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

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: $u ( c ) = \frac { c ^ { 1 - y } } { ( 1 - y ) }$
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.