The Demand for Money
Theories and Evidence
The Demand for Money
• So far we have considered the money supply
and how a central bank goes about changing it.
• Where does money demand come from?
• Understanding the demand for money will allow
us to examine the links between monetary
policy, inflation, and unemployment.
• The quantity of money circulating around the
economy and the interest rate at which it
circulates are determined by both money supply
and money demand.
The Quantity Theory of Money
• How much money would you need to purchase the
economy’s annual output of goods and services?
– Suppose GDP (P*Y) was $14 trillion.
– Would you need a money supply of $14 trillion to buy all this
output over the course of a year?
– No! Each dollar is used multiple times. You would need
considerably less M than P*Y.
• Velocity is defined as the number of times a dollar bill
changes hands over the course of a year in an economy.
– It tells us the turnover rate for money in the economy.
• Equation of Exchange: M*V ≡ P*Y
– The total money supply multiplied by the number of times this
money changes hands must be equal to nominal income (or
nominal GDP)
– Total expenditure (M*V) = Total production (P*Y)
– Everything produced is consumed
The Quantity Theory of Money
• When the money market is in equilibrium, Md =
Ms = M.
• The quantity theory of money can be re-written
as:
– Md = (1/V)*PY
– Md = k*PY
(k = 1/V = constant if V is a constant)
• The demand for money is solely a function of
nominal GDP
• Money demand is not directly affected by
interest rates.
Is Velocity Constant?
The Liquidity Preference Theory of Money
• As seen, velocity cannot be accurately treated as a
constant.
– If velocity can change, then the link between prices and money
is muddled.
• J.M. Keynes postulated that individuals hold money for
three reasons:
– Transactions Motive  You need money to buy things
– Precautionary Motive  You might need money on hand for an
unexpected purchase
– Speculative Motive  You hold your wealth as money (as
opposed to bonds) to store value
• The biggest innovation was to identify a link between
money and interest rates (an inverse relationship.)
The Liquidity Preference Function
• What people really care about is the purchasing power of
their money
– If prices rise, then the real value of money falls.
– Want to look at the demand for real money balances
• Md/P = f(i,Y)
– Real money demand is a decreasing function of nominal interest
rates
– Real money demand is an increasing function of real income.
• Recall that M*V ≡ P*Y
– V = P*Y/M
– P/Md = 1/f(i,Y)
– V = Y/f(i,Y) when the market for money is in equilibrium.
– As i↑, f(i,Y)↓, and V↑  Velocity is not constant!
The Transactions Motive for Holding Money
• Suppose you earn $3000 per month and consume $100 per day.
– We’ll assume 30 day months and a constant rate of consumption over
this period.
• Case 1: You hold the entire $3000 in cash to carry out your
transactions.
– You have $3000 at the beginning of the month and $0 at the end.
– Your average cash balance is $1500.
– Your annual income (P*Y) $36,000 and your holdings of money (M)
average $1500.
– V = PY/M = 36,000/1500 = 24
• Case 2: You hold $1500 in cash and buy $1500 in bonds at the
beginning of each month
– After 15 days, you sell your bonds and use the principal ($1500) to
make your purchases, keeping any earned interest for yourself.
– Your average cash balance is now $750 (1500 at day 1, 0 at day 15,
1500 at day 16, 0 at day 30: (1500+0+1500+0)/4 = 750.
– V = PY/M = 36,000/750 = 48
– If i = 1% per month, you also earned (i/2)*1500 = .005*1500 = $7.50
Two Cases
Cash on Hand
Cash on Hand
3000
1500
1500
750
0
½
1
2
Time
0 ¼ ½
1
1.5
2
Time
The Transactions Motive for Holding Money
• Case 3: Now suppose you hold $500 in cash and buy $2500 in
bonds.
– Every 5 days (1/6th month) you run out of cash and have to sell $500
worth of bonds to make your purchases.
– Your average cash holdings over the course of the month is M = $250.
– V = 36,000/250 = 144
– At 1% monthly interest, you earn
(1/6*1%*$2500)+(1/6*1%*$2000)+…+(1/6*1%*500) = $12.50
• As your average cash balance shrinks, both velocity and the interest
earned on bonds increases.
• So why not hold the smallest amount of cash possible?
• Transactions costs of bonds!
– Brokerage fees
– Time costs
• As interest rates rise, people want to hold smaller average cash
balances, causing money demand to fall and velocity to rise.
• As transactions costs of bonds rise, people want to hold more
money at any given point, causing money demand to rise and
velocity to fall.
The Speculative Motive
• A weakness of Keynes’ original analysis of the
speculative motive is that it has a knife edge solution
– If the return on bonds is higher, then all speculation is in bonds.
If the return on money is higher, then all speculation is in money.
– Only when the two assets have identical returns (an uncommon
occurrence) will people hold money and bonds for speculative
purposes.
• James Tobin offered a refinement in 1958 by arguing that
people care about both expected returns and risk.
– Money has a certain nominal return: zero
– Bonds have more volatile returns that may in fact be negative.
– Through carrying a diversified portfolio of money and bonds, the
overall risk of the portfolio may be minimized relative to expected
returns.
• However, it is not clear that money offers any greater
diversification benefits than near risk-free bonds such as
U.S. treasury bills.
– No speculative motive for holding money?
Friedman’s Modern Quantity Theory of Money
• Milton Friedman built upon Keynes’ idea and
introduced his own model of the demand for money:
Md


e
 f  YP , rb  rm , re  rm ,   rm 
P
( )
()
 (  ) ( )

• Real money demand is a function of…
– Permanent income (YP), expected average income over the
course of one’s life. (+)
– The excess return on bonds over money (-)
– The excess return on equities over money (-)
– The rate at which money loses purchasing power. Can also be
thought of as the excess return on goods over money. (-)
Conclusions of Friedman’s Refinement
• Includes alternative assets to money
• Views money and goods as substitutes
• While the expected return on money is not a constant,
the excess return on bonds (rb – rm) is assumed to be a
constant.
– Thus, interest rates (because they cause the returns on all
assets to rise by the same proportion) will not affect money
demand.
• Therefore, the demand for money is predictable  a
direct function of permanent income.
– Thus, Velocity is predictable and stable!
– MV = PY  Money is the primary determinant of aggregate
spending.
Empirical Evidence
• Money and Interest Rates
– Money demand does appear to be sensitive to interest rates
– In the extreme case, money demand is so sensitive to interest
rates that it is a flat curve at the current rate.
• Known as a liquidity trap, since monetary policy cannot affect
interest rates in this case.
– Very little evidence that money demand hits a liquidity trap at
interest rates above zero.
– When nominal interest rates approach zero, we can fall into such
a trap (see Japan).
• The Money Demand function is variable and
unpredictable in Keynes’ model, but stable in Friedman’s
model
– Before 1970, Md was fairly stable.
– Since 1970, Md has been much less stable due to the rapid pace
of financial innovation.
– Greater instability in Md makes monetary policy harder to control
and less predictable.