Practice Problems
Consumption Over Time
University of California, Los Angeles
1. Courtney has an income of
$50
today and
$20
tomorrow.
She has the
following production technology:
Q
2
= 20
I
1
2
1
, where
I
1
is the investment
today and
Q
2
is the gross return of the investment. The interest rate is
100%
.
(a) Suppose that Courtney wants to consume
$45
tomorrow. How much
should she consume and invest today?
(b) Find the net present value of Courtney±s maximum attainable wealth.
(c) Her utility function is
U
(
C
1
; C
2
) =
C
1
2
1
C
1
2
2
. Find her optimal invest
ment and consumption.
2. Sarah has
$100
today. She has the following production technology:
Q
2
=
110 ln (
I
1
)
, where
I
1
is the investment today and
Q
2
is the gross return of
the investment a year from now. Sarah can borrow at a rate of
10%
. Her
utility function between consumption today
C
1
and consumption a year
from now
C
2
is
U
(
C
1
; C
2
) =
C
1
C
2
.
(a) Find Sarah±s optimal investment choice.
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 Summer '08
 cunningham
 Courtney, C1 C2, C2 C1 C2

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