Econ 110 TA sections
January 14, 2009
1
Problem 1
Suppose the household in the twoperiod model has the utility function
u
(
c
1
; c
2
; l
1
; l
2
) =
v
(
c
1
) +
1
1 +
°
v
(
c
2
) +
(
l
1
; l
2
)
where
v
(
c
) =
c
1
°
°
°
1
1
°
±
and
(
l
1
; l
2
)
is some unspeci°ed function of
l
1
and
l
2
. The constants
°
and
±
are both assumed to be positive.
(a) What is the household±s marginal rate of substitution between
c
1
and
c
2
?
(b) Assuming that the interest rate,
R
, is equal to
°
, how will
c
1
compare
to
c
2
? What is the growth rate of consumption between periods?
(c) If the interest rate rises to some
R
0
> R
what happens to the growth
rate of consumption? How does your answer depend on the value of
±
?
2
Problem 2
It is quite common in macroeconomics to assume that households are impatient
...
that other things equal, they prefer to consume sooner rather than later.
Suppose the household±s utility function is
u
(
c
1
; c
2
; l
1
; l
2
) = ln (
c
1
) +
²
ln (
T
°
l
1
) +
1
1 +
°
[ln (
c
2
) +
²
ln (
T
°
l
2
)]
where
c
1
+
c
2
1 +
r
=
w
1
l
1
+
w
2
l
2
1 +
r
In this example we assume that
° >
0
.
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 Spring '08
 SchmittGrohe
 Economics, Macroeconomics, Utility, c2 w2 l2

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