Question 1:

i) Suppose an investor has initial wealth

W

0

and has the opportunity for an investment such

that the end-of-period wealth is

W

=

W

0

+

H

. If the investor uses exponential utiliy, show that

W

C

W

0

does not depend on

W

0

.

ii) Suppose an investor has initial wealth

W

0

and has the opportunity for an investment such that the

end-of-period wealth is

W

=

HW

0

. If the investor uses power utility show that

W

C

W

0

does not depend on

W

0

.

Question 2:

Let

W

, a random variable, represent the amount of future wealth held by an investor, and

let

u

1

and

u

2

be two different utility functions. The certainty equivalent of

W

under

u

1

is denoted

W

(1)

C

,

and the certainty equivalent of

W

under

u

2

is denoted

W

(2)

C

. Using the definition of certainty equivalent

and the definition of equivalent utility functions, show that if

u

1

u

2

then

W

(1)

C

=

W

(2)

C

. You may assume

u

1

and

u

2

are strictly increasing.