Question

Suppose, as usual, Elmos utility function over gambles satisfies the expected utility property. Consider two gambles g and h such that E[g] > E[h]. (a) Suppose Elmo is risk-averse. Will Elmo necessarily prefer g to h? Explain. (b) What if Elmo is risk-neutral? Explain. (c) What if Elmo is risk-loving? Explain.

Answer 1

(a) When Elmo is risk-averse, then he would prefer a guaranteed lower return than to an expected higher return as it involves zero risks (almost). Hence, if Elmo is risk-averse and gets a sure lower return, then he would choose the lower returns than higher returns with substantial risk.

(b) If Elmo is risk-neutral, then he would be indifferent between the two risk situations. He would be inclined more towards the one which gives higher returns irrespective of the risk involved.

(c) If Elmo is risk-loving, then he would prefer high-risk situations. Moreover, we relate high risks with high expected returns. Hence, risk-lover will prefer a high risk higher return outcome to a lower risk low expected return outcome.