《宏观经济学》课程教学资源（英文版）Lecture 2 Answers to Textbook Questions and Problems_Mankiw

Chapter 4 Money and Inflation inflation. A nominal variable is one that is measured in current dollars the value of the variable is not adjusted for inflation. For example a real variable could be a hershey's candy bar; the nominal variable is the current-price value of the Hershey's candy bar- 5 cents in 1960, say, and 75 cents in 1999. The interest rate you are quoted by your bank--8 percent, say-is a nominal rate, since it is not adjusted for inflation. If infla- tion is, say, 3 percent, then the real interest rate, which measures your purchasing power, is 5 percent. Problems and applications 1. Money functions as a store of value a medium of exchange, and a unit of account a. A credit card can serve as a medium of exchange because it is accepted in exchange for goods and services. a credit card is, arguably, a(negative) store of lue because you can accumulate debt with it. a credit card is not a unit of ccount--a car, for example, does not cost 5 VISA cards b. A Rembrandt painting is a store of value only c. A subway token, within the subway system, satisfies all three functions of money Yet outside the subway system, it is not widely used as a unit of account or a medium of exchange, so it is not a form of money 2. The real interest rate is the difference between the nominal interest rate and the infla tion rate. The nominal interest rate is 11 percent, but we need to solve for the inflation rate. We do this with the quantity identity expressed in percentage- change form M + Change in V=% Ch in P+% Change in Y. Rearranging this equation tells us that the inflation rate is given by %o Change in P+% Change in M + Change in V-% Change in Y. Substituting the numbers given in the problem, we thus find %o Change in P=14%+0%0-5% =9% Thus, the real interest rate is 2 percent: the nominal interest rate of 11 percent minus the inflation rate of 9 percent. 3. a. Legislators wish to ensure that the real value of Social Security and other benefit stays constant over time. This is achieved by indexing benefits to the cost of living as measured by the consumer price index with indexing, nominal benefits change at the same rate as prices. b. Assuming the inflation is measured correctly(see Chapter 2 for more on this issue), senior citizens are unaffected by the lower rate of inflation. Although they get less money from the government, the goods they purchase are cheaper; their purchasing power is exactly the same as it was with the higher inflation rate. 4. The major benefit of having a national money is seigniorage--the ability of the govern- ment to raise revenue by printing money. The major cost is the possibility of inflation, or even hyperinflation, if the government relies too heavily on seigniorage. The benefit and costs of using a foreign money are exactly the reverse: the benefit of foreign money is that inflation is no longer under domestic political control, but the cost is that the domestic government loses its ability to raise revenue through seigniorage. (There is lIso a subjective cost to having pictures of foreign leaders on your currency. The foreign country's political stability is a key factor. The primary reason for using another nations money is to gain stability. If the foreign country is unstable, then the home country is definitely better off using its own currency-the home econo- my remains more stable, and it keeps the seigniorage 5. A paper weapon might have been effective for all the reasons that a hyperinflation is bad. For example, it increases shoeleather and menu costs; it makes relative prices more variable; it alters tax liabilities in arbitrary ways; it increases variability in rela-

inflation. A nominal variable is one that is measured in current dollars; the value of the variable is not adjusted for inflation. For example, a real variable could be a Hershey’s candy bar; the nominal variable is the current-price value of the Hershey’s candy bar— 5 cents in 1960, say, and 75 cents in 1999. The interest rate you are quoted by your bank—8 percent, say—is a nominal rate, since it is not adjusted for inflation. If infla￾tion is, say, 3 percent, then the real interest rate, which measures your purchasing power, is 5 percent. Problems and Applications 1. Money functions as a store of value, a medium of exchange, and a unit of account. a. A credit card can serve as a medium of exchange because it is accepted in exchange for goods and services. A credit card is, arguably, a (negative) store of value because you can accumulate debt with it. A credit card is not a unit of account—a car, for example, does not cost 5 VISA cards. b. A Rembrandt painting is a store of value only. c. A subway token, within the subway system, satisfies all three functions of money. Yet outside the subway system, it is not widely used as a unit of account or a medium of exchange, so it is not a form of money. 2. The real interest rate is the difference between the nominal interest rate and the infla￾tion rate. The nominal interest rate is 11 percent, but we need to solve for the inflation rate. We do this with the quantity identity expressed in percentage-change form: % Change in M + % Change in V = % Change in P + % Change in Y. Rearranging this equation tells us that the inflation rate is given by: % Change in P + % Change in M + % Change in V – % Change in Y. Substituting the numbers given in the problem, we thus find: % Change in P = 14% + 0% – 5% = 9%. Thus, the real interest rate is 2 percent: the nominal interest rate of 11 percent minus the inflation rate of 9 percent. 3. a. Legislators wish to ensure that the real value of Social Security and other benefits stays constant over time. This is achieved by indexing benefits to the cost of living as measured by the consumer price index. With indexing, nominal benefits change at the same rate as prices. b. Assuming the inflation is measured correctly (see Chapter 2 for more on this issue), senior citizens are unaffected by the lower rate of inflation. Although they get less money from the government, the goods they purchase are cheaper; their purchasing power is exactly the same as it was with the higher inflation rate. 4. The major benefit of having a national money is seigniorage—the ability of the govern￾ment to raise revenue by printing money. The major cost is the possibility of inflation, or even hyperinflation, if the government relies too heavily on seigniorage. The benefits and costs of using a foreign money are exactly the reverse: the benefit of foreign money is that inflation is no longer under domestic political control, but the cost is that the domestic government loses its ability to raise revenue through seigniorage. (There is also a subjective cost to having pictures of foreign leaders on your currency.) The foreign country’s political stability is a key factor. The primary reason for using another nation’s money is to gain stability. If the foreign country is unstable, then the home country is definitely better off using its own currency—the home econo￾my remains more stable, and it keeps the seigniorage. 5. A paper weapon might have been effective for all the reasons that a hyperinflation is bad. For example, it increases shoeleather and menu costs; it makes relative prices more variable; it alters tax liabilities in arbitrary ways; it increases variability in rela￾Chapter 4 Money and Inflation 25

26 Answers to Textbook questions and problems tive prices; it makes the unit of account less useful; and finally, it increase es uncerta and causes arbitrary redistributions of wealth. If the hyperinflation is sufficiently extreme, it can undermine the publics confidence in the economy and economic policy Note that if foreign airplanes dropped the money, then the government would not receive seigniorage revenue from the resulting inflation, so this benefit usually associ- ated with inflation is lost 6. One way to understand Coolidge's statement is to think of a government that is a net debtor in nominal terms to the private sector. Let b denote the government's outstand ing debt measured in U.S. dollars. The debt in real terms equals B/P, where P is the price level. By increasing inflation, the government raises the price level and reduces in real terms the value of its outstanding debt. In this sense we can say that the govern- ment repudiates the debt. This only matters, however when inflation is unexpected. If inflation is expected, people demand a higher nominal interest rate. Repudiation still occurs (l.e. e real valu ue of the debt still falls when the price level rises), but it is not t the expense of the holders of the debt, since they are compensated with a higher 7. A deflation means a fall in the general price level, which is the same as a rise in the value of money. Under a gold standard, a rise in the value of money is a rise in the value of gold because money and gold are in a fixed ratio. Therefore, after a deflation an ounce of gold buys more goods and services. This creates an incentive to look for new gold deposits and, thus, more gold is found after a deflation. 8. An increase in the rate of money growth leads to an increase in the rate of inflation Inflation, in turn, causes the nominal interest rate to rise, which means that the oppor- tunity cost of holding money increases. As a result, real money balances fall. Since money is part of wealth, real wealth also falls. A fall in wealth reduces consumption, and, therefore increases saving. The increase in saving leads to an outward shift of the saving schedule, as in Figure 4-1. This leads to a lower real interest rate 4 Investment S The classical dichotomy states that a change in a nominal variable such as infla- tion does not affect real variables. In this case the classical dichotomy does not hold; the increase in the rate of inflation leads to a decrease in the real interest rate. the Fisher effect states that i=r +I. In this case. since the real interest rate r falls. a 1 percent increase in inflation increases the nominal interest rate i by less than 1 per

tive prices; it makes the unit of account less useful; and finally, it increases uncertainty and causes arbitrary redistributions of wealth. If the hyperinflation is sufficiently extreme, it can undermine the public’s confidence in the economy and economic policy. Note that if foreign airplanes dropped the money, then the government would not receive seigniorage revenue from the resulting inflation, so this benefit usually associ￾ated with inflation is lost. 6. One way to understand Coolidge’s statement is to think of a government that is a net debtor in nominal terms to the private sector. Let B denote the government’s outstand￾ing debt measured in U.S. dollars. The debt in real terms equals B/P, where P is the price level. By increasing inflation, the government raises the price level and reduces in real terms the value of its outstanding debt. In this sense we can say that the govern￾ment repudiates the debt. This only matters, however, when inflation is unexpected. If inflation is expected, people demand a higher nominal interest rate. Repudiation still occurs (i.e., the real value of the debt still falls when the price level rises), but it is not at the expense of the holders of the debt, since they are compensated with a higher nominal interest rate. 7. A deflation means a fall in the general price level, which is the same as a rise in the value of money. Under a gold standard, a rise in the value of money is a rise in the value of gold because money and gold are in a fixed ratio. Therefore, after a deflation, an ounce of gold buys more goods and services. This creates an incentive to look for new gold deposits and, thus, more gold is found after a deflation. 8. An increase in the rate of money growth leads to an increase in the rate of inflation. Inflation, in turn, causes the nominal interest rate to rise, which means that the oppor￾tunity cost of holding money increases. As a result, real money balances fall. Since money is part of wealth, real wealth also falls. A fall in wealth reduces consumption, and, therefore, increases saving. The increase in saving leads to an outward shift of the saving schedule, as in Figure 4–1. This leads to a lower real interest rate. The classical dichotomy states that a change in a nominal variable such as infla￾tion does not affect real variables. In this case, the classical dichotomy does not hold; the increase in the rate of inflation leads to a decrease in the real interest rate. The Fisher effect states that i = r + π. In this case, since the real interest rate r falls, a 1- percent increase in inflation increases the nominal interest rate i by less than 1 per￾cent. 26 Answers to Textbook Questions and Problems Real interest rate r A B I, S Investment, Saving I (r) S1 S2 r 2 r 1 Figure 4–1

Chapter 4 Money and Inflation Most economists believe that this Mundell-Tobin effect is not important becaus real money balances are a small fraction of wealth. Hence, the impact on saving illustrated in Figure 4-1 is small 9.TheEconomist(www.economist.com)isausefulsiteforrecentdata[notE:unfortu- nately, as of this writing (February 2002), you need a paid subscription to get access to many of the tables online. Alternatively, the International Monetary Fund has links to countrydatasources(www.imf.orgfollowthelinkstostandardsandcodesandthento data dissemination) For example, in the twelve months ending in November 2001, consumer prices in Turkey rose 69 percent from a year earlier MI rose 55 percent while M2 rose 52 per- cent, and short-term interest rates were 54 percent. By contrast, in the United States in the twelve months ending in December 2001, consumer prices re Mi rose 8 percent, M2 rose 14 percent; and short-term interest rates were a little under 2 percent. These data are consistent with the theories in the chapter, in that high-infla tion countries have higher rates of money growth and also higher nominal interest rates More Problems and applications to Chapter 4 1. With constant money growth at rate u, the question tells us that the Cagan model a. One way to interpret this result is to rearrange to ln ations of this equation. implies that p,=m,+yu. This question draws out the impli That is, real balances depend on the money growth rate. As the growth rate of money rises, real balances fall. This makes sense in terms of the model in this chapter, since faster money growth implies faster inflation, which makes it less desirable to hold money balances b. With unchanged growth in the money supply, the increase in the level of the money supply m, increases the price level p, one-for-one. c. With unchanged current money supply m, a change in the growth rate of money u changes the price level in the same direction. d. When the central bank reduces the rate of money growth u, the price level will immediately fall. To offset this decline in the price level, the central bank can increase the current level of the money supply mu, as we found in part(b). These answers assume that at each point in time private agents expect the growth rat of money to remain unchanged, so that the change in policy takes them by sur- prise--but once it happens, it is completely credible. a practical problem is that the private sector might not find it credible that an increase in the current money als a decrease in future money growth rates e. If money demand does not depend on the expected rate of inflation, then the price level changes only when the money supply itself changes. That is, changes in the growth rate of money u do not affect the price level. In part(d), the central bank can keep the current price level p, constant simply by keeping the current money supply m, constant

Most economists believe that this Mundell–Tobin effect is not important because real money balances are a small fraction of wealth. Hence, the impact on saving as illustrated in Figure 4–1 is small. 9. The Economist (www.economist.com) is a useful site for recent data. [Note: unfortu￾nately, as of this writing (February 2002), you need a paid subscription to get access to many of the tables online.] Alternatively, the International Monetary Fund has links to country data sources (www.imf.org; follow the links to standards and codes and then to data dissemination). For example, in the twelve months ending in November 2001, consumer prices in Turkey rose 69 percent from a year earlier, M1 rose 55 percent while M2 rose 52 per￾cent, and short-term interest rates were 54 percent. By contrast, in the United States in the twelve months ending in December 2001, consumer prices rose about 2 percent, M1 rose 8 percent, M2 rose 14 percent; and short-term interest rates were a little under 2 percent. These data are consistent with the theories in the chapter, in that high-infla￾tion countries have higher rates of money growth and also higher nominal interest rates. More Problems and Applications to Chapter 4 1. With constant money growth at rate µ, the question tells us that the Cagan model implies that pt = mt + γµ. This question draws out the implications of this equation. a. One way to interpret this result is to rearrange to find: mt – pt = –γµ. That is, real balances depend on the money growth rate. As the growth rate of money rises, real balances fall. This makes sense in terms of the model in this chapter, since faster money growth implies faster inflation, which makes it less desirable to hold money balances. b. With unchanged growth in the money supply, the increase in the level of the money supply mt increases the price level pt one-for-one. c. With unchanged current money supply mt, a change in the growth rate of money µ changes the price level in the same direction. d. When the central bank reduces the rate of money growth µ, the price level will immediately fall. To offset this decline in the price level, the central bank can increase the current level of the money supply mt, as we found in part (b). These answers assume that at each point in time, private agents expect the growth rate of money to remain unchanged, so that the change in policy takes them by sur￾prise—but once it happens, it is completely credible. A practical problem is that the private sector might not find it credible that an increase in the current money supply signals a decrease in future money growth rates. e. If money demand does not depend on the expected rate of inflation, then the price level changes only when the money supply itself changes. That is, changes in the growth rate of money µ do not affect the price level. In part (d), the central bank can keep the current price level pt constant simply by keeping the current money supply mt constant. Chapter 4 Money and Inflation 27

CHAPTER The Open Economy Questions for Review 1. By rewriting the national income accounts identity we show in the text that This form of the national income accounts identity shows the relationship between the international flow of funds for capital accumulation, S-l, and the international flow of goods and services, NX. Net foreign investment refers to the (s-D) part of this identity: it is th of mestic saving over domestic investment. In an open economy, domestic saving need not equal domestic investment, because investors can borrow and lend in world finan- cial markets. The trade balance refers to the (NX) part of the identity: it is the differ ence between what we export and what we import Thus, the national accounts identity shows that the international flow of funds to finance capital accumulation and the international flow of goods and services are two sides of the same coin 2. The nominal exchange rate is the relative price of the currency of two countries. The real exchange rate, sometimes called the terms of trade, is the relative price of the goods of two countries. It tells us the rate at which we can trade the goods of one country for the goods of another. B. a cut in defense spending increases government saving and, hence, increases national saving Investment depends on the world rate and is unaffected. Hence the increase in saving causes the(s-n schedule to shift to the right, as in Figure 5-1. The trade bal ce rises, and the real exchange rate falls. Figure 6-1 -----B Net exports

Questions for Review 1. By rewriting the national income accounts identity, we show in the text that S – I = NX. This form of the national income accounts identity shows the relationship between the international flow of funds for capital accumulation, S – I, and the international flow of goods and services, NX. Net foreign investment refers to the (S – I) part of this identity: it is the excess of domestic saving over domestic investment. In an open economy, domestic saving need not equal domestic investment, because investors can borrow and lend in world finan￾cial markets. The trade balance refers to the (NX) part of the identity: it is the differ￾ence between what we export and what we import. Thus, the national accounts identity shows that the international flow of funds to finance capital accumulation and the international flow of goods and services are two sides of the same coin. 2. The nominal exchange rate is the relative price of the currency of two countries. The real exchange rate, sometimes called the terms of trade, is the relative price of the goods of two countries. It tells us the rate at which we can trade the goods of one country for the goods of another. 3. A cut in defense spending increases government saving and, hence, increases national saving. Investment depends on the world rate and is unaffected. Hence, the increase in saving causes the (S – I) schedule to shift to the right, as in Figure 5–1. The trade bal￾ance rises, and the real exchange rate falls. 28 ∋ ∋ ∋ Real exchange rate A B NX NX Net exports ∋) ( NX2 NX1 S1 – I S2 – I 1 2 Figure 5–1 CHAPTER 5 The Open Economy

Chapter 5 The Open Economy 4. If a small open economy bans the import of Japanese VCRs, then for any given real exchange rate, imports are lower, so that net exports are higher. Hence the net export schedule shifts out, as in Figure 5-2 52 MX(∈) MXx1∈) Net exports The protectionist policy of banning VCRs does not affect saving, investment, or the world interest rate, so the S-I schedule does not change Because protectionist policies do not alter either saving or investment in the model of this chapter, they cannot alter the trade balance. Instead a protectionist policy drives the real exchange rate highe 5. We can relate the real and nominal exchange rates by the expression N Real Ratio of Exchang Rat Rate Let P be the Italian price level and P be the german price level. The nominal exchange rate e is the number of Italian lira per german mark (this is as if we take germany to be the "domestic"country). We can express this in terms of percentage changes over time as % Change in e=% Change in∈+(π-π), e t is the italian inflation rate and t is the german inflation rate. If Italian infla- is higher than German inflation, then this equation tells us that a mark buys an increasing amount of lira over time: the mark rises relative to the lira. alternatively, viewed from the Italian perspective, the exchange rate in terms of marks per lira falls

4. If a small open economy bans the import of Japanese VCRs, then for any given real exchange rate, imports are lower, so that net exports are higher. Hence, the net export schedule shifts out, as in Figure 5–2. The protectionist policy of banning VCRs does not affect saving, investment, or the world interest rate, so the S – I schedule does not change. Because protectionist policies do not alter either saving or investment in the model of this chapter, they cannot alter the trade balance. Instead, a protectionist policy drives the real exchange rate higher. 5. We can relate the real and nominal exchange rates by the expression Nominal Real Ratio of Exchange = Exchange × Price Rate Rate Levels e = × (P*/P). Let P* be the Italian price level and P be the German price level. The nominal exchange rate e is the number of Italian lira per German mark (this is as if we take Germany to be the “domestic” country). We can express this in terms of percentage changes over time as % Change in e = % Change in + (π* – π), where π* is the Italian inflation rate and π is the German inflation rate. If Italian infla￾tion is higher than German inflation, then this equation tells us that a mark buys an increasing amount of lira over time: the mark rises relative to the lira. Alternatively, viewed from the Italian perspective, the exchange rate in terms of marks per lira falls. Chapter 5 The Open Economy 29 ∋ ∋ ∋ ∋ Real exchange rate B A NX NX2( ) NX ∋ 1( ) Net exports 2 1 S - I ∋ ∋ Figure 5–2