Question

(a) State the expected utility theorem.

(b)State the four axioms from which it can be derived from expecetd utility theory.

Answer 1

a) The expected utility theorem states that a function, U (w) can be constructed representing an investor’s utility of wealth, w, at some future date. Decisions are made on the basis of maximising the expected value of utility under the investor’s particular beliefs about the probability of different outcomes.
(b) The expected utility theorem can be derived formally from the following four axioms.
(1) Comparability. An investor can state a preference between all available certain outcomes.
(2) Transitivity. If A is preferred to B and B is preferred to C, then A is preferred to C.
(3) Independence.If an investor is indifferent between two certain outcomes, A and B, then he is also indifferent between the following two gambles;
(a) A with probability p and C with probability (1 - p); and
(b) B with probability p and C with probability (1 - p).
(4) Certainty equivalence.Suppose that A is preferred to B and B is preferred to C. Then there is a unique probability, p, such that the investor is indifferent between B and a gamble giving A with probability p and C with probability (1 - p). B is known as the certainty equivalent of the above gamble.

The expected utility theorem states that a function, U (w) can be constructed
representing an investor’s utility of wealth, w, at some future date.