international econ

Exchange Rates II: The Asset Approachin the Short Run

1. Use the money market and FX diagrams to answer the following questions about therelationship between the British pound (£) and the U.S. dollar ($). The exchange rateis in U.S. dollars per British pound, E$/£. We want to consider how a change in theU.S. money supply affects interest rates and exchange rates. On all graphs, label theinitial equilibrium point A.

a. Illustrate how a temporary decrease in the U.S. money supply affects the moneyand FX markets. Label your short-run equilibrium point B and your long-runequilibrium point C.

Answer: See the diagram below.

S-23

4

iRs

i 1Rs

i 2Rs

MS 1 MS 2

MD 1

A C

B

ER

i 1R$

i 2R$

DR 1

DR 2

FR 1

FR 2

E 1 E 2E 3M 2IN

P 2IN

A C

B

ERs/$M 1IN

P 1IN

M2IN

P1IN

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b. Using your diagram from (a), state how each of the following variables changesin the short run (increase/decrease/no change): U.S. interest rate, British interestrate, E$/£, Ee

$/£, and the U.S. price level.

Answer: The U.S. interest rate increases, the British interest rate does notchange, E$/£ decreases, Ee

$/£ does not change, and the U.S. price level does notchange.

c. Using your diagram from (a), state how each of the following variables changesin the long run (increase/decrease/no change relative to their initial values atpoint A): U.S. interest rate, British interest rate, E$/£, Ee

$/£, and U.S. price level.

Answer: All of the variables return to their initial values in the long run. This isbecause the shock is temporary, implying the central bank will increase themoney supply from M2 to M1 in the long run.

2. Use the money market and FX diagrams from (a) to answer the following questions.This question considers the relationship between the Indian rupees (Rs) and the U.S.dollar ($). The exchange rate is in rupees per dollar, ERs/$. On all graphs, label the ini-tial equilibrium point A.

a. Illustrate how a permanent increase in India’s money supply affects the money andFX markets. Label your short-run equilibrium point B and your long-run equi-librium point C.

Answer: See the following diagram.

S-24 Solutions ■ Chapter 4 Exchange Rates II: The Asset Approach in the Short Run

iRs

i 1Rs

i 2Rs

MS 1 MS 2

MD1

A C

B

ER

i 1R$

i 2R$

DR1

DR2

FR 1

FR 2

E 1 E 2E 3M 2IN

P 2IN

A C

B

ERs/$M 1IN

P 1IN

M 2IN

P 1IN

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3. Is overshooting (in theory and in practice) consistent with PPP? Consider the rea-sons for the usefulness of PPP in the short run versus the long run and the assump-tion we’ve used in the asset approach (in the short run versus the long run). Howdoes overshooting help to resolve the empirical behavior of exchange rates in theshort run versus the long run?

Answer:Yes, overshooting is consistent with PPP. Investors forecast the expected ex-change rate based on the theory of PPP. When there is some change in the market,the investors know the exchange rate will change to equate relative prices in the longrun. This is why we observe overshooting in the short run—the investors incorpo-rate this information into their short-run forecasts. Exchange rates are volatile in theshort run. The theory’s implication that there is exchange rate overshooting (in re-sponse to permanent shocks) is one explanation for short run volatility in exchangerates.

4. Use the money market and foreign exchange (FX) diagrams to answer the followingquestions. This question considers the relationship between the euro (€) and the U.S.dollar ($). The exchange rate is in U.S. dollars per euro, E$/€. Suppose that with fi-nancial innovation in the United States, real money demand in the United States de-creases. On all graphs, label the initial equilibrium point A.

a. Assume this change in U.S. real money demand is temporary. Using the FX andmoney market diagrams, illustrate how this change affects the money and FXmarkets. Label your short-run equilibrium point B and your long-run equilib-rium point C.

Answer: See the following diagram. The long-run values are the same as the ini-tial values because the shock is temporary. Also because the shock is temporary,we assume that the reversal of real money demand occurs before the price leveladjusts—that is, MD returns from MD2 to MD1 before the price level changes.


i$

i 1$

i2$

i1$

i2$

MS1

MD1

MD2

A C A C

B

ER

DR1

DR2

FR1

E1M1US / P1

US E2

B

E$/€

b. Assume this change in U.S. real money demand is permanent. Using a new dia-gram, illustrate how this change affects the money and FX markets. Label yourshort-run equilibrium point B and your long-run equilibrium point C.

Answer: See the following diagram. In this case, the expected exchange ratechanges because the shock is permanent. In the long run, the price level will haveto increase to adjust for the drop in real money demand (assuming the central bankdoes not change the money supply, M). That is, the nominal interest rate returns toits initial value in the long run. This requires that the price level increase to re-

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The U.S. dollar was pegged to the value of gold along with other major currencies,including the British pound, the French franc, and so on. Many researchers haveblamed the severity of the Great Depression on the Federal Reserve and its failure toreact to economic conditions in 1929 and 1930. Discuss how the policy trilemma ap-plies to this situation.

Answer: The United States was committed to the fixed exchange rate with gold;consequently, policy makers had to sacrifice either monetary policy autonomy or cap-ital mobility, just as the trilemma suggests. Based on the information given in thequestion, we can assume that the policy did not respond to the U.S. business cycle(policy makers did not exercise monetary policy autonomy). Thus, if we assume in-ternational capital mobility, the United States could not react to the business cyclewith a monetary expansion until it abandoned the gold standard.

9. On June 20, 2007, John Authers, investment editor of the Financial Times, wrote thefollowing in his column, “The Short View”:

The Bank of England published minutes showing that only the narrowest pos-sible margin, 5–4, voted down [an interest] rate hike last month. Nobody fore-saw this. . . . The news took the sterling back above $1.99, and to a 15-year highagainst the yen.

Can you explain the logic of this statement? Interest rates in the United Kingdomhad remained unchanged after the vote and were still unchanged after the minuteswere released. What was contained in the news that caused traders to react? Use theasset approach.

Answer: The news item indicates that investors did not expect the decision to leaveinterest rates unchanged would be divisive. They thought that any increases in inter-est rates would happen further in the future. Higher interest rates would lead to anappreciation in the pound sterling. When the minutes showed that interest rate in-creases were more likely than previously thought, investors came to expect an appre-ciation sooner rather than later. This caused an appreciation in the current spot ex-change rate.

10. We can use the asset approach both to make predictions about how the market willreact to current events and to understand how important these events are to investors.Consider the behavior of the Union/Confederate exchange rate during the CivilWar. How would each of the following events affect the exchange rate, defined asConfederate dollars per Union dollar, EC$/$?

a. The Confederacy increases the money supply by 2,900% between July and De-cember of 1861.

Answer: The home money supply increases, the exchange rate increases, and theConfederate dollar depreciates.

b. The Union Army suffers a defeat in Battle of Chickamauga in September 1863.

Answer: Appreciation in the Confederate dollar is expected because a militaryvictory means decreased risk, the exchange rate decreases, and the Confederatedollar appreciates.

c. The Confederate Army suffers a major defeat with Sherman’s March in the au-tumn of 1864.

Answer: Depreciation in the Confederate dollar is expected because of militarydefeat/increased risk; the exchange rate increases, and the Confederate dollardepreciates.


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S-36 Solutions ■ Chapter 5 National and International Accounts

3. Show how each of the following would affect the U.S. BOP. Include a description ofthe debit and credit items, and in each case say which specific account is affected (e.g.,imports of goods and services, IM; exports of assets, EXA; and so on).

a. A California computer manufacturer purchases a $50 hard disk from a Malaysiancompany, paying the funds from a bank account in Malaysia.

Answer:

b. A U.S. tourist to Japan sells his iPod to a local resident for yen worth $100.

Answer:

c. The U.S. central bank sells $500 million of its holdings of U.S. Treasury bonds toa British financial firm and purchases pound sterling foreign reserves.

Answer:

d. A foreign owner of Apple shares receives $10,000 in dividend payments, whichare paid into a New York bank.

Answer:

e. The central bank of China purchases $1 million of export earnings from a firmthat has sold $1 million of toys to the United States, and the central bank holdsthese dollars as reserves.

Answer:

Description BOP Account Account (detail) Credit/Debit

Hard disk imported from Malaysia CA (↓) �IM (↑), TB (↓) –$50Decrease in Malaysian deposits owned by U.S. firm FA (↑) �IMF

A (↓) �$50


iPod exported to Japan CA (↑) �EX (↑), TB (↑) �$100Increase in Japanese currency owned by U.S. tourist FA (↓) �IMF

A (↑) �$100


U.S. bonds sold to British firm FA (↑) �EXHA (↑) �$500 mil.

Pound-sterling reserves imported from Britain FA (↓) �IMFA (↑) �$500 mil.


Import of factor service (ownership) from ROW CA (↓) �IMFS (↑), NFIA (↓) �$10,000New York bank deposits paid to ROW FA (↑) �EXH

A (↑) �$10,000


Import of toys from China CA (↓) �IM (↑), TB (↓) �$1 mil.China central bank buys U.S. dollars FA (↑) �EXH

A (↑) �$1 mil.

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Solutions ■ Chapter 5 National and International Accounts S-37

f. The U.S. government forgives a $50 million debt owed by a developing country.

Answer:

4. In 2010 the country of Ikonomia has a current account deficit of $1 billion and anonreserve financial account surplus of $750 million. Ikonomia’s capital account is ina $100 million surplus. In addition, Ikonomian factors located in foreign countriesearn $700 million. Ikonomia has a trade deficit of $800 million. Assume Ikonomianeither gives nor receives unilateral transfers. Ikonomia’s GDP is $9 billion.

a. What happened to Ikonomia’s net foreign assets during 2010? Did it acquire orlose foreign assets during the year?

Answer: BOP � CA � FA � KA � 0CA � KA � �FA

Current account deficit of $1 billion ($1,000 million) and the capital account isin a $100 million surplus.

�$1,000 � $100� �FA

FA � $900 � EXA � IMA

The financial account records financial flows into and out of the country. In thiscase, the FA surplus indicates that on net, foreigners purchased more Ikonomianassets than Ikonomians purchased foreign assets. Therefore, net foreign assets forIkonomia declined by $900 million.

b. Calculate the official settlements balance. Based on this number, what happenedto the central bank’s (foreign) reserves?

Answer:The financial account can be split into those transactions conducted bythe central bank (official settlements balance) and those conducted by everyoneelse (nonreserve financial account):

FA � Official settlements balance � Nonreserve financial account

Nonreserve financial account is a $750 million surplus.

$900 � Official settlements balance � $750

Official settlements balance � $150

The official settlements balance is in a $150 million surplus. This means that for-eign central banks purchased more Ikonomian assets (paid for with foreign cur-rency) than the Ikonomian central bank purchases of foreign assets (paid for withdomestic currency, $ in this case). Therefore, Ikonomia’s central bank experiencedan increase in its foreign reserve holdings.


Debt forgiveness (gift) KA (↓) �KAOUT (↑) �$50 mil.Decrease in external assets owned by U.S. entities FA (↑) �IMF

A (↓) �$50 mil.

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c. How much income did foreign factors of production earn in Ikonomia during2010?

Answer: The current account can be split into three components: the trade bal-ance (final goods and services), the net factor income from abroad (paymentsto/from factor services), and the net unilateral transfers.

CA � TB � NFIA � NUT

�$1000 � �$800 � NFIA � 0. In the question, we are given the trade balance (�$800 million) and the current account (�$1,000 million).

NFIA � �$200. Net factor income from abroad is �$200 million.This implies that foreign factors of production located in Ikonomia earned more than Ikonomian factors abroad.

NFIA � EXFS � IMFS. We know that Ikonomian factors abroad earned $600 million.

�$200 � $600 � IMFS

IMFS � $800. Foreign factors located in Ikonomia earned $900 million.

d. Calculate NFIA.

Answer: See (c). NFIA � �$200 million.

e. Using the identity BOP � CA � FA � KA, show that BOP � 0.

Answer: To check our work, we can verify the BOP identity:

BOP � CA � FA � KA

BOP � [TB � NFIA � NUT] � FA � KA

BOP � [�$800 � �$200 � $0] � [$750 � $150] � $100 � 0

f. Calculate Ikonomia’s GNE, GNI, and GNDI.

Answer: We know that GDP � C � I � G � (EX � IM) � GNE � TB

GNE � GDP � TB

GNE � $9,000 � (�$800)

GNE � $9,800

GNI � GDP � NFIA � GNE � TB � NFIA

GNI � $9,000 � (�$200) � $9,800 � (�800) � (�$200)

GNI � $8,800 � $8,800

GNDI � GDP � NFIA � NUT � GNI � NUT.Because NUT � $0, GNDI � GNI

GNDI � $8,800

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5. To answer this question, you must obtain data from the Bureau of Economic Analy-sis (BEA), http://www.bea.gov, on the U.S. BOP tables. Go to interactive tables toobtain annual data for 2008 (the default setting is for quarterly data). It may take yousome time to get familiar with how to navigate the website. You need only refer toTable 1 on the BOP accounts. Using the BOP data, calculate the following for theUnited States:

Answers will vary because of data revisions. The figures below are based on thosegiven in the Table 5-3.

a. TB, NFIA, NUT, and CA

Answer: TB � �$375 billion (Lines 1 � 3)

NFIA � �$121 billion (Lines 2 � 4)

NUT � �$125 billion (Line 5)

CA � �$379 billion (Lines 1 � 2 � 3 � 4 � 5)

b. FA

Answer: FA � �$166 billion (Lines 7 � 8)

c. Official settlements balance, referred to as “U.S. official reserve assets” and “For-eign official assets in the United States.”

Answer: Official settlements balance � �$398 billion (Lines 7a � 8a)

d. Nonreserve financial account (NRFA)

Answer: Nonreserve financial account � �$232 billion (Lines 7b � 8b)

e. BOP. Note that this may not equal zero because of statistical discrepancy. Verifythat the discrepancy is the same as the one reported by the BEA.

Answer: BOP � CA � FA � KA � �$379 � $166 � $0 � �$213

(statistical discrepancy � �$213 million)

6. Continuing from the previous question, find nominal GDP for the United States in2008 (you can find it elsewhere on the BEA site). Use this information along withyour previous calculations to calculate the following:

Answers will vary because of data revisions. The figures below use data from Table 5-2.

a. GNE, GNI, GNDI

Answer: GNE � $14,649 billion (row 4)

GNI � $14, 362 billion (row 8)

GNDI � $14, 237 billion (row 10)

b. In macroeconomics, we often assume the U.S. economy is a closed economywhen building models that describe how changes in policy and shocks affect theeconomy. Based on the previous data (BOP and GDP), do you think this is a rea-sonable assumption to make? Do international transactions account for a largeshare of total transactions (involving goods and services, or income) involving theUnited States?

Answer: Based on Table 5-2, we see that GDP � $14,257 billion, whereas thetrade balance accounts for a small share of this total (TB � �$392 billion). Sim-ilarly, if we compare the share of GNI ($14,362 billion) that is attributed to thecurrent account (CA � �$412 billion), we can see that international transactionsaccount for a relatively small share of U.S. production and income. Therefore, theassumption of a closed economy is a reasonable one.

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7. During the 1980s, the United States experienced “twin deficits” in the current ac-count and government budget. Since 1998, the U.S. current account deficit hasgrown steadily, along with rising government budget deficits. Do government bud-get deficits lead to current account deficits? Identify other possible sources of the cur-rent account deficits. Do current account deficits necessarily indicate problems in theeconomy?

Answer: “Twin deficits” are possible, but there are other factors that influence thecurrent account. Since 1998, the decline in the current account has been associatedwith movements in investment and national savings. Note the following expressionfrom the textbook:

CA � SP � SG � I

It is not clear that budget deficits cause current account deficits. There are two pos-sibilities besides a budget deficit (SG � 0):• Private savings (SP) may change when the government changes taxes (e.g., tax

rates). Suppose tax rates decrease, causing a decrease in government saving. Ac-cording to Ricardian equivalence, households will respond to a tax cut today byincreasing savings in anticipation of a future tax increase needed to finance thecurrent budget deficit. This implies private savings will increase, possibly offset-ting the effect on national saving.

• The current account may move independently of saving, namely because ofchanges in investment (I). An increase in domestic investment opportunitiescould lead to current account deficits.

8. Consider the economy of Opulenza. In Opulenza, domestic investment of $400 mil-lion earned $20 million in capital gains during 2009. Opulenzans purchased $120million in new foreign assets during the year; foreigners purchased $160 million inOpulenzan assets. Assume the valuation effects total $1 million in capital gains.

Note that we need to assume a value for the capital account. We will assume KA �0 in the following transactions.

a. Compute the change in domestic wealth in Opulenza.

Answer: The change in domestic wealth is the sum of additions to the capitalstock plus capital gains earned on domestic assets:

Change domestic wealth � I � Capital gains on K � $400 � $20 � $420 million

b. Compute the change in external wealth for Opulenza.

Answer: The change in external wealth is:

∆W � Valuation effects � (�FA) � $1 � ($160� $120) � –$39 million

c. Compute the total change in wealth for Opulenza.

Answer: The change in total wealth is:

Change total wealth � Change domestic wealth � Change in external wealth � $420 � (�$39) � $381 million

d. Compute domestic savings for Opulenza.

To calculate national savings, note that the change in total wealth is:

Change total wealth � S � KA � Capital gains on K � Capital gains on (A � L)$381 � S � $0 � ($20 � $1)S � $360 million

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e. Compute Opulenza’s current account. Is the CA in deficit or surplus?

Answer: Using the current account identity: S � I � CA:

S � I � CA$360 � $400 � CACA � �$40 million

Or, we could use the definition of the change in total wealth:

Change total wealth � I � (CA � KA) � Capital gains on K � Capital gainson (A � L)

$381 � $400 � CA � $0 � $20 � $1CA � �$40 million

f. Explain the intuition for the CA deficit/surplus in terms of savings in Opulenza,financial flows, and its domestic/external wealth position.

Answer: We see that Opulenza experienced a $420 million increase in its do-mestic wealth while losing $39 million in external wealth. $360 million of thisincrease in domestic wealth was financed through domestic savings, plus wealthgrew because of capital gains on the existing stock of wealth ($20). This leaves$20 million financed from foreign sources. The way that Opulenza pays for thisgrowth in domestic wealth is through borrowing from abroad—this is why itsexternal wealth declined. It is also the reason for the CA deficit. Opulenzans en-joy relatively high spending (GNE � GDP) through running a CA deficit andthrough borrowing from abroad (∆W � 0).

g. How would a depreciation in Opulenza’s currency affect its domestic, external,and total wealth? Assume that foreign assets owned by Opulenzans are denomi-nated in foreign currency.

Answer: The answer to this question depends on how Opulenzan external as-sets and external liabilities are denominated. If, as in the case of the United States,most liabilities are denominated in the home currency whereas a smaller share isdenominated in the foreign currency, then a depreciation leads to a larger in-crease in external liabilities than assets. In turn, this would decrease in financialaccount. This would improve Opulenza’s external wealth position, reducing itsCA deficit. Note that this implies they will have to cut back on spending (re-ducing the CA deficit).

9. This question asks you to calculate valuation effects for the United States in 2004using the same methods mentioned in the chapter. Use the http://www.bea.govwebsite to collect the data needed for this question: look under the “International”heading.

Visit the BEA’s balance of payments data page and obtain the U.S. BOP for 2004in billions of dollars. Be sure to get the annual data, not quarterly.

Visit the BEA’s net international investment position data page and obtain the U.S.net international investment position for end 2003 to end 2004.Answers may vary based on data revisions. The data below were obtained in Novem-ber 2007:

a. What was the U.S. current account for 2004?

Answer: CA � �$640,148 million

b. What was the U.S. financial account for 2004?

Answer: FA � $556,742 million

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Therefore, the country’s initial external wealth, W0 � (1 � r*)W�1, is equal tothe present value of the country’s future trade deficits.

d. How would the expressions in (a) and (b) change if the economy had net laborincome (positive or negative) to or from abroad or net unilateral transfers? Ex-plain briefly.

Answer: Net labor income to or from abroad would affect the stock of externalwealth each period through changing the NFIA from NFIA � r*W0 (with onlycapital) to NFIA � r*K0 � net labor income from abroad, in which K denotesinitial capital held abroad. Assume that labor abroad, Lx is paid a world wage, w*:

�W0 � TB0 � r*K�1 � 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 coun-try receives net unilateral transfers, this would also add to the country’s initialwealth.

3. In this question assume all dollar units are real dollars in billions, so $150 means $150 bil-lion. It is year 0. Argentina thinks it can find $150 of domestic investment projectswith an MPK of 10% (each $1 invested pays off $0.10 in every later year). Argentinainvests $84 in year 0 by borrowing $84 from the rest of the world at a world real in-terest 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. In-terest is paid in perpetuity, in year 1 and every year thereafter. In addition, assume thatif 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:

��

�

QK� � r*

Because MPK � 10% � r* (� 5%), the country will benefit from the investmentproject.

b. Why might Argentina be able to borrow only $84 and not $150?

Answer: Argentina may face borrowing limits. Because 150 units of output ac-counts for three fourths of the country’s total production, lenders might be un-willing to lend this much, even for a productive investment project (e.g., a sud-den stop).

c. From this point forward, assume the projects totaling $84 are funded and com-pleted in year 0. If the MPK is 10%, what is the total payoff from the projects infuture 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 dol-lars, what is Argentina’s Q � GDP in year 0, year 1, and later years?

Answer: Q0 � 200, Q � 208.4 in subsequent years.

Solutions ■ Chapter 6 Balance of Payments I: The Gains from Financial Globalization S-45

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e. At year 0, what is the new PV(Q) in dollars? Hint: To simplify, calculate the valueof the increment in PV(Q) due to the extra output in later years.

Answer: The present value of output is:

PV(Q) � Q0 � �Qr*

� � 200 � �200.80.54

� � 4,368

f. At year 0, what is the new PV(I) in dollars? Therefore, what does the LRBC sayis 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 inPV(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 (comparedwith the case with no investment project) is 2% (� 84 / 4,200). The new levelof consumption in all years is:

PV(C) � C � �Cr*

�

4,284 � C � �0.C05� → C � 204

Yes, Argentina is better off because consumption increases from 200 to 204 inevery period.

h. For the year the projects go ahead, year 0, explain Argentina’s balance of pay-ments 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 � �88NFIA � 0CA � �88FA � 88 (from the balance of payments, CA � FA � KA and KA � 0 by as-sumption in this question)

i. What happens in later years? State the levels of CA, TB, NFIA, and FA in year 1and every later year.

Answer: In subsequent years, the values are as follows:

TB � Q � C � I � 208.4 � 204 � 0 � 4.4NFIA � �4.4 (� r* �K � 0.05 88)CA � 0 � FA

4. Continuing from the previous question, we now consider Argentina’s external wealthposition.

a. What is Argentina’s external wealth W in year 0 and later? Suppose Argentina hasa 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 Argentinastick 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 year0 and thereafter. The interest payments needed to service its debt rise from $4.4to $13.2 (� 0.15 88). The only way that Argentina can make these paymentsis through reducing consumption.

S-46 Solutions ■ Chapter 6 Balance of Payments I: The Gains from Financial Globalization

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b. Suppose Argentina decides to unilaterally default on its debt. Why might Ar-gentina do this? State the levels of CA, TB, NFIA, and FA in year N and all sub-sequent years. What happens to the Argentine level of C in this case?

Answer: If Argentina defaults on this debt, NFIA � 0 because external wealthrises to 0. This means Argentina no longer needs to run a trade surplus, so its con-sumption 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 de-crease in wealth.

d. External wealth data for Argentina and ROW are recorded in the net interna-tional investment position account. Is this change in wealth recorded as a finan-cial flow, a price effect, or an exchange rate effect?

Answer: In the net international investment position, this is recorded as a fi-nancial flow.

5. Using production function and MPK diagrams, answer the following questions. Forsimplicity, 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, illus-trate how the poor country will converge with the rich country. Describe howthis mechanism works.

Answer: See the following figure.


qR

qP

q

MPK

kP kR

MPKP

MPKR

A

B

k

kP and qP riseuntil qP � qR.

kP kR

A

B

k

Because MPKP � MPKR, capital flows into P.

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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 la-bor production). France can buffer the effects on income through diversifying. Inthis case, France experiences a decline in output (from the labor stoppage), but stillcontinues to enjoy relatively high capital income from its portfolio investment inthe Czech Republic. This income can finance France’s GNE. Likewise, the CzechRepublic’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. TheCzech Republic continues to earn income from its capital investments in France,buffering its total income against the shock. In this case, capital income flowsfrom France to the Czech Republic.

10. Assume that a country produces an output Q of 50 every year. The world interest rateis 10%. Consumption C is 50 every year, and I � G � 0. There is an unexpected dropin output in year 0, so output falls to 39 and is then expected to return to 50 in everyfuture year. If the country desires to smooth consumption, how much should it bor-row 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 presentvalue of consumption is:

PV(C) � PV(Q) � PV(G) � 39 � �05.100

� � 539

To determine the level of consumption each period, we know that the countrywantsto maintain a given level of consumption:

PV(C) � C � �Cr*

�

539 � C � �0.C10� → C � 49

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. Alterna-tively, the change in consumption can be calculated using the following:

�C � �1 �

r*r*

� �Q � �1 �

0.100.10

�(�11) � �1

Consumption decreases by one unit, to C � 49.

11. Assume that a country produces an output Q of 50 every year. The world interest rateis 10%. Consumption C is 50 every year, and I � G � 0. There is an unexpected warin year 0, which costs 11 units and is predicted to last one year. If the country desiresto smooth consumption, how much should it borrow in period 0? What will the newlevel of consumption be from then on?

The country wakes up in year 1 and discovers that the war is still going on and willeat up another 11 units of expenditure in year 1. If the country still desires to smoothconsumption 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 bor-rowing (e.g., running a current account deficit). To determine how much the countryshould 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 increasein government spending. Therefore, the present value of consumption is:


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PV(C) � PV(Q) � PV(G) � 50 � �05.100

� � 11 � 539

To determine the level of consumption each period, we know that the country wantsto maintain a given level of consumption:

PV(C) � C � �Cr*

�

539 � C � �0.C10� → C � 49

If the government needs to borrow again, then we can use the same approach to findconsumption each period. Note that for every 10 units borrowed, consumption is re-duced by one unit, as NFIA � 0.10 10 in subsequent periods. Therefore, in pe-riod 0, C � 49. Thereafter, when the government needs another 11 units, beginningin 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 hasan average output of 9 and desires to smooth consumption. All income takes the formof capital income and is fully consumed each period.

a. Initially there are two states of the world, Pestilence (P) and Flood (F). Each hap-pens with 50% probability. Pestilence affects Highland and lowers the output thereto 8, leaving Lowland unaffected with an output of 10. Flood affects Lowland andlowers 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). Inthree 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.

b. Two more states of world appear: Armageddon (A) and Utopia (U). Each happenswith 50% probability but is uncorrelated with the P-F state. Armageddon affectsboth 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 withfour rows corresponding to each state (rows marked PA, PU, FA, FU). In threecolumns, show income to three portfolios: the portfolio of 100% H capital, theportfolio of 100% L capital, and the portfolio of 50% H � 50% L capital.

Answer: See the following table.

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 torisk through investing equally in capital at home and abroad. This is because allshocks in this part are idiosyncratic and are negatively correlated. In (b), the


State 100% L Capital 100% H Capital 50-50 portfolio

P 10 8 9F 8 10 9

State 100% L Capital 100% H Capital 50-50 portfolio

PU 10 8 9FU 8 10 9PA 6 4 5PA 4 6 5

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countries are able to reduce some of the volatility in capital income through di-versification, but not completely. This is because both countries are subject tocommon shocks (Armageddon) that cannot be diversified away. This state uni-formly reduces capital income in both countries.

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