Ch a p ter
The Demand for Money
In earlier chapters, we spent a lot of time and effort learning what the money supply
is, how it is determined, and what role the Federal Reserve System plays in it. Now
we are ready to explore the role of the money supply in determining the price level
and total production of goods and services (aggregate output) in the economy. The
study of the effect of money on the economy is called monetary theory, and we
examine this branch of economics in the chapters of Part VI.
When economists mention supply, the word demand is sure to follow, and the discussion of money is no exception. The supply of money is an essential building block
in understanding how monetary policy affects the economy, because it suggests the
factors that influence the quantity of money in the economy. Not surprisingly, another
essential part of monetary theory is the demand for money.
This chapter describes how the theories of the demand for money have evolved.
We begin with the classical theories refined at the start of the twentieth century by
economists such as Irving Fisher, Alfred Marshall, and A. C. Pigou; then we move on
to the Keynesian theories of the demand for money. We end with Milton Friedman’s
modern quantity theory.
A central question in monetary theory is whether or to what extent the quantity
of money demanded is affected by changes in interest rates. Because this issue is crucial to how we view money’s effects on aggregate economic activity, we focus on the
role of interest rates in the demand for money.1
Quantity Theory of Money
Developed by the classical economists in the nineteenth and early twentieth centuries,
the quantity theory of money is a theory of how the nominal value of aggregate
income is determined. Because it also tells us how much money is held for a given
amount of aggregate income, it is also a theory of the demand for money. The most
important feature of this theory is that it suggests that interest rates have no effect on
the demand for money.
In Chapter 24, we will see that the responsiveness of the quantity of money demanded to changes in interest
rates has important implications for the relative effectiveness of monetary policy and fiscal policy in influencing
aggregate economic activity.
Velocity of Money
and Equation of
A brief biography and summary
of the writings of Irving Fisher.
The clearest exposition of the classical quantity theory approach is found in the work of
the American economist Irving Fisher, in his influential book The Purchasing Power of
Money, published in 1911. Fisher wanted to examine the link between the total quantity
of money M (the money supply) and the total amount of spending on final goods and
services produced in the economy P Y, where P is the price level and Y is aggregate
output (income). (Total spending P Y is also thought of as aggregate nominal income
for the economy or as nominal GDP.) The concept that provides the link between M and
P Y is called the velocity of money (often reduced to velocity), the rate of turnover of
money; that is, the average number of times per year that a dollar is spent in buying the
total amount of goods and services produced in the economy. Velocity V is defined more
precisely as total spending P Y divided by the quantity of money M:
If, for example, nominal GDP (P Y ) in a year is $5 trillion and the quantity of
money is $1 trillion, velocity is 5, meaning that the average dollar bill is spent five
times in purchasing final goods and services in the economy.
By multiplying both sides of this definition by M, we obtain the equation of
exchange, which relates nominal income to the quantity of money and velocity:
The equation of exchange thus states that the quantity of money multiplied by the
number of times that this money is spent in a given year must be equal to nominal
income (the total nominal amount spent on goods and services in that year).2
As it stands, Equation 2 is nothing more than an identity—a relationship that is true
by definition. It does not tell us, for instance, that when the money supply M changes,
nominal income (P Y ) changes in the same direction; a rise in M, for example, could
be offset by a fall in V that leaves M V (and therefore P Y ) unchanged. To convert
the equation of exchange (an identity) into a theory of how nominal income is determined requires an understanding of the factors that determine velocity.
Irving Fisher reasoned that velocity is determined by the institutions in an economy that affect the way individuals conduct transactions. If people use charge accounts
and credit cards to conduct their transactions and consequently use money less often
when making purchases, less money is required to conduct the transactions generated
by nominal income (M↓ relative to P Y ) , and velocity (P Y )/M will increase.
Conversely, if it is more convenient for purchases to be paid for with cash or checks
(both of which are money), more money is used to conduct the transactions generated
by the same level of nominal income, and velocity will fall. Fisher took the view that
Fisher actually first formulated the equation of exchange in terms of the nominal value of transactions in the
P average price per transaction
T number of transactions conducted in a year
VT PT/M transactions velocity of money
Because the nominal value of transactions T is difficult to measure, the quantity theory has been formulated
in terms of aggregate output Y as follows: T is assumed to be proportional to Y so that T vY, where v is a
constant of proportionality. Substituting vY for T in Fisher’s equation of exchange yields MVT vPY, which can
be written as Equation 2 in the text, in which V VT /v.
The Demand for Money
the institutional and technological features of the economy would affect velocity only
slowly over time, so velocity would normally be reasonably constant in the short run.
Fisher’s view that velocity is fairly constant in the short run transforms the equation
of exchange into the quantity theory of money, which states that nominal income is
determined solely by movements in the quantity of money: When the quantity of
money M doubles, M V doubles and so must P Y, the value of nominal income.
To see how this works, let’s assume that velocity is 5, nominal income (GDP) is initially $5 trillion, and the money supply is $1 trillion. If the money supply doubles to
$2 trillion, the quantity theory of money tells us that nominal income will double to
$10 trillion ( 5 $2 trillion).
Because the classical economists (including Fisher) thought that wages and prices
were completely flexible, they believed that the level of aggregate output Y produced
in the economy during normal times would remain at the full-employment level, so
Y in the equation of exchange could also be treated as reasonably constant in the short
run. The quantity theory of money then implies that if M doubles, P must also double in the short run, because V and Y are constant. In our example, if aggregate output is $5 trillion, the velocity of 5 and a money supply of $1 trillion indicate that the
price level equals 1 because 1 times $5 trillion equals the nominal income of $5 trillion. When the money supply doubles to $2 trillion, the price level must also double
to 2 because 2 times $5 trillion equals the nominal income of $10 trillion.
For the classical economists, the quantity theory of money provided an explanation of movements in the price level: Movements in the price level result solely from
changes in the quantity of money.
Quantity Theory of
Because the quantity theory of money tells us how much money is held for a given
amount of aggregate income, it is in fact a theory of the demand for money. We can
see this by dividing both sides of the equation of exchange by V, thus rewriting it as:
where nominal income P Y is written as PY. When the money market is in equilibrium, the quantity of money M that people hold equals the quantity of money
demanded M d, so we can replace M in the equation by M d. Using k to represent the
quantity 1/V (a constant, because V is a constant), we can rewrite the equation as:
Md k PY
Equation 3 tells us that because k is a constant, the level of transactions generated by a
fixed level of nominal income PY determines the quantity of money M d that people
demand. Therefore, Fisher’s quantity theory of money suggests that the demand for money
is purely a function of income, and interest rates have no effect on the demand for money.3
Fisher came to this conclusion because he believed that people hold money only to
conduct transactions and have no freedom of action in terms of the amount they want
to hold. The demand for money is determined (1) by the level of transactions generated
While Fisher was developing his quantity theory approach to the demand for money, a group of classical economists in Cambridge, England, came to similar conclusions, although with slightly different reasoning. They
derived Equation 3 by recognizing that two properties of money motivate people to hold it: its utility as a medium
of exchange and as a store of wealth.
by the level of nominal income PY and (2) by the institutions in the economy that affect
the way people conduct transactions and thus determine velocity and hence k.
Is Velocity a Constant?
A summary of how various
factors affect the velocity of
The classical economists’ conclusion that nominal income is determined by movements
in the money supply rested on their belief that velocity PY/M could be treated as reasonably constant.4 Is it reasonable to assume that velocity is constant? To answer this, let’s
look at Figure 1, which shows the year-to-year changes in velocity from 1915 to 2002
(nominal income is represented by nominal GDP and the money supply by M1 and M2).
What we see in Figure 1 is that even in the short run, velocity fluctuates too much
to be viewed as a constant. Prior to 1950, velocity exhibited large swings up and
down. This may reflect the substantial instability of the economy in this period, which
included two world wars and the Great Depression. (Velocity actually falls, or at least
its rate of growth declines, in years when recessions are taking place.) After 1950,
velocity appears to have more moderate fluctuations, yet there are large differences in
F I G U R E 1 Change in the Velocity of M1 and M2 from Year to Year, 1915–2002
Shaded areas indicate recessions. Velocities are calculated using nominal GNP before 1959 and nominal GDP thereafter.
Sources: Economic Report of the President; Banking and Monetary Statistics; www.federalreserve.gov/releases/h6/.
Actually, the classical conclusion still holds if velocity grows at some uniform rate over time that reflects changes
in transaction technology. Hence the concept of a constant velocity should more accurately be thought of here as
a lack of upward and downward fluctuations in velocity.
The Demand for Money
the growth rate of velocity from year to year. The percentage change in M1 velocity
(GDP/M1) from 1981 to 1982, for example, was 2.5%, whereas from 1980 to 1981
velocity grew at a rate of 4.2%. This difference of 6.7% means that nominal GDP was
6.7% lower than it would have been if velocity had kept growing at the same rate as
in 1980–1981.5 The drop is enough to account for the severe recession that took
place in 1981–1982. After 1982, M1 velocity appears to have become even more
volatile, a fact that has puzzled researchers when they examine the empirical evidence
on the demand for money (discussed later in this chapter). M2 velocity remained
more stable than M1 velocity after 1982, with the result that the Federal Reserve
dropped its M1 targets in 1987 and began to focus more on M2 targets. However,
instability of M2 velocity in the early 1990s resulted in the Fed’s announcement in
July 1993 that it no longer felt that any of the monetary aggregates, including M2, was
a reliable guide for monetary policy.
Until the Great Depression, economists did not recognize that velocity declines
sharply during severe economic contractions. Why did the classical economists not
recognize this fact when it is easy to see in the pre-Depression period in Figure 1?
Unfortunately, accurate data on GDP and the money supply did not exist before
World War II. (Only after the war did the government start to collect these data.)
Economists had no way of knowing that their view of velocity as a constant was
demonstrably false. The decline in velocity during the Great Depression years was so
great, however, that even the crude data available to economists at that time suggested
that velocity was not constant. This explains why, after the Great Depression, economists began to search for other factors influencing the demand for money that might
help explain the large fluctuations in velocity.
Let us now examine the theories of money demand that arose from this search for
a better explanation of the behavior of velocity.
Keynes’s Liquidity Preference Theory
A brief history of
John Maynard Keynes.
In his famous 1936 book The General Theory of Employment, Interest, and Money, John
Maynard Keynes abandoned the classical view that velocity was a constant and developed
a theory of money demand that emphasized the importance of interest rates. His theory
of the demand for money, which he called the liquidity preference theory, asked the
question: Why do individuals hold money? He postulated that there are three motives
behind the demand for money: the transactions motive, the precautionary motive, and
the speculative motive.
In the classical approach, individuals are assumed to hold money because it is a medium
of exchange that can be used to carry out everyday transactions. Following the classical
tradition, Keynes emphasized that this component of the demand for money is determined primarily by the level of people’s transactions. Because he believed that these
transactions were proportional to income, like the classical economists, he took the
transactions component of the demand for money to be proportional to income.
We reach a similar conclusion if we use M2 velocity. The percentage change in M2 velocity (GDP/M2) from 1981
to 1982 was 5.0%, whereas from 1980 to 1981 it was 2.3%. This difference of 7.3% means that nominal
GDP was 7.3% lower than it would have been if M2 velocity had kept growing at the same rate as in 1980–1981.
Keynes went beyond the classical analysis by recognizing that in addition to holding
money to carry out current transactions, people hold money as a cushion against an
unexpected need. Suppose that you’ve been thinking about buying a fancy stereo; you
walk by a store that is having a 50%-off sale on the one you want. If you are holding
money as a precaution for just such an occurrence, you can purchase the stereo right
away; if you are not holding precautionary money balances, you cannot take advantage of the sale. Precautionary money balances also come in handy if you are hit with
an unexpected bill, say for car repair or hospitalization.
Keynes believed that the amount of precautionary money balances people want
to hold is determined primarily by the level of transactions that they expect to make
in the future and that these transactions are proportional to income. Therefore, he
postulated, the demand for precautionary money balances is proportional to income.
If Keynes had ended his theory with the transactions and precautionary motives,
income would be the only important determinant of the demand for money, and he
would not have added much to the classical approach. However, Keynes took the
view that money is a store of wealth and called this reason for holding money the speculative motive. Since he believed that wealth is tied closely to income, the speculative
component of money demand would be related to income. However, Keynes looked
more carefully at the factors that influence the decisions regarding how much money
to hold as a store of wealth, especially interest rates.
Keynes divided the assets that can be used to store wealth into two categories:
money and bonds. He then asked the following question: Why would individuals
decide to hold their wealth in the form of money rather than bonds?
Thinking back to the discussion of the theory of asset demand (Chapter 5), you
would want to hold money if its expected return was greater than the expected return
from holding bonds. Keynes assumed that the expected return on money was zero
because in his time, unlike today, most checkable deposits did not earn interest. For
bonds, there are two components of the expected return: the interest payment and the
expected rate of capital gains.
You learned in Chapter 4 that when interest rates rise, the price of a bond falls. If
you expect interest rates to rise, you expect the price of the bond to fall and therefore
suffer a negative capital gain—that is, a capital loss. If you expect the rise in interest
rates to be substantial enough, the capital loss might outweigh the interest payment,
and your expected return on the bond would be negative. In this case, you would want
to store your wealth as money because its expected return is higher; its zero return
exceeds the negative return on the bond.
Keynes assumed that individuals believe that interest rates gravitate to some normal value (an assumption less plausible in today’s world). If interest rates are below this
normal value, individuals expect the interest rate on bonds to rise in the future and so
expect to suffer capital losses on them. As a result, individuals will be more likely to
hold their wealth as money rather than bonds, and the demand for money will be high.
What would you expect to happen to the demand for money when interest rates
are above the normal value? In general, people will expect interest rates to fall, bond
prices to rise, and capital gains to be realized. At higher interest rates, they are more
likely to expect the return from holding a bond to be positive, thus exceeding the
expected return from holding money. They will be more likely to hold bonds than
money, and the demand for money will be quite low. From Keynes’s reasoning, we can
conclude that as interest rates rise, the demand for money falls, and therefore money
demand is negatively related to the level of interest rates.
Putting the Three
The Demand for Money
In putting the three motives for holding money balances together into a demand for
money equation, Keynes was careful to distinguish between nominal quantities and
real quantities. Money is valued in terms of what it can buy. If, for example, all prices
in the economy double (the price level doubles), the same nominal quantity of money
will be able to buy only half as many goods. Keynes thus reasoned that people want
to hold a certain amount of real money balances (the quantity of money in real
terms)—an amount that his three motives indicated would be related to real income
Y and to interest rates i. Keynes wrote down the following demand for money equation, known as the liquidity preference function, which says that the demand for real
money balances M d/P is a function of (related to) i and Y:6
f (i, Y )
The minus sign below i in the liquidity preference function means that the demand
for real money balances is negatively related to the interest rate i, and the plus sign
below Y means that the demand for real money balances and real income Y are positively related. This money demand function is the same one that was used in our
analysis of money demand discussed in Chapter 5. Keynes’s conclusion that the
demand for money is related not only to income but also to interest rates is a major
departure from Fisher’s view of money demand, in which interest rates can have no
effect on the demand for money.
By deriving the liquidity preference function for velocity PY/M, we can see that
Keynes’s theory of the demand for money implies that velocity is not constant, but
instead fluctuates with movements in interest rates. The liquidity preference equation
can be rewritten as:
f (i, Y )
Multiplying both sides of this equation by Y and recognizing that M d can be replaced
by M because they must be equal in money market equilibrium, we solve for velocity:
f (i, Y )
We know that the demand for money is negatively related to interest rates; when i
goes up, f (i, Y ) declines, and therefore velocity rises. In other words, a rise in interest rates encourages people to hold lower real money balances for a given level of
income; therefore, the rate of turnover of money (velocity) must be higher. This reasoning implies that because interest rates have substantial fluctuations, the liquidity
preference theory of the demand for money indicates that velocity has substantial
fluctuations as well.
An interesting feature of Equation 5 is that it explains some of the velocity movements in Figure 1, in which we noted that when recessions occur, velocity falls or its
rate of growth declines. What fact regarding the cyclical behavior of interest rates (discussed in Chapter 5) might help us explain this phenomenon? You might recall that
The classical economists’ money demand equation can also be written in terms of real money balances by dividing both sides of Equation 3 by the price level P to obtain:
interest rates are procyclical, rising in expansions and falling in recessions. The liquidity preference theory indicates that a rise in interest rates will cause velocity to rise
also. The procyclical movements of interest rates should induce procyclical movements in velocity, and that is exactly what we see in Figure 1.
Keynes’s model of the speculative demand for money provides another reason why
velocity might show substantial fluctuations. What would happen to the demand for
money if the view of the normal level of interest rates changes? For example, what if
people expect the future normal interest rate to be higher than the current normal interest rate? Because interest rates are then expected to be higher in the future, more people will expect the prices of bonds to fall and will anticipate capital losses. The expected
returns from holding bonds will decline, and money will become more attractive relative to bonds. As a result, the demand for money will increase. This means that f (i, Y )
will increase and so velocity will fall. Velocity will change as expectations about future
normal levels of interest rates change, and unstable expectations about future movements in normal interest rates can lead to instability of velocity. This is one more reason
why Keynes rejected the view that velocity could be treated as a constant.
Keynes’s explanation of how interest rates affect the demand for money will be easier
to understand if you think of yourself as an investor who is trying to decide whether
to invest in bonds or to hold money. Ask yourself what you would do if you expected
the normal interest rate to be lower in the future than it is currently. Would you rather
be holding bonds or money?
To sum up, Keynes’s liquidity preference theory postulated three motives for
holding money: the transactions motive, the precautionary motive, and the speculative motive. Although Keynes took the transactions and precautionary components of
the demand for money to be proportional to income, he reasoned that the speculative
motive would be negatively related to the level of interest rates.
Keynes’s model of the demand for money has the important implication that
velocity is not constant, but instead is positively related to interest rates, which fluctuate substantially. His theory also rejected the constancy of velocity, because changes
in people’s expectations about the normal level of interest rates would cause shifts in
the demand for money that would cause velocity to shift as well. Thus Keynes’s liquidity preference theory casts doubt on the classical quantity theory that nominal
income is determined primarily by movements in the quantity of money.
Further Developments in the Keynesian Approach
After World War II, economists began to take the Keynesian approach to the demand
for money even further by developing more precise theories to explain the three
Keynesian motives for holding money. Because interest rates were viewed as a crucial
element in monetary theory, a key focus of this research was to understand better the
role of interest rates in the demand for money.
William Baumol and James Tobin independently developed similar demand for
money models, which demonstrated that even money balances held for transactions