Understanding Money
Demand
Money can be anything that satisfies:
•Store of Value
•Unit of account
•Medium of exchange
Lots of things satisfy these properties
Standard Definitions of Money




Monetary Base (M0): Direct liabilities of the central bank
 Currency in circulation + Bank Reserves
M1:
 Currency in circulation + Traveler's Checks +
Checking accounts
M2:
 M1 + Savings accounts + Money Market Accounts +
Small Time Deposits
M3:
 M2 + Large Time Deposits + Eurodollars
Think of this as a portfolio allocation problem. You have
a fixed amount of income and you are allocating it over
several assets.
More Liquid
Lower Return
Less Liquid
Higher Return
$5,000/month
Cash
$400
Checking Account
$2,000
M1
Savings Account
$600
M2
Stock/Bonds
$2,000
M1 Money Demand

Suppose you plan on
spending $120 over
the upcoming month.
You can withdraw the
$120 from your
savings account
immediately, or you
can make several trips
to the ATM.
Suppose you go to the bank three times per month
(every 10 days)
ATM Withdrawals
Cash Balance Hits Zero

More generally, you make plan on Spending PY
dollars per month. If you make N trips to the ATM
PY
Average Cash
Balances
0 +
N
=
= Money Demand
2
Real
Money =
Demand
M
P
=
Y
2N
Choosing N

There are two costs associated with money:
yi
Interest Cost 
2N
If you make very few
trips to the bank (N
is small), you will
need to withdraw
more cash – having
more cash entails
more lost interest
Transactio n Cost  tN
If you make a lot of
trips to the bank,
you will withdraw
less each time (less
interest cost), but
you will pay more in
transaction costs
 yi

Minimize 
 tN 
N
 2N

yi

t  0
2
2N
yi
N
2t
Take the derivative with
respect to ‘N’
Solve for N
M1 Money Demand
This is the optimal
behavior (i.e. trips to
the ATM per month)
yi
N
2t
As the interest rate
goes up, you hold less
cash. Therefore, you
make more trips to the
bank
As ATM fees rise, you
make less trips to the
bank, but withdraw more
each time
M1 Money Demand
Real Income
d
M
y


P
2N
yt
2i
Nominal
Interest Rate
Real Money Demand
Transaction
Costs
Generally Speaking….
“is a function of…”
d
M
 M  y, i, t 
P
Real Income (+)
Transactions Costs
(Cost of obtaining
money) (+)
Real Money Demand
Nominal Interest
Rate (-)
Cambridge Money
Demand
A common form of money demand can be written as
follows:
d
M
 k (i, t ) y
P
Money demand is equal to a fraction (k is between zero and one) of
real income. That fraction depends on interest rates (-) and
transaction costs
The Quantity Theory of
Money
MV = Py
Money Supply
Nominal Income
Velocity – Measures
the number of times a
dollar changes hands
For example, if PY = $100 (there are $100 worth of goods and services
to buy) and M = $50 (there are $50 worth of cash available), the V = 2
(each dollar changes hands twice)
The Quantity Theory of Money and
Cambridge Money Demand
M
 k (i, t ) y
P
MV  Py
1
V
k (i, t )
When money demand drops (either interest rates rise or transaction
costs fall), individuals do not want to hold onto as much money as
before. To get rid of it, they pass it on to someone else – velocity
increases.
In 1995, we saw a dramatic change in household
portfolio decisions…why?
M1 Money Demand
falls dramatically
starting in 1995
Money Demand Rises
from 1980 - 1993
Trend
Is interest rates rose, households switched out of checking accounts and
into savings accounts….technology (online banking, ATMs, etc. made this
transition easier)
Falling demand
for M2
Rising Demand
for M2
M2 Money Demand

Recall that M2 includes everything in M1
(cash + checking accounts) plus savings
accounts. Therefore, any model of M2
demand would need to explain why
households hold savings/checking
accounts rather than less liquid assets
such as T-Bills
M2 Money Demand

Any M2 money demand should have the
same characteristics as the previously
derived M1 demand
Positively related to income/consumption
 Negatively related to interest rates

M2 Money Demand
Positively related to
consumption
mt  .05  .23%mt 1   .08%mt 2   .45%ct  
 .24%ct 1   .002R  RM 2t  .003R  RM 2t 1  .11mt 1 
 .11~
y  .002R  RM 2  .0072T  .03D83Q1
t 1
t 1
Negatively related to
interest rates
t