Chapter 10: The Theory of Economic Growth
Introduction
1. We measure growth as sustained change in real GDP per
person. Does this reflect a welfare gain? How does this related
to the LRAS curve?
2. Why the rate of compounding results in substantial differences
in welfare gain? What is the ‘rule of 72’?
3. Why we study growth theory. Several important questions in
chapters 10-11:
a. What determines economic growth in natural real GDP per
person? (Ch. 10)
b. Why are some countries ‘rich’ and others ‘poor’? (Ch. 11)
c. What explains the ebb and flow of productivity growth in
the U.S.? (Ch. 11)
Standards of Living as a Consequence of Economic Growth
1. How does U.S. per capita income compare to the United
Kingdom?
2. Why can we conclude that Minor differences in economic
growth rates over a long period build up into substantial
differences in relative living standards.
3. How does economic growth shift the production possibility
curve to avoid a ‘zero sum’ game.
The Production Function and Economic Growth
1. How does neoclassical theory explains output as a function of
labor, capital, and exogenous total factor productivity?
2. How is this converting to output per worker as a function of
capital per worker?
3. Why are the sources of growth per person dependent on capital
per person and autonomous growth factor, A?
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4. What sources of growth are included in A?
Example of Cobb-Douglas production function
1. If the Cobb-Douglas production specification is used, variables
are expressed as an index. (See appendix to chapter 10).
2. Cobb-Douglas Y = A Kb L1-b assumes constant returns to scale.
3. Suppose initially 1.0 = 1.0(1.0 0.25 1.0 0.75)
a. Suppose labor input increases 4% to 1.04, then Y
increases to 1.03 (or 3%).
b. Suppose capital input increases 4% to 1.04, then Y
increases 1.01 (or 1%).
c. If both input increase 4%, then Y increases 4%
d. uppose A increases 4% to 1.04, then Y increases to 1.04
(or 4%).
4. (Note that exponents are elasticity of real GDP with respect to a
change in an input (0.75 for labor, 0.25 for capital).
5. Assume that L can be estimated by total population, N, then the
Cobb-Douglas specification after dividing by N, gives the
following relationship: Y/N = A (K/N) b Note that the function
results in diminishing returns from capital, since MPPk =
Ab(K/N) b-1 = Ab(K/N)b)/(K/N) decreases as K/N increases.
(see figure 10-1)
The Theory of Economic Growth
Goal: To understand forces causing differences in income over time
and across countries.
 Why is economic growth is based upon the production function of
the economy?
 Why must differences in income and growth over time come from
differences or changes in capital, labor, and/or technology?
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 Why do changes in the production function result in shifts in the
aggregate supply curve (to the right) so that higher output occurs
for a given price level?
Our Primary Task in chapter 10 is to develop the Solow model of
economic growth.
Our Secondary Task is to examine how economic policy can
influence the level and growth in our standard of living.
Finally, we will look at some endogenous forces that may affect
economic growth.
The Solow Growth Model without Technology Change
1. What determines the supply of goods in the economy?
a. The Solow model assumes that the supply of goods and
services depends upon a production function with constant
returns to scale. zY = F(zK, zN)
b. Hence, with substitution if z = 1/N, then Y/N = F(K/N, 1),
i.e. output per worker depends upon capital per worker.
c. The marginal productivity of capital MPK will diminish if
the amount of labor and technology is fixed. (See Figure 101)
d. Clearly changes in the stock of capital will result in an
increase in the supply of goods and services, even with the
supply of labor and technology fixed.
2. What determines the link between investment and the growth in
capital?
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a. The Solow model assumes that the demand for goods
depends upon consumption and investment. This rate of
income equates the savings rate per capita with the rate of
investment per capita.
c. For a given propensity to save, s, this occurs when I/N = s
(Y/N), i.e. investment is proportional to income.
d. Hence, the savings rate determines the allocation of Y/N
between consumption and investment for every value of K/N.
e. Net investment adds to the capital stock. This occurs only if
gross investment is greater than depreciation. If depreciation
is given by d (K/N), then change in the capital stock is = s
f(Y/N)) - d (K/N)
4. What is the Steady State?
a. The steady state occurs when net investment equals zero, i.e.
investment equals depreciation. Then s f(Y/N) = d (K/N).
b. Output and capital grow at the same rate, so that Y/K is
fixed.
c. Also, Y/N and K/N are fixed, so that the growth rate in
capital, k, and the growth rate in labor, n, are the same, i.e. k
= n.
f. At this Steady State I = (n + d)K or s(Y/K) = n + d
5. What is the impact of a higher savings rate on income per
capita?
a. A higher savings rate increases the rate of investment and
adds to net investment, K/N and Y?N.
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b. It results in a higher Steady State equilibrium income and
higher economic welfare of a country.
c. Is a higher domestic savings rate always desirable?
6. What is the impact on income per capita of population growth?
a. Population growth increases output but lower income per
capita
b. The change in capital must now be sufficient to meet
depreciation plus the erosion in the productivity of capital
due to less capital per worker as the number of workers
increase.
c. Hence, the steady state level of capital per worker falls with
more population as population growth widens (as opposed to
deepens) the capital stock and in effect ‘depreciates’ the
amount of capital available to each worker.
d. Graphically, this causes the depreciation plus population
growth function to rotate upwards compared to its value if
population is fixed.
e. This lowers steady state output per capita and consumption
per capita in populated countries.
7.. What is the impact of technological Progress in the Solow
Model?
a. Solow explains technological progress as the residual
between the rate of growth in output and the amount
explained by the rate of growth in capital and the rate of
growth in labor inputs. This is called the “Solow Residual.”
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b. The growth in autonomous growth factors, a, is the amount
that is not explained by capital and labor inputs, so that (with
small letters representing rates of change) If Y/N – A (K/N)b
, then
a = (y – n) – b(k – n)
c. Since, k and n face diminishing returns only technological
progress (changes in a) can explain persistently rising
living standards.
d. Neutral technological change makes labor and capital more
efficient, so that the growth factor A grows over time.
Education, innovations, and research increase A every year
so that GDP per capita increases with a constant output per
capital ratio. K/N and Y/N both rise in the steady state at the
same rate, supported by statistical evidence in developed
economies, such as the U.S.
What insight does the Solow Model give regarding growth, and
economic policy?
1. What does the model predict to be the impact of policies to
change the rate of savings?
2. What about polices to allocate investment?
3. What about policies that control population growth?
4. What about policies to encourage advances in technology and
education?
What are some Puzzles that Solow’s Theory Cannot Explain
1. Long-run economic growth per capita depends primarily on the
‘Solow residual’ (rate of change in A) that is exogenous to the
model. We are left with little understanding of the principal
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determinants of differences in long-term growth rates among
countries.
Conflict 1: Income per capital varies too much across countries to
be explained by neoclassical theory which depends primarily on
savings rate or slope of steady-state investment line. Obviously,
all countries do not have the same production function in terms of
technology and knowledge.
Conflict 2: Poor countries do not have a higher rate of return on
capital. Again, poor countries do not operate on the same
production function as rich countries.
Conflict 3: Convergence of income is not occurring among ‘rich’
versus ‘poor’ countries or even within regions in the same country.
Convergence occurs among regions in the same ‘club’ but not
among regions outside the ‘club’.
Beyond the Solow Model: What are the elements of new
(endogenous) growth theory?
1. The basic model: Y/N= A (K/N)b
What determines A?
2. What is the role of human capital with constant or increasing
returns. How are ideas tuned into innovations? Adding human
capital to capital in the production function substantially
increases the value of b to b + c where c is the rate of return on
human capital. (An Increase of b + c to 0.9 rather than b only of
0.25 adds to percent growth explained by the production
function, while increasing returns allows output to increase
more than proportional to inputs.)
3. What determines the production of ideas?: “standing on
shoulders” versus “stepping on toes”. Technology relates to
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innovation in production, including business and organization,
development of intellectual property rights, public
infrastructure, research and development, market structure to
reinforce patents and copyrights, political stability
Chapter 11. The Big Questions of Economic Growth
The Big Questions (revisited):
1.
2.
Why is the disparity of income among countries so large when
the neoclassical model predicts convergence of income?
What creates a growth ‘miracle’ that elevates countries from the
ranks of the poor?
Why are we so rich and they so poor?
1. The groupings of countries among the consistently rich (U.S.
Britain, etc.), the rapidly growing countries achieving income
convergence with the rich (Korea, Taiwan, Hong Kong, and
Singapore), and the poor nations that have failed to converge India,
Bangladesh, African and Latin American countries).
2. What are the Solow model predictions?
a. Higher income per person due to higher capital per person,
achieved through savings and investing.
b. But, the differences between countries’ income per capita is
several times larger than differences in both the amounts of
capital per person and rates of return on capital investment.
c. Part of the difference can be explained by differences in
human capital per worker, but then how can a migrant worker
earn so much additional income in a ‘rich’ country with no
change in their education?
d. The answer is a shift upward in the production function or
higher total factor productivity allowing countries to be much
more productive than others in using the capital that they
have.
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What creates a growth miracle?
1. How have countries been able to catch up to the technological
frontier established by rich countries?
2. Solow model predictions:
a. Assume a production function with diminishing returns that
allows a higher income (output) per person to be reached by
increasing the rate of capital per person through higher rates
of savings and investment, including human capital.
b. But, the economy eventually slows to its stationary state
without expansion of its technological frontier.
How does the standard of living relate to labor productivity?
1. The Solow Model assumes that ‘output per person’ is the same as
labor ‘productivity’ symbolized as y – n, where y is the rate of
change in output and n is the rate of change in population.
2. But, if q is the rate of change in work hours and n is the rate of
change in population, then it is possible for q > n or q < n to exist
and the rate of change in standard of living may not be the same as
the rate of change in labor productivity.
3. In Europe, labor productivity has grown faster than their standard
of living because hours of work have grown more slowly than
population.
4. Europe has longer vacations, a lower labor force participation rate,
and a higher average unemployment rate than in the United States.
Growth rate in labor’s share = (w – p) – (y – n)
Why has convergence not occurred?
Recall that the Solow model without technological change predicts
convergence of income per person at a steady state based on the
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country’s production function and savings rate. A poor country
differs from a rich country only because it has a lower capital per
labor ratio, since there is no difference between the per person
production function of rich versus poor nations.
Technology does not alter the conclusions of the Solow model if
assumed that it is freely available to all countries. The key empirical
prediction is that poorer nations have lower capital per person ratios,
but they also have higher subsequent growth rates that eventually
converge at the same capital per person and income per person.
The facts show that the prices of labor-intensive services (like
haircuts) are much higher in rich countries, but prices of high-tech
goods (like computers) tend to be lower in rich countries. If prices
were the same, poor countries would improve their relative standing
to rich countries, but even if adjusted for prices convergence is not
universal. (See fig. 11-3 and Table 11-1 that shows indexes of
relative income of countries to U.S. income)
Despite the failure to converge among all countries, among rich
countries the negative relationship between initial income per person
and subsequent growth in income per person is quite strong. The
prediction toward convergence breaks down when poor countries are
included.
What are some solutions to the issues of convergence suggested
from a study of the Solow Model?
1. The Solow model is unrealistic because it assumes the
production function does not shift.
a. Even higher saving rates that speed up the rate of growth
toward the stationary state may not explain differences in
income per person among countries that have different
production functions.
b. Investment in human capital shifts up the production
function for a given amount of physical capital. Poor
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countries cannot afford high levels of investment in
physical and human capital.
c. Technological change shifts up the production function for
a given amount of physical capital and also requires
greater human capital to operate modern equipment and
software.
2. At the stationary state the only increase in growth comes from
TFP that is gained from innovation higher technology.
a. Developing countries may import technology through (a)
copying products from developed countries, (b) importing
machinery containing embodied technology, and (c) direct
foreign investment by higher technology firms.
b. Still the absorption of imported technology is increased
when combined with higher rates of human capital
investment.
How do political capital, infrastructure, and geography
encouraging growth and innovation?
1. The free-market system reward entrepreneurship and innovation
if risk taking is rewarded by higher profits.
a. This required protection of private property rights from
thieves, a fairly administered tax system, and opportunity
to open new businesses (without costly permits or bribes).
b. Government infrastructure as highways, airports, ports,
telecommunication networks, and electricity systems
encourage investment.
c. Geography may impede development and cannot be easily
altered. (Adverse effect of temperate zones on diseases
and crop productivity; low economies of scale in
innovative absorption)
2. The role of diversion
a. Entrepreneurial activity must take precedence over
pirating activity, which extract rents without contributing
to value.
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b. Policies should not only minimize diversion but also make
government policies predictable.
c. Douglas North explains the government motive for
diversionary policies to maximize income or power or to
minimize the nuisance of trying to get rid of offenders
(Mafia).
d. Favorable political capital shifts the production function
upward in much the same way as favorable human capital,
adding to TFP.
3. What is the difference between an exchange and a transaction?
a. An exchange does not depend on trust like a transaction
that involves future promises to pay.
How can we integrating exogenous factors into economic growth
theory?
Y = A(G, P, T) F(K, R, H, N)
Y is output that depends on the function A that depends on
geographic location, G; political capital, P; and the level of
technology, T, that is multiplied by the more traditional production
function, F, that depends on the stock of physical capital, K;
infrastructure investment, R; human capital, H; and labor input, N.
1. The more comprehensive production function explains why
incomes do not always converge and why there is so much
disparity in income among countries.
2. Some countries in unfavorable geographic areas may never
converge.
3. Other countries will need to make substantial changes in
political capital and infrastructure to encourage foreign
investment and entrepreneurship and innovation among their
own population.
4. Human capital is a catalyst that is often complementary with
other inputs.
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How do labor supply shifts relate to productivity growth?
1. Adverse labor supply shocks that lower productivity and real
wages result if the labor supply curve shifts outward. (Higher
labor force participation or in migration)
2. Adverse labor demand shocks that lower productivity and real
wages result if the labor demand curve shifts inward. (Union
rules change, loss of capital stock)
3. Over the last two decades, the U.S. has a superior record over
Europe in creating jobs and maintaining a relatively low
unemployment rate, but has achieved slower growth in real
wages.
4. The U.S. labor market is more “flexible” than Europe with
weaker bargaining position of workers and less job security,
contributing to more service workers, slower growth in average
productivity, and slower growth in average real wages among
workers in the U.S. versus workers in Europe.
5. However, the recent “New Economy” gave a boost to labor
productivity and income among workers from 1995 and 2002.
Higher wages increases occurred without driving up labor costs
and inflation.
6. Some have questioned whether this New Economy growth rate
is sustainable.
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