Midterm Exam1
Viktor Tsyrennikov
Graduate Macroeconomics
September 23, 2011
The exam is designed to be finished in 75 minutes.
There are 2 problems, worth 40 and 60 points respectively.
Read carefully the
whole problem
before answering.
Show your work – guessed answers will not be accepted.
Name:
1
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Question 1.
Consumption tax
Consider a saving model with endogenous labor supply and
˜
u
(
c
t
, l
t
) =
log
parenleftBigg
c
t

l
1+1
/η
t
1 + 1
/η
parenrightBigg
,
η >
1
.
Government taxes consumption purchases in period
t
at rate
τ
t
. Wage rate
is constant and equals
w
= 1. Agent starts with
a
0
= 0.
a)
Derive the consumption Euler equation.
b)
Compute per period tax revenue as a function of tax rate
τ
in the
case with
βR
t
+1
= 1
,
∀
t
and
τ
t
=
τ,
∀
t
. How does
η
affects the tax revenue
schedule? Interpret your result.
c)
Suppose the interest rate increases temporarily and the government
increases taxes to pay high interest on its debt:
{
R
t
+1
}
∞
0
=
{
β

1
, β

1
+
e, β

1
, β

1
, ...
}
,
{
τ
t
}
∞
0
=
{
0
, τ,
0
,
0
, ...
}
, τ <
1
/η
.
Characterize the path of
c
t
, l
t
.
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 Spring '11
 ViktorTsyrennikov
 Economics, Macroeconomics, Supply And Demand, producer, high cost producers

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