MATH451-Unit 4 Intellipath - Utility Theory

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MATH451 – Unit 4 Intellipath Utility Theory One can consider the decision making based on monetary values, but it would be strictly money. However, a person might be willing to take a risk of performing some function knowing very well that the outcomes may not be in his or her favor. In this section, you would look at these cases and define the attitude of a person toward risk as a utility theory. You would consider the issues involved in determination of utility function and decide if the person is a risk avoider, risk indifferent, or risk seeker. In other applications, the decisions are made based on the monetary values strictly. However, most of the times people are willing to take risks knowing very well that the outcome of the risks they are taking are not in his or her favor. People spend money on gambling or lottery tickets knowing very well that the chance of winning is almost 0. Example Suppose Mary is trying to start a business that if it turned out to be a success, she gets a payoff of $40,000. However, if she fails, she would lose $20,000 in the investment. Assume the probability of success to be 0.50 and the probability of failure to be 0.50. You need to determine her utility’s value to decide if she should get into the business. You assign a value of 1 for the utility value of success for the best payoff and 0 for the utility value of failure for the worst payoff. Suppose she is approached by another competitor who is performing the same types of business in the neighborhood, and he wants to discourage her to enter in his territories by offering her $6,000. The question is whether or not she should ignore the offer and goes on to the business or takes the money and forgets the idea. Expected Monetary Value The expected monetary value (EMV) of this business is: $40,000 * 0.50 − 20,000 * 0.50 = $10,000. If she accepts the money, $6,000 would be the EMV value and not the calculated $10,000.

U($6,000) = U($40,000) * 0.5 + U(−$20,000) * 0.5 = 1 * 0.5 + 0 * 0.5 = 0.5. Risk Avoider Because she accepted lower than the EMV, she is considered to be a risk avoider. Calculate the Risk Premium Indeed, you calculate the risk premium as the difference between the monetary amounts that a decision maker is willing to give up to avoid the risk associated with a gamble. In the case of Mary, the risk premium is: (EMV of gamble) − (Certainty equivalent) =$10,000 − $6,000 = $4,000. Risk Avoider If the value of risk premium is positive, the person is risk avoider . Risk Neutral If the risk premium is 0, the person is considered to be risk indifferent or risk neutral person . Risk Seeker However, if the risk premium is negative, the person is risk seeker. The utility value changes from one person to another for the very same situations depending how important is to take or avoid the risk to them. Indeed, a person’s utility risk can also vary as the EMV goes higher. People do not mind betting on few dollars for a game or other types of gambling while the same people will not gamble on high price activities. Using a Treeplan A treeplan is used to make a decision. You can replace the monetary values by the utility values and the results may or may not turn out to be the same. Suppose Mary has the utility values of U(−20,000) = 0, U($0) = 0.2, and U($40,000) = 1.0. She wishes to get into that business by rejecting the offer. You can use the treeplan by first performing the calculation based on EMV and then replacing EMV by utility values.

Figure 1 shows the treeplan suggesting she goes to the business purely based on the monetary values. Figure 1: Treeplan Used to Calculate EMV for Mary’s Decision-Making Problem Figure 2 shows the same treeplan with the exception that utility values are replacing the monetary values. In this case both tree diagrams suggest that she needs to go on with the business. Figure 2: Treeplan Used to Calculate Utility Value for Mary’s Decision- Making Problem

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