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Chapter 6 Long-Run Economic Growth
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Learning Objectives
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)
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I.
Class Notes
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
3. Application: the post-1973 slowdown in productivity growth
What caused the decline in productivity?
a. Measurement—inadequate accounting for quality improvements
b. The legal and human environment—regulations for pollution control and worker safety, crime, and
declines in educational quality
c. Oil prices—huge increase in oil prices reduced productivity of capital and labor, especially in basic
industries
d. New industrial revolution—learning process for information technology from 1973 to 1990 meant slower
growth
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 work force grow at same rate n
b. Economy is closed and G  0
c. Ct  Yt  It
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
2. The per-worker production function
a. yt  f(kt)
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
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
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
4. Reaching the steady state
a. Suppose saving is proportional to current income:
St  sYt,
(6.9)
(6.4)
(6.5)
(6.6)
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)
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
h. To summarize, with no productivity growth, the economy reaches a steady state, with constant capitallabor 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 fixed
(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
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 continuously
e. Summary: The rate of productivity improvement is the dominant factor determining how quickly living
standards rise
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
1.
(6.12)
Constant MPK
a. Human capital
(1) Knowledge, skills, and training of individuals
(2) Human capital tends to increase in same proportion as physical capital
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)
C. Summary
1. Endogenous growth theory attempts to explain, rather than assume, the economy’s growth rate
2. The growth rate depends on many things, such as the saving rate, that can be affected by government
policies
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
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