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Prof. Chow YingFoon, Ph.D.
Room 201A, Leung Kau Kui Building
Department of Finance
The Chinese University of Hong Kong
2009—2010 First Term
Phone: (+852) 2609 7638
Fax: (+852) 2603 6586
Email: yfchow@cuhk.edu.hk
FIN 4160
Intermediate Financial Theory
Suggested Outline of Answers to Assignment 1
1.
a. No capital market, so Robinson Crusoe’s problem is
max
U
(
Y
0
,Y
1
)
s.t. F
(
Y
0
,Y
1
)=0
.
The
f
rstorder conditions imply
Y
∗
0
≈
66
.
8699
and
Y
∗
1
≈
36
.
1138
.S
in
c
eh
eb
eg
an
with 100 dollars, we see that he has invested
100
−
66
.
8699 = 33
.
1301
dollars in real
assets, which provides him with an average rate of return of approximately 8.5%.
Note that Robinson Crusoe’s savings decision is tied directly to his investment
decision – he consumes 66.8699 dollars and saves 33.1301 dollars. The decision
abouthowmuchtoconsumeandsavewasmadeatthesametimeastheinvestment
decision. The reason for this is simple: There are no capital markets in which
Robinson Crusoe can borrow and lend, thus all the monies needed to
f
nance his
investment must come from his own savings.
b. By the Fisher Separation Theorem, Robinson Crusoe’s optimal consumption bun
dles
(
C
0
,C
1
)
arefoundonthel
inew
iths
lope
−
1
.
075
that is tangent to the curve
F
(
Y
0
,Y
1
)=0
.W
es
o
l
v
e
dY
1
/dY
0
=
−
(1 +
r
)
for
(
Y
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 Fall '09
 Prof.Chow
 Finance, Robinson Crusoe, Robinson Crusoe

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