In class we have learned that, given an indirect utility function u(w), there are two relevant measures u" (w) of risk aversion, namely absolute risk aversion, A(w) = and relative risk aversion, R(w) u' (w)' A(w)w. The following questions relate to risk aversion in general, and relationships around these two measures. 1. Utility function u(w) is risk averse if it is concave. Show mathematically that the set of all risk averse functions is a convex set. 2. It is often argued that absolute risk aversion should satisfy DARA (i.e. absolute risk aversion is decreasing in w). Show that, (i) a neccesary but not sufficient condition for DARA is that v(w) = -u'(w) is concave, and (ii) that a necessary and sufficient condition for DARA is that v(w) = -u' (w) is more risk averse than u(w). TC 1 = LORDA 1

In class we have learned that, given an indirect utility function u(w), there are two relevant measures u" (w) of risk aversion, namely absolute risk aversion, A(w) = and relative risk aversion, R(w) u' (w)' A(w)w. The following questions relate to risk aversion in general, and relationships around these two measures. 1. Utility function u(w) is risk averse if it is concave. Show mathematically that the set of all risk averse functions is a convex set. 2. It is often argued that absolute risk aversion should satisfy DARA (i.e. absolute risk aversion is decreasing in w). Show that, (i) a neccesary but not sufficient condition for DARA is that v(w) = -u'(w) is concave, and (ii) that a necessary and sufficient condition for DARA is that v(w) = -u' (w) is more risk averse than u(w). TC 1 = LORDA 1

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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