# Week 11

Document Sample

```					                              Week 11
Chapter 16
Determinants of the Money Supply

The monetary base is

MB  R  C

where R represents the reserves in the banking system and C the currency in the
hands of the nonblank public. The money supply is

M  DC

where D is the amount of deposits in the banking system. Suppose that we look
at how some the banking system will respond to an increase in reserves if

1. all excess reserves are driven to zero
2. the public does not change its holdings of currency.
3. the proceeds from all loans are put into a deposit.

In that case

MB  R  C
M  D  C

By assumption (1.) banks will lend out all excess reserves and by (3.) all the
proceeds will end up in a deposit. For that reason D will change. By assumption
(2.) the nonblank public does not change its money holding, so

C  0

and

MB  R
M  D
If excess reserves have been driven to zero, then all reserves will be required
reserves so

R  rD D

and

MB  R  rD D  rD M
MB  rD M                                       (1)
1
M        MB  m  MB
rD

so there should be a relationship between the monetary base and the money
supply. We will write that relationship as

M  m  MB

where m is called the money multiplier. It is a variable not a constant. The
equation indicates how much the money supply will change for a given change in
the monetary base. Recall that the Fed has control of the monetary base. Its
supply of the money supply would be as complete if the three assumptions
mentioned above are true. To the extent they are not true the Feds control of the
money supply will not be as complete. That is why m is a variable and not a
constant.

The expansion of the money supply will not be as great as Equation (1) indicates
because banks will not drive excess reserves to zero and because the public
may decide to keep some of the proceeds of the borrowing and lending in the
form of cash. Assume that the public has some preferred ratio of currency to
currency to deposit holdings

C D     currency ratio

and that banks maintain a certain level of excess reserves relative to deposits

 ER D    excess reserve ratio
Recall total reserves are made up of required reserves plus excess reserves so

R  RR  ER

and required reserves are a multiple of demand deposits

RR  rD D

so

R  rD D  ER

Putting this into the equation for MB = R + C

MB  rD D  ER  C
MB  rD D   ER D  D  C D  D
MB   rD   ER D   C D  D

This gives us a relationship between MB and D

1
D                          MB                (2)
rD   ER D   C D 

Now lets play with the money supply equation briefly

M  D  C  D  C D  D
(3)
M  1  C D  D

Now take the representation for D in equation (2) and put it into equation (3)

M  1  C D  D  1  C D 
1
 MB
 rD   ER D  C D 
M
1  C D         MB
 r   ER D  C D 
D
Now we have our relationship between MB and M. The money multiplier is

m
1  C D
 r   ER D  C D 
D

Example in Text on page 415

rD  0.1
C  \$400 (all money values in billions)
D  \$800
ER  \$0.8
M  C  D  \$1200
C   400  0.5
 D  800
0.8
 ER D       0.001
800
1  0.5       1.5
m                         2.5
0.1  0.001  0.5 0.601

So if the Fed were to increase the monetary base by \$10 billion, this would
create \$25 billion new money in the economy (assuming the ratios do not change
in the meantime)

Factors that affect the money multiplier

Changes in the reserve ratio

A change in the reserve ratio affects the money multiplier. Suppose that the Fed
increases the reserve ratio. This means that banks will have to increase required
reserves and likely excess reserves as well. To do this banks may have to
restrict loans. This limits the amount of demand deposit expansion
Banks A with a reserve ratio of 0.10

Figure 16.1

Consider bank A in Figure 16.1 This bank has excess reserves of \$1000 if the
reserve ratio is 0.10. The bank can lend \$1000 and this will start the demand
deposit expansion. Suppose the Fed raises the reserve ratio to 0.20. Now bank
A has \$0 in excess reserves and can lend nothing.

Bank A with a reserve ratio of 0.20

This banks will also try to build up its excess reserve holdings by calling in loans.
This will further reduce demand deposit creation and spending. This is built into
the money multiplier by the ER/D ratio.
Using the values of the previous example except for the reserve ratio which is
changed from 10 percent to 20 percent we have

rD  0.2
C  \$400 (all money values in billions)
D  \$800
ER  \$0.8
M  C  D  \$1200
C   400  0.5
 D  800
0.8
 ER D        0.001
800
1  0.5       1.5
m                         2.14
0.2  0.001  0.5 0.701

So the result of increasing the reserve ratio is to make the money multiplier
smaller and lead to a smaller amount of money creation for a given increase in
the monetary base.
Changes in the publics desire to hold cash.

Suppose that the public decides to increase its cash holdings. In this case the
[C/D] ratio increases (the public converts some demand deposits to currency).
This will initially decrease reserves in the banking system.

Bank A before a cash withdrawal

Bank A after \$1000 has been withdrawn

The reduction in excess reserves will inhibit possible demand deposit expansion.
The bank may decide to increase its excess reserve holdings. This will further
decrease any money creation.

Let’s see what the multiplier tells us.

If the public decides to increase its cash holdings the [C/D] ratio will increase.
Recall initially that

C D   0.5
 ER D   0.001
rD  0.1
1  C D                   1  0.5
m                                                  2.5
rD  C D    ER D        0.1  0.5  0.001
Suppose now the public decides to hold more cash so that C D  0.8 . In that
case

C D   0.8
 ER D   0.001
rD  0.1
1  C D                   1  0.8
m                                                  2.0
rD  C D    ER D        0.1  0.8  0.001

Banks decide to increase excess reserves.

Suppose that the banks decide to increase excess reserves. As we have seen
earlier this will tend to reduce lending which, in turn, will reduce increases in the
money supply. Suppose that we look at the multiplier with our original data
where rD  0.1, C D  0.5, and  ER D  0.001 . In that case the multiplier was
m  2.5 . Suppose that the excess reserve ratio increases to 0.01

C D   0.5
 ER D   0.01
1  C D            1  0.5
m                                           2.46
rD  C D    ER D  0.1  0.5  0.01

As expected the multiplier becomes smaller if banks increase excess reserves. If
the costs of holding excess reserves increases banks will hold less excess
reserves. If the benefits of holding excess reserves increase, then banks will
hold more of them.

Market interest rates If interest rates on loans increase banks will find it more
costly to hold excess reserves rather than lending the funds. So one would
expect to find the multiplier to increase when interest rates increase. See the
graph on the next page
The relationship between interest rates and [ER/D]

Expected deposit outflows. Another factor that affects a banks decision of
whether to increase holdings of excess reserves is whether it thinks deposits will
increase or decrease. If the bank feels that deposits are likely to flow out of the
bank, then it may try to build up its supply of excess reserves (perhaps by not
making new loans). If the bank feels that deposits are likely to increase, it may
be willing to make more loans.
Other factors that determine the money supply

We have been assuming that the Fed has complete control of the monetary
base. The Fed can restrict discount loans to banks but cannot force banks to
borrow. Thus the Fed does not have complete control over reserves. It can
influence banks decisions of whether to borrow, but cant control the decision.

We will break the monetary base into two parts, the borrowed and nonborrowed
monetary base.

MBn  MB  DL
MBn  the nonborrowed monetary base
MB  the monetary base
DL  discount loans.

where it is presumed that the Fed has greater control of the nonborrowed base.
Then the multiplier relation can be written as

M  m  MBn  DL

Effect of changing MBn

There is nothing new here. If the Fed buys securities then nonborrowed reserves
will increase. An increase in MBn then supports an expansion of the money
supply. A sale of securities by the Fed will decrease nonborrowed reserves and
hence the money supply.

Effect of changing DL

If banks borrow from the Fed this will increase reserves and hence increase the
monetary base. There is nothing new here either.

Market interest rates and the discount rate

There is something new here. When banks borrow from the Fed they can make
loans or buy securities with the funds they borrow. Suppose that the interest rate
that a bank can earn from a loan or security (pretend the interest rate is the same
on each, it just makes life easier) is i and that the interest rate the bank pays for
a discount loan is id . Now consider i  id . A bank may be willing to lose money
and borrow if id  i in certain circumstances. Suppose a very good customer
needs a quick loan. The larger id gets relative to i the less likely this will occur,
however. If i increases the banks may be tempted to make loans even though
their ER position is weak and then borrow from the Fed as a means of building
up ER. If banks do lend more because of the increase in market interest rates,
then the money supply will expand.

The whole point here is that the money supply is not absolutely independent of
interest rates as we pretended in earlier chapters. In earlier chapters we
assumed that the money supply could be set absolutely without regard to the
interest rate. This assumption is not quite true. The money supply is also
affected to some extent by interest rates. Note also the Fed can affect the
money supply by manipulating the discount rate.
Money supply growth since 1980

It has varied a lot, from –0.11% to 13.1%
MB was mostly nonborrowed reserves save for the period in 1984
when the Fed made massive loans to the Continental Illinois
National Bank.

Note the change in m means it will be difficult for the Fed to control
the money supply. Note particularly the sharp decline in the
multiplier after about 1994. This suggest that we might expect a
sharp decline in M1.
The Great Depression Bank Panics.

During the Great Depression a large number of banks failed and bank panics
ensued. One would expect to find that the [C/D] ratio to increase as people
converted D into C.

One would also expect that banks would tend to increase the [ER/D] ratio in anticipation
of runs on deposits.

If [C/D] and [ER/D] decline we would expect to see a decline in m and hence in the
money supply.
The money supply declined about 25%. This is true even though there was a20%
increase in MB. Now since

M  m  MB

this decline in M must be the result of the decline in m.

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 23 posted: 3/14/2010 language: English pages: 17