Notes on Money Demand
The simplest money demand function is constructed from the quantity equation in
which velocity is constant:
M
t
V
P
t
Y
t
and this states that real money balances are proportional to real income:
M
t
P
t
Y
t
where
is the inverse of constant velocity. Note that in this model, the price level is
affected by either changes in the money supply at date
t
or by output at date
t
.
Now we consider a model in which velocity exhibits the "hot potato" effect. That is, if
consumers expect higher inflation in the future, they will try to get rid of money and
thus velocity rises. In this case, velocity depends on expected inflation:
V
t
V
t
1
e
where
t
1
e
is expected inflation between today and tomorrow.
The simplest model of this process is called the
Cagan model of money demand
.
The model is given by:
m
t
−
p
t
−
p
t
1
e
−
p
t
,
or
m
t
−
p
t
−
t
1
e
Here, lower case letters are all the natural logs of the relevant variables
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 Spring '08
 Serra
 Inflation, price level, money demand

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