Download A Two-Period International Investment Model Setting Up the The

Chapter 10
The Economics of International Investment
The foreign-investment fuss ignores facts, economics
and history.
(The Economist, 1989)
International
Economics
The Goals of this Chapter
• Show how international investment raises the total value of
world output and income, and why all countries share in
the net gains.
• Explain how international investment permits investors to
spread their risk among a greater variety of assets.
• Present evidence and models suggesting that international
investment also facilitates the flow of technology between
countries.
• Explain why international investment is still small
compared to what it could be.
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Economics
A Two-Period International Investment Model
• The first model presented in this chapter shows
how two economies with different time-preferences
gain from being able to borrow and lend.
• The model simplifies by assuming that people live
for just two periods, which permits us to use a twodimensional graphic version of the model.
• The model also assumes away the problems of risk
and default that normally plague intertemporal
transactions.
• This model makes it clear that international trade
and international investment are closely related.
International
Economics
The Principal Assumptions of the Two-Period Model:
• Output Y is produced using capital, K, and labor, L,
according to the production function Y = F(K,L).
• Output Y can be used for consumption C or as a
productive capital good K.
• If the labor force, L, remains constant, investment
in new capital is subject to diminishing returns.
• Technology does not change.
• The economy begins period 1 with a certain
endowment of labor and capital.
• Suppose, finally, that capital goods last just one
period, after which point they must be replaced by
newly-produced capital inputs.
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Economics
Setting Up the The Supply Side of the Model
• Output in period 1, Y1, is a
function of the amount of
capital produced, K1.
• The two-period intertemporal
consumption-possibilities
frontier (ICPF) shows that
the larger is saving in period
1 (equal to the difference
between Y1 and C), the
greater is period 2’s output.
• If consumption in period 1 is
C”, then saving/investment is
Y1 ! C”, and second period
output will be Y”2.
Output in
period 2
Figure 10.1
The Intertemporal Consumption
Possibilities Frontier
Y’2
Y”2
ICPF
C’
C” Y Output in
1 period 1
International
Economics
Setting Up the The Supply Side of the Model
• On the other hand, if first
period consumption is less,
say C’, then investment is Y1
! C’, and second period
output will be Y’2.
• Period 2 output and
consumption, Y’2 > Y”2 , is
greater in this case because
(Y1 ! C’) > (Y1 ! C”).
• The curvature of the ICPF
reflects diminishing returns to
investment; equal additions to
investment in period 1 result
in smaller and smaller
additions to period 2 output .
Output in
period 2
Figure 10.1
The Intertemporal Consumption
Possibilities Frontier
Y’2
Y”2
ICPF
C’
C” Y Output in
1 period 1
International
Economics
Setting Up the The Demand Side of the Model
• Intertemporal preferences are
represented by intertemporal
indifference curves, such as I.
• It is assumed that people only
live for two periods, so that they
only choose consumption over
two periods.
• People always prefer more
consumption in both periods to
less consumption in both
periods; a higher the
intertemporal indifference
curve, like I’, represents a
higher level of total welfare.
Figure 10.2
The Suply and Demand Sides
of Intertemporal Trade
Y2= c 2
A
I
P
I’
ICPF
c’
Y1
International
Economics
Setting Up the The Demand Side of the Model
• At A, the rate at which the economy
can substitute period 1 consumption
for period 2 consumption equals the
rate at which consumers are willing to
substitute period 1 consumption for
period 2 consumption.
• The slope of the intertemporal price
line P is equal to (1+r), where r
Y=c
represents the % premium to induce
consumers to voluntarily give up
current consumption.
• In intertemporal equilibrium, period 1
consumption c’ enables investment of
Y1 ! c’ create the capital to produce
output Y2 = c2 in period 2.
2
Figure 10.2
The Suply and Demand Sides
of Intertemporal Trade
A
2
I
P
ICPF
c’
Y1
International
Economics
A Two-Period International Investment Model
The Intertemporal Equilibrium
• A single, isolated economy
can do no better than point
A.
• However, if people acquire
foreign assets or they sell
assets to foreigners, they can
reach intertemporal
consumption combinations
that lie outside the ICPF.
• To keep the analysis simple,
suppose that the economy is
very “small.”
Figure 10.3
Intertemporal Equilibrium with Asset Trade
Output in
Period 2
ICPF
e
B
f
A
I’
g
k
I
D
P*
0
j i
h Y1
P
Output in
Period 1
International
Economics
The Intertemporal Equilibrium
• Suppose, finally, that ROW’s
interest rate, denoted as r*, is
higher than the small
economy’s interest rate, r.
• If people in the small
country are free to borrow or
lend in ROW, they will
select the intertemporal
consumption pattern given
by the point B.
• Consumers are thus able to
reach a higher intertemporal
indifference curve, which
confirms that international
investment raises welfare.
Figure 10.3
Intertemporal Equilibrium with Asset Trade
Output in
Period 2
ICPF
e
B
f
A
I’
g
k
I
D
P*
0
j i
h Y1
P
Output in
Period 1
International
Economics
The Intertemporal Equilibrium
• The small country’s savers
invest hY1 in domestic
capital, which creates
output 0g in period 2.
• In addition, international
investment of jh gives
small-country savers a
return in period 2 of
(1+r*)jh = ge.
• Summing the returns to
domestic investment hY1
and international
investment jh gives period
2 consumption of 0e.
Figure 10.3
Intertemporal Equilibrium with Asset Trade
Output in
Period 2
ICPF
e
B
f
A
I’
g
k
I
D
P*
0
j i
h Y1
P
Output in
Period 1
International
Economics
The Intertemporal Equilibrium
• By being able to lend, export, and import, the small
country’s consumers to achieve the combination of period
1 and 2 consumption levels that lie on a higher indifference
curve than the best closed-economy consumption point A.
• Notice that for the small country to take advantage of
international investment opportunities, it must engage in
international trade.
• Notice also that the gains from intertemporal trade require
that countries run trade deficits or trade surpluses in the
short run; that is, trade deficits or surpluses can be quite
desirable and are not necessarily “problems” that need to
be corrected.
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Economics
Determinants of Intertemporal Comparative Advantage
• Differences in interest rates between countries are the
result of (1) different indifference curves (consumer
preferences) or (2) different ICPFs (different rates of return
to investment).
• Differences in intertemporal preferences reflect differences
in people’s tastes, age, household responsibilities, present
and expected future income, and willingness to bear risk.
• Differences in returns to investment are the result of
differences in (1) the availability of other factors to
combine with capital, (2) technology, (3) the efficiency of
the financial system in allocating savings to investors, and
(4) institutions such as the protection of property, the rule
of law, contract enforcement, and sound monetary policy.
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Many Periods Instead of Just Two Periods
• In multi-period models with technological progress, it
remains true that savings will flow to countries where
investment or R&D activity promises the highest returns.
• Economies with the greatest growth potential will be net
borrowers and have trade deficits in the short run.
• Rapidly growing economies have an intertemporal
comparative advantage with their high return investments.
• Economies whose residents, firms, and governments are
relatively more frugal will lend to foreigners in the short run
and run trade surpluses.
• Both the two-period and multi-period models of international
investment show that the lifetime welfare of people is higher
than it would be in a closed economy.
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Economics
A Partial Equilibrium Model of International Savings
• The two-period, two-country intertemporal model of
investment and trade does not explicitly tell us who
actually enjoys the intertemporal welfare gains and who
suffers the potential welfare losses.
• A partial equilibrium model can be used to show how the
welfare gains from international investment are distributed
among savers and borrowers in one period of time.
• This model is “partial” in nature because it looks at
international savings flows in one period; this partial view
is ignores the many other savings and trade flows that
occur in other periods of time, as suggested by the twoperiod model.
International
Economics
A Partial Equilibrium Model of International Savings
• In general, the demand curve
for savings, or “loanable
funds,” is downward sloping
to reflect the descending
order of the real and financial
investment opportunities.
• The supply curve of loanable
funds is shown as an upwardsloping curve, suggesting
people save more the higher
is the interest rate.
• The equilibrium in the market
for loanable funds occurs at
the interest rate of 10 percent
in the Figure.
Figure 10.4
The Market for Loanable Funds
%
S
10%
D
Loanable Funds
International
Economics
A Partial Equilibrium Model of International Savings
• Borrowers earn a surplus equal
to the area a.
Figure 10.4
The Market for Loanable Funds
%
S
a
10%
D
Loanable Funds
International
Economics
A Partial Equilibrium Model of International Savings
• Borrowers earn a surplus equal
to the area a.
• Savers earn a surplus over and
above their perceived value of
foregone consumption equal to
the area b.
Figure 10.4
The Market for Loanable Funds
%
10%
S
a
b
D
Loanable Funds
International
Economics
A Partial Equilibrium Model of International Savings
• Borrowers earn a surplus equal
to the area a.
• Savers earn a surplus over and
above their perceived value of
foregone consumption equal to
the area b.
• The area under the supply of
funds curve, area c, represents
the opportunity cost of savers’
foregone consumption.
Figure 10.4
The Market for Loanable Funds
%
10%
S
a
b
c
D
Loanable Funds
International
Economics
A Partial Equilibrium Model of International Savings
• The area under the supply of
funds curve, area c, represents
the opportunity cost of savers’
foregone consumption.
• Borrowers earn a surplus equal
to the area a.
• Savers earn a surplus over and
above their perceived value of
foregone consumption equal to
the area b.
• The area under D (a+b+c)
represents the total returns to
the investments on the
loanable funds demand curve.
Figure 10.4
The Market for Loanable Funds
%
S
10%
D
D
Loanable Funds
International
Economics
A Two-Country Partial Equilibrium
Model of International Investment
• The single country model
can be expanded into a
two-country model to show
how international
investment affects lender
and borrower surpluses.
• Suppose that the world
consists of two countries,
India and Pakistan.
• Because of different supply
and demand conditions, the
rates of return in the two
countries are 12 percent
and 8 percent, respectively.
Figure 10.5
Two-Country Partial Equilbrium Investment Model
%
India
%
Pakistan
SI
SP
12%
8%
DI
DP
Loanable Funds
Loanable Funds
International
Economics
A Two-Country Partial Equilibrium
Model of International Investment
• In the absence of
barriers, savings will
move from Pakistan to
India.
• The supply curve of
funds to purchase assets
in India therefore shifts
to the right.
• The supply of savings
in Pakistan shifts to the
left by an equal amount.
• This arbitrage tends to
equalize the interest rate
in both countries.
Two-Country Partial Equilbrium Investment Model
%
India
%
Pakistan
SI
SP
12%
8%
DI
DP
Loanable Funds
Loanable Funds
International
Economics
The Welfare Effects of International Investment
Figure 10.7
Two-Country Partial Equilbrium Investment Model
%
India
%
SI
International Investment
Pakistan
SI!F
%
SI+F
Si
12%
a
b
B
D
8%
II
Loanable Funds
d
Di
DI
e f g
c
SP
DP
0
k
II
Loanable Funds
h i
j
Loanable Funds
II
International
Economics
The Welfare Effects of International Investment
• Savers in India
lose the area a.
• But Indian
borrowers find
that the lower
interest rate
provides gains
equal to the areas
a and b.
• The net gain to
Indian citizens is
the area b.
Figure 10.7
Two-Country Partial Equilbrium Investment Model
%
India
%
SI
International Investment
Pakistan
SI!F
%
SI+F
Si
12%
a
b
B
D
8%
e f g
II
d
Di
DI
Loanable Funds
c
SP
DP
0
k
II
Loanable Funds
h i
j
Loanable Funds
II
International
Economics
The Welfare Effects of International Investment
• Pakistani savers gain
areas c and d.
• The area c is not a
net gain for the
country; it represents
returns that were
captured by
Pakistani borrowers
but now accrue to
Pakistani savers.
• The net gain to
Pakistani citizens is
the area d.
Figure 10.7
Two-Country Partial Equilbrium Investment Model
%
12%
India
%
SI
International Investment
Pakistan
SI!F
%
SI+F
Si
a
b
B
D
8%
II
Loanable Funds
d
Di
DI
e f g
c
SP
DP
0
k
II
Loanable Funds
h i
j
Loanable Funds
II
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Economics
The Welfare Effects of International Investment
• Total investment
falls in Pakistan by
ij and rises in India
by fg.
• Pakistan is a net
gainer because, by
sending savings to
India and increasing
India’s assets,
Pakistan’s savers
enjoy higher returns
and total Pakistani
income rises.
Figure 10.7
Two-Country Partial Equilbrium Investment Model
%
12%
India
%
SI
International Investment
Pakistan
SI!F
%
SI+F
Si
a
b
B
D
8%
II
Loanable Funds
d
Di
DI
e f g
c
SP
DP
0
k
II
Loanable Funds
h i
j
Loanable Funds
II
International
Economics
The Gains from Asset Diversification
• Asset holders generally have two goals: (1) maximize
returns and (2) minimize risk.
• These two goals often seem to conflict; safer assets
generally offer lower returns because wealth holders are
more willing to acquire such assets.
• Risk can be reduced by diversifying asset holdings (Don’t
put all your eggs in one basket).
• Successful risk reduction requires that asset earnings not
be perfectly correlated.
• Since international asset prices and returns are less likely
to be correlated, international investment provides
opportunities for risk-reducing asset diversification.
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Summarizing the Gains
from International Investment
• International asset exchanges permit consumers to more
efficiently allocate their consumption expenditures over
time.
• International asset exchanges permit savings to be channeled
to the highest-return investments wherever they may be in
the world.
• International investment permits investors to reduce risk by
pooling assets from different countries, which are less
closely correlated than assets located within a single country.
• These three motives for international investment are often
referred to as intertemporal consumption smoothing, the
efficient allocation of savings, and risk diversification.
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International Investment in
the Solow Growth Model
• In the Solow model, the
return to investment is the
slope of the production
function Y = f(K).
• A steep slope implies a high
return because each increase
in K causes a large increase
in output.
• The slope of the production
function depends on the
stock of capital, the stock of
other factors of production,
and the level of technology.
The Solow Model
Y
f(K)
Y*
b

K
a
0
K*
f(K)
K
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The Rate of Return to Investment Depends Jointly
on the Capital Stock, Other Factors, and Technology
• Diminishing returns implies
that as more capital is added
to a fixed amount of other
productive resources, each
additional unit of capital
increases output by smaller
and smaller amounts.
• At the lower stock of capital
K1, the slope of the
production function r1 is
greater than the slope r2 at
the larger stock of capital K2
(point a versus point b).
Dimishing Returns to Capital
Y
r1
r2
f1(K,L1)
b
a
K1
K2
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Economics
The Rate of Return to Investment Depends Jointly
on the Capital Stock, Other Factors, and Technology
• The return to capital also
depends on the stocks of
other factors of production.
• For example, an increase in
the amount of labor from L1
to L2 raises the production
function from f1(K,L1) to
f1(K,L2).
• For a given capital stock
K*, the increase in labor
causes the marginal rate of
return to investment
(capital) to rise from r2 to r3
(point c versus point b).
An Increase in the Stock of Labor
.
Y
r3
c
f1(K, L2)
r2
b
f1(K, L1)
K*
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Economics
The Rate of Return to Investment Depends Jointly
on the Capital Stock, Other Factors, and Technology
• Technological progress
shifts the production
function, as from f1(K,L1)
to f2(K,L1).
• If technological progress
causes the slope of f2(K,L1)
at K* to be steeper than the
slope of f1(K,L1) at K*, the
return to investment rises
from r2 to r3.
Technological Progress
.
Y
r3
c
f2(K,L1)
r2
b
f1(K,L1)
K*
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Economics
International Investment and Economic Growth
• International investment has been linked to economic growth.
• To understand the possible links, recall the Schumpeterian
model of technological progress, summarized as:
q = f( B, r, R, $ ).
• The variable q is the quantity of innovations generated in the
economy, R the supply of resources in the economy, B is the
profit from innovating, $ the efficiency of R&D activities in
terms of the resources necessary to generate an innovation,
and r is the interest rate that reflects people’s valuation of
future gains versus current income and at which the returns
from investments in R&D must be discounted.
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Economics
International Investment and Economic Growth
• International investment is likely to affect technological
progress through B, the profit from innovation.
• Because it contributes to globalization, which is essentially
the integration of separate economies into a single world
economy, international investment raises the potential profits
from innovation.
• International investment can reduce the cost of innovation,
$, because it facilitates the flow of ideas.
• There is evidence that foreign direct investment leads to the
transfer of technology to the recipient countries, and other
forms of investment may also facilitate information flows
between economies, thereby reducing $.
• Foreign investment may also stimulate innovation be
increasing competition.
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Why Is International Investment So Small?
• Investment is subject to some degree of risk.
• Investment is an intertemporal transaction where
one party agrees to accept payment(s) at some
future date.
• It is impossible to foresee the future with certainty.
• There are also some perverse incentives that
increase the likelihood that future payments will fall
short of agreed-to levels.
• International investment faces greater difficulties in
foreseeing the future and countering perverse
incentives.
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Economics
Why Is International Investment So Small?
• Information available to lenders and borrowers is often
asymmetric, with lenders knowing less than borrowers
about the eventual payout of assets.
• Asymmetric information can result in adverse selection,
which is the case where, because buyers have difficulty in
verifying the quality of assets, a disproportionate amount
of “bad” assets are likely to be offered for sale.
• Moral hazard refers to the likelihood that once borrowers
have acquired a loan, sold stock, or sold a bond, they will
behave differently than they would had they not gained the
financing, thereby reducing the eventual earnings from an
asset.
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