Balance of Payments I: The Gains
from Financial Globalization
6
1. Using the notation from the text, answer the following questions. You may assume
that net labor income from abroad is zero, there are no capital gains on external
wealth, and there are no unilateral transfers.
a. Express the change in external wealth (W0) at the end of period 0 as a function of the economy’s trade balance (TB), the real interest rate (a constant, r*),
and initial external wealth (W1).
Answer: The total amount added to (or subtracted from) external wealth is equal
to the trade balance plus interest earned on external wealth from the previous
period: W0 TB0 r*W1.
b. Using (a), write an expression for the stock of external wealth at the end of period 0 (W0). This should be written as a function of the economy’s trade balance
(TB0), the real interest rate, and initial external wealth (W1).
Answer: Rewriting the previous expression, solving for W0:
W0 W0 W1 TB0 r*W1
W0 TB0 (1 r*)W1
c. Using (a) and (b), write an expression for the stock of external wealth at the end
of period 1 (W1).This should be written as a function of the economy’s trade balance (TB) each period, the real interest rate, and initial external wealth (W1).
Answer: From (a), we know that the change in wealth in period 1 is equal to
the trade balance in period 1 plus interest earned on external wealth from period 0:
W1 TB1 r*W0
Rewriting this expression to solve for W1:
W1 TB1 (1 r*)W0
Plugging in the expression from (b) for W0:
W1 TB1 (1 r*)[TB0 (1 r*)W1]
W1 TB1 (1 r*)TB0 (1 r*)2W1
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
d. Using your answers from (a), (b), and (c), write an expression for the stock of external wealth at the end of period 2 (W2). This should be written as a function
of the economy’s trade balance (TB) each period, the real interest rate, and initial external wealth (W1).
Answer: Using the same method from (c) to solve for W2:
W2 TB2 r*W1
W2 TB2 (1 r*)W1
W2 TB2 (1 r*)[TB1 (1 r*)TB0 (1 r*)2W1]
W2 TB2 (1 r*)TB1 (1 r*)2TB0 (1 r*)3W1
e.
Suppose we require that W2 equal 0. Write down the condition that the three
trade balances (in periods 0, 1, and 2) must satisfy. Arrange the terms in present
value form.
Answer: If W2 0, then
TB2 (1 r*)TB1 (1 r*)2TB0 (1 r*)3W1 0
(1 r*)3W1 TB2 (1 r*)TB1 (1 r*)2TB0
In present value terms:
TB1
TB2
(1 r*)W1 TB0 2
(1 r*)
(1 r*)
2. Using the assumptions and answers from the previous question, complete the following:
a. Write an expression for the future value of the stock of external wealth in period
N (WN).This should be written as a function of the economy’s trade balance (TB)
each period, the real interest rate r*, and initial external wealth.
Answer: The future value of external wealth in period N is the sum of the trade
balance in each period (compounded by the interest earned or paid) plus compounded interest earned on initial external wealth:
WN TBN (1 r*)TBN1 (1 r*)2TBN2 . . . (1 r*)N TB0 (1 r*)N1W1
b. Using the answer from (a), write an expression for present value of the stock of
external wealth in period N (WN).
Answer: In present value terms, divide both sides of the previous expression by
(1 r*)N:
WN
TB1
TB2
TBN
TB0 2 . . . (1 r*)W1
N
(1 r*)
(1 r*)
(1 r*)
(1 r*)N
c. The “no Ponzi game” conditions force the present value of WN to tend to 0 as
N gets large. Explain why this implies that the economy’s initial external wealth
is equal to the present value of future trade deficits.
Answer: The “no Ponzi game” condition means that the county cannot have
negative or positive external wealth as N gets large (in the limit, N → ):
WN
0
lim N→ (1 r*)N
Therefore, we can rewrite the expression from (b), imposing this condition:
TB1
TB2
TBN
(1 r*)W1 TB0 2 . . . (1 r*)
(1 r*)
(1 r*)N
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
Therefore, the country’s initial external wealth, W0 (1 r*)W1, is equal to
the present value of the country’s future trade deficits.
d. How would the expressions in (a) and (b) change if the economy had net labor
income (positive or negative) to or from abroad or net unilateral transfers? Explain briefly.
Answer: Net labor income to or from abroad would affect the stock of external
wealth each period through changing the NFIA from NFIA r*W0 (with only
capital) to NFIA r*K0 net labor income from abroad, in which K denotes
initial capital held abroad. Assume that labor abroad, Lx is paid a world wage, w*:
W0 TB0 r*K1 w*L0 NUT
The country can effectively finance trade deficits through both capital income
(as in the standard model) and labor income from abroad. Similarly, if the country receives net unilateral transfers, this would also add to the country’s initial
wealth.
3. In this question assume all dollar units are real dollars in billions, so $150 means $150 billion. It is year 0. Argentina thinks it can find $150 of domestic investment projects
with an MPK of 10% (each $1 invested pays off $0.10 in every later year). Argentina
invests $84 in year 0 by borrowing $84 from the rest of the world at a world real interest rate r* of 5%. There is no further borrowing or investment after this.
Use the standard assumptions: Assume initial external wealth W (W in year 1) is 0.
Assume G 0 always; and assume I 0 except in year 0. Also, assume
NUT KA 0 and that there is no net labor income so that NFIA r*W.
The projects start to pay off in year 1 and continue to pay off all years thereafter. Interest is paid in perpetuity, in year 1 and every year thereafter. In addition, assume that
if the projects are not done, then GDP Q C $200 in all years, so that
PV(Q) PV(C) 200 200/0.05 4,200.
a. Should Argentina fund the $84 worth of projects? Explain your answer.
Answer: Yes. The criterion for undertaking an investment project is:
Q
r*
K
Because MPK 10% r* ( 5%), the country will benefit from the investment
project.
b. Why might Argentina be able to borrow only $84 and not $150?
Answer: Argentina may face borrowing limits. Because 150 units of output accounts for three fourths of the country’s total production, lenders might be unwilling to lend this much, even for a productive investment project (e.g., a sudden stop).
c. From this point forward, assume the projects totaling $84 are funded and completed in year 0. If the MPK is 10%, what is the total payoff from the projects in
future years?
Answer: The project will result in an 8.4 increase in Q each period
( MPK K 0.10 84).
d. Assume this is added to the $200 of GDP in all years starting in year 1. In dollars, what is Argentina’s Q GDP in year 0, year 1, and later years?
Answer: Q0 200, Q 208.4 in subsequent years.
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
e.
At year 0, what is the new PV(Q) in dollars? Hint: To simplify, calculate the value
of the increment in PV(Q) due to the extra output in later years.
Answer: The present value of output is:
f.
Q
208.4
PV(Q) Q0 200 4,368
r*
0.05
At year 0, what is the new PV(I) in dollars? Therefore, what does the LRBC say
is the new PV(C) in dollars?
Answer: The present value of investment is:
PV(I) K 84
Using the LRBC, we can calculate the present value of consumption:
PV(C) PV(Q) PV(I) 4,368 84 4,284
g. Assume that Argentina is consumption smoothing. What is the percent change in
PV(C)? What is the new level of C in all years? Is Argentina better off?
Answer: The percent change in the present value of consumption (compared
with the case with no investment project) is 2% ( 84 / 4,200). The new level
of consumption in all years is:
C
PV(C) C r*
C
4,284 C → C 204
0.05
Yes, Argentina is better off because consumption increases from 200 to 204 in
every period.
h. For the year the projects go ahead, year 0, explain Argentina’s balance of payments as follows: State the levels of CA, TB, NFIA, and FA.
Answer: In year 0, the values are as follows:
TB = Q C I 200 204 84 88
NFIA 0
CA 88
FA 88 (from the balance of payments, CA FA KA and KA 0 by assumption in this question)
i.
What happens in later years? State the levels of CA, TB, NFIA, and FA in year 1
and every later year.
Answer: In subsequent years, the values are as follows:
TB Q C I 208.4 204 0 4.4
NFIA 4.4 ( r* K 0.05 88)
CA 0 FA
4. Continuing from the previous question, we now consider Argentina’s external wealth
position.
a. What is Argentina’s external wealth W in year 0 and later? Suppose Argentina has
a one-year debt (i.e., not a perpetual loan) that must be rolled over every year.
After a few years, in year N, the world interest rate rises to 15%. Can Argentina
stick to its original plan? What are the interest payments due on the debt if
r* 15%? If I G 0, what must Argentina do to meet those payments?
Answer: Argentina borrows $88 in year 0, so its external wealth is $88 in year
0 and thereafter. The interest payments needed to service its debt rise from $4.4
to $13.2 ( 0.15 88). The only way that Argentina can make these payments
is through reducing consumption.
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
b. Suppose Argentina decides to unilaterally default on its debt. Why might Argentina do this? State the levels of CA, TB, NFIA, and FA in year N and all subsequent years. What happens to the Argentine level of C in this case?
Answer: If Argentina defaults on this debt, NFIA 0 because external wealth
rises to 0.This means Argentina no longer needs to run a trade surplus, so its consumption can increase by the $4.4 that was previously paid on its debt. TB NFIA CA FA 0 and C $208.4.
c. When the default occurs, what is the change in Argentina’s external wealth, W?
What happens to the rest of the world’s (ROW’s) external wealth?
Answer: External wealth rises to 0.The rest of the world experiences an $88 decrease in wealth.
d. External wealth data for Argentina and ROW are recorded in the net international investment position account. Is this change in wealth recorded as a financial flow, a price effect, or an exchange rate effect?
Answer: In the net international investment position, this is recorded as a financial flow.
5. Using production function and MPK diagrams, answer the following questions. For
simplicity, assume there are two countries: a poor country (with low living standards)
and a rich country (with high living standards).
a. Assuming that poor and rich countries have the same production function, illustrate how the poor country will converge with the rich country. Describe how
this mechanism works.
Answer: See the following figure.
q
A
qR
B
qP
kP and qP rise
until qP ⫽ qR.
kP
kR
k
MPK
B
MPKP
Because MPKP ⬎ MPKR,
capital flows into P.
A
MPKR
kP
kR
k
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
We know that living standards are measured by output per capita—this is directly
correlated with output per worker (denoted q on the diagram) and income per
worker. Therefore, according to the benchmark model (in which we assume the
same production functions in both countries), the reason the rich country is rich
is simple: it saves more and therefore has more capital per worker (denoted k on
the diagram) and therefore more output per worker. This is shown by the two
points A (rich country) and B (poor country). According to the benchmark
model, the gap in living standards should not persist. Because the marginal product of capital is higher in the poor country, it will attract capital from abroad,
converging to the level of output per capita and output per worker observed in
the rich country. Over time, countries will converge to the same living standards.
b. In the data, countries with low living standards have capital-to-worker ratios that
are too high to be consistent with the model used in (a). Describe and illustrate
how we can modify the model used in (a) to be consistent with the data.
Answer: See the following figure.
q
A
qR
D
q 2P
qP
B
C
kP and qP rise,
but qP ⬍ qR.
k dataP
kP
k 2P
kR
k
MPK
B
MPKP
MPKdataP
C
A
MPKR
D
kP
k dataP
k 2P
kR
k
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
In the two graphs on the previous page, we observe a gap in living standards (qR
versus qP) that is inconsistent with the gap in capital to worker ratios (kR versus kP).
Specifically, the poor countries are saving a lot more than that implied by the model
(once we’ve pinned down the parameters ␪ and A). This is shown by point C in
the figure.The way we can address this gap is to assume the two countries have different production functions—specifically, they have different productivity levels, A
(see [a]). From the diagram that follows, we see that this implies poorer countries
will not completely converge with their richer counterparts. With lower productivity levels, these countries will achieve a point at which MPK r* at a lower level
of capital per worker; therefore, they will have a lower output per worker. We see
the poor country converges to point D, at which the marginal products are equal,
but the poor country has a lower level of capital (and output) per worker.
c. Given your assumptions from (b), what does this suggest about the ability of poor
countries to converge with rich countries? What do we expect to happen to the
gap between rich and poor countries over time? Explain.
Answer: With lower productivity levels, these countries will achieve a point
where MPK r* at a lower level of capital per worker; therefore, they will have
a lower output per worker. The gap will persist as long as the productivity levels
differ.
Using the model from (b), explain and illustrate how convergence works in the
following cases.
d. The poor country has a marginal product of capital that is higher than that of the
rich country.
Answer: See figure for (b). Since the poor country's MPK is higher, capital flows
into the poor country, raising its living standards.
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
e.
The marginal products in each country are equal. Then, the poor country experiences an increase in human capital through government funding of education.
Answer: See the following diagrams. This implies an increase in productivity
level. The gap between the living standards will be reduced because the poor
country is able to maintain a higher capital-to-worker ratio.
q
A
qR
E
q 2P
D
qP
kP and qP rise with
increase in AP.
kP
k 2P
kR
k
MPK
MPKP rises as
AP increases.
E
r*
A
D
kP
k 2P
kR
k
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
The marginal products in each country are equal. Then, the poor country experiences political instability such that investors require a risk premium to invest in
the poor country.
Answer: See the following diagrams.This implies that investors require r* RP MPKR to invest in the poor country. To pay the higher return to capital, MPKP must
decrease.To pay the higher return to capital, MPKP must increase, which means that
kp must decrease.
q
A
qR
D
qP
q 2P
E
kP and qP fall with a
rise in risk premium.
k 2P
kP
kR
k
MPK
Because MPKP ⫽ r* ⫹ RP,
kP falls.
r* ⫹ RP
E
A
r*
D
k 2P
kP
kR
k
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
6. Assume that Brazil and the United States have different production functions q f(k)
where q is output per worker and k is capital per worker. Let q Ak1/3.You are told
that relative to the U.S. 1, Brazil has an output per worker of 0.32 and capital per
worker of 0.24. Can A be the same in Brazil as in the United States? If not, calculate
the level of A for Brazil. What is Brazil’s MPK relative to the United States?
Answer: We can calculate the implied ratio of productivity levels ABrazil/AUS. Let P
denote Brazil (the poor country) and R denote the United States (the rich country).
Note the ratio of the marginal product of capital in each country is:
0.32
MPKP
qP/qR
1.333
0.24
MPKR
kP/kR
Therefore, the ratio of the MPK in each country is 1.333. To find the difference in
productivity levels, we assume the capital share ␪ 1/3, and substitute in the production functions:
AP/AR
AP k␪P/AR k␪R
AP/AR
MPKP
qP/qR
AP/AR
1.33
1␪
2/3
(kP/kR)
kP/kR
0.386
MPKR
kP/kR
(0.24)
AP/AR 0.51
Therefore, Brazil’s productivity level is 51% of that in the United States. We can see
from the previous expression that it is not possible that Brazil’s productivity level is
equal to that of the United States.
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
7. Use production function and MPK diagrams to examine Turkey and the EU. Assume
that Turkey and the EU have different production functions q f(k) where q is output per worker and k is capital per worker. Let q Ak1/3. Assume that the productivity level A in Turkey is lower than A in the EU.
a. Draw a production function diagram (with output per worker, q, as a function of
capital per worker, k) and MPK diagram (MPK versus k) for the EU. (Hint: Be
sure to draw the two diagrams with the production function directly above the
MPK diagram so that the level of capital per worker, k, is consistent on your two
diagrams.)
Answer: See the following diagram.
b. For now, assume capital cannot flow freely in and out of Turkey. On the same diagrams, plot Turkish production function and MPK curves, assuming that the
productivity level A in Turkey is half the EU level and that Turkish MPK exceeds
EU MPK. Label the EU position in each chart EU and the label the Turkish position T1.
Answer: See the following diagram.
c. Assume capital can now flow freely between Turkey and the EU and the rest of
the world and that EU is already at the point where MPK r*. Label r* on the
vertical axis of the MPK diagram. Assume no risk premium. What will be
Turkey’s capital per worker level k? Label this outcome point T2 in each diagram.
Will Turkey converge to the EU level of q? Explain.
Answer: See the following diagram. Turkey’s capital per worker will be equal to
the levels in the EU once capital flows freely between the two regions. This is
because Turkey’s high MPK will attract capital from abroad, increasing output per
worker in Turkey.Yes, Turkey will converge to the EU level of q.
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
q
A
qEU
T2
q 2T
qT
T1
kT and qT rise,
but qT ⬍ qEU.
kT
k 2T
kEU
k
MPK
Capital flows into Turkey
from EU, kT rises, and qT
rises, but qT ⬍ qEU.
MPKT
T1
A
r* ⫽ MPKR
T2
kT
k 2T
kEU
k
8. This question continues from the previous problem, focusing on how risk premiums
explain the gaps in living standards across countries.
a. Investors worry about the rule of law in Turkey and also about the potential for
hyperinflation and other bad macroeconomic policies. Because of these worries,
the initial gap between MPK in Turkey and r* is a risk premium, RP. Label RP
on the vertical axis of the MPK diagram. Now where does Turkey end up in
terms of k and q?
Answer: Turkey will be forced to remain at a lower capital per worker (versus
the EU) because the risk premium means MPKT RP r*. Turkey’s k and q
will be lower than those in the EU.
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
q
A
qEU
T2
qT
q 3T
T3
kT and qT fall with a
rise in risk premium.
k 3T
kT
kEU
k
MPK
Because MPKT ⫽ r* ⫹ RP,
kT falls.
r* ⫹ RP
T3
A
r*
T2
k 3T
kT
kEU
k
b. In light of (a), why might Turkey be keen to join the EU?
Answer: If Turkey were to join the EU, it would be required to adopt policies
that are in line with those used in international trade and finance in the EU. This
would potentially allay investors’ concerns, reducing Turkey’s risk premium. Joining the EU gives Turkey the opportunity to signal a credible move towards
“good” policy.
c. Some EU countries are keen to exclude Turkey from the EU. What might be the
economic arguments for that position?
Answer: The countries in the EU most likely to be opposed to Turkey’s entrance
into the EU (based on economic arguments) would be those that are relatively
poor. It is possible that when Turkey enters the EU, it would attract some of the
capital that would have been bound for the EU’s relatively poorer members. Although these countries might not be as poor as Turkey, they will now have to
compete with Turkey for capital (now that Turkey would not be required to pay
a risk premium).
9. In this chapter, we saw that financial market integration is necessary for countries to
smooth consumption through borrowing and lending. Consider two economies: the
Czech Republic and France. For each of the following shocks, explain how and to
what extent each country can trade capital to better smooth consumption.
a. The Czech Republic and France each experience an EU-wide recession.
Answer: This is an example of a common shock. The Czech Republic and
France would be unable to use diversification to eliminate the volatility in capital income created by this negative shock. Both countries would seek to borrow.
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
b. A strike in France leads to a reduction in French income.
Answer: This is an idiosyncratic shock to France’s output (from a reduction in labor production). France can buffer the effects on income through diversifying. In
this case, France experiences a decline in output (from the labor stoppage), but still
continues to enjoy relatively high capital income from its portfolio investment in
the Czech Republic. This income can finance France’s GNE. Likewise, the Czech
Republic’s output is relatively high (compared with France), so its GNI GNE,
with the difference flowing to France in the form of capital income.
c. Floods destroy a portion of the Czech capital stock, lowering Czech income.
Answer: This is a negative idiosyncratic shock to the Czech Republic. The
Czech Republic continues to earn income from its capital investments in France,
buffering its total income against the shock. In this case, capital income flows
from France to the Czech Republic.
10. Assume that a country produces an output Q of 50 every year. The world interest rate
is 10%. Consumption C is 50 every year, and I G 0.There is an unexpected drop
in output in year 0, so output falls to 39 and is then expected to return to 50 in every
future year. If the country desires to smooth consumption, how much should it borrow in period 0? What will the new level of consumption be from then on?
Answer: There is a one-time decrease in output of 11 units. Therefore, the present
value of consumption is:
50
PV(C) PV(Q) PV(G) 39 539
0.10
To determine the level of consumption each period, we know that the countrywants
to maintain a given level of consumption:
C
PV(C) C r*
C
539 C → C 49
0.10
Note that for every 10 units borrowed, consumption is reduced by one unit, as NFIA 0.10 10 in subsequent periods.Therefore, C 49 in period 0 and thereafter. Alternatively, the change in consumption can be calculated using the following:
r*
0.10
C Q (11) 1
1 r*
1 0.10
Consumption decreases by one unit, to C 49.
11. Assume that a country produces an output Q of 50 every year.The world interest rate
is 10%. Consumption C is 50 every year, and I G 0. There is an unexpected war
in year 0, which costs 11 units and is predicted to last one year. If the country desires
to smooth consumption, how much should it borrow in period 0? What will the new
level of consumption be from then on?
The country wakes up in year 1 and discovers that the war is still going on and will
eat up another 11 units of expenditure in year 1. If the country still desires to smooth
consumption looking forward from year 1, how much should it borrow in period 1?
What will be the new level of consumption from then on?
Answer: If the war is temporary, the increase in G should be financed through borrowing (e.g., running a current account deficit). To determine how much the country
should borrow, we first must calculate the change in the present value of consumption.
The present value of government spending is equal to 11, as this is a one-time increase
in government spending. Therefore, the present value of consumption is:
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
50
PV(C) PV(Q) PV(G) 50 11 539
0.10
To determine the level of consumption each period, we know that the country wants
to maintain a given level of consumption:
C
PV(C) C r*
C
539 C → C 49
0.10
If the government needs to borrow again, then we can use the same approach to find
consumption each period. Note that for every 10 units borrowed, consumption is reduced by one unit, as NFIA 0.10 10 in subsequent periods. Therefore, in period 0, C 49. Thereafter, when the government needs another 11 units, beginning
in period 1, C 48 (as NFIA increases by one additional unit).
12. Consider a world of two countries, Highland (H) and Lowland (L). Each country has
an average output of 9 and desires to smooth consumption. All income takes the form
of capital income and is fully consumed each period.
a. Initially there are two states of the world, Pestilence (P) and Flood (F). Each happens with 50% probability. Pestilence affects Highland and lowers the output there
to 8, leaving Lowland unaffected with an output of 10. Flood affects Lowland and
lowers the output there to 8, leaving Highland unaffected with an output of 10.
Devise a table with two rows corresponding to each state (rows marked P, F). In
three columns, show income to three portfolios: the portfolio of 100% H capital,
the portfolio of 100% L capital, and the portfolio of 50% H 50% L capital.
Answer: See the following table.
State
P
F
100% L Capital
10
8
100% H Capital
50-50 portfolio
8
10
9
9
b. Two more states of world appear: Armageddon (A) and Utopia (U). Each happens
with 50% probability but is uncorrelated with the P-F state. Armageddon affects
both countries equally and lowers income in each country by a further 4 units,
whatever the P-F state. Utopia leaves each country unaffected. Devise a table with
four rows corresponding to each state (rows marked PA, PU, FA, FU). In three
columns, show income to three portfolios: the portfolio of 100% H capital, the
portfolio of 100% L capital, and the portfolio of 50% H 50% L capital.
Answer: See the following table.
State
PU
FU
PA
PA
100% L Capital
10
8
6
4
100% H Capital
8
10
4
6
50-50 portfolio
9
9
5
5
c. Compare your answers to (a) and (b) and consider the optimal portfolio choices.
Does diversification eliminate consumption risk in each case? Explain.
Answer: In (a), Lowland and Highland are each able to eliminate exposure to
risk through investing equally in capital at home and abroad. This is because all
shocks in this part are idiosyncratic and are negatively correlated. In (b), the
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Chapter 6 Balance of Payments I: The Gains from Financial Globalization
countries are able to reduce some of the volatility in capital income through diversification, but not completely. This is because both countries are subject to
common shocks (Armageddon) that cannot be diversified away. This state uniformly reduces capital income in both countries.