The demand for money
How much of their wealth will people choose to hold in
the form of money as opposed to other assets, such
as stocks or bonds? The answer to this question
determines the demand for money.
What is the opportunity cost of holding money?
The opportunity cost is the interest rate forgone on
alternative assets, which we can lump together
generically and call “bonds.”
The opportunity cost of holding money is the nominal
interest rate, not the real interest rate.
Recall that
real interest rate = nominal interest rate – expected inflation rate
which implies that
nominal interest rate = real interest rate + expected inflation rate.
Why is the opportunity cost of holding money the
nominal interest rate and not the real interest rate?
If an individual chooses to hold, say, $100 in the
form of money, he or she is giving up the opportunity
to hold $100 of bonds which would pay a certain
nominal interest rate. This nominal interest rate
provides both some additional purchasing power at
the end of the loan period as well as compensation
for inflation.
Because the nominal interest rate is the opportunity
cost of holding wealth in the form of money instead
of in the form of other assets, it follows that the
quantity of money demanded depends inversely on
the nominal interest rate.
The higher the nominal interest rate, the lower is the
quantity of money demanded; the lower the nominal
interest rate, the higher is the quantity of money
demanded:
Factors that shift the money demand curve:
price level
real GDP
technology of payments.
If the price level increases, the demand for money
increases, i.e., the money demand curve shifts to
the right.
Recall that “” means “change in.”
The demand for money changes proportionally to
the price level (%MD = %P). For example, a one
percent increase in the price level causes a one
percent increase in the demand for money.
If real GDP increases, the demand for money
increases, i.e., the money demand curve shifts to
the right.
Any technological innovation that makes it possible
to undertake transactions with smaller money
holdings, e.g., credit cards, will cause a decrease
in the demand for money, i.e., the money demand
curve will shift to the left.
The supply of money is determined by the Fed and
does not vary with interest rates:
The market clearing equilibrium nominal interest rate
is the nominal interest rate at which the quantity of
money demanded is equal to the quantity supplied:
To understand the adjustment to equilibrium in the
market for money, it is important to understand that
there is an inverse relationship between interest
rates and bond prices.
Suppose a bond pays $10 in interest per year. The
interest rate depends on how much the buyer paid
for the bond. If the buyer paid $80 for the bond,
then the interest rate is ($10/$80) X 100% = 12.5%.
But if the buyer paid $50 for the same bond, the
interest rate is ($10/$50) X 100% = 20%.
Thus, the lower the price paid for a bond, the higher
is the interest rate.
Returning to the previous graph, at a nominal interest
rate of 6%, the quantity of money supplied is greater
than the quantity of money demanded, i.e., there is an
excess supply of money. Individuals will use up their
excess money holdings by buying bonds, driving bond
prices up and the interest rate down toward
equilibrium.
At a nominal interest rate of 4%, the quantity of
money demanded is greater than the quantity of
money supplied, i.e., there is an excess demand for
money. Individuals will sell bonds to convert them
into money, driving bond prices down and the
interest rate up toward equilibrium.
Changes in the equilibrium interest rate are caused
by shifts of the money supply and/or money demand
curves.
For example, if the Fed increases the money supply,
the market clearing equilibrium nominal interest rate
will decrease in the short run:
The money supply increases from MS0 to MS1, i.e.,
from $2 trillion to $3 trillion, causing the market
clearing equilibrium nominal interest rate to decrease
from 5% to 4%.
However, in the long run, the decrease in the interest
rate will cause households and firms to borrow more
and spend more on consumption and investment.
Aggregate demand therefore increases, which
causes an increase in the price level and therefore an
increase in the demand for money.
Recall that the demand for money increases in the
same proportion, i.e., by the same percentage amount,
as the increase in the price level.
The price level increases by the same percentage
amount as the increase in the money supply (we’ll see
why later).
Therefore the demand for money increases by the
same percentage amount as the increase in the
money supply.
To summarize:
%MD = %P,
%P = %MS,
therefore,
%MD = %MS,
i.e., the money supply and the demand for
money curves both shift to the right by the same
amount and the market clearing equilibrium
nominal interest rate increases back to 5%:
Therefore, we can conclude that an increase in the
money supply has no long-run permanent effect on
interest rates, but it does cause a permanent
increase in the price level. A given percentage
change in the money supply causes an equal
percentage change in the price level.
This analysis assumes that potential GDP is
constant. What if potential GDP increases? To
answer this question we need the Quantity Theory
of Money.
The starting point for this theory is the definition of
the velocity of money, V. Velocity is the number of
times the average dollar is spent on final goods and
services in a given time period.
___
V = P.Y
M
where,
P = aggregate price level,
Y = real GDP = real output = real income,
P.Y = nominal GDP, the current dollar value of the
amount spent on final goods and services, or the
current dollar value of income earned,
M = money supply,
V = velocity of money.
For example, if nominal GDP = P.Y = $500 billion per
year and the money supply = M = $100 billion, then
$500 billion
___ = ___________
V = P.Y
=
M
$100 billion
5.
This means that each dollar changes hands an
average of five times per year.
Multiplying both sides of the velocity equation by M,
M.V = P.Y,
Which is called the equation of exchange. Total
nominal expenditure on final goods and services can
be measured either by nominal GDP, P.Y, or by M.V.
Dividing both sides of the equation of exchange by Y,
M.V .
____
P =
Y
According to the quantity theory of money, V is
relatively stable over time, or at least is independent
of changes in the money supply, M.
If, in addition, Y is interpreted as potential GDP and
potential GDP is constant, then any percentage
change in M will cause an equal percentage change
in P.
For example, if the Fed increases the money supply
by 5% per year, this will cause the price level to
increase by 5% per year, i.e., the inflation rate will be
5%.
However, over time it is likely that potential GDP will
grow, as a result of capital accumulation and
technological innovation.
If M increases and Y is also increasing, then the
inflation rate will be the difference between the
growth rate of the money supply and growth rate of
real GDP.
In general, %P = %M - %Y (assuming %V = 0).
For example, if the Fed allows the money supply to
grow at 5% per year and potential GDP is growing at
2% per year, then the inflation rate will be 3%.
The late Milton Friedman said that “inflation is
always and everywhere a monetary phenomenon,”
i.e., the only thing that causes inflation is the money
supply growing faster than real GDP.