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

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

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Definitions:

Hypotheticals

Hypotheticals refer to situations or scenarios that are imagined or speculated about, often used in reasoning or in discussing possible outcomes.

Principle

A basic principle or statement that forms the basis for a belief system or for logical thinking.

Rational

The quality of being based on or in accordance with reason or logic, often related to the ability to think, understand, and form judgments by a process of logic.

Fully Rational Being

An entity capable of comprehensive reasoning, capable of making logically consistent decisions based on full information.