ap macro ch25

Solution

Long-Run Economic Growth1. The accompanying table shows data from the Penn World Table, Version 6.1, for real

GDP per capita in 1996 U.S. dollars for Argentina, Ghana, South Korea, and theUnited States for 1960, 1970, 1980, 1990, and 2000.

99

1960 real GDP

per capita

2000 real GDP

per capita

Real GDP per capita

(1996 dollars)

1960 $7,395 ? ? $832 ? ?

1970 9,227 ? ? 1,275 ? ?

1980 10,556 ? ? 1,204 ? ?

1990 7,237 ? ? 1,183 ? ?

2000 10,995 ? ? 1,349 ? ?

Year

Percentage of 1960

real GDP per capita

2000 real GDP

per capita

Real GDP per capita

(1996 dollars)

Percentage of

Argentina Ghana

1960 real GDP

per capita

2000 real GDP

per capita

Real GDP per capita

(1996 dollars)

1960 $1,571 ? ? $12,414 ? ?

1970 2,777 ? ? 16,488 ? ?

1980 4,830 ? ? 21,337 ? ?

1990 9,959 ? ? 26,470 ? ?

2000 15,881 ? ? 33,308 ? ?

Year

Percentage of 1960

real GDP per capita

2000 real GDP

per capita

Real GDP per capita

(1996 dollars)

Percentage of

South Korea United States

a. Complete the table by expressing each year’s real GDP per capita as a percentageof its 1960 and 2000 levels.

b. How does the growth in living standards from 1960 to 2000 compare across thesefour nations? What might account for these differences?

1. a. The accompanying table shows each nation’s real GDP per capita in terms of its1960 and 2000 levels.

1960 $7,395 100% 67% $832 100% 62%

1970 9,227 125 84 1,275 153 95

1980 10,556 143 96 1,204 145 89

1990 7,237 98 66 1,183 142 88

2000 10,995 149 100 1,349 162 100

1960 real GDP

per capita

2000 real GDP

per capita

Real GDP per capita

(1996 dollars)Year

Percentage of 1960

real GDP per capita

2000 real GDP

per capita

Real GDP per capita

(1996 dollars)

Percentage of

Argentina Ghana ch

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KrugmanMacro_SM_Ch08.qxp 11/9/05 4:47 PM Page 99

b. South Korea experienced the greatest increase in living standards from 1960 to2000; in 2001 it produced 1,011% ($15,881/$1,571 × 100) of what it produced in1960. Argentina and Ghana experienced only a modest growth in living standardsover the same period. Argentina’s path was less consistent than that of Ghana,where living standards remained low throughout the period. Compared with realGDP per capita in 1960, the United States in 2000 produced 268%($33,308/$12,414 × 100) of what it produced in 1960. The growth in living stan-dards in Argentina, Ghana, and South Korea reflects the pattern for their differentregions of the world. South Korea, like many other East Asian countries, had highproductivity growth because of high savings and investment rates, a good educa-tion system, and substantial technological progress. Living standards grew moremodestly in Argentina, as in other Latin American countries, because of low sav-ings and investment spending rates, underinvestment in education, political insta-bility, and irresponsible government policies. Although the growth in living stan-dards was similar in Ghana and Argentina, Ghana had started from a much lowerlevel. Real GDP per capita in Ghana was only 11% of that in Argentina in 1960and 12% in 2000. Living standards in Africa suffered from major political insta-bilities, poor education and infrastructure, and disease.

2. The accompanying table shows the average annual growth rate in real GDP per capi-ta for Argentina, Ghana, and South Korea using data from the Penn World Table,Version 6.1, for the past few decades.

a. For each decade and for each country, use the Rule of 70 where possible to calcu-late how long it would take for that country’s real GDP per capita to double.

b. Suppose that the average annual growth rate that each country achieved over theperiod 1990–2000 continues indefinitely into the future. Starting from 2000, usethe Rule of 70 to calculate, where possible, the year in which a country will havedoubled its real GDP per capita.

Average annual growth rate of real GDP per capita

Years Argentina Ghana South Korea

1960–1970 2.24% 4.36% 5.86%

1970–1980 1.35 −0.57 5.69

1980–1990 −3.70 −0.18 7.51

1990–2000 4.27 1.33 4.78

1960 $ 1,571 100% 10% $12,414 100% 37%

1970 2,777 177 17 16,488 133 50

1980 4,830 307 30 2 1,337 172 64

1990 9,959 634 63 26,470 213 79

2000 15,881 1,011 100 33,308 268 100

1960 real GDP

per capita

2000 real GDP

per capita

Real GDP per capita

(1996 dollars)Year

Percentage of 1960

real GDP per capita

2000 real GDP

per capita

Real GDP per capita

(1996 dollars)

Percentage of

South Korea United States

100 M A C R O E C O N O M I C S , C H A P T E R 8E C O N O M I C S , C H A P T E R 2 5


Solution

Solution2. a. The accompanying table shows the number of years it would take for real GDP percapita to double according to the Rule of 70 using the average annual growth ratein real GDP per capita per decade in each country. Values corresponding to yearswith negative growth rates are left uncalculated because we cannot apply the Ruleof 70 to a negative growth rate.

b. If each nation continues to grow as it did from 1990 to 2000, real GDP per capitawill have doubled in Argentina by 2016, in Ghana by 2052, and in South Korea by 2014.

3. 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) andoutput per worker (Y/L) is given by the curve labeled Productivity1 in the accompa-nying diagram. Albernia is at point A and Brittania is at point B.

a. In the relationship depicted by the curve Productivity1, 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 areheld fixed in each country, can you recommend a policy to generate a doubling ofreal GDP per capita in each country?

c. How would your policy recommendation change if the amount of human capitalper worker and the technology were not fixed? Draw a curve on the diagram thatrepresents 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 andtechnology fixed. Both Albernia and Brittania experience diminishing returns tophysical capital since in both countries equal successive increases in physical capi-tal per worker—holding human capital per worker and technology constant—willresult in smaller and smaller increases in real GDP per worker.

b. Albernia should increase its physical capital per worker to (K/L)B. Brittania willhave to add a huge amount of physical capital per worker.

Real GDPper worker

Physical capital per worker

BProductivity1

A

(Y/L)B

(Y/L)A

(K/L)A (K/L)B

Years for real GDP per capita to double according to the Rule of 70Years Argentina Ghana South Korea

1960–1970 31.3 16.1 11.9

1970–1980 51.9 — 12.3

1980–1990 — — 9.3

1990–2000 16.4 52.6 14.7

L O N G - R U N E C O N O M I C G R O W T H 101


Solution

c. If it were possible to increase the amount of human capital per worker or improvethe technology, or both, then Productivity1 could shift to Productivity2 andAlbernia could double real GDP per worker without a change in the physical capi-tal per worker. On the accompanying diagram, Albernia would move from point Ato point C.

4. Why would you expect real GDP per capita in California and Pennsylvania to exhibitconvergence but not in California and Baja California, a state of Mexico that bordersthe United States? What changes would allow California and Baja California to con-verge?

4. According to the conditional convergence hypothesis, other things equal, countrieswith relatively low real GDP per capita tend to have higher rates of growth thancountries with relatively high real GDP per capita. We can apply this hypothesis toregions as well. It is more likely that the factors that affect growth will be equal inCalifornia and Pennsylvania: both states have similar educational systems, infra-structure, rule of law, and so on. But that is not true of California and BajaCalifornia: in comparing them, the factors that affect growth are not likely to beequal. California and Baja California have very different educational systems, differ-ent infrastructures, and there are differences in how the rule of law is applied. So itis less likely that they will converge. For California and Baja California to converge inreal GDP per capita, they would have to become more similar in the factors thataffect growth.

5. The economy of Profunctia has estimated its aggregate production function, whenholding human capital per worker and technology constant, as

= 100 × ��KL

YL

Real GDPper worker

Physical capitalper worker

BProductivity1

Productivity2

A

C(Y/L)B

(Y/L)A

(K/L)A (K/L)B


102_KrugmanMacro_SM_Ch08.qxp 11/10/05 1:07 PM Page 102

Solution


Y is real GDP, L is the number of workers, and K is the quantity of physical capital.Given that Profunctia has 1,000 workers, calculate real GDP per worker and thequantity of physical capital per worker for the differing amounts of physical capitalshown in the accompanying table.

a. Plot the aggregate production function for Profunctia.

b. Does the aggregate production function exhibit diminishing returns to physicalcapital? Explain your answer.

5. a. The accompanying table and diagram show the aggregate production function forProfunctia.

0.05 0.060.040.03 0.08 0.090.070.02$0.010

$30

20

10

Real GDPper worker,

Y/L

Physical capital per worker, K/L

K L K/L Y/L

$0 1,000 $0.00 $0.00

10 1,000 0.01 10.00

20 1,000 0.02 14.14

30 1,000 0.03 17.32

40 1,000 0.04 20.00

50 1,000 0.05 22.36

60 1,000 0.06 24.49

70 1,000 0.07 26.46

80 1,000 0.08 28.28

90 1,000 0.09 30.00

100 1,000 0.10 31.62

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 ? ?


Solution

Solution

Solution

b. The aggregate production function does exhibit diminishing returns to physicalcapital. For example, the table shows that as K increases from $30 to $40, Y/Lincreases by $2.68, but as K increases from $70 to $80, Y/L increases only by$1.82.

6. The Bureau of Labor Statistics regularly releases the “Productivity and Costs” reportfor the previous month. Go to www.bls.gov and find the latest report. (On theBureau of Labor Statistics home page, click on “Productivity” under Latest Numbersand then choose the latest “Productivity and Costs” report.) What were the percentchanges in business and nonfarm business productivity for the previous quarter?How does the percent change in that quarter’s productivity compare to previousdata?

6. Answers will vary with the latest data. For the third quarter of 2005, business andnonfarm business productivity grew by 4.8% and 4.1%, respectively. These were high-er than the productivity growth figures for the second quarter of 2005, which were0.81% and 2.1%, respectively.

7. What roles do physical capital, human capital, technology, and natural resources playin influencing long-run economic growth of aggregate output per capita?

7. Physical capital, human capital, technology, and natural resources play importantroles in influencing long-run growth in real GDP per capita. Increases in both physi-cal capital and human capital help a given labor force to produce more over time.Although economic studies have suggested that increases in human capital mayexplain 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 produc-tivity, they play a less important role in increasing productivity than do increases inhuman or physical capital in most countries today.

8. Through its policies and institutions, how has the United States influenced U.S. long-run economic growth? Why might persistently large borrowing by the U.S. govern-ment ultimately limit long-run economic growth in the future?

8. Institutions and policies in the United States have greatly aided U.S. economicgrowth. The country has been politically stable, and its laws and institutions protectprivate property. The economy has attracted significant savings, both domestic andforeign, that have allowed investment spending to spur the growth of the capitalstock and fund research and development. The government has directly supportedeconomic growth through its support of public education as well as research anddevelopment. However, the government’s persistently large borrowing may reduceprivate investment spending (a phenomenon known as “crowding out”), conse-quently slowing economic growth.

9. Over the next 100 years, real GDP per capita in Groland is expected to grow at anaverage annual rate of 2.0%. In Sloland, however, growth is expected to be somewhatslower, at an average annual growth rate of 1.5%. If both countries have a real GDPper capita today of $20,000, how will their real GDP per capita differ in 100 years?(Hint: A country that has a real GDP today of $x and grows at y% per year willachieve a real GDP of $x × (1 + 0.0y)z in z years.)



Solution

Solution9. If real GDP per capita in Groland grows at an average annual rate of 2.0%, real GDPper capita in 100 years will be $144,893 [$20,000 � (1 � 0.02)100]. At an averageannual rate of growth of 1.5%, real GDP per capita in Sloland in 100 years will be$88,641 [$20,000 � (1 � 0.015)100]. Although both nations start with the same realGDP per capita today, the differential growth rates will result in living standards inSloland that are 61.2% ($88,641/$144,893 � 100) of those in Groland.

10. The accompanying table shows data from the Penn World Table, Version 6.1, for realGDP per capita (1996 U.S. dollars) in France, Japan, the United Kingdom, and theUnited States in 1950 and 2000. Complete the table. Have these countries convergedeconomically?

10. The accompanying table shows real GDP per capita (1996 U.S. dollars) in France,Japan, and the United Kingdom as a percentage of real GDP per capita in the UnitedStates.

Real GDP per capita in France and Japan, the two nations with the lowest real GDPper capita in 1950, closed some of the gap in living standards with the United States.Japan’s real GDP per capita grew from only 23.1% of that in the United States to73.5%, and France’s rose from 52.5% to 66.8%. But living standards in the UnitedKingdom relative to those in the United States actually declined; real GDP per capitafell from 70.7% of that in the United States to 68.6%. France and Japan have con-verged, but the United Kingdom has not.

1950 2000Real GDP Real GDPper capita Percentage of U.S. per capita Percentage of U.S.

(1996 dollars) real GDP per capita (1996 dollars) real GDP per capita

France $5,561 52.5% $22,254 66.8%

Japan 2,445 23.1 24,495 73.5

United Kingdom 7,498 70.7 22,849 68.6

United States 10,601 100.0 33,308 100.0

1950 2000Real GDP Percentage Real GDP Percentage per capita of U.S. per capita of U.S. (1996 real GDP (1996 real GDP dollars) per capita dollars) per capita

France $5,561 ? $22,254 ?

Japan 2,445 ? 24,495 ?

United Kingdom 7,498 ? 22,849 ?

United States 10,601 ? 33,308 ?



Solution

11. The accompanying table shows data from the Penn World Table, Version 6.1, for realGDP per capita (1996 U.S. dollars) for Argentina, Ghana, South Korea, and the UnitedStates in 1960 and 2000. Complete the table. Have these countries converged economi-cally?

11. The accompanying table shows real GDP per capita (1996 U.S. dollars) in Argentina,Ghana, and South Korea as a percentage of real GDP per capita in the United States.

There is little evidence of convergence for either Argentina or Ghana. Living stan-dards in both nations declined relative to those in the United States. In Argentinareal GDP per capita 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 real GDP per capita showedsigns of convergence with those in the United States; real GDP per capita rosefrom 12.7% of that in the United States to 47.7%.

1960 2000Real GDP Real GDPper capita Percentage of U.S. per capita Percentage of U.S.

(1996 dollars) real GDP per capita (1996 dollars) real GDP per capita

Argentina $7,395 59.6% $10,995 33.0%

Ghana 832 6.7 1,349 4.0

South Korea 1,571 12.7 15,881 47.7

United States 12,414 100.0 33,308 100.0

1960 2000Real GDP Percentage Real GDP Percentage per capita of U.S. per capita of U.S. (1996 real GDP (1996 real GDP dollars) per capita dollars) per capita

Argentina $7,395 ? $10,995 ?

Ghana 832 ? 1,349 ?

SouthKorea 1,571 ? 15,881 ?

United States 12,414 ? 33,308 ?



ap macro ch25

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