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Solution Manual of Macroeconomics, 9th Edition Abel, Bernanke _ Croushore, sm

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Solution Manual of Macroeconomics, 9th Edition Abel, Bernanke _ Croushore, sm

Chapter 6
Long-Run Economic Growth
 Learning Objectives
I. Goals of Chapter 6
A. Discuss the sources of economic growth and the fundamentals of growth accounting (Sec. 6.1)
B. Explain the factors affecting long-run living standards in the Solow model (Sec. 6.2)
C. Summarize endogenous growth theory (Sec. 6.3)
D. Discuss government policies for raising long-run living standards (Sec. 6.4)
II. Notes to Eighth Edition Users
A. We shortened and simplified the discussion of the post-1973 slowdown in productivity growth
B. We renamed the application on “The Recent Surge in U.S. Productivity Growth” to “The
Rebound in U.S. Productivity Growth,” with modified data
122 Abel/Bernanke/Croushore • Macroeconomics, Ninth Edition
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 Teaching Notes
I. The Sources of Economic Growth (Sec. 6.1)
A. Production function
Y  AF(K, N) (6.1)
1. Decompose into growth rate form: the growth accounting equation
 Y/Y  A/A  aK K/K  aN N/N (6.2)
2. The a terms are the elasticities of output with respect to the inputs (capital and labor)
3. Interpretation
a. A rise of 10% in A raises output by 10%
b. A rise of 10% in K raises output by aK times 10%
c. A rise of 10% in N raises output by aN times 10%
4. Both aK and aN are less than 1 due to diminishing marginal productivity
B. Growth accounting
1. Four steps in breaking output growth into its causes (productivity growth, capital input
growth, labor input growth)
a. Get data on Y/Y, K/K, and N/N, adjusting for quality changes
b. Estimate aK and aN from historical data
c. Calculate the contributions of K and N as aK K/K and aN N/N, respectively
d. Calculate productivity growth as the residual: A/A  Y/Y – aK K/K – aN N/N
Numerical Problems 1 and 2 are growth accounting exercises.
2. Growth accounting and productivity trends
a. Denison’s results for 1929–1982 (text Table 6.3)
(1) Entire period output growth 2.92%; due to labor 1.34%; due to capital 0.56%; due to
productivity 1.02%
(2) Pre-1948 capital growth was much slower than post-1948
(3) Post-1973 labor growth slightly slower than pre-1973
(4) Productivity growth is major difference
(a) Entire period: 1.02%
(b) 1929–1948: 1.01%
(c) 1948–1973: 1.53%
(d) 1973–1982: –0.27%
b. Productivity growth slowdown occurred in all major developed countries
Theoretical Application
Growth accounting provides the basis for the real business cycle (RBC) model of the economy,
which we will discuss in greater detail in Chapter 10. The RBC model takes movements in total
factor productivity to be the primary source of business cycle fluctuations.
3. Application: the post-1973 slowdown in productivity growth
What caused the decline in productivity?
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a. The legal and human environment—regulations for pollution control and worker safety,
crime, and declines in educational quality
Data Application
Mark Wynne’s article, “The Comparative Growth Performance of the U.S. Economy in the
Postwar Period,” Federal Reserve Bank of Dallas Economic Review, First Quarter 1992,
pp. 1–16, argues that the postwar period up to the mid-1970s showed extraordinary productivity
growth. After the mid-1970s, productivity returned to more normal levels.
b. Oil prices—huge increase in oil prices reduced productivity of capital and labor,
especially in basic industries
c. New industrial revolution—learning process for information technology from 1973 to
1990 meant slower growth
4. Application: the rebound in U.S. productivity growth
a. Labor productivity growth increased sharply in the second half of the 1990s
b. Labor productivity and TFP grew steadily from 1982 to 2008 (text Fig. 6.1)
c. Labor productivity growth has generally exceeded TFP growth since 1995 (Fig. 6.2)
d. The gap between labor productivity growth and TFP growth can be seen in the equation
            (6.3)
(1) Equation (6.3) suggests that labor productivity growth (the left-side term) exceeds
TFP growth (the first right-side term) when capital growth exceeds labor growth
e. The increase in labor productivity can be traced to the ICT (information and
communications technologies) revolution
(1) But other countries also had an ICT revolution, and their labor productivity did not
rise as much as in the United States
(2) European labor productivity did not rise as much as in the United States because of
government regulations
f. Why is there such a lag between ICT investment and increases in productivity?
(1) Because productivity improvements require not just technological advances, but also
investment in intangible capital—research and development, reorganization of firms,
and worker training
g. Is the recent episode unique in U.S. history?
(1) Not really: 1873–1890—steam power, trains, telegraph; 1917–1927—electrification
in factories; 1948–1973—transistor
II. Long-Run Growth: The Solow Model (Sec. 6.2)
A. Two basic questions about growth
1. What’s the relationship between the long-run standard of living and the saving rate,
population growth rate, and rate of technical progress?
2. How does economic growth change over time? Will it speed up, slow down, or stabilize?
B. Setup of the Solow model
1. Basic assumptions and variables
a. Population and workforce grow at same rate n
b. Economy is closed and G  0
c. Ct  Yt  It (6.4)
d. Rewrite everything in per-worker terms: yt  Yt/Nt; ct  Ct/Nt; kt  Kt/Nt
e. kt is also called the capital-labor ratio
124 Abel/Bernanke/Croushore • Macroeconomics, Ninth Edition
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2. The per-worker production function
a. yt  f(kt) (6.5)
b. Assume no productivity growth for now (add it later)
c. Plot of per-worker production function—text Figure 6.3
d. Same shape as aggregate production function
Numerical Problem 3 and Analytical Problem 6 work with the per-worker production function.
3. Steady states
a. Steady state: yt, ct, and kt are constant over time
b. Gross investment must
(1) Replace worn out capital, dKt
(2) Expand so the capital stock grows as the economy grows, nKt
c. It  (n  d)Kt (6.6)
d. From Eq. (6.4),
Ct  Yt  It  Yt  (n  d)Kt (6.7)
e. In per-worker terms, in steady state
c  f(k)  (n  d)k (6.8)
f. Plot of c, f(k), and (n  d)k (Figure 6.1; identical to text Figure 6.4)
g. Increasing k will increase c up to a point
(1) This is kG in the figure, the Golden Rule capital-labor ratio
(2) For k beyond this point, c will decline
(3) But we assume henceforth that k is less than kG, so c always rises as k rises
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Figure 6.1
4. Reaching the steady state
a. Suppose saving is proportional to current income:
St  sYt, (6.9)
where s is the saving rate, which is between 0 and 1
b. Equating saving to investment gives
sYt  (n  d)Kt (6.10)
c. Putting this in per-worker terms gives
sf(k)  (n  d)k (6.11)
d. Plot of sf(k) and (n  d)k (Figure 6.2; identical to text Figure 6.5)
126 Abel/Bernanke/Croushore • Macroeconomics, Ninth Edition
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Figure 6.2
e. The only possible steady-state capital-labor ratio is k
f. Output at that point is y
*  f(k
); consumption is c
*  f(k
)  (n  d)k
g. If k begins at some level other than k
, it will move toward k
(1) For k below k
, saving > the amount of investment needed to keep k constant,
so k rises
(2) For k above k
, saving < the amount of investment needed to keep k constant,
so k falls
Numerical Problems 5, 6, and 7 look at equilibrium in the Solow model.
h. To summarize, with no productivity growth, the economy reaches a steady state, with
constant capital-labor ratio, output per worker, and consumption per worker
C. The fundamental determinants of long-run living standards
1. The saving rate
a. Higher saving rate means higher capital-labor ratio, higher output per worker, and higher
consumption per worker (shown in text Figure 6.6)
b. Should a policy goal be to raise the saving rate?
(1) Not necessarily, since the cost is lower consumption in the short run
(2) There is a trade-off between present and future consumption
2. Population growth
a. Higher population growth means a lower capital-labor ratio, lower output per worker,
and lower consumption per worker (shown in text Figure 6.7)
b. Should a policy goal be to reduce population growth?
(1) Doing so will raise consumption per worker
(2) But it will reduce total output and consumption, affecting a nation’s ability to defend
itself or influence world events
c. The Solow model also assumes that the proportion of the population of working age is
(1) But when population growth changes dramatically this may not be true
(2) Changes in cohort sizes may cause problems for social security systems and areas
like health care
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3. Productivity growth
a. The key factor in economic growth is productivity improvement
b. Productivity improvement raises output per worker for a given level of the capital-labor
ratio (text Fig. 6.8)
c. In equilibrium, productivity improvement increases the capital-labor ratio, output per
worker, and consumption per worker
(1) Productivity improvement directly improves the amount that can be produced at
any capital-labor ratio
(2) The increase in output per worker increases the supply of saving, causing the
long-run capital-labor ratio to rise
d. Can consumption per worker grow indefinitely?
(1) The saving rate can’t rise forever (it peaks at 100%) and the population growth rate
can’t fall forever
(2) But productivity and innovation can always occur, so living standards can rise
e. Summary: The rate of productivity improvement is the dominant factor determining how
quickly living standards rise
Analytical Problems 1, 2, 3, and 4 look at how changes in the fundamentals affect an economy’s
economic growth.
4. Application: The growth of China
a. China is an economic juggernaut
(1) Population 1.4 billion people
(2) Real GDP per capita is low but growing (Table 6.4)
(3) Starting with low level of GDP, but growing rapidly (Fig. 6.10)
b. Fast output growth attributable to
(1) Huge increase in capital investment
(2) Fast productivity growth (in part from changing to a market economy)
(3) Increased trade
c. Will China be able to keep growing rapidly?
(1) Rapid growth because of use of underemployed resources, using advanced
technology developed elsewhere, and making the transition from a centrally-planned
economy to a market economy
(2) Such gains may not last
d. So, it may take China a long time to catch up with the rest of the developed world

III. Endogenous Growth Theory—Explaining the Sources of Productivity Growth (Sec. 6.3)
A. Aggregate production function
Y  AK (6.12)
1. Constant MPK
a. Human capital
(1) Knowledge, skills, and training of individuals
(2) Human capital tends to increase in same proportion as physical capital
128 Abel/Bernanke/Croushore • Macroeconomics, Ninth Edition
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Data Application
For more information and a look at the data on the returns to human capital, see Ellis W. Tallman
and Ping Wang, “Human Capital Investment and Economic Growth: New Routes in Theory
Address Old Questions,” Federal Reserve Bank of Atlanta Economic Review, September/October
1992, pp. 1–12. For an excellent and more detailed overview of endogenous growth theory, see
the symposium in the Journal of Economic Perspectives, Winter 1994.
b. Research and development programs
c. Increases in capital and output generate increased technical knowledge, which offsets
decline in MPK from having more capital
B. Implications of endogenous growth
1. Suppose saving is a constant fraction of output: S  sAK
2. Since investment  net investment  depreciation, I  K  dK
3. Setting investment equal to saving implies:
K  dK  sAK (6.13)
4. Rearrange (6.13):
K/K  sA  d (6.14)
5. Since output is proportional to capital, Y/Y  K/K, so
 Y/Y  sA  d (6.15)
6. Thus the saving rate affects the long-run growth rate (not true in Solow model)
Theoretical Application
The Wall Street Journal discussed the theory of endogenous growth and the contributions of
Stanford economist Paul Romer, in the article “Wealth of Notions,” January 21, 1997.
C. Summary
1. Endogenous growth theory attempts to explain, rather than assume, the economy’s growth
2. The growth rate depends on many things, such as the saving rate, that can be affected by
government policies
Policy Application
For a good review of how government policy can contribute to economic growth, see Satyajit
Chatterjee, “Making More Out of Less: The Recipe for Long-Term Economic Growth,” Federal
Reserve Bank of Philadelphia Business Review, May/June 1994.
Chapter 6 Long-Run Economic Growth 129
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Data Application
Is the Solow model or the model of endogenous growth a better representation of how economic
growth is determined? To find out, Ben S. Bernanke and Refet S. Gürkaynak of Princeton
University examined data from many different countries from 1960 to 1998 (“Is Growth
Exogenous? Taking Mankiw, Romer, and Weil Seriously,” NBER Macroeconomics Annual 2001,
in Ben S. Bernanke and Kenneth Rogoff, eds., Cambridge, MA: MIT Press, 2002). They tested
whether the Solow model or several alternative models of endogenous growth were more
consistent with the data.
Bernanke and Gürkaynak tested a key implication of the Solow model: that the steady-state
growth rate of a country does not depend on variables such as the rate of human capital
accumulation and the saving rate. They found that, in fact, countries’ growth rates are closely
correlated with both the saving rate and the rate of human capital accumulation, which suggests
either that the Solow model does not work well or that the economies are not in steady state.
However, the Solow model implies that even if an economy is not in a steady state, the growth
rate of total factor productivity (TFP) is exogenous: it does not depend on the saving rate or on
any other behavioral variable, such as the level of education in a country or the growth rate of the
labor force. After constructing measures of long-run TFP growth for about 50 countries,
Bernanke and Gürkaynak examined the relationship between it and other variables. They found
that there is, in fact, a strong relationship between TFP growth and the saving rate, some
relationship between TFP growth and the growth rate of the labor force, and a weaker
relationship between TFP growth and the level of education. Thus, the data do not support the
Solow model.
Models of endogenous growth imply that human capital formation and physical capital
accumulation should be related to the long-run growth rate of output. Bernanke and Gürkaynak
found that there is indeed such a relationship in the data across many countries. However, the
models they test are not perfect, as they cannot explain why savings rates and rates of human
capital accumulation differ so much across countries.
Overall, the research of Bernanke and Gürkaynak suggests that models of endogenous growth
hold more promise than the Solow model in explaining economic growth.
IV. Government Policies to Raise Long-Run Living Standards (Sec. 6.4)
A. Policies to affect the saving rate
1. If the private market is efficient, the government shouldn’t try to change the saving rate
a. The private market’s saving rate represents its trade-off of present for future consumption
b. But if tax laws or myopia cause an inefficiently low level of saving, government policy to
raise the saving rate may be justified
2. How can saving be increased?
a. One way is to raise the real interest rate to encourage saving; but the response of saving to
changes in the real interest rate seems to be small
b. Another way is to increase government saving
(1) The government could reduce the deficit or run a surplus
(2) But under Ricardian equivalence, tax increases to reduce the deficit won’t affect
national saving
B. Policies to raise the rate of productivity growth
1. Improving infrastructure
a. Infrastructure: highways, bridges, utilities, dams, and airports
b. Empirical studies suggest a link between infrastructure and productivity
130 Abel/Bernanke/Croushore • Macroeconomics, Ninth Edition
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c. U.S. infrastructure spending has declined in the last two decades
d. Would increased infrastructure spending increase productivity?
(1) There might be reverse causation: Richer countries with higher productivity spend
more on infrastructure, rather than vice versa
(2) Infrastructure investments by government may be inefficient, since politics, not
economic efficiency, is often the main determinant
2. Building human capital
a. There’s a strong connection between productivity and human capital
b. Government can encourage human capital formation through educational policies,
worker training and relocation programs, and health programs
c. Another form of human capital is entrepreneurial skill
Government could help by removing barriers like red tape
3. Encouraging research and development
a. Support scientific research
b. Fund government research facilities
c. Provide grants to researchers
d. Contract for particular projects
e. Give tax incentives
f. Provide support for science education
Policy Application
Many issues relating to government policy and its effects on growth are discussed in a special issue
of the Journal of Monetary Economics, December 1993. The articles were presented at a World
Bank Conference on the research project, “How Do National Policies Affect Long-Run Growth?”


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