Certainty equivalent as function of risk-aversion parameter

Question

Explain Certainty equivalent as a function of the risk-aversion parameter.

Answer 1

When the wealth is random, and all outcomes can be assigned a probability, one can ask what amount of certain wealth has the same utility as the expected utility of the unknown outcomes. Simply solve

U(Wc) = E[U(W)].

The quantity of wealth Wc that solves this equation is called the certainty equivalent wealth. One is therefore indifferent between the average of the utilities of the random outcomes and the guaranteed amount Wc. As an example, consider the

Figure: Certainty equivalent as a function of the risk-aversion parameter

Figure demonstrates a plot of the certainty equivalent for example like a function of the risk-aversion parameter η. See how it decreases the greater the risk aversion.