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A Widely Used Utility Function in the Economics Literature Is u(c)=c1y(1y)u ( c ) = \frac { c ^ { 1 - y } } { ( 1 - y ) }

question 27

Essay

A widely used utility function in the economics literature is the constant rate of risk aversion utility function, of which log utility is a special case. It is given by: u(c)=c1y(1y)u ( c ) = \frac { c ^ { 1 - y } } { ( 1 - y ) }
With this utility function, the marginal utility of consumption is c- γ\gamma . What is the Euler equation for this utility function? Show that if y=1y = 1
, the Euler equation is the same as if we used log utility.

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