This preview shows pages 1–2. Sign up to view the full content.
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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Summer '08
 cunningham

Click to edit the document details