Question

A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(25000) + (1 -p)(5000). If the utility of 25,000 is 0 and of 5000 is 1, then the utility of 10,000 is

A. 5
B. 6
C. 4
D. 4

Answer 1

The utility of losing $10,000 is equivalent to the expected utility of a lottery, calculated as 0.6 based on the given probabilities and utilities of $25,000 and $5,000. However, the answer choices do not match the correct utility value

Step-by-step explanation:

The utility of an outcome in decision theory represents the individual's satisfaction or preference for that outcome. In this case, the decision maker has assigned a utility of 0 to the outcome of receiving $25,000 and a utility of 1 to the outcome of receiving $5,000. The utility of $10,000 can be found by using the concept of expected utility.

Let's calculate the expected utility for the lottery:

Expected utility = (p * utility of $25,000) + ((1 - p) * utility of $5,000)

where p is the probability of winning $25,000.

Substituting the given values,

Expected utility = (0.4 * 0) + ((1 - 0.4) * 1)

Expected utility = 0 + 0.6

Expected utility = 0.6

Therefore, the utility of $10,000 is 0.6.