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Unformatted text preview: x ) r 1 ( x ) for all x , where r i ( x ) = u 00 i ( x )/ u i ( x ). The number r ( x ) = u 00 ( x )/ u ( x ) is called the coefFcient of absolute risk aversion of u at x . We will see that a higher coefFcient of absolute risk aversion means a more risk-averse decision maker. To see that (3) and (4) are equivalent, note the following chain of equivalences: DeFnition (3) (that is, u 1 u 1 2 is concave) is satisFed iff the function d / dt [ u 1 ( u 1 2 ( t )) ] is nonincreasing in t iff u 1 ( u 1 2 ( t ))/ u 2 ( u 1 2 ( t )) is nonincreasing in t iff (since ( 1 ) ( t ) = 1 / ( 1 ( t )) ) u 1 ( x )/ u 2 ( x ) is nonincreasing in x (since u 1 2 ( t ) is increasing in t ) iff...
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- Fall '10