"Case 8.

Derive Your Own Utility Function" of 01 Note.

Note 1. Expected Utility Theory

People often face decision making under uncertainty. Popular method to understand

this behavior is the utility function and the expected utility theory. Suppose you face the

following three gambles with a combination of income and uncertainty. Assume you are

Individual 1 with Figure 1 utility function. Examine your mean value (MV) of each gamble

based on probability and income you can earn (US$).

First, you attempt to maximize the average income (MV) based on equation (1)

MV = P1 X1 + P2 X2 (1)

Second, you attempt to maximize utility associated with income you can earn. Under

certain conditions, your expected utility (EU) is calculated as the following equation:

EU = P1 U(X1) + P2 U(X2) (2)

Based on expected utility, you will choose gamble 2, 1, and 3 in this order because the

corresponding expected utility is higher in this order.

Case 8. Derive Your Own Utility Function

Next we discuss how you derive your own utility function. We will introduce the notion of

"Certainty Equivalent (C.E.) of income." Assume you ask yourself what amount of income is

required to give up the gamble 1. For example, you answer that it is $2,000 which is the exact

amount to give up the gamble 1. Then this is certainty equivalent income of the gamble 1. Exactly

with this amount of money, you can give up the gamble 1 and the utility associated with gamble 1 is

same for the certainty equivalent income for the gamble 1. Certain income of $2,000 has utility of

0.50, $5,500 is 0.67, $-4,000 is 0.20. This is a utility function of an individual 1. Certainty equivalent

income depends on people and various conditions. You should ask yourself repeatedly with the

various gambles. With this simulation, you can draw your own utility function.