Economics 202A Lecture Outline, November 29, 2007
(Version 2.0)
Maurice Obstfeld
Issues in Monetary Policy
In this lecture I survey several issues important in the design and imple
mentation of monetary policy in practice. Some of these are related to the
government’s revenue needs, as discussed in the last lecture, but we also go
beyond that question to consider other problems.
Money and welfare: Milton Friedman’s \optimum quantity of
money"
A useful dynamic framework for thinking about monetary policy in a
world of
flexible
prices was provided by Miguel Sidrauski and William Brock.
1
The representative consumer maximizes
Z
1
t
u
[
c
(
s
)
; m
(
s
)] e
(
s
t
)
d
s;
where
c
is consumption and
m
M=P
the stock of real balances held. Above,
interest rate. We are motivating a demand for money by assuming that the
individual derives a ±ow of utility from his/her holdings of real balances
 implicitly, these help the person economize on transaction costs, provide
liquidity, etc.
Total real ²nancial assets
a
are the sum of real money
m
and real bonds
b
, which pay a real rate of interest
r
(
t
) at time
t
:
a
=
m
+
b:
1
See Miguel Sidrauski, \Rational Choice and Patterns of growth in a Monetary Econ
omy,"
American Economic Review
57 (May 1967): 53444; and William A. Brock, \Money
and Growth: The Case of Long Run perfect Foresight,"
International Economic Review
15 (October 1974): 75077.
1
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(
t
) be a transfer that the individual receives from the government each
instant.
2
Then if we assume an endowment economy with output
y
(
t
), the
_
a
=
y
+
rb
+
c
±m
=
y
+
ra
+
c
(
r
+
±
)
m:
Since this last constraint incorporates the portfolio constraint that
a
=
m
+
b
, we need no longer worry about it. Under an assumption that we have
perfect foresight, so that actual
±
=
_
P=P
equals expected in±ation, the
Fisher equation tells us that the nominal interest rate is
i
=
r
+
±;
so the last constraint becomes
_
a
=
y
+
ra
+
c
im:
We can analyze the individual optimum using the Maximum Principle.
If
²
denotes the costate variable, the (currentvalue) Hamiltonian is
H
=
u
(
c; m
) +
²
(
y
+
ra
+
im
)
:
In the maximization problem starting at time
t
,
a
(
t
) is predetermined at
the level of the individual, who chooses optimal paths for
c
and
m
. The
Pontryagin necessary conditions are
@H
@c
=
u
c
²
= 0
;
@H
@m
=
u
m
²i
= 0
;
_
²
³²
=
@H
@a
=
²r:
2
Beware: in the last lecture the same symbol
denoted taxes, or negative transfers, so
all signs preceding
are reversed in this lecture compared to the last.
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 Fall '07
 AKERLOF
 Inflation, Interest Rates, Monetary Policy, Interest Rate, Real Balances

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