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: $u ( c ) = \frac { c ^ { 1 - y } } { ( 1 - y ) }$
With this utility function, the marginal utility of consumption is c^{- $\gamma$}. What is the Euler equation for this utility function? Show that if $y = 1$
, the Euler equation is the same as if we used log utility.

Question

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 ) = \frac { c ^ { 1 - y } } { ( 1 - y ) }

With this utility function, the marginal utility of consumption is c^{- $\gamma$}. What is the Euler equation for this utility function? Show that if

y = 1

, the Euler equation is the same as if we used log utility.

Quizplus · Accepted Answer

The Answer of 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: $u ( c ) = \frac { c ^ { 1 - y } } { ( 1 - y ) }$ With this utility function, the marginal utility of consumption is c^-$\gamma$. What is the Euler equation for this utility function? Show that if $y = 1$ , the Euler equation is the same as if we used log utility.

A Widely Used Utility Function in the Economics Literature Is u(c)=c1−y(1−y)u ( c ) = \frac { c ^ { 1 - y } } { ( 1 - y ) }u(c)=(1−y)c1−y​

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