves start drying out, prices should rise. This will cause a fall in the quantity demanded, extending the time during which proven oil reserves will last. 14. The accompanying table shows the annual growth rate for the years 2000 in emissions of carbon dioxide (CO 2 ) and the annual growth rate in real GDP for selected countries average annual growth rate of: per CO 2 emissions Country capita Argentina 2.81% 1.01% Bangladesh Canada China Germany Ireland Japan South Korea Mexico Nigeria Russia South Africa United Kingdom United States Sources: Energy Information Administration: International Monetary Fund. a. Rank the countries in terms of their growth in CO 2 emissions, from highest to lowest. What five countries have the highest growth rate in emissions? What five countries have the lowest growth rate in emissions? b. Now rank the countries in terms of their growth in, from highest to lowest. What five countries have the highest growth rate? What five countries have the lowest growth rate? c. Would you infer from your results that CO 2 emissions are linked to growth in output? d. Do high growth rates necessarily lead to high CO 2 emissions? KrugWellsECPS3e_Macro_CH09.indd S-130

11 14. a. As shown in the accompanying table, the five countries with the highest growth rate in CO 2 emissions are China, Bangladesh, South Korea, Argentina, and South Africa. The five countries with the lowest growth rate in CO 2 emissions are Nigeria, Ireland, the United States, Canada, and the United Kingdom. Country b. As shown in the accompanying table, the five countries with the highest growth rate in are China, Nigeria, Russia, Bangladesh, and South Korea. The five countries with the lowest growth rate in are Mexico, Japan, the United States, Germany, and Canada. Country 2000 average annual growth rate of CO 2 emissions China 11.11% Bangladesh 5.47 South Korea 1.68 Argentina 1.01 South Africa 0.80 Russia 0.52 Mexico 0.44 Japan 1.03 Germany 1.23 United Kingdom 1.35 Canada 1.46 United States 1.78 Ireland 2.10 Nigeria 2.46 Sources: Energy Information Administration; International Monetary Fund average annual growth rate of China 9.85% Nigeria 6.07 Russia 5.22 Bangladesh 4.17 South Korea 3.48 Argentina 2.81 South Africa 2.39 Ireland 1.05 United Kingdom 0.88 Canada 0.68 Germany 0.59 United States 0.58 Japan 0.29 Mexico 0.18 Sources: Energy Information Administration; International Monetary Fund. LONG-RUN ECONOMIC GROWTH S-131 KrugWellsECPS3e_Macro_CH09.indd S-131

12 S-132 MACROECONOMICS, CHAPTER 9 ECONOMICS, CHAPTER 24 c. Yes. Three of the five countries with the highest growth rate in CO 2 emissions also have the highest growth rate in : China, Bangladesh, and South Korea. Two of the five countries with the lowest growth rate in CO 2 emissions also have the lowest growth rate in per capita: the United States and Canada. d. Although growth rates in GDP and CO 2 emissions are linked, the experience of Nigeria and, to a lesser extent, Ireland shows that it is possible both to have a high growth rate of GDP and to reduce CO 2 emissions. This can be done in a variety of ways, including using alternative energy sources and better designs for buildings and automobiles. Estimates suggest that large CO 2 reductions would put only a minor dent in long-run GDP growth. KrugWellsECPS3e_Macro_CH09.indd S-132

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