SECTION C: ANALYTICAL REASONING AND DECISION MAKING

Read the following and choose the best alternative (Questions 86-89):

Decisions are often 'risky' in the sense that their outcomes are not known with certainty. Presented with a choice between a risky prospect that offers a 50 percent chance to win $200 (Otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. (Expected value is the sum of possible outcomes weighted by their probability of occurrence.) Preference for a sure outcome over a risky prospect of equal expected value is called risk averse; indeed, people tend to be risk averse when choosing between prospects with positive outcomes. The tendency towards risk aversion can be explained by the notion of diminishing sensitivity, first formalized by Daniel Bernoulli in 1738. Just as the impact of a candle is greater when it is brought into a dark room then into a room that is well lit so, suggested Bernoulli, the utility resulting from a small increase in wealth will be inversely proportional to the amount of wealth already in one's possession. It has since been assumed that people have a subjective utility function, and that preferences should be described using expected utility instead of expected value. According to expected utility, the worth of a gamble offering a 50 percent chance to win $200 (otherwise nothing) is 0.50*u($200), where u is the person's concave utility function. (A function is concave or convex if a line joining two points on the curve lies entirely below or above the curve, respectively). It follows from a concave function that the subjective value attached to a gain of $100 is more than 50 percent of the value attached to a gain of $200, which entails preference for the sure $100 gain and, hence, risk aversion.

Consider now a choice between losses. When asked to choose between a prospect that offers a 50 percent chance to lose $200 (otherwise nothing) and the alternative of losing $100 for sure, most people prefer to take an even chance at losing $200 or nothing over a sure $100 loss. This is because diminishing sensitivity applies to negative as well as to positive outcomes: the impact of an initial $100 loss is greater than that of the next $100. This results in a convex function for losses and a preference for risky prospects over sure outcomes of equal expected value, called risk seeking. With the exception of prospects that involve very small probabilities, risk aversion is generally observed in choices involving gains, whereas risk seeking tends to hold in choices involving losses.

Based on the above passage, analyse the decision situations faced by three persons: Babu, Babitha and Bablu.

86. Suppose instant and further utility of each unit of gain is same for Babu. Babu has decided to play as many times as possible, before he dies. He expected to live for another 50 years. A game does not last more than ten seconds. Babu is confused which theory to trust for making decision and seeks help of renowed decision making consultant: Roy Associates. what should be Roy Associates' advice to Babu?

A. Babu can decide on the basis of Expected Value hypothesis.

B. Babu should decide on the basis of Expected Utility hypothesis.

C. "Mr.Babu, I'm redundant".

D. A and B

E. A, B and C

Solution:

From the given games it is clear that the expected value is same in all options i.e. 0.1 ´ $1000 = 0.25 ´ $400 = 0.5 ´ $200 = 1 ´ $100

It is given that the instant and further utility of each unit of gain is same for Babu.

Let us assume that expected utility is 0.8 for Babu for each unit of gain.

\ The expected utility is also equal.

i.e. 0.1 ´ $1000 ´ 0.8 = 0.25 ´ $400 ´ 0.8 = 0.5 ´ $200 ´ 0.8 = 1 ´ $100 ´ 0.8

Hence, either theory is going to be the same. Choice (C)

87. Babitha played a game wherein she had three options with following probabilities: 0.4, 0.5 and 0.8. The gains from three outcomes are likely to be $100, $80 and $50. An expert has pointed out that Babitha is a risk taking person. According to expected utility hypotheis, which option is Babitha most likely to favour?

A. First

B. Second

C. Third

D. Babitha would be indifferent to all three actions.

E. None of the above.

Solution:

Since Babita is a risk taking person, the expected value function is convex. i.e. she prefers riskier prospect over sure or less risky prospect. Hence, she would most likely to favour the first option. Choice (A)

88. Continuing with previous question, suppose Babitha can only play one more game, which theory would help in arriving at better decision?

A. Expected Value.

B. Expected Utility.

C. Both theories will give same results.

D. None of the two.

E. Data is insufficient to answer the question.

Solution:

Since, Babita is risk seeking, she would go for higher gain with less probability, expected value theory does not apply here, because expected value is equal in all options. Since Babita is not going for sure gains, it is clear that she is going by utility function. Choice (B)

89. Bablu had four options with probability of 0.1, 0.25, 0.5 and 1. The gains associated with each options are: $1000, $400, $200 and $100 respectively. Bablu chose the first option. As per expected value hypothesis:

A. Bablu is risk taking.

B. Expected value function is concave.

C. Expected value function is convex.

D. It does not matter which option should Babu choose.

E. None of above.

Solution:

Bablu has chosen the option which gives highest gain but has a low probability. It means that he preferred a risky prospect over sure outcome, the fourth option. Hence, He is risk taking. Choice (A)