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11 MONEY, INTEREST, REAL GDP, AND THE PRICE LEVEL**

* * This is Chapter 27 in Economics.

C h a p t e r K e y I d e a s

Ripple Effects of Money

A. There is enough money in the United States for everyone to have $2,300 in notes and coins and another $19,000 in the bank. Why do we hold all this money?

B. Starting in 2001 and continuing in 2002 and 2003, the Fed lowered interest rates, but just a few years earlier in 1999 and 2000, the Fed was more concerned about inflation and had raised interest rates.

C. How does the Fed change interest rates, and how does that influence real GDP and inflation?

O u t l i n e

I. The Demand for Money

A. The Influences on Money Holding

1. Four factors influence the quantity of money that people plan to hold: the price level, the interest rate, real GDP, and financial innovation.

2. A rise in the price level increases the nominal quantity of money but doesn’t change the real quantity of money that people plan to hold.

a) Nominal money is the amount of money measured in dollars.

b) The quantity of nominal money demanded is proportional to the price level — a 10 percent rise in the price level increases the quantity of nominal money demanded by 10 percent.

3. The interest rate is the opportunity cost of holding wealth in the form of money rather than an interest-bearing asset. A rise in the interest rate decreases the quantity of money that people plan to hold.

4. An increase in real GDP increases the volume of expenditure, which increases the quantity of real money that people plan to hold.

C h a p t e r

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5. Financial innovation that lowers the cost of switching between money and interest-bearing assets decreases the quantity of money that people plan to hold.

B. The Demand for Money Curve

1. The demand for money curve is the relationship between the quantity of real money demanded, M/P, and the interest rate when all other influences on the amount of money that people wish to hold remain the same.

2. Figure 11.1 illustrates the demand for money curve.

3. The demand for money curve slopes downward—a rise in the interest rate raises the opportunity cost of holding money and brings a decrease in the quantity of money demanded, which is shown by a movement up along the demand for money curve.

C. Shifts in the Demand for Money Curve

1. The demand for money changes and the demand for money curve shifts if real GDP changes or if financial innovation occurs. Figure 11.2 illustrates an increase and a decrease in the demand for money.

2. An increase in real GDP increases the demand for money and shifts the demand curve rightward.

3. A decrease in real GDP or a financial innovation decreases the demand for money and shifts the demand curve leftward.

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D. The Demand for Money in the United States

Figure 11.3 shows scatter diagrams of the interest rate against real M1 and real M2 from 1970 through 2003 and interprets the data in terms of movements along and shifts in the demand for money curves.

II. Interest Rate Determination

A. An interest rate is the percentage yield on a financial security such as a bond or a stock.

1. The price of a bond and the interest rate are inversely related. If the price of a bond falls, the interest rate on the bond rises. If the price of a bond rises, the interest rate on the bond falls.

2. We can study the forces that determine the interest rate in the market for money.

B. Money Market Equilibrium

1. The Fed determines the quantity of money supplied and on any given day, that quantity is fixed. The real quantity of money supplied is equal to the nominal quantity supplied divided by the price level.

2. The supply of money curve is vertical at the given quantity of money supplied.

3. Money market equilibrium determines the interest rate, as Figure 11.4 illustrates.

4. If the interest rate is above the equilibrium interest rate, the quantity of money that people are willing to hold is less than the

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quantity supplied. They try to get rid of their “excess” money by buying financial assets. This action raises the price of these assets and lowers the interest rate.

5. If the interest rate is below the equilibrium interest rate, the quantity of money that people want to hold exceeds the quantity supplied. They try to get more money by selling financial assets. This action lowers the price of these assets and raises the interest rate.

C. Changing the Interest Rate

1. When the Fed changes the quantity of money, the interest rate changes. Figure 11.5 shows how the Fed changes the interest rate.

2. If the Fed conducts an open market sale of securities, the quantity of money decreases, the money supply curve shifts leftward, and the interest rate rises.

3. If the Fed conducts an open market purchase of securities, the quantity of money increases, the money supply curve shifts rightward, and the interest rate falls.

III. Short-Run Effects of Money on Real GDP and the Price Level

A. Ripple Effects of the Interest Rate

1. If the Fed raises the interest rate, three events follow:

a) Investment and consumption expenditures decrease, because the interest rate is the opportunity cost of funds used to finance investment and big-ticket consumer purchases.

b) With interest rates in other countries unchanged, funds move into the United States, the exchange rate rises, and net exports decrease.

c) These changes in the components of aggregate expenditure set off a multiplier process that magnifies the initial effects.

2. Figure 11.6 summarizes these ripple effects.

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B. The Fed Tightens to Avoid Inflation

1. Figure 11.7 illustrates the effect of fighting inflation with monetary policy in three panels. The first shows the money market, the second interest-sensitive expenditure, and the third shows the aggregate supply and aggregate demand curves.

2. A decrease in the quantity of money in part (a) raises the interest rate. The rise in the interest rate decreases expenditure in part (b). The decrease in expenditure shifts the AD curve leftward with a multiplier effect in part (c). Real GDP decreases and the price level falls.

C. The Fed Eases to Fight Recession

1. Figure 11.8 illustrates the effect of fighting recession with monetary policy in three panels. The first shows the money market, the second interest-sensitive expenditure, and the third shows the aggregate supply and aggregate demand curves.

2. An increase in the quantity of money in part (a) lowers the interest rate. The fall in the interest rate increases expenditure in part (b). The increase in expenditure shifts the AD curve rightward with a multiplier effect in part (c). Real GDP increases and the price level rises.

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IV. Long-Run Effects of Money on Real GDP and the Price Level

A. An Increase in the Quantity of Money at Full Employment

1. Figure 11.9 illustrates the effect of an increase in the quantity of money at full employment in two panels. The first shows the money market and the second shows the SAS, LAS, and AD curves.

2. An increase in the quantity of money in part (a) lowers the interest rate. The fall in the interest rate shifts the AD curve rightward in part (b). The inflationary gap brings a rise in the money wage rate and a leftward shift in the SAS curve. In the long run, an increase in the quantity of money leaves real GDP unchanged but raises the price level.

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B. The Quantity Theory of Money

1. The quantity theory of money is the proposition that in the long run, an increase in the quantity of money brings an equal percentage increase in the price level.

2. The quantity theory of money is based on the velocity of circulation and the equation of exchange.

a) The velocity of circulation is the average number of times a dollar of money is used annually to buy goods and services that make up GDP. Calling the velocity of circulation V, then V = PY/M. Figure 11.10 graphs the velocity of circulation for M1 and M2 for 1963–2003.

b) The equation of exchange states that the quantity of money, M, multiplied by the velocity of circulation, V, equals the price level, P, multiplied by real GDP, Y. That is:

MV = PY.

3. The quantity theory assumes that velocity and potential GDP are not affected by the quantity of money. So

P = (V/Y)M.

4. Because (V/Y) does not change when M changes, a change in M brings a proportionate change in P. That is, the change in P, ∆P, is related to the change in M, ∆M, by the equation:

∆P = (V/Y)∆M.

Divide this last equation by the previous one and the term (V/Y) cancels to give:

∆P/P = ∆M/M.

∆P/P is the inflation rate and = ∆M/M is the growth rate of the quantity of money.

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C. The Quantity Theory and the AS-AD Model

1. The quantity theory of money can be interpreted in terms of the AS-AD model. In the long run, real GDP equals potential GDP and according to the AS-AD model, an increase in the quantity of money brings an equal percentage rise in the price level.

2. The AS-AD model also makes clear why the quantity theory is a long-run theory. In the short run, an increase in the quantity of money brings an increase in real GDP and a smaller than proportionate rise in the price level.

D. Historical Evidence on the Quantity Theory of Money

1. Historical evidence shows that U.S. money growth and inflation are correlated, more so in the long run than the short run, which is broadly consistent with the quantity theory.

2. Figure 11.11 graphs money growth and inflation in the United States from 1963 to 2003.

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E. International Evidence on the Quantity Theory of Money

1. International evidence shows a marked tendency for high money growth rates to be associated with high inflation rates.

2. Figure 11.12 shows scatter diagrams of money growth and inflation for various countries and regions during the 1980s and 1990s.

F. Correlation, Causation, and Other Influences

1. Correlation is not causation; money growth and inflation could be correlated because money growth causes inflation, or because inflation causes money growth, or because a third factor caused both. But the combination of historical, international, and other independent evidence gives us confidence that in the long run, money growth causes inflation.

2. In the short run, however, the quantity theory is not correct. To understand the short-term fluctuations in inflation, we need the AS-AD model.

R e a d i n g B e t w e e n t h e L i n e s The news article reports the fears of renewed inflation in Argentina following its currency crises of 2001. The analysis examines the history of money growth and inflation in Argentina between 1971 and 2000 and shows that the quantity theory of money provides a good explanation for Argentina’s inflation of the 1970s and 1980s and price stability of the 1990s and why people fear renewed inflation.

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N e w i n t h e S e v e n t h E d i t i o n This chapter combines material from Chapters 27 and 28 in the sixth edition to focus on the economic theory of money demand and how the Fed uses monetary policy to influence interest rates, real GDP, and the price level. The material on how the Fed controls the quantity of money is moved to Chapter 26. The updated discussion and organization makes a clear distinction between the short-run and long-run effects of monetary policy.

Data and figures are updated to 2003.

Te a c h i n g S u g g e s t i o n s 1. The Demand for Money It is worth reminding students that “money” has a jargon sense in economics; students are often

confused by the phrase “demand for money” and it is worth tackling it head-on by emphasizing this does not equate to “wanting to be rich,” but refers to how much of total wealth (assets) the public want to hold in the particular form “money.” Students often try to understand ideas in terms of their own lives; few will make a clear connection between interest rates and demand for money from their own introspection. There are two ways to overcome this: one is to ask them to think in terms of extreme situations (get what short-term interest rates are in a high-inflation country); the other is to get them to imagine themselves in the job of treasurer of a corporation with large liquid resources, and to think how their behavior with respect to those funds might differ according to the short-term interest rates available.

2. Interest Rate Determination The reason that an increase in the money supply lowers the interest rate can be easily developed by

focusing on banks. To increase the money supply, the Fed increases excess reserves. Banks want to loan these new excess reserves, and thus the supply of loans increases. As a result, the interest rate on loans falls as they struggle to make more loans. This type of intuitive explanation often can be quite helpful in supplementing the formal analysis.

3. Short-Run Effects of Money on Real GDP and the Price Level We bring in here the expenditure multiplier; it is important to ensure that students do not get

confused between the multiplier impact of open market operations on money supply, and the multiplier process that magnifies autonomous expenditure changes. In using the AS-AD model to explain the impact of deflationary monetary policy, it is important to stress the text’s point that the model is a stationary simplification, whereas in reality output and the price level both tend to grow, so that rather than reducing real GDP and the price level, the Fed’s anti-inflation policy would slow their growth.

4. Long-Run Effects of Money on Real GDP and the Price Level This section of the chapter has a lot of analytic content, and includes a number of things that can

easily confuse students. Velocity of circulation. Emphasize that velocity is defined by the equation V = PY/M, and is not the

average number of times a given piece of paper changes hands in a year. Nor is V the transactions velocity because most transactions are not payments for goods and services. (Transactions are twice PY because they also include payments for the services of factors of production, which equals PY, plus all the purely financial transactions such as buying and selling stocks, bonds, foreign currency, and real estates.)

The quantity theory of money. Given that V is defined as PY/M, the equation of exchange, MV = PY is an identity. The quantity theory is not the equation of exchange but the propositions that (1) V is

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independent of M and (2) Y equals potential GDP, which is independent of M. Given these assumptions, the inflation rate equals the growth rate of the quantity of money.

The quantity theory of hyperinflation. A possible exercise is to ask students whether we would expect the correlation between money growth and inflation to remain strong in a hyperinflation. Most will see that in a hyperinflation, velocity will increase. Emphasize that the level of velocity is greater in hyperinflation but if the inflation rate remains constant (and high) velocity also is constant (and high), so the quantity theory still holds. It does not hold in the move from low inflation to high inflation. The inflation rate overshoots the growth rate of the quantity of money.

T h e B i g P i c t u r e

Where we have been

Chapter 11 presumes knowledge on the part of the students about the role played by Fed in creating money. This topic was discussed extensively and was one of the key points in Chapter 10. It also briefly utilizes the notion of GDP, covered in depth in Chapter 5; investment demand, from Chapter 8; and the AS-AD model of Chapter 7. But it does not directly draw on much material except for that in Chapter 26.

Where we are going

Chapter 11 is the second of three chapters that examine money, aggregate demand, and inflation. The material presented in this chapter (and in the closely related Chapter 10) is used in Chapter 12 when the relationship between money and inflation is more fully developed. It also is necessary in Chapter 16 wherein the government’s monetary policy is discussed. Finally, without a thorough grasp from this chapter of how a change in the money supply affects the equilibrium interest rate, the students will be unable to understand key points in Chapter 12 about the relationships among monetary growth, the inflation rate, and the nominal interest rate. Therefore this chapter is crucial because of its underpinning of topics in succeeding chapters.

O v e r h e a d Tr a n s p a r e n c i e s

Transparency Text figure Transparency title

63 Figure 11.1 The Demand for Money

64 Figure 11.2 Changes in the Demand for Money

65 Figure 11.4 Money Market Equilibrium

66 Figure 11.5 Interest Rate Changes

67 Figure 11.7 Monetary Stabilization: Avoiding Inflation

68 Figure 11.8 Monetary Stabilization: Avoiding Recession

69 Figure 11.9 Long-Run Effects of a Change in the Quantity of Money

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A d d i t i o n a l D i s c u s s i o n Q u e s t i o n s 1. “Ask anyone if he or she has enough money. No one ever has enough money, that is, everyone

demands more money. Thus theorizing about the demand for money makes no sense because this demand obviously is infinite.” Correct and comment on the error in this assertion.

2. If the interest rate exceeds the equilibrium interest rate, what forces drive the interest rate back to its equilibrium level?

3. What is the effect on the interest rate of a decrease in the supply of money? No credit will be given unless the correct diagram is used to support your answer.

4. What is the effect on the interest rate of an increase in the demand for money? No credit will be given unless the correct diagram is used to support your answer.

5. How should the Fed behave if it fears recession is about to begin? Illustrate with diagrams showing effects in the money market, the investment market, and AS-AD.

6. Suppose non-economic events in the rest of the world cause the exchange rate of the dollar to fall when the U.S. economy is at full employment. How should the Fed react in order to maintain macroeconomic stability? Why?

17. Why is there a difference between the short-run and long-run effects from an increase in the quantity of money?

18. What is velocity? Why might it be an important concept? 9. What is the relationship between the quantity theory and the AD/AS model?

10. If the price level was already doubling every month and inflation accelerating, what would you expect to happen to the velocity of circulation and why? How close would you expect the relation between the quantity of money and the price level to be?

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A n s w e r s t o t h e R e v i e w Q u i z z e s

Page 261 (page 633 in Economics) 1. The quantity of money demanded depends on four factors: the price level, the interest rate, real

GDP, and financial innovation. An increase in the price level increases the nominal demand for money but does not change the real quantity demanded. An increase in the interest rate decreases the quantity of money demanded, because the interest rate is the opportunity cost of holding assets in the form money. An increase in real GDP increases the demand for money, because more GDP implies more transactions and therefore a demand for more money to finance the transactions. And, financial innovations that make it less costly to get by with less money on hand decreases the demand for money.

2. The demand for money curve shows how the quantity of money demanded depends on the interest rate. The demand for money curve is downward sloping, showing that an increase (decrease) in the interest rate decreases (increases) the quantity of money demanded.

3. An increase in the interest rate decreases the quantity of money demanded. An increase in the interest rate creates an upward movement along the demand curve for real money.

4. An increase in real GDP increases the demand for money. An increase in real GDP shifts the demand for curve for real money to the right.

5. Financial innovations have generally decreased the demand for M1. These same innovations (for instance, increased usage of credit cards) initially either increased or had no effect on the demand for M2 but later financial innovations have decreased the demand for M2.

Page 262 (page 634 in Economics) 1. The short-term interest rate is determined by the demand for and supply of money. When the

quantity of money demanded equals the quantity supplied, the interest rate is at its equilibrium level.

2. If people are holding more money than they plan to hold, the interest rate is above its equilibrium level. In this case people use their “excess” money to buy financial securities such as bonds. As people buy more bonds, the price of bonds rises and the interest rate falls to its equilibrium level.

3. If the Fed wants to increase the interest rate, the Fed sells securities and decreases the quantity of money. If the Fed wants to decrease the interest rate, the Fed buys securities and increases the quantity of money.

Page 265 (page 637 in Economics) 1. To decrease the quantity of money, the Fed sells securities. Bank reserves and the quantity of

money contract; the interest rate rises; the value of the dollar increases; net exports, investment, and consumption fall; Aggregate demand decreases, and real GDP growth and inflation slow.

2. Investment, consumption, and net exports decrease when the interest rate rises and they increase when the interest rate falls.

3. A change in the U.S. interest rate means that the interest rate differential with other countries changes. For example, a rise in the U.S. interest rate, other things remaining the same, means that the differential increases. As a result, people will want to move funds from other countries into the United States in order to obtain the higher returns on U.S. assets implied by the higher interest rate. To move funds into the United States, people buy dollars and sell other currencies, driving the price of the dollar up. A higher dollar means that foreigners must pay more for U.S.-made goods and services and Americans pay less for foreign goods and services. Thus, the rise in the

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interest rate means that exports decrease and imports increase, corresponding to a fall in net exports.

4. The answer should look like panel (c) in Figure 11.8; or even better, should show the AD curve tending to move leftward and the Fed’s actions attempting to counter that and hold the AD curve at a level consistent with the LAS curve.

5. The answer should look like panel (c) in Figure 11.7.

Page 71 (page 643 in Economics) 1. In the short run, an increase in the quantity of money increases aggregate demand and increases

both the price level and real GDP. In the long run, however, an increase in the quantity of money increases only the price level and has no effect on real GDP. The difference between the short-run and long-run effects reflects the economy’s adjustment back to potential GDP. In the short run, money wages do not immediately change to reflect the higher price level so that real wages fall. Real GDP exceeds potential GDP. But, as time passes, money wages rise, thereby decreasing short-run aggregate supply. In the long run, money wages rise in the same proportion as the price level so that real wages return to their initial level. At this time, short-run aggregate supply has decreased so that real GDP has decreased to equal potential GDP. The long-run change in real GDP is zero.

2. The quantity theory of money is the proposition that in the long run an increase in the quantity of money causes an equal percentage increase in the price level. Put in terms of growth rates, the quantity theory of money asserts that the inflation rate (the percentage change in the price level) equals the growth rate of money (the percentage change in the quantity of money), so long as velocity does not change.

3. Yes, the long-run historical and international evidence on the relationship between money growth and the inflation rate supports the quantity theory. The data suggest a marked tendency for nations with high money growth rates to have high inflation rates. Thus the long-run cause of inflation is growth in the quantity of money.

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A n s w e r s t o t h e P r o b l e m s 1. a. People buy bonds, and the interest rate falls. b. People sell bonds, and the interest rate rises. c. People neither buy nor sell bonds, and the interest rate remains constant at 4 percent a year.

With real GDP of $20 billion (Y1 in the spreadsheet), column C shows the demand for money schedule. The quantity of money supplied is $3 billion, so the equilibrium interest rate is 4 percent a year. If the interest rate exceeds 4 percent a year, people are holding more money than they demand. So they try to decrease the amount of money held by buying bonds. The prices of bonds rise, and the interest rate falls. If the interest rate is less than 4 percent a year, people are holding less money than they demand. So they try to increase the amount of money held by selling bonds. The prices of bonds fall, and the interest rate rises. If the interest rate equals 4 percent a year, people are holding exactly the quantity of money that they demand. So they take no actions to try to change the amount of money held. The interest rate remains constant.

2. a. People buy bonds, and the interest rate falls. b. The equilibrium interest rate is 3 percent a year.

If the interest rate equals 3 percent a year, people are holding exactly the quantity of money that they demand.

c. When real GDP falls to $10 billion, the interest rate falls. With real GDP of $20 billion (Y1 in the spreadsheet), column C shows the demand for money schedule. The quantity of money supplied is $3 billion, so the equilibrium interest rate is 4 percent a year. With real GDP of $10 billion (Y0 in the spreadsheet), column B shows the demand for money schedule. The quantity of money supplied is $3 billion, so the equilibrium interest rate is 3 percent a year. When real GDP decreases from $20 billion to $10 billion, the demand for money decreases. The demand for money curve shifts leftward and the real interest rate falls.

3. a. The interest rate rises to 5 percent a year. b. The interest rate falls to 3 percent a year.

When real GDP increases in an expansion to $30 billion (Y2 in the spreadsheet), column D shows the demand for money schedule. The quantity of money supplied is $3 billion, so the equilibrium interest rate is 5 percent a year. When real GDP decreases in a recession to $10 billion (Y0 in the spreadsheet), column B shows the demand for money schedule. The quantity of money supplied is $3 billion, so the equilibrium interest rate is 3 percent a year.

4. a. The interest rate falls to 3 percent a year. b. The interest rate remains at 4 percent a year.

Initially when real GDP is $20 billion (Y2 in the spreadsheet), column D shows the demand for money schedule. When people plan to hold $0.5 billion less than the numbers in the spreadsheet, the demand for money when real GDP is $20 billion becomes column C. The quantity of money supplied is $3 billion, so the equilibrium interest rate is 3 percent a year. When the central bank decreases the quantity of money by $0.5 billion the quantity of money supplied decreases to $2.5 billion. When the demand for money as shown by column C is $2.5 billion, the real interest rate is 4 percent a year.

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5. a. The money supply curve is vertical at 1 trillion 1990 yaks. When the real money supply is 1 trillion 1990 yaks, the equilibrium interest rate is 3 percent a year at the intersection of the demand for money and supply of money curves.

b. Must increase the quantity of real money by 0.5 trillion 1990 yaks. When the quantity of real money increases to 1.5 trillion 1990 yaks, the equilibrium interest rate falls to 2 percent a year.

6. a. The demand for money curve shifts rightward, leftward, or remains the same. The new smart card decreases the demand for money and the demand for money curve shifts leftward. The new smart card also causes business to boom and real GDP increases. The demand for money increases and the demand for money curve shifts rightward. The direction in which the demand for money curve shifts depends on the overall effect of the new smart card. If the decrease in demand equals the increase in demand, the demand for money curve does not change.

b. If the demand for money changes then the supply of money must change to keep the interest rate from changing. If the demand for money increases, then the supply of money must also increase. If the demand for money decreases, then the supply of money must also decrease. If the demand for money does not change, then the supply of money must remain the same.

c. If the demand for money increases, then to increase the supply of money, the Upland Fed must make an open market purchase. If the demand for money decreases, then to decrease the supply of money the Upland Fed must make an open market sale. If the demand for money does not change, then the supply of money must remain the same so the Upland Fed makes no open market operation.

7. The AD and SAS curves intersect at a real GDP that exceeds potential GDP and there is an inflationary gap. An open market sale decreases the quantity of money and decreases aggregate demand. The AD curve shifts leftward and the inflationary gap shrinks. If the size of the open market sale is appropriate, this monetary policy action can avoid inflation. Real GDP in the long run is determined by potential GDP and the decrease in the quantity of money has no effect on real GDP in the long run.

8. The AD and SAS curves intersect at a real GDP that is below potential GDP and there is a recessionary gap. An open market purchase increases the quantity of money and increases aggregate demand. The AD curve shifts rightward and the recessionary gap shrinks. If the size of the open market purchase is appropriate, this monetary policy action restores full employment. The price level rises but there is no inflation. Real GDP in the long run is determined by potential GDP and the increase in the quantity of money has no effect on real GDP in the long run.

9. a. Aggregate demand increases. b. The price level rises and real GDP increases in the short run. c. In the long run, real GDP returns to potential GDP and the price level is higher than it

otherwise would have been by the same percentage as the percentage increase in the quantity of money.

10. a. The quantity of money decreases because deposits decrease. b. Aggregate demand decreases. c. In the short run, the decrease in aggregate demand causes the price level to fall and real GDP to

decrease. d. In the long run, real GDP returns to potential GDP and the price level is lower than it otherwise

would have been by the same percentage as the percentage decrease in the quantity of money.

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11. a. $40 million. Because the equation of exchange tells us that MV = PY, we know that M = PY/V. Then, with P = 200, Y = $400 million, and V = 20, M = $40 million.

b. $48 million. Money grows by 20 percent, which is $8 million.

c. 240. Because the quantity theory holds and because the factors that influence real GDP have not changed, the price level rises by the same percentage as the increase in money, which is 20 percent.

d. $400 billion. Because the factors that influence real GDP have not changed, real GDP is unchanged.

e. 20. Because the factors that influence velocity have not changed, velocity is unchanged.

12. a. $9.6 million. From solution 11b, the quantity of money in year 2 was $48 million. Therefore the quantity of money in year 3 is $48 million/5 = $9.6 million.

b. The price level is 48. Because the quantity theory holds and because the factors that influence real GDP have not changed, the price level falls by the same percentage as the decrease in money, which is 80 percent.

c. $400 billion. Because the factors that influence real GDP have not changed, real GDP is unchanged.

d. 20. Because the factors that influence velocity have not changed, velocity is unchanged.

e. If the quantity theory results are obtained only with a lag, then in the short run—the first year—real GDP will decrease and the price level will fall, though it will not fall all the way to its long-run value of 48.