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1 KrugmanMacro_SM_Ch08.qxp 11/9/05 4:47 PM Page 99 Long-Run Economic Growth 1. The accompanying table shows data from the Penn World Table, Version 6.1, for real GDP in 1996 U.S. dollars for Argentina, Ghana, South Korea, and the United States for, 1970, 1980, 1990, and. Year Argentina Ghana $7,395?? $832?? ,227?? 1,275?? ,556?? 1,204?? ,237?? 1,183?? 10,995?? 1,349?? Year South Korea United States $1,571?? $12,414?? ,777?? 16,488?? ,830?? 21,337?? ,959?? 26,470?? 15,881?? 33,308?? 8chapter 25 macroeconomics economics 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 Ghana $7, % 67% $ % 62% , , , , , , , ,

2 KrugmanMacro_SM_Ch08.qxp 11/9/05 4:47 PM Page MACROECONOMICS, CHAPTER 8 ECONOMICS, CHAPTER 25 Year South Korea United States $ 1, % 10% $12, % 37% , , , , , , ,881 1, , b. South Korea experienced the greatest increase in living standards from to ; in 2001 it produced 1,011% ($15,881/$1, ) of what it produced in. Argentina and Ghana experienced only a modest growth in living standards over the same period. Argentina s path was less consistent than that of Ghana, where living standards remained low throughout the period. Compared with real GDP in, the United States in produced 268% ($33,308/$12, ) 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. Although the growth in living standards was similar in Ghana and Argentina, Ghana had started from a much lower level. in Ghana was only 11% of that in Argentina in and 12% in. Living standards in Africa suffered from 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 6.1, for the past few decades. Average annual growth rate of Years Argentina Ghana South Korea % 4.36% 5.86% 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 1990 continues indefinitely into the future. Starting from, use the Rule of 70 to calculate, where possible, the year in which a country will have doubled its.

3 KrugmanMacro_SM_Ch08.qxp 11/9/05 4:47 PM Page 101 LONG-RUN ECONOMIC GROWTH 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 b. If each nation continues to grow as it did from 1990 to, will have doubled in Argentina by 2016, in Ghana by 2052, and in South Korea by You are hired as an economic consultant to the countries of Albernia and Brittania. Each country s current relationship between physical capital per worker (K/L) and output per worker (Y/L) is given by the curve labeled Productivity 1 in the accompanying diagram. Albernia is at point A and Brittania is at point B. per worker (Y/L) B B Productivity 1 (Y/L) A A (K/L) A (K/L) B Physical capital per worker a. In the relationship depicted by the curve Productivity 1, what factors are held fixed? Do these countries experience diminishing returns to physical capital per worker? b. Assuming that the amount of human capital per worker and the technology are held fixed in each country, can you recommend a policy to generate a doubling of in each country? c. How would your policy recommendation change if the amount of human capital per worker and the technology were not fixed? Draw a curve on the diagram that represents this policy for Albernia. 3. a. The curve reflecting the relationship between physical capital per worker (K/L) and output per worker (Y/L) is drawn holding human capital per worker and technology fixed. Both Albernia and Brittania experience diminishing returns to physical capital since in both countries equal successive increases in physical capital per worker holding human capital per worker and technology constant will result in smaller and smaller increases in per worker. b. Albernia should increase its physical capital per worker to (K/L) B. Brittania will have to add a huge amount of physical capital per worker.

4 102_KrugmanMacro_SM_Ch08.qxp 11/10/05 1:07 PM Page MACROECONOMICS, CHAPTER 8 ECONOMICS, CHAPTER 25 c. If it were possible to increase the amount of human capital per worker or improve the technology, or both, then Productivity 1 could shift to Productivity 2 and Albernia could double per worker without a change in the physical capital per worker. On the accompanying diagram, Albernia would move from point A to point C. per worker Productivity 2 (Y/L) B C B Productivity 1 (Y/L) A A (K/L) A (K/L) B Physical capital per worker 4. 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? 4. 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 there are 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. 5. The economy of Profunctia has estimated its aggregate production function, when holding human capital per worker and technology constant, as Y L = 100 K L

5 KrugmanMacro_SM_Ch08.qxp 11/9/05 4:47 PM Page 103 LONG-RUN ECONOMIC GROWTH 103 Y is, L is the number of workers, and K is the quantity of physical capital. Given that Profunctia has 1,000 workers, calculate per worker and the quantity of physical capital per worker for the differing amounts of physical capital shown in the accompanying table. K L K/L Y/L $0 1,000?? 10 1,000?? 20 1,000?? 30 1,000?? 40 1,000?? 50 1,000?? 60 1,000?? 70 1,000?? 80 1,000?? 90 1,000?? 100 1,000?? a. Plot the aggregate production function for Profunctia. b. Does the aggregate production function exhibit diminishing returns to physical capital? Explain your answer. 5. a. The accompanying table and diagram show the aggregate production function for Profunctia. K L K/L Y/L $0 1,000 $0.00 $ , , , , , , , , , , per worker, Y/L $ $ Physical capital per worker, K/L

6 KrugmanMacro_SM_Ch08.qxp 11/11/05 5:31 PM Page MACROECONOMICS, CHAPTER 8 ECONOMICS, CHAPTER 25 b. The aggregate production function does exhibit diminishing returns to physical capital. For example, the table shows that as K increases from $30 to $40, Y/L increases by $2.68, but as K increases from $70 to $80, Y/L increases only by $ 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, click on Productivity under Latest Numbers and then choose the latest 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 previous data? 6. Answers will vary with the latest data. For the third quarter of 2005, business and nonfarm business productivity grew by 4.8% and 4.1%, respectively. These were higher than the productivity growth figures for the second quarter of 2005, which were 0.81% and 2.1%, respectively. 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 increases in physical capital per worker, technological progress is probably the most important driver of productivity growth. While natural resources played a prominent role historically in determining productivity, they play a less important role in increasing productivity than do increases in human or physical capital in most countries today. 8. Through its policies and institutions, how has the United States influenced U.S. longrun economic growth? Why might persistently large borrowing by the U.S. government ultimately limit long-run economic growth in the future? 8. Institutions and policies in the United States have greatly aided U.S. economic growth. The country 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. However, the government s persistently large borrowing may reduce private investment spending (a phenomenon known as crowding out ), consequently slowing economic growth. 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 ( y) z in z years.)

7 KrugmanMacro_SM_Ch08.qxp 11/9/05 4:47 PM Page 105 LONG-RUN ECONOMIC GROWTH If in Groland grows at an average annual rate of 2.0%, in 100 years will be $144,893 [$20,000 (1 0.02) 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. 10. The accompanying table shows data from the Penn World Table, Version 6.1, 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 $5,561? $22,254? Japan 2,445? 24,495? United Kingdom 7,498? 22,849? United States 10,601? 33,308? 10. The accompanying table shows U.S. in France, Japan, and the United Kingdom as a percentage of in the United States U.S. U.S. France $5, % $22, % Japan 2, , United Kingdom 7, , United States 10, , in France and Japan, the two nations with the lowest in 1950, closed some of the gap in living standards with the United States. Japan s grew from only 23.1% of that in the United States to 73.5%, and France s rose from 52.5% to 66.8%. But living standards in the United Kingdom relative to those in the United States actually declined; fell from 70.7% of that in the United States to 68.6%. France and Japan have converged, but the United Kingdom has not.

8 KrugmanMacro_SM_Ch08.qxp 11/9/05 4:47 PM Page MACROECONOMICS, CHAPTER 8 ECONOMICS, CHAPTER The accompanying table shows data from the Penn World Table, Version 6.1, for real GDP 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 $7,395? $10,995? Ghana 832? 1,349? South Korea 1,571? 15,881? United States 12,414? 33,308? 11. The accompanying table shows U.S. in Argentina, Ghana, and South Korea as a percentage of in the United States. U.S. U.S. Argentina $7, % $10, % Ghana , South Korea 1, , United States 12, , There is little evidence of convergence for either Argentina or Ghana. Living standards in both nations declined relative to those in the United States. In Argentina fell from 59.6% of that of the United States to 33.0%; Ghana s fell from 6.7% to 4.0%. But South Korea s showed signs of convergence with those in the United States; rose from 12.7% of that in the United States to 47.7%.

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