ECO 320LHW2
Due March 23, 2010 Classtime
1. Consider the consumptionsaving problem of a consumer. His current income is
y
and his future income is
y
0
.
The real interest rate is
r
. Consumer’s utility function is ln(
C
) + ln(
C
0
)
.
The government taxes capital income
to raise tax revenues. There are no other taxes. The capital income tax is
t
k
(i.e. Consumer pays
t
k
units of
consumption good for each unit he earns from savings).
(a) Write down the ﬁrst period and second period budget constraint for the consumer.
(b) Write down the lifetime budget constraint.
(c) What is the relative price of future consumption in terms of current consumption? How does it depend
capital income tax
t
k
?
(d) Write down the optimality condition.
(e) Using the optimality condition and the lifetime budget constraint, solve the optimal
C
,
C
0
, and savings
s
as functions of
y,y
0
,r,
and
t
k
.
(f) Now assume that
y
= 100 and
y
0
= 50
. r
= 20% and
t
k
= 50%
.
Calculate
C
,
C
0
,
s,
and government’s tax
revenue in the future period.
2. Consider the consumptionsaving problem of a consumer. His current income is
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 Fall '08
 KURUSCU
 Macroeconomics, Utility, tax revenues, lifetime budget constraint

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