Reference no: EM133393262

Case: Pretending for real that you are given two choices: (1) a gamble with a bowl of 100 red and white balls such that if a randomly selected ball from the bowl is red, then you win $1 million (Outcome A); otherwise, you get nothing (Outcome C); (2) a large amount of money between $0 and $1 million for sure (Outcome B).

Assume that you are happier with more money than less money, and artificially assign your utility or degree of happiness of getting Outcome A, $1 million, to be 100; and Outcome C, $0, to be 0. If the bowl contains all 100 red balls, clearly you will choose the gamble. On the other hand, if the bowl contains all 100 white balls, you will definitely choose B because you will get more money than nothing and thus be happier.

Now, if the fraction of red balls in the bowl gradually decreases from 100 to 0, you will feel that Outcome B becomes more and more attractive. Let p* be the fraction for which if the actual fraction of red balls in the bowl, p > p*, you will still prefer the gamble, but if p<p*, you will prefer the sure money. In this case, if p=p*, you will feel that your utilities or degrees of happiness of these two choices are about the same. In this case, by Utility Theory, the utility of the sure money, U(B at p*) = p*U(A)+(1-p*)U(C) = 100p*.

6a. If the sure money is $500,000, what will be your p* and U($500,000), and is the utility more or less than 50?

6b. If the sure money is $200,000, what will be your p* and U($200,000), and is the utility more or less than 20?

6c. Connect your utilities for $0, $200,000, $500,000, and $1 million in a Utility and Amount of Money diagram, which is the outline of your utility curve for money. If it lies above a straight line connecting 0 utility at $0 and 100 utility at $1 million, then you are risk-averse; if it lies exactly on the straight line, then you are risk neutral; finally, if it lies below the straight line, then you are risk-preferring. Which one are you?

7. Christopher's utility function for money is the cubic root of the amount of money. He is interested in buying a collector's item but is not sure about how much he should pay. After much contemplation, he feels that he would be equally happy with the collector's item and a gamble in which he has a 3% chance of winning $1 million and a 97% chance of getting nothing. Use this information and his utility function for money to determine the maximum monetary value Chris should pay for the collector's item.