Chapter 20
ANSWERS TO QUESTIONS
1. How would you expect velocity to typically behave over the course of the business cycle?
Since nominal GDP falls during recessions, and as a result expansionary monetary policy,
which increases the money supply is implemented, in most cases velocity will decline during
2. If velocity and aggregate output are reasonably constant (as the classical economists
believed), what will happen to the price level when the money supply increases from $1
trillion to $4 trillion?
The price level will quadruple.
3. If credit cards were made illegal by congressional legislation, what would happen to
velocity? Explain your answer.
Velocity would fall because a greater quantity of the money supply (M) would be needed to
4. “If nominal GDP rises, velocity must rise.” Is this statement true, false, or uncertain?
Explain your answer.
False. Velocity is equal to nominal GDP divided by the money supply. If nominal GDP
5. Why would a central bank be concerned about persistent, long-term budget deficits?
Persistent long-term budget deficits can lead to the perception or worry that policymakers
will satisfy the government budget constraint by monetizing the debt in the future, leading to
6. “Persistent budget deficits always lead to higher inflation.” Is this statement true, false, or
uncertain? Explain your answer.
Uncertain. As long as a country (such as the United States) has reliable access to bond
7. Why might a central bank choose to monetize the debt, knowing that it could lead to higher
inflation?
If the government is running large deficits, this could lead to higher interest rates, which
could be contractionary to the economy or be misaligned from the central bank’s optimal
8. Consider two central banks: one with a history of maintaining price stability and low
inflation, and the other with a history of high inflation and poor inflation management. All
else equal, if the same level of government budget deficit is monetized in both countries, how
is inflation likely to behave in each country?
Central banks with a poor history of inflation management can easily experience an
unanchoring of (or sharp increase in) inflation expectations. So if the monetary base
9. Some payment technologies require infrastructure (e.g., merchants need to have access to
credit card swiping machines). In most developing countries historically this infrastructure
has either been nonexistent or very costly however recent mobile payment systems have
expanded rapidly in developing countries as they have become cheaper. Everything else
being equal, would you expect the transaction component of the demand for money to be
increasing or decreasing in a developing country relative to a rich country?
In general the need for costly infrastructure to support new payment technologies would
mean that cash would be used more in developing countries relative to rich countries. As a
10. What three motives for holding money did Keynes consider in his liquidity preference theory
of the demand for real money balances? On the basis of these motives, what variables did he
think determined the demand for money?
The three motives are: precautionary, speculative, and transactions motives. From these three
11. In Keynes’s analysis of the speculative demand for money, what will happen to demand for
money if people suddenly expect that the normal level of the interest rate has fallen? Explain
your answer.
Because it indicates that money demand and hence velocity is affected by interest rates, and
since interest rates fluctuate a lot, velocity will as well. Furthermore, changes in people’s
12. Why is Keynes’s analysis of the speculative demand for money important to his view that
velocity will undergo substantial fluctuations and thus cannot be treated as constant?
Because it indicates that money demand and hence velocity is affected by interest rates, and
since interest rates fluctuate a lot, velocity will as well. Furthermore, as the answer to
problem 11 suggests, changes in people’s expectations about what the normal level of
13. According to the portfolio theories of money demand, what are the four factors that
determine money demand? What changes in these factors can increase the demand for
money?
The four factors determining money demand under portfolio theory are: interest rates
14. Explain how the following events will affect the demand for money according to the portfolio
theories of money demand:
a. The economy experiences a business cycle contraction.
Since risk of alternative assets increases, liquidity of alternative assets likely decreases, and
15. Suppose a given country experienced low and stable inflation rates for quite some time, but
then inflation picked up and over the past decade has been relatively high and quite
unpredictable. Explain how this new inflationary environment would affect the demand for
money according to portfolio theories of money demand. What would happen if the
government decided to issue inflation-protected securities?
The demand for money would likely fall. Compared to other assets, money would be more
16. Consider the portfolio choice theory of money demand. How do you think the demand for
money would be affected during a hyperinflation (i.e., monthly inflation rates in excess of
50%)?
The demand for money would decrease, similar to problem 15 above, but much more
17. Both the portfolio choice and Keynes’s theories of the demand for money suggest that as the
relative expected return on money falls, demand for it will fall. Why does the portfolio choice
approach predict that money demand is affected by changes in interest rates? Why did
Keynes think that money demand is affected by changes in interest rates?
In Keynes’s view, a rise in interest rates leads to a lower relative expected return of money
and hence a lower demand for money. In the portfolio choice view, a rise in interest rates
18. Why does the Keynesian view of the demand for money suggest that velocity is unpredictable?
In Keynes’s view, velocity is unpredictable because interest rates, which have large
19. What evidence is used to assess the stability of the money demand function? What does the
evidence suggest about the stability of money demand, and how has this conclusion affected
monetary policymaking?
Velocity is used to indicate if the money demand function is stable. If velocity is predictable
and stable, then the money demand function is also stable, and vice versa. Up until the early
20. Suppose that a plot of the values of M2 and nominal GDP for a given country over 40 years
shows that these two variables are very closely related. In particular, a plot of their ratio
(nominal GDP/M2) yields very stable and easy-to-predict values. On the basis of this
evidence, would you recommend that the monetary authorities of this country conduct
monetary policy by focusing mostly on the money supply rather than on setting interest
rates? Explain.
This stable relationship implies that the velocity of the M2 money supply is very stable, and
ANSWERS TO APPLIED PROBLEMS
21. Suppose the money supply M has been growing at 10% per year, and nominal GDP, PY, has
been growing at 20% per year. The data are as follows (in billions of dollars):
2018
2019
2020
M
100
110
121
Calculate the velocity for each year. At what rate is the velocity growing?
22. Calculate what happens to nominal GDP if velocity remains constant at 4 and the money
supply increases from $250 billion to $375 billion.
23. What happens to nominal GDP if the money supply grows by 17% but velocity declines by
24%?
24. If velocity and aggregate output remain constant at 5 and $1,000 billion, respectively, what
happens to the price level if the money supply declines from $400 billion to $300 billion?
25.
Period
1
Period
2
Period
3
Period
4
Period
5
Period
6
Y (in billions)
12,000
12,500
12,250
12,500
12,800
13,000
Interest rate
0.05
0.07
0.03
0.05
0.07
0.04
Period 1
Period 2
Period 3
Period 4
Period 5
Period 6
Period 7
Y (in billions)
12,000
12,500
12,250
12,500
12,800
13,000
13,200
Interest Rate
L(i, Y)
1492.5
1512.5
ANSWERS TO DATA ANALYSIS PROBLEMS
1. Go to the St. Louis Federal Reserve FRED database, and find data on the M1 Money Stock
(M1SL), M1 Money Velocity (M1V), and Real GDP (GDPC1). Convert the M1SL data series
to “quarterly” using the frequency setting, and for all three series, use the “Percent Change
from Year Ago” setting for units.
a. Calculate the average percentage change in real GDP, the M1 money stock, and velocity
b. Based on your answer to part (a), calculate the average inflation rate since 2000 as
predicted by the quantity theory of money.
Based on part (a), the average inflation rate should be about %ΔM + %ΔV – %ΔY = 6.74
– 2.32 – 1.95 = 2.46%.
2. Go to the St. Louis Federal Reserve FRED database and find data on the budget deficit
(FYFSD), the amount of federal debt held by the public (FYGFDPUN), and the amount of
federal debt held by the Federal Reserve (FDHBFRBN). Convert the two “debt held” series
to “Annual” using the frequency setting. Download all three series into a spreadsheet. Make
sure that the rows of data align properly to the correct dates. Note that for the deficit series,
a negative number indicates a deficit; multiply the series by –1 so that a deficit is indicated
by a positive number. Manipulate the three series so that all data are given in terms of the
same units (either millions or billions of dollars). To do this, if a series is in millions and you
are converting it to billions, divide the series by 1000. Finally, for each year, convert the two
“debt held” series into one “changes in debt holdings by the public and the Federal
Reserve” series by calculating, for each year, the difference in bond holdings from the
preceding year.
a. Create a scatter plot showing the deficit on the horizontal axis and the change in bond
holdings by the public on the vertical axis, using the data from 1980 through the most
recent period of data available. Insert a fitted line into the scatter plot, and comment on
the relationship between the deficit and the change in public bond holdings.
a. See below. Not surprisingly, from 1980 to 2016, there appears to be a very strong
new debt issued.
b. See graph below. For the change in holdings by the Federal Reserve, there appears to be a
positive relationship suggesting some monetization of the debt, but this is much less
obvious (and using a fitted regression line indicates a much smaller relationship, with less
predictive power). In particular, for each $1 of deficit, the Fed absorbs about 23 cents of
it in debt holdings.
c. See graph below. There appears to be some amount of debt monetization in the
scatterplot data in the post-crisis period: in general, as the deficits get significantly larger
during 2008 to 2016, the change in bond holdings by the Fed gets larger, indicating the