Econ 387L: Macro II
Spring 2008, University of Texas
Instructor: Dean Corbae
Problem Set #11 Due 4/24/08
1. We will consider a cashinadvance environment to study “Unpleasant Monetarist
Arithmetic". The technology is given by
y
t
=
n
t
where
n
t
∈
[0
,
1]
is fraction of
hours worked. Preferences are given by
P
∞
t
=0
β
t
{
U
(
c
t
)
−
γn
t
}
where
U
(
c
t
) =
c
1
−
θ
t
1
−
θ
.
Households can hold money and/or government bonds. Let
M
t
+1
and
B
t
+1
be money
(dollars) and nominal bonds (claims to dollars next period) held by households between
t
and
t
+ 1
. The government expands or contracts the money supply at a constant rate
μ
according to
M
t
+1
= (1 +
μ
)
M
t
.
Let
p
t
be the dollar price of consumption goods and
q
t
be the consumption good price of a bond (so that
p
t
q
t
is the dollar price of a bond). Let
τ
t
be real lump sum taxes/transfers the government levies to help pay for its constant real
expenditure
g
on goods. Assume that only money
M
t
accumulated last period can be used
to purchase consumption goods
c
t
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 Spring '07
 CORBAE
 Inflation, nominal terms, unpleasant monetarist arithmetic

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