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Chapter3
Introduction to Economic Growth
Macroeconomics Chapter 3
1
Fact 1 on Economic Growth


Large variations in per capita
income across countries.
Real GDP in 2000, PPP-adjusted, in
1996 US$
Per capita Rel. USA Per worker Rel. USA
USA
33290
100
64540
100
Canada
26900
81
52300
81
India
3750
11
6170
9. 6
Uganda
940
2. 8
1970
3. 1
Macroeconomics Chapter 3
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Rise in Income Inequality
Macroeconomics Chapter 3
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Fact 2 – Cont’

Large variations in growth rates of
income across countries.
Real GDP per Worker
1960 2000
Growth Rate
South Korea 4470 36850
5. 3
Spain
12150 44110
3. 2
Canada
27870 52300
1. 6
Veneguela
25290 17750
0. 9
Chad
3090
0. 4
2600
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Macroeconomics Chapter 3
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Fact 3 – Cont’

A country’s relative position in the
world distribution of per capita
incomes may experience large
changes over time. Countries can
move from "poor" to "rich", and vice
versa.
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Fact 4 – Cont’
In the Unites States over the last century:
 the real rate of return to capital, r , shows no
trend upward or downward;
 the share of income devoted to capital, rK/Y , and
labor, wL/Y , show no trend;
 the average growth rate of output per person has
been positive and relatively constant over time i.e., the Unites States exhibited steady, sustained
per capita income growth (or, the U.S. economy is
on the balanced growth path).
The above three features of the United States are
also called Kaldor facts (balanced growth).
Macroeconomics Chapter 3
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Macroeconomics Chapter 3
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Long Term Economic Growth in OECD Countries
Macroeconomics Chapter 3
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Productivity Slowdown

The decline in the growth rate of
real GDP per person from 3.1% per
year for 1960–1980 to 1.8% per
year for 1980–2000 is sometimes
called the productivity slowdown.
Macroeconomics Chapter 3
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Growth Questions


What factors caused some countries to
grow fast and others to grow slow over
periods such as 1960 to 2000?
In particular, why did the East Asian
countries do so much better than the subSaharan African countries?
Macroeconomics Chapter 3
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Growth Questions

How did countries such as the United
States and other OECD members sustain
growth rates of real GDP per person of
around 2% per year for a century or more?
Macroeconomics Chapter 3
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Growth Questions

What can policymakers do to increase
growth rates of real GDP per person?
Macroeconomics Chapter 3
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Production Function
Y = A· F(K, L)



A  Technology Level
K  Capital Stock – machines and
buildings used by business.
L  Labor Force – number of workers
Macroeconomics Chapter 3
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Macroeconomics Chapter 3
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Macroeconomics Chapter 3
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Production Functions

MPL – Marginal Product of Labor


Diminishing Marginal Product of labor
MPK – Marginal Product of Capital

Diminishing Marginal Product of Capital
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Constant Returns to Scale

Constant Returns to Scale



Double K and L and Y will also double
Therefore, if we multiply K and L by
the quantity 1/L we also multiply Y
by 1/L to get
Y/L = A· F(K/L, L/L)
Macroeconomics Chapter 3
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Per Worker Production Function

y=f(k)


y  output per worker
k  capital per worker
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An example:
Cobb-Douglas Production Function
Y  AK  L1
Y
y
L
K
k
L
AK  L1
y
 AK  L  Ak 
L
dY
MPK 
 AK  1 L1  AK  L1 / K  Y / K
dK
   MPK  K / Y
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Contributions to GDP Growth



∆Y/Y = ∆A/A + α·(∆K/K) + β·(∆L/L)
The growth rate of real GDP, ∆Y/Y, equals
the growth rate of technology, ∆A/A, plus
the contributions from the growth of capital,
α·(∆K/K), and labor, β·(∆L/L).
Solow residual
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Contributions to GDP Growth

α+β=1
Share of capital income (α) + share of labor income (β) = 1

∆Y/Y = ∆A/A + α·(∆K/K) + β·(∆L/L)
 0 < α < 1
 0 < β < 1
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Solow Growth Model

Model ignores:

Government


No taxes, public expenditures, debt, or
money
International Trade

No trade in goods or financial assets
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Solow Growth Model

Labor force, L = ( labor force/
population) · population



Labor-force participation rate
Assume labor force participation rate is
constant.
Labor force growth rate is the
population growth rate
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Solow Growth Model

Growth rate in population


We assume that population grows at a
constant rate, denoted by n, where n is
a positive number (n > 0).
∆L/L = n
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Solow Growth Model
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Solow Growth Model

Assume ∆A/A = 0

∆Y/Y= α·(∆K/K) + (1−α)·(∆L/L)

The growth rate of real GDP is a
weighted average of the growth
rates of capital and labor.
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Solow Growth Model

From the per worker production
function

∆y/y = ∆Y/Y − ∆L/L

∆k/k = ∆K/K − ∆L/L
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Solow Growth Model
 ∆Y/Y= α·(∆K/K) + (1−α)·(∆L/L)

∆Y/Y= α·(∆K/K) − α·(∆L/ L) + ∆L/ L

∆Y/Y − ∆L/L = α · (∆K/K − ∆L/L)

∆y/y = α·(∆k/k)
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Solow Growth Model



Each household divides up its real income
in a fixed proportion s to saving and 1 − s
to consumption ( C ).
Capital depreciate at the same constant
rate δ
δK is the amount of capital that depreciates
each year
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Solow Growth Model


Real saving = s · (Y −δK)
Real saving = (saving rate) · (real
income)
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Solow Growth Model

Y−δK=C+s·(Y−δ K)
Real income = consumption + real saving
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Solow Growth Model




Y=C+I
Real GDP = consumption + gross
investment
Y−δK = C + (I−δK)
Real NDP = consumption + net
investment
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Solow Growth Model

C+s·(Y−δK) = C+I−δK
or


s·(Y−δK) = I−δK
Real saving = net investment
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Solow Growth Model



∆K = I−δK
Change in capital stock = gross investment
− depreciation,
or
Change in capital stock = net investment
∆K = s·(Y−δK)
Change in capital stock = real saving
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Solow Growth Model


Divide both sides by K
∆K/K = s·Y/K − sδ
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Solow Growth Model

∆k/k = ∆K/K − ∆L/L

∆k/k = s· (Y/K) − sδ − n
Macroeconomics Chapter 3
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Solow Growth Model

Y/K =(Y/L) / (K/L)

Y/K = y/k
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Solow Growth Model



∆k/k = s·(y/k) − sδ − n
∆y/y = α·(∆k/k)
∆y/y = α·[ s·(y/k) − sδ − n]
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Solow Growth Model
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Solow Growth Model
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Solow Growth Model

steady state.



When k = k∗, ∆k/k equals zero.
∆k/k = 0, k stays fixed at the value k∗.
y* = f(k*)
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Solow Growth Model
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Solow Growth Model

In the steady state, ∆k/k equals zero.
s·(y*/k*) − sδ − n= 0

s·(y* −δ k*) = nk*


Steady-state saving per worker = steadystate capital provided for each new worker
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