How the Fed controls
the money supply?
• Recall:
• money supply = currency plus deposits at banks
• Decisions are made by FOMC
– FOMC meets next Tuesday
– markets will be speculating about what the Fed
will do to the short-term interest rate (Federal
funds rate)
– we will see that the decisions about the money
supply are directly linked to this interest rate
Simplest Case:
currency is whole money supply
• Then the Fed simply prints all the money
and the total amount of money is easily
determined
• But this is not the real world: deposits are a
major part of the money supply
– At the end of last year, for example,
• currency = $426 billion
• M1 = $1,069 billion
• M2 = $4,019 billion
More relevant case: deposits at
banks are part of the money supply.
24_01
First observe where deposits fit in to
banks’ business
Deposits
Savers
(lenders)
Loans
Investors
(borrowers)
Banks
Interest payments
on deposits
Interest payments
on loans
Direct loans
(bonds)
Interest payments
on direct loans
In order to control the money supply,
the Fed must have a link to deposits
at banks.
• Why?
– Because deposits are part of money supply
• In symbols, the money supply is:
• M = CU + D
– where
• M = money supply
• CU = currency
• D = deposits at banks
First key idea in the story:
people want to hold a fixed mix
of deposits and currency.
• This is a reasonable simplifying assumption
• An equation to describe this assumption is
• CU = kD where k is a constant called the
• currency to deposit ratio
– example: k = 0.2, so that people hold currency equal to 20
percent of their deposits
– k depends on custom, crime enforcement, etc.
– it is possible for k to change over time (banking panics),
but we assume k is fixed for now
Second key idea in the story:
banks are required to hold “bank
reserves” equal to a certain
fraction of their deposits
• Bank reserves are deposits a (commercial)
bank holds at the central bank (Fed)
• An equation describing this requirement is
• BR = rD where r is a constant called the
• required reserve ratio
– example: r = .1, so that banks are required to hold bank
reserves equal to 10 percent of deposits
• The above equation is a link for the Fed to control
the money supply
Third key idea in the story:
The Fed can control the amount
of bank reserves in the economy
• How? (Recall that bank reserves are simply
deposits that banks have at the Fed)
• By buying and selling “things” and paying
or getting paid with the reserves, the Fed
can determine the total amount of reserves
– what are the things?
• Ketchup? No, there is not enough of it.
• Government bonds? Yes, there are plenty of them.
The monetary base
• Defined as currency plus bank reserves
• In symbols, MB = CU + BR where
• MB = monetary base
• CU = currency
• BR = bank reserves
• Because the Fed can control bank reserves,
it can control the monetary base
Look at what we have so far:
M = CU + D
CU = kD
BR = rD
MB = CU + BR
Logical implication of what we have so far:
M = CU + D = kD + D = (k+1)D
MB = CU + BR = kD + rD = (k+r)D
Thus: M = [(k+1)/(k+r)]MB
Example: k = .2 and r = .1 implies
[(k+1)/(k+r)] = (1.2)/(0.3) = 4
The blue term is the money multiplier
The money multiplier
• The end of the story. We (and the Fed) now
know how much the money supply will
increase as a result of an increase in the
monetary base.
• The term multiplier is used because the number is
greater than one, e.g. 4.
• Since the Fed can control the monetary base
it can control the money supply.
• example: say the money multiplier is 4
• Fed increases the monetary base (MB) by $1
• money supply (M) will increase by $4 billion.
The Gory Detail I
Assets
Liabilities
Loans 70
Deposits 100
Bonds 20
Reserves 10
The Gory Detail II
Assets
Liabilities
Loans 70
Deposits 100
Bonds 10
Reserves 20
The Gory Detail III
Assets
Liabilities
Loans 80
Deposits 100
Bonds 10
Reserves 10
The Gory Detail….
Set k = 0 to focus on deposits at banks
Bank2
Bank3
Bank4
Bank5
Bank6
Bank7
Deposits
10.00
9.00
8.10
7.29
6.56
5.90
Loans
9.00
8.10
7.29
6.56
5.90
Reserves
1.00
0.90
0.81
0.73
0.66
If you sum up the numbers in the
first column of the previous table
you get:
10(1 +.9 +.92 + .93 …)
= 10/(1 - .9) = 100
So the money multiplier is 10
just what we get from the earlier
analysis if k = 0 and r = .1
Wrap up of Long Run Analysis
• Factors affecting long-run real GDP growth
• Growth rate of aggregate hours (working age
population, employment to population ratio, hours
per worker)
• Growth rate of productivity (capital, technology-use SAM and the growth accounting formula)
• Factors affecting long-run rate of inflation
• Money growth (Fed and the money multiplier)
• Velocity growth
• Use quantity equation of money
• Now on to economic fluctuations next week
Finally, use quantity equation of
money to determine the appropriate
growth rate of the money supply
Potential GDP growth rate ( 2.3)
+ inflation rate (2.3)
- velocity growth rate (0.0)
= money growth rate (4.6)
END
OF
LECTURE