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

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the expected utility theory. We know that the decision maker values a certain gain of 5,000 with a utility of 1. Therefore, we can set up the following equation:

U(5,000) = 1

We also know that the decision maker cannot choose between a certain loss of 10,000 and the lottery p(-25,000) + (1-p)(5,000) when p = 0.4. This means that the decision maker is indifferent between these two options:

U(-10,000) = EU(p(-25,000) + (1-p)(5,000))

We can solve for U(-10,000) as follows:

U(-10,000) = p*U(-25,000) + (1-p)*U(5,000)
U(-10,000) = 0.4*0 + 0.6*1
U(-10,000) = 0.6

Therefore, the utility of a loss of 10,000 is 0.6. Now we need to determine the best choice based on expected utility.

The expected utility of the lottery is:

EU(p(-25,000) + (1-p)(5,000)) = p*U(-25,000) + (1-p)*U(5,000)

When p = 0.4, this becomes:

EU(0.4*(-25,000) + 0.6*(5,000)) = 0.4*0 + 0.6*1
EU(-7,000) = 0.6

The expected utility of the certain loss is:

EU(-10,000) = U(-10,000) = 0.6

Since EU(-7,000) < EU(-10,000), the decision maker should choose the certain loss of 10,000. Therefore, the best choice is B.

A Decision Maker Has Chosen