I.A.1.4.2 Introducing the Utility Function

Question 1

Axiom of non-satiation

Answer 1

The utility function, u(x), should be non-decreaseing in as much as more cash is preferred to less

Question 2

Utility Function - u(x)

Answer 2

• x is a cash amount expressing wealth and u(x) its utility to the owner of the wealth
• Should be a continuous, non-decreasing function of x
• Should be continuous in as much as cas itself can be considered as continuous and a small increase in cash sould produce a small increase in utility
• Free to choose the origin and unit of scale without affecting preferences

Question 3

Utility Function Note

Answer 3

Common practice to choose the current level of wealth as the origin of the cash scale to have a zero utility for the current level of wealth

This is so becasue future wealth is valued against the current level of wealth rather than in absolute terms

Since both the level of wealth and risk attiude may change over time it is prudent to check the utility function being used regularly to see if it is representative of the risk preferences