Homework 3
Econ 4721002: Money and Banking, Fall 2011
Due Tuesday, November 22, beginning of class
Problem 1: Risks
Consider an individual consumer who lives for two periods, endowed with
y
= 40 goods when
young and nothing when old.
The consumer wants to save half of the endowment (thus,
20 goods).
Saving can be done in either a
safe
asset (asset
a
) or a
risky
asset (asset
b
). The real
rate of return on asset
b
is uncertain, and depends upon which event occurs in the second period,
as summarized in the following table:
Event
H
Event
L
probability of occuring
π
H
= 0
.
5
π
L
= 0
.
5
return on asset
a
r
H
= 1
.
25
r
L
= 1
.
25
return on asset
b
r
H
= 2
r
L
= 0
.
5
The consumer cares about
expected utility
from consumption, defined as
ln (
c
1
) +
β
[
π
H
ln (
c
2
,H
) +
π
L
ln (
c
2
,L
)]
where
β
= 0
.
5 and
c
2
,H
and
c
2
,L
are consumption in Event
H
and consumption in Event
L
, respec
tively.
(a)
Investment plan 1: Invest all 20 goods in asset
a
. Calculate the expected rate of return on this
investment plan and the expected utility for the consumer using the formula above.
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 Fall '11
 Triece
 Economics, Fractionalreserve banking, bank deposits, investment plan

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