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Chapter 11
The Theory of
Economic Growth
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Welfare Gains from Growth
• The profound importance of growth comes from
the power of compound arithmetic.
– Even small changes in growth rates make a huge
difference in the standard of living in the long run.
• Example: Korea and Philippines had the same level
of real income per capita in 1965.
– By 2010, Korea’s real income per capita was six times that
of the Philippines thanks to Korea’s rapid economic growth.
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Great Questions of Economic Growth
•
•
•
Economic Growth is the study of the causes and
consequences of sustained growth in natural real GDP
per person.
What secrets did countries with rapid economic growth
like Korea discover?
Why is there a growing chasm between “rich” and
“poor” countries?
– “Rich” countries are from North America, much of Europe, Japan, some of
the successful Asian countries and Australasia.
– “Poor” countries include much of the rest of the world except for “middle
income” countries like most former members of the Soviet Bloc.
•
What explains the ebb and flow of economic growth?
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International Perspective
The Growth Experience of Seven Countries
over the Last Century
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International Perspective
The Growth Experience of Seven Countries
over the Last Century
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The Production Function
• Traditional growth theory divides output growth into two
categories:
– Growth of Factor Inputs that directly produce real GDP such as
capital (K) and labor (N).
– Growth in output relative to growth in factor inputs.
• The Production Function shows how much output (Y) can
be produced by a given quantity of factor inputs and some
autonomous growth factor, A:
Y = AF(K, N)
• In per capita terms, the production function becomes:
Y
K
A f  
N
N
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Figure 11-1 A Production Function Relating
per Person Output to per Person Capital Input
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Solow’s Theory of Economic Growth
• We will first study an economy that has no technical change,
implying that A is constant.
• The economy is in a Steady State when Y, K and N are all
growing at the same rate.
– Implication: Y/K and K/N are both fixed in the steady state.
• Some new variables:
–
–
–
–
–
–
–
I = private investment
K = Capital stock
d = depreciation rate  dK units of capital depreciate each yr
K1 = K0 + I – dK  ∆K = I - dK or I = ∆K + dK
S = National saving (previously notated NS)
s = S/Y is the country’s saving rate
k, n, and y refer to the growth rates of K, N and Y.
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Derivation of the Steady State
Condition
• At the steady state, ∆K/K = k = n.
• Investment adds to the capital stock (∆K) plus
replaces worn out or depreciate capital (dK):
I = ∆K + dK = (∆K/K + d)K = (n + d)K
• Assuming NX = 0  S = I
• Using S = sY  sY = (n + d)K
• Dividing through by N yields:
sY
K
 (n  d )
N
N
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Interpretation of Solow’s Result
sY
K
 (n  d )
N
N
• The LHS gives per person national savings
• The RHS gives the amount of per person steadystate investment.
• Thus, in order for the economy to be at a steady
state, the economy must save enough to pay for the
investment required to replace worn out capital and
to maintain per person capital.
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Figure 11-2 Output, Saving,
and Steady-State Investment per Person
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Figure 11-3 Equilibrium of Saving and
Investment in the Solow Growth Model
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Figure 11-4 The Effect of a Higher
Saving Rate on Capital and Income per
Person
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What Affects the Solow Model?
• A higher saving rate leads to higher standard of
living, but *not* a permanent higher growth rate
of output per person.
• A lower population growth rate leads to higher
standard of living.
• A lower depreciation rate also leads to a higher
standard of living.
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Two Types of Technological Change
• Growth in technology in all forms includes better
schooling, improved organization, better health
care, and the fruits of innovation and research.
• Technology that makes each worker more efficient
is called Labor-Augmenting Technological
Change.
– Instead of counting the number of workers, we count
N = the Effective Labor Input
• Technology that shifts the per person production
function is called Neutral Technological
Change.
– This is represented by the growth of the autonomous
growth factor, A, in the per person production function.
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The “Solow Residual”
• The per person production function in terms of
growth rates is given by: y – n = a + b(k – n)
(where b is the elasticity of output with respect to K)
• Solving for a yields the “Solow Residual:”
a = (y – n) – b(k – n)
• The Solow Residual is the amount that remains
after subtracting from the rate of real GDP growth
all of the identifiable sources of economic growth.
– a is also known as the growth in Multifactor
Productivity
or Total Factor Productivity.
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Puzzles for Solow’s Theory
• Conflict #1: Income per capita varies too much
across countries.
– The theory implies that a country that is 10 times richer
than a poor country must have vastly greater amounts of
capital per worker (like 10,000 times the amount of K/N!)
• Conflict #2: Poor countries do not have a higher
rate of return on capital.
• Conflict #3: Convergence has not been uniform.
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Figure 11-5 A Production Function Relating
per Person Output to per Person Capital Input
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Human Capital and Solow Puzzles
•
Human capital (H) is the value for a person or for
society as a whole, of the extra future earnings made
possible by education.
– The new production function: Y = AF(K, H, N)
•
Including human capital suggests that rich countries
having 10 times the per person income of a poor nation
need to have about 12.6 times the combined human and
physical capital.
• Including human capital also removes the need for rich
countries to have much lower returns on human and
physical capital as compared to poor countries.
• The immigration puzzle: why do immigrants suddenly earn more
for the same low-skilled work in the U.S?
– All factors (beyond human capital) contribute to immigrants higher MPL
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Endogenous Growth Theory
• Endogenous Growth Theory attempts to
explain technical change as the outcome of
market activity in response to economic
incentives rather than just assuming that
technical changes happens exogenously.
– Some models have the key to growth being the
development of ideas for new goods, assuming monopoly
power granted by patents and copyright.
– Other models look at the role of international trade in
disseminating ideas.
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