# Expected Utility, Relative Risk Aversion

Not what you're looking for?

An expected utility maximizing individual has utility of eno-of-period wealth given by

u(W)= W^(1-y)-1, if y is not equal to 1

ln(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, Wo but his end of period wealth is subject to random income shock given as follows

$y, with probably p

$0, with probability 1-p

where 0<p<1

He can purchase 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 the risk?

##### Purchase this Solution

##### Solution Summary

Expected Utility and Relative Risk Aversion are assessed.

##### Solution Preview

See the attached file. The symbols and text here may not print correctly. I have tried to be as simple as possible and have written all the steps so that it is easier for you to understand the solution. Thanks

An expected utility maximizing individual has utility of end-of-period wealth given by

u(W)= W^(1-y)-1, if y is not equal to 1

ln(W), if y=1

1. Show that this individual has constant relative risk aversion and decreasing absolute risk aversion.

u'(W)=(1-y)*W^(1-y-1)= (1-y)*W^(-y) if y is not equal to 1

=W^-1 if y=1

u"(W)=(1-y)*(-y)*W^(-y-1) if y is not equal to 1

=-W^-2 if y=1

Coefficient of Relative Risk Aversion = -W*u"(W)/u'(W)

When y is not equal to 1 we ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

##### Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.

##### Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.

##### Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.

##### Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.