Download THE DEMAND FOR MONEY

___________________________________________________CHAPTER 13______________
THE DEMAND FOR MONEY
____________________________________________________________________________
The introduction of money into an economy makes households better off, and in many
ways it is like an improvement in technology. Once the "invention" arrived, and it arrives early
in the development process, households must decide how much money they want to hold. In this
chapter we study this decision.
But, before we begin, we need to agree on the meaning of the word money. In ordinary
conversation the word money can have several different meanings. If you ask someone how
much money you make in a particular job, money means income. When you see a large house
with fancy cars in the driveway you might say that those people have a lot of money. In this case
money means wealth. If someone points a gun at you and asks for your money, you will give
him, or her, your cash. When we talk about money we have the same meaning in mind as the
mugger - currency and coin. Later, in chapter 20, we will discuss some different definitions of
money that are in common use.
Average Money Balances
The amount or quantity of money that you hold fluctuates each day. On the weekends you
may hold large money balances while in the middle of week you may only have lunch money.
Right after payday your wallet may be full, but near the end of the pay period you may be short
of cash. Fluctuations in daily money balances depend on the idiosyncrasies of individual tastes,
the weather, pay periods, and so forth. To avoid dealing with the erratic behavior of daily money
balances, economists focus on the demand for and behavior of average money balances.
money demand
2
Let's look at a simple example to see what we mean by average money balances. Suppose
at 5:00 P.M. on each of the next seven days you count the money (coins and bills) that you have
on you. After the week you could make a table something like Table 13.1.
Table 13.1
M
T
W
R
F
S
SN
money
$65
$90
$85
$75 $100 $15
$60
balances
Your money holdings fluctuate substantially as we expected. To calculate your average
money holdings, we add up the balance for each day. This gives $490. Since there were 7 days
in this experiment, the average money balances are $490/7 = $70. We say that over this week
your demand for (average) money balances was $70. If this was a typical week, then $70 equals
your demand for money balances or demand for money for short.
The quantity of average money balances results from a choice, implicit or explicit, that you
make. For example, on Monday you could have spent $10 more or put $10 in your savings
account. This would have reduced your money holdings by $10 on Monday and on each
succeeding day. Your average money balances would have fallen to $60. On the other hand, a
reduction of spending by $10 on Monday would have increased your average money balances to
$80. By doing neither, you reveal a preference to hold $70 in average money balances.
Real Money Balances
Households use money to purchase goods and services, and they are therefore interested in
the quantity of goods that their money balances will buy. It is one thing to have $200 in money
balances when the price level is $2 per bundle and quite another to have $200 in money balances
when the price level is $2000 per bundle. In the first instance money balances represent 100
bundles of goods, while in the second case money balances represent only 1/10th of a bundle.
The number of bundles of goods that a household's nominal balances will buy is called the
household's real money balances. In symbols real money balances are written as
3 chapter 13
real money balances = M/P.
For a given price level, nominal money balances and real money balances behave in the
same way. As a matter of fact, if the price level is fixed, we don't have to worry much about the
distinction between real and nominal money balances. It is when the price level is allowed to
change that it becomes important to differentiate between the two. For now we keep the price
level fixed so that we do not have to worry about the distinction.
Money Demand
It is costly to hold money balances since they represent bundles of goods that could be
consumed. Therefore, no one will voluntarily hold money unless they receive some benefits.
One possible motive for carrying money from one period to another is savings. However, money
is a poor vehicle in which to save because it bears no interest. We will have to look for a reason
to hold money somewhere else.
Money is the medium of exchange and the final payment in most transactions involves the
transfer of money. But this alone is not enough to generate a demand for money. To see why,
suppose that there are two assets in the economy: bonds that pay risk free interest and money
that bears no interest, but is used in all transactions. Also assume that it is free to exchange
money for bonds and vice versa. In this world it would be optimal to hold bonds until the
moment you were ready to make a purchase. Right at the instant of purchase you would sell just
enough bonds to make payment. The seller would take the cash and immediately buy bonds. No
one would hold money for more than a moment.
The crucial assumption in the above example is that it is free to swap bonds for money and
money for bonds. When we drop this assumption and assume instead that it involves a transactions cost to convert assets from one form to another things change. Transactions costs may be
fees paid to brokers when you buy or sell stocks and bonds, so-called brokerage costs, or they
may be the time and inconvenience of going to and from the bank or ATM machine, so-called
shoe leather costs. Once we recognize transactions costs, it is no longer optimal to hold only
bonds. The transactions costs would be too high. Every time you wanted to buy a drink from a
machine or pay for lunch, you would have to go to the bank; and this would grow old rapidly.
money demand
4
For most households it will also not be optimal to hold only money. When you hold money
it means that you are not holding bonds, and are thus foregoing the interest income that bonds
yield. The interest income given up because of holding money balances is called interest
opportunity cost. The decision on how much money to hold involves a trade-off between transactions costs and interest opportunity costs. If you hold a large quantity of money balances, you
only go to the bank infrequently. But, you also have little interest income. On the other hand, if
you hold low money balances in favor of more bonds, you enjoy a higher interest income. But,
you must make frequent trips to the bank.
An Example of the Trade-Off
A simple example helps to illustrate the nature of the trade-off between the two types of
costs. Consider a household that receives $700 each Monday morning for the previous week's
work. All purchases are made with cash and the household spends $100 each day. The house hold has a savings account at a bank that is open 7 days a week, but it is costly in terms of shoe
leather cost to go to and from the bank.
Table 13.2
Balances with Seven Trips to the Bank
M
T
W
R
F
S
SN
money balances
$100
$100
$100
$100
$100
$100
$100
savings balances
$600
$500
$400
$300
$200
$100
$0
spending
$100
$100
$100
$100
$100
$100
$100
Begin by assuming that the household chooses to go to the bank each morning to withdraw
$100 for the day's purchases. In this case the household makes 7 trips to the bank and holds
$100 in (average) money balances. The average balance in their savings account is $300 (just
sum the daily balances in savings and divide by 7). Table 13.2 reports the data for daily spend ing, money balances, and savings account balances.
5 chapter 13
Now suppose that the household makes just 3 trips to the bank. On Monday they withdraw
$200, on Tuesday $200, and on Friday $300. Table 13.3 summarizes the balances for this case.
Table 13.3
Balances with Three Trips to the Bank
M
T
W
R
F
S
SN
money balances
$200
$100
$200
$100
$300
$100
$100
savings balances
$500
$500
$300
$300
$0
$0
$0
spending
$100
$100
$100
$100
$100
$100
$100
The household's average money balances have increased to $171.43, while average
balances in the savings account have fallen to $228.57. Making fewer trips to the bank increases
average money balances because the household must make a larger withdrawal on each trip to
the bank. Transactions costs decrease because of the fewer number of trips, but, since savings
balances are smaller, interest income is also smaller. Lower transactions costs are enjoyed only
at the expense of higher interest opportunity costs.
The Determinants of Money Demand
In the face of transactions costs, money is held to finance spending and an increase in trans actions costs raises money demand. To see why, suppose, for instance, that your bank reduces
the number of tellers or closes down an ATM machine so it takes longer to make withdrawals.
This increase in transaction costs encourages you to make fewer trips to the bank. But, if you
make fewer trips to the bank, on each trip you have to take out more money, and this increases
your holdings of average money balances, just as in the example.
Higher spending also increases the demand for money since more money is required to
carry out more expenditures. On the other hand, a higher interest rate makes it more attractive to
hold bonds. Bond holdings, the savings balance in the earlier example, increase, and the demand
for money falls.
money demand
6
Because the price level has been held constant, our analysis applies to both the demand for
real money balances and the demand for nominal money balances. It is convenient to summarize
our discussion in terms of the demand for real money balances, and we write
Md/P = L(r, Y, γ),
- + +
where Md/P is the demand for real money balances, r is the rate of interest, Y is real income and
represents total spending, and the Greek letter γ (gamma) is the transactions cost of swapping
money and savings balances (bonds). The negative sign under r means that an increase in r
lowers the demand for real money balances. The positive sign under Y means that an increase in
income raises the demand for real money balances. Finally, the positive sign under γ means that
an increase in transactions costs raises the demand for real money balances.
The Cost of Holding Nominal Money Balances
It is now time to let the price level vary and consider the demand for nominal money
balances. To see how changes in the price level affect the demand for nominal money balances,
we need to find out how much current consumption is given up when you hold $1. Suppose that
the price of a bundle of goods is $.50. In this case each dollar of money balances that you hold
represents 2 bundles. This is an easy calculation and can be written down in symbols as
$1/$.50 per bundle = 2 bundles.
This means that the opportunity cost of holding $1 in average money balances is two bundles of
goods.
Now suppose that the price of a bundle increases to $2.00. The cost of holding $1 in
money balances falls to 1/2 a bundle. In symbols
$1/$2 per bundle = 1/2 bundle.
7 chapter 13
The cost of holding the $1 has fallen because the $1 represents fewer bundles than it did before
prices rose. In general, the cost of holding $1 in money balances is
$1/P = cost of holding $1 in money balances
in terms of bundles of goods
An increase in the current price level lowers the cost of holding $1 in money balances
because holding the $1 represents fewer bundles of goods foregone. It is easy to get confused
here if a sharp distinction isn't drawn between the current price level and the future price level.
If you expect prices to rise in the future, you would try to spend your money today before prices
went up. This would lower your demand for money. On the other hand, if the current price level
increases, and no subsequent changes are expected, it is too late to spend your money. It has
already lost some of its value. Instead, you will hold more money because the dollar value of
your spending willincrease. Our conclusions are:
1)
An increase in the current price level lowers the cost
of holding money balances and thus increases money demand.
2)
An expected increase in the future price level raises
the cost of holding money and thus reduces the demand
money.
A change in the future price level would mean that inflation is expected, so we may rephrase the
second conclusion to read that an increase in the expected rate of inflation lowers the demand for
real money balances.
The first conclusion is represented graphically in Figure 13.1. In this figure the cost of
holding each dollar, $1/P, is measured on the vertical axis and the quantity of nominal money
balances, M, is measured on the horizontal axis. The initial price level is $10 per bundle, so the
cost of holding $1 is 1/10th of a bundle. At this price level households want to hold $200 in
nominal money balances. If the price level increases to $20 per bundle (and afterwards is
expected to remain at $20), the cost of holding nominal money declines to 1/20th bundle per
dollar. This decline leads households to increase their demand for nominal money balances to
$400. We could do this for all price levels and this would trace out the nominal money demand
money demand
8
curve. The demand curve for nominal
money balances has a negative slope and
can be thought of in the same way as a
1/P
demand curve for any good.
The demand for nominal money
1/10
balances is just Md and can be written in
symbols as
1/20
Md = P*L(r, Y, γ, πexpected )
- + + -
$200
where we have now added the expected rate
of inflation as a determinant of money
$400
M
Figure 13.1 The Demand for Nominal
Money Balances
demand. On the Md curve the quantity of nominal money balances demanded and the price
level, P, are the only variables that are changing. This means that the real rate of interest, r, the
real income stream, Y, transactions costs, γ, and the expected rate of inflation, πexpected, are held
constant along the Md curve. A change in the price level causes a movement along the Md curve,
while changes in the remaining variables that determine money demand cause shifts in the Md
curve. We analyze how the Md curve shifts in the same way that we studied shifts in consumption demand, investment demand, and in labor demand. The effect of a change in the income
will be taken up first.
The first order of business is to find a benchmark. In Figure 13.2 the Md curve is drawn so
that at the price level P 0 the demand for nominal money balances is M d0 . Now assume that there
is an increase in income. If the price level stays the same, what will happen to the demand for
nominal money balances? Since income is higher, expenditures are higher as well, and house holds will want to hold larger nominal money balances. The demand for nominal money
∏
balances will increase, say, to M d0 . This means that an increase in (real) income shifts the Md
∏
curve upwards and to the right. The new curve is labeled M d .
The same thought experiment reveals how the Md curve shifts when the interest rate
increases. In Figure 13.3 we start with the same benchmark. Instead of changing income, we
now let the interest rate increase. If the price level stays the same, what happens to the demand
9 chapter 13
for nominal money balances? The higher
interest rate raises interest opportunity cost.
Households substitute towards bonds and
1/P
lower their demand for nominal money
∏
balances to, say, M d0 . The money demand
curve shifts down and to the left.
An increase in expected inflation also
increases the cost of holding money because
1/P
0
money is losing its purchasing power at a
more rapid rate. In response to this higher
cost, households will reduce their average
money holdings. A picture of this result
would look just like Figure 13.3.
Md '
Md
Md
M d'
M
0
0
Figure 13.2 The Effect on Money
Demand of an Increase
in Income
Now consider an increase in the transactions cost, γ. It is now more costly to go to the
bank, and households will make fewer trips. Since fewer trips are made, withdrawals each time
are larger, and average money balances increase. A picture of this result would look just like
Figure 13.2.
Extensions
1/P
The above analysis emphasizes the
relationship between money demand and
the price level. Many economists prefer to
emphasize the influence of money on the
interest rate, and plot the demand for real
money balances against the interest rate r.
To see the shape of this money demand
curve suppose at the interest rate r 1 the
demand for real money balances is (Md/P)1.
This is shown in Figure 13.4. As r falls, in
1/P
0
Md
Md '
Md'
Md
M
0
0
Figure 13.3 The Effect on Money
Demand of an Increase
in the Interest Rate
money demand
10
the figure from r1 to r2, households shift
away from bonds into money, and the
demand for real money balances increases to
r
(Md/P)2This gives us the downward sloping
curve labeled L. The economics of money
r
demand are the same, no changes have been
1
made. Indeed, if we so chose, we could plot
the demand for money against real income,
r
2
L
Y. We show this picture here because it
turns out to be useful later when we study
sticky wage models.
Summary
d
M/P
(M /P)
(Md/P)
1
2
Figure 13.4 The Demand for Real
Money Balances Plotted
Against the Interest
Rate
In this chapter we studied the demand
for money. In this context money means currency and coin, and the demand for money is the
demand for average money balances. It is important to be clear on the distinction between real
and nominal money balances. The demand for real money balances depends positively on
income and transactions costs, and negatively on the real interest rate and the expected rate of
inflation.
_____________________________________________________________________________
_____________________________________________________________________________
Review Questions
1)
How would you expect the introduction of credit cards into an economy to affect the money
demand curve?
2)
Plot the money demand curve against real income Y. What is the slope of this curve? How
would it shift if interest rates fall?
11 chapter 13
3)
Germany experienced a so-called hyperinflation from August of 1922 to November of
1923. Something that cost 1 mark in August of 1922 cost 10,000,000,000 marks by November of 1923. The average rate of inflation was 322% per month. What do you think
happened to the demand for real money balances over this period?
4)
Consider the path of daily money balances given below.
money
balances
M
T
W
R
F
S
SN
$100
$65
$80
$85
$140
$30
$60
What are average money balances? If the price level is $5, what are real money balances?
5)
If the demand for real money balances is 20 bundles and the price level is $130, what is the
demand for nominal money balances?