Econ 387L: Macro II
Spring 2006, University of Texas
Instructor: Dean Corbae
Problem Set #7 Question I Due 3/10/06, II Due 3/21/06
I. Consider the following version of the Lucas asset pricing model. Preferences are
given by
U
(
c
t
) = ln(
c
t
)
.
Each household is endowed with project that generates dividends
y
t
∈
D
⊂
R
++
where
D
is a
fi
nite set. The dividends follow a markov process with
π
(
y
t
+1

y
t
) =
prob
(
y
t
+1
=
y
0

y
t
=
y
)
.
The government spends amount
g
t
=
ε
t
y
t
per capita
where
ε
t
∈
[0
,
1)
which does not enter preferences. Government spending follows a markov
process
φ
(
ε
t
+1
=
ε
0

ε
t
=
ε
)
.
The only assets traded are shares (or titles) to trees.
1. Assume that all goverment expenditures are
fi
nanced by a lump sum tax
τ
t
per
household which is independent of the shares owned by the household. Calculate the
equilibrium share price function.
2. Assume that there is an income tax on dividends. Speci
fi
cally dividends are taxed at
the rate
τ
t
y
t
so that
τ
t
units of the time
t
good are collected on dividends. Assume a balanced
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 Spring '07
 CORBAE
 Macroeconomics, per capita, equilibrium share price, share price function, T JT

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