Explain the denotation a utility function

Question

Explain the denotation a utility function and how it can vary between investors?

Answer 1

If we denote a utility function by U (W) here W is the ‘wealth,’ subsequently one would expect utility functions to have specific commonsense properties. In the given a prime (‘) denotes differentiation respecting W.

• The function U (W) can vary between investors each will have a various attitude to risk for illustration.

• U’ (W) ≥ 0: more is preferred to less. When this is a strict inequality then satiation is not possible, the investor will all the time prefer more than he has. Such slope measures the marginal improvement in utility along with changes in wealth.

• Usually U’’ (W) < 0: there utility function is strictly concave.

Since it is the rate of change of the marginal ‘happiness,’ this gets harder and harder to raise happiness as wealth increases. An investor along with a concave utility function is said to be risk averse. That property is frequently referred to as the law of diminishing returns.