1. An expected utility maximizing individual has utility of end-of-period wealth given by wl-r –1 , if y #1 u(W)={ 1-y In(W), if y = 1 (1) Show that this individual has constant relative risk aversion and decreasing absolute risk aversion. (2) Consider the special case where y = 2. Suppose that this individual is endowed with an initial wealth W, but his end-of-period wealth is subject to a random income shock given as follows: S $y, with probability p s0, with probability 1-p where 0

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1. An expected utility maximizing individual has utility of end-of-period wealth given by
wl-Y – 1
-, if y #1
1-7
u(W)=
In(W), if y =1
(1) Show that this individual has constant relative risk aversion and decreasing absolute risk
aversion.
(2) Consider the special case where y= 2. Suppose that this individual is endowed with an initial
wealth W, but his end-of-period wealth is subject to a random income shock given as follows:
$y, with probability p
|$0, with probability 1-p
where 0<p<1.
He can purchase an insurance at a cost of $c to remove the risk of receiving no income. At what
level of initial wealth will he be indifferent between taking on the risk of getting no income and
buying the insurance that removes this risk?
Transcribed Image Text:1. An expected utility maximizing individual has utility of end-of-period wealth given by wl-Y – 1 -, if y #1 1-7 u(W)= In(W), if y =1 (1) Show that this individual has constant relative risk aversion and decreasing absolute risk aversion. (2) Consider the special case where y= 2. Suppose that this individual is endowed with an initial wealth W, but his end-of-period wealth is subject to a random income shock given as follows: $y, with probability p |$0, with probability 1-p where 0<p<1. He can purchase an insurance at a cost of $c to remove the risk of receiving no income. At what level of initial wealth will he be indifferent between taking on the risk of getting no income and buying the insurance that removes this risk?
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