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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 .

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.

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