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Chapter 5
International Trade and Economic Growth
The international trading system...has enhanced competition
and nurtured what Joseph Schumpeter a number of decades
ago called “creative destruction,” the continuous scrapping of
old technologies to make way for the new.
(Alan Greenspan, 2001)
International
Economics
The Goals of this Chapter for ECN 665
• Extend the analysis of trade beyond the traditional static
models of international trade and analyze the relationship
between international trade and economic growth.
• Show how the power of compounding makes international
trade’s effect on economic growth much more important for
human welfare than the static gains in welfare.
• Familiarize students with the recent statistical evidence on
the relationship between trade and economic growth.
• Introduce the Solow growth model and use it show how
international trade affects economic growth when investment
is subject to diminishing returns and depreciation.
• Explain the Schumpeterian model of technological progress
and use it to show how international trade affects the
determinants of long-run technological progress.
International
Economics
Trade and Growth Achieve
Similar Gains in Welfare
• Trade and growth both
enable the economy to reach
a higher indifference curve.
• Trade leads to a new
consumption point at C.
• Growth leads to a new
consumption point at D.
• Both points lie on the same
higher indifference curve.
Food
400
P
D
300
A
C
200
CPL
p
100
0
100
200
300
400
500
Clothing
International
Economics
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• An economy with the red
production possibilities
frontier can reach the
indifference curve I2 with
trade.
• However, it takes
continued growth (a large
shift in the indifference
curve) to reach the much
higher level of welfare
given by I20.
• Can trade help stimulate
such economic growth?
F
o
o
d
I20
I2
I1
I1
Clothing
International
Economics
Figure 5.3
World Economic Growth During the
Past 200 Years Has Been Impressive
Per Capita
Real Output
$5,000
$4,000
$3,000
$2,000
$1,000
0
1,000 AD
Based on data from Angus Maddison (2001)
150 0
1820 2000
Time
International
Economics
Figure 5.4
The Recent Growth Has Varied
Greatly Across Regions of the World
Western
Offshoots
Per Capita Real GDP
Western
Europe
$15000
$10000
Southern
Europe
Latin America
Eastern Europe
$5000
World
Asia
Africa
1820
1870
1900
1929
1950
1973
1992
Source: Angus Maddison (1995), Monitoring the World Economy 1820-1992, Paris: OECD, Table 1-1(a), p.
19, and Tables G-1, G-2, G-3, pp. 226-8.
International
Economics
Figure 5.5
Are Economic Growth and
International Trade Related?
Exports/
GDP
Per Capita
Real GDP
$6,000
14%
$5,000
12%
10%
$4,000
Exports/GDP
8%
$3,000
6%
$2,000
4%
Per Capita
Real GDP
$1,000
1820
1870
1900
1929
2%
1950
1973
1998
International
Economics
The Power of Compounding
If per capita real GDP (PCGDP) grows at an annual
rate of R, then after T years PCGDP will be:
PCGDPT = PCGDPt=0(1 + R)T
(5-1)
International
Economics
The Power of Compounding
For a country with a per capita real GDP of
$2,000, a 2.5 percent annual growth rate implies
that in 10 years per capita real GDP will grow to:
PCGDPt=10 = $2000(1 + .025)10 = $2,560
International
Economics
The Power of Compounding
Suppose that another country grows a little faster at
3.5 percent per year. After ten years, this economy’s
per capita real GDP will be:
PCGDPT=10 = $2000(1 + .035)10 = $2,821
After ten years, a difference of 1% per year causes a
per capita income difference greater than 10%.
International
Economics
The Power of Compounding
Two countries that grow at 2.5 percent and 3.5
percent, respectively, for 100 years will find
their standards of living growing far apart:
PCGDPT=100 = $2000(1 + .025)100 = $23,627
PCGDPT=100 = $2000(1 + .035)100 = $62,383
The power of compounding is great.
International
Economics
The statistical analysis of the relationship between
international trade and economic growth shows that:
! International trade is closely and positively related to
economic growth.
! The potential size of trade’s “growth effect” is large.
Statistical analysis thus suggests that international
trade is very important for future human welfare.
International
Economics
The Solow Growth Model
• Production function Y =
f(K,L) with diminishing
returns.
• If labor supply is fixed,
then the function can be
written as Y = f(K).
• Diminishing returns
implies a decreasing
slope; each additional
unit of capital adds less
to output than the
previous unit
Y
0
f(K)
K
International
Economics
The Solow Growth Model
• Solow assumes
that the saving
rate is constant
and between 0
and 1.
• Saving is
assumed to be a
constant fraction
of income.
Y
f(K)
Consumption
f(K)
Saving
0
K
International
Economics
The Solow Growth Model
• Depreciation is
assumed to be a
constant fraction of
the stock of capital K.
• Thus, depreciation is
a straight-line
function of K.
Y
f(K)

K
f(K)
0
K
International
Economics
The Solow Growth Model
• The capital stock continues
to grow until saving and
investment are equal.
• This occurs where the
depreciation line and the
savings function intersect.
• In equilibrium, a capital
stock of K* results in output
Y* = f(K*).
• K* and Y* are referred to as
the steady state levels of
capital and output/income.
Y
f(K)
Y*

K
f(K)
0
K*
K
International
Economics
The Solow Growth Model
• The steady state level
of K* is a stable
equilibrium.
• If K < K*, investment
exceeds depreciation
and K grows.
• If K > K*, depreciation
exceeds investment and
K shrinks.
Y
f(K)
b
Y*

K
f(K)
a
0
K1
K*
K2
K
International
Economics
The Solow Growth Model
• The Solow model
depicts an economy
with a stable
equilibrium.
• Income depends on
the rate of saving,
the rate of
depreciation, and the
shape of the
production function.
Y
f(K)
Y*

K
C*
f(K)
I*
0
K*
K
International
Economics
Figure 5.8
A Rise in the Saving Rate
Increases the Steady State
Y
f(K)
Y2*

K
Y1*
2f(K)
I2*
1 f(K)
I1*
0
K1*
K2*
K
International
Economics
Figure 5.12
Trade’s Transitional Effect on Output
According to the Solow Growth Model
• The static gain from trade
raises the value of output,
which raises output to Y’
= g(K*).
• Given a constant saving
rate, the saving function
shifts up proportionately
to the production function.
• Trade therefore leads to
transitional growth as the
economy adjusts to a new
steady state equilibrium at
K** and Y** = g(K**).
Y
Y**
g(K)
Y’
Y*
f(K)

K
g(K)
f(K)
0
K*
K**
International
Economics
Figure 5.9
The Role of Technological Progress
• Technological progress
raises the production
function
• Technological progress
neutralizes diminishing
returns; it is possible for
output to double when
the capital stock is
doubled, as from a to b
• Without technological
progress, the increase in
capital from 1 to 2 would
only take the economy to
point c, where output
rises by only 40%
Y
f2(K)
200
b
f1(K)
140
c
100
0
a
1
2
K
International
Economics
Figure 5.10
Continual Technological Progress
Y
Y***
c f3(K)
Y**
f2(K)
b
Y*
f1(K)
a

K
f3(K)
f2 (K)
f1(K)
0
K*
K**
K***
International
Economics
Trade and Growth
• International trade seems to produce only
temporary growth according to the Solow model.
• Indeed, the Solow model suggests that continued
economic growth is not possible without
technological progress.
• Hence, for trade to raise standards of living in the
long run, it must influence technological progress.
International
Economics
The statistical evidence on trade and growth is not
entirely convincing, however:
• Statistical studies cannot provide definitive proof
that international trade causes economic growth.
• It is difficult for statistical procedures and the
available data to accurately distinguish between
the effects of trade and those of the other factors.
• Statistical research has not yet distinguished why
trade and growth are positively related.
For further insights, we need logical reasoning and
consistent models that can explain the statistical
relationship between trade and growth.
International
Economics
The Solow Model and Technological Progress
• The Solow growth model shows that for a given
production function economic growth will eventually stop
when the economy reaches its steady state.
• Continued economic growth is only possible if the
production function continually shifts up, which requires
continued technological progress.
• The Solow model highlights the importance of
technological progress, but it does not explain what
determines technological change.
• Several insightful models of models of technological
progress have been developed to complement the Solow
growth model.
International
Economics
Figure 5.14
The Learning Curve
• Many studies of industrial
productivity have noted
that unit costs tend to
decline in proportion to
accumulated experience.
• This process is often
referred to as learning by
doing.
• The learning curve depicts
the learning process, but it
does not explain its
causes.
Unit Costs
Cumulative Output
International
Economics
The Schumpeterian Model of Technological Progress
In Schumpeterian innovation models, R&D activity depends on:
! The productivity with which R&D activity generates innovations.
! The costs of acquiring the resources to carry out R&D activities.
! The benefits that entrepreneurs expect to reap from an innovation.
The first two items above determine the costs of innovation. The
latter item reflects the gains from innovation. The equilibrium level
of R&D activity is found by maximizing benefits subject to the costs
of innovation.
International
Economics
Figure 5.16
The Innovation Function
• The quantity of
innovations depends on
the quantity of resources
applied to R&D activity q
and the productivity of
R&D activity.
• Defining q as the quantity
of innovations, $ as
the quantity of resources
per innovation, and RR&D 0
as the resources applied to
innovation, then:
q = 1/$(RR&D).
1/$(R R&D )
RR&D
International
Economics
Figure 5.17
The Cost of Innovation
• The cost of innovation
(CoI) depends on the cost
of resources and the
productivity of R&D
activity
• The cost of resources
depends on total resources
R and the demand by
innovators RR&D
• Therefore:
CoI = h(RR&D, R, $).
CoI
CoI [$
, R]
0
RR&D
International
Economics
Profit in an Imperfectly-Competitive Market
• The present value of
innovation (PVI) depends on
the size of the profit box B
and on how long a successful
innovator enjoys its
monopoly position.
• The life of a monopoly is the
inverse of the number of
innovations per year, q.
• Expected profit from an
innovation is equal to B/q
= B/[RR&D / $] = B$ /
RR&D.
Price
f
p
B
MC
e
C
MR
0
a
D
Quantity
International
Economics
The Present Value of Innovation (PVI) Curve
• PVI is a negative function of
the rate of interest with
which future profit is
discounted, r, and the
amount of resources
employed in R&D activity
RR&D..
• PVI is a positive function of
the profit markup B and the
resource requirements in
R&D activity, $.
• The present value of
innovation is:
PVI = f( B, r, RR&D, $ ).
PVI
PVI (B, r, $
)
RR&D
International
Economics
Figure 5.20
Equilibrium Innovation
• The intersection of the
CoI and PVI curves
determines the amount
of resources devoted to
R&D activity, RR&D.
• The curve 1/$ in the
bottom half of the
figure relates the
amount of resources to
the expected number of
actual innovations.
CoI,
PVI
CoI ($
, R)
PVI (B, r, $
)
RR&D
q
1/$
Innovations
per Year
International
Economics
Figure 5.21
The Effects on Innovation
of an Increase in B or R
CoI,
PVI
• An increase in B shifts the
PVI curve upward to PVI1,
and, all other things equal,
the number of resources
devoted to innovative
activity increases.
• The increase in RR&D in
turn raises the number of
innovations per year from q
to q1.
CoI
PVI1
PVI
RR&D
q
q1
1/$
Innovations
per Year
International
Economics
Figure 5.22
The Effects on Innovation
of an Increase in R
• An increase in R lowers
the cost of resources.
• The lowering of
resource costs imply a
downward shift in the
CoI curve, say to CoI1.
• This causes profitmotivated entrepreneurs
to employ more
resources in R&D, which
increases the number of
innovations q.
CoI,
PVI
CoI
CoI1
PVI
RR&D
q
q1
1/$
Innovations
per Year
International
Economics
Figure 5-21
The Effects on Innovation
of an Increase in $
• A change in $ is complex
because it affects all curves.
• An increase in $ rotates
the 1/$ line
counterclockwise.
• An increase in $ implies
that R&D activity requires
more costly resources,
which shifts the CoI curve
up.
• The PVI curve also shifts up
because creative destruction
slows when it becomes
harder to innovate, which
makes each innovation that
does occur more profitable.
CoI,
PVI
CoI2
CoI
PVI2
PVI
q1
q
RR&D
1/$
1
Innovations
per Year
1/$
International
Economics
The number of innovations per year is determined by the function:
q = f( B, r, R, $ )
All other things equal, innovation in the economy will be greater:
! The larger is the potential profit for the successful innovator;
! The more innovators value future gains relative to current costs;
! The greater is the supply of resources available to innovators;
! The more efficiently innovators use resources in R&D activity.
International
Economics
How Trade Influences Technological Progress
• For example, integrating
two identical economies
through trade doubles
the market, effectively
shifting the demand
curve from D to Dt.
• The marginal revenue
curve also shifts,
doubling the equilibrium
quantity.
• This doubles the
potential profit accruing
to innovators from B to
2B.
Price
p
Dt
B
B
MC
C
MR
0
a
2a
MR 2 D
Quantity
International
Economics
How Trade Influences Technological Progress
• The doubling of the
profit area, all other
things equal, shifts the
PVI curve up.
• The amount of
resources that profitseeking innovators
apply to R&D activity
expands, and the
number of innovations
rises.
CoI,
PVI
CoI
PVI
RR&D
q1
q2
1/$
Innovations
per Year
International
Economics
How Trade Influences Technological Progress
• The supply of
resources in the
combined economy is
doubled, making more
resources available to
innovators.
• The CoI curve slopes
up less steeply because
the price of resources
rises less rapidly.
• This expands R&D
activity and innovation
further.
CoI,
PVI
CoI
CoI2
PVI
RR&D
q1
q2
q3
1/$
Innovations
per Year
International
Economics
How Trade Influences Technological Progress
• Trade and specialization
also improve the allocation
of resources, thus
increasing the effective
stock of resources.
• An effective increase in R
lowers the CoI curve.
• This efficiency of resource
use is in addition to profit
and resource effects
already described.
CoI,
PVI
CoI
CoI2
PVI
RR&D
q1
q2
q3
q4
1/$
Innovations
per Year
International
Economics
How Trade Influences Technological Progress
• Finally, comparative
advantage also applies to
innovative activity.
• The improvement in the
overall productivity of
innovation decreases $
• A decrease in $ shifts
all three curves.
• Shifts in CoI and PVI are
likely to cancel each other
out, but 1/$ also shifts
out, likely causing an
overall increase in
innovation.
CoI,
PVI
CoI
CoI2
PVI
RR&D
q1
q2
q3
q4
q5
1/$
Innovations
per Year
International
Economics