MCom I Semester Managerial Economics Theory Consumer Choice Under Risk Study Material Notes

MCom I Semester Managerial Economics Theory Consumer Choice Under Risk Study Material Notes : The problem ofThor of Consumer Choice Under RIsk The Bernoulli Hypothesis managerial Economics One of the Most Important Topic for MCom Students So Gurujionlinestudy is Present a Topic-wise Nots study Material for Mcom I Semester Students :

MCom I Semester Business Environment Collaboration Light Recent Changes Study Material Notes

THEORY OF CONSUMER CHOICE UNDER RISK

THE PROBLEM OF THEORY OF CONSUMER CHOICE UNDER RISK

The cardinal approach of the traditional utility analysis is concerned with consumer behaviour among riskless choices. The ordinal approach of the mordern utility analysis is the outcome of the failure of the indifference curve technique to explain consumer behaviour among risky or uncertain choices. In reality, many goods and services involve risk or uncertainty such as investment in shares of stock, insurance and gambling. It was Neumann and Margenstern who is their book Theory of Games and Economic Behaviour studied the behaviour of an individual in risky situations. The solution to the problem of risky situation was provided by Daniel Bernoulli who tried to solve St. Petersburg Paradox.

THE BERNOULLI HYPOTHESIS

The neo-classical theory assumes that the consumer is a rational human being who does not indulge in gambling or even in fair bet with 50-50 odds. Daniel Bernoulli, a swiss mathematician, found that Russians were unwilling to make bets even at better than 50-50 odds knowing fully that their mathematical expectations of winning money in a particular kind of gamble were greater the more money they bet. This contradiction is known as St. Petersburg Paradox.

Bernoulli resolved the St. Petersburg Paradox by suggesting that the reason why people would not be prepared to pay their entire income to play such a game is that the marginal utility of money diminishes as income rises.

A person who stakes Rs. 100 at even odds of winning or losing Rs. 10 will not play the game if he is a rational being. For if he wins, he will have Rs. 110, which are equal to the gain of utility from Rs. 10 won added to Rs. 100. If he losses, he will have Rs. 90 which are equal to the loss of utility from Rs. 10 lost subtracted from Rs. 100. Though the monetary gain or loss is equal, the loss in utility is greater than the gain in utility in this game. Thus, in Bernoulli’s view, rational decisions in the case of risky choices would be made on the basis of expectations of total utility rather than the mathematical expectations of monetary value. This is illustrated in Figure 1.

Where TU is the total utility curve which becomes less and less steep at higher levels of income, indicating diminishing marginal utility of income. Suppose the person is at the income level OY (Rs. 100 in our example) which gives him utility OU. He is considering whether or not to accept a fair bet with a 50-50 probability of either increasing his income of OY (Rs. 110) or reducing it to OY, (Rs. 90) by an equal amount. He will consider its effect on his utility.

Assumptions of the N-M- Utility Index

The N-M utility index is based on the following assumptions:

1 The individual behaves in risky situations in order to maximise expected utility

2. His choices are transitive: if he prefer A prize (win) to B prize and B to C, then he prefers A to C.

3.There is probability* P which lies between 0 and 1 (0<P<1) such that the individual is indifferent between prize A which is certain and the lottery tickets offering prizes C and B with probability P and 1-P respectively.

4. If two lottery tickets offer the same prizes, the individual prefers the lottery ticket with the higher probability of winning. * Probability is a mathematical term which can be understood as the possibility of an event to happen, out of given events. The probability of tossing a coin is 1/2, for the coin has two sides. The probability of a “four” in a six-sided dice is 1/6 for the possibility of getting a “four is one in six turn”. In the above formula if the probability of winning prize Cin a lottery is 50-50, i.e., 1/2, then the chance of losing B is (1-1/2). If it 40-60 of C, it is 40/100 2.5 and B (1-2/5) = 3/5.

5.. The individual can completely order probability combinations of uncertain choices.

6. Uncertainty or risk does not possess utility or disutility of its own.

The N-M Utility Index

Neumann and Morgenstern have suggested the following method of measuring the utility index.

“Consider three events, C, A, B for which the order of individual’s preferences is the one stated. Let a be real number between 0 and 1, such that A is exactly eqully desirable with the combined event consisting of a change of probability 1-a for B and the remaining chance of probability a for C. Then we suggest the use of a as a numerical estimate for the ratio of the preference of A over B to that of Cover B.”

Their formula becomes A =B (1-a+aC). Substituting P for a probability, we have

A =B (1-P)+ P.C. Given the assumptions, it is possible to derive a cardinal utility index based on the above formula. Suppose there are three events (lottries) C, A, B. Out of these, event (lottery) A is certain, Chas probability P, and B probability (1-P), and if their respective utilities are U,,U, and U, then

U.EU, U. + (1+P)U Since the consumer is expected to maximize utility, the utility of A with certainty must be equal to some value P, the expected utility of the events (lotteries) C and B.

In order to construct a utility index based on the N-M equation, we have to assign utility values C and B. These utility values are arbitrary except for the fact that higher value should be assigned to a preferred event (lottery). Suppose we assign the following arbitrary utility values :U. = 100 utils, U.=0 util, and P = 4/5 or 0.8, then

U = (4/5) 100+ (1-4/5) (0)

= 80+ (1/5) (0) = 80 Thus, the utility index in this situation is Situation

1. 800

100 Proceeding this way, one can derive utility values for U,,U,U,, etc. and construct a complete N-M utility index for all possible combinations starting from two arbitrary situations involving probabilities of risk.

An Appraisal of the N-M Utility Index

The N-M utility index provides conceptual measurement of cardinal utility under risky choices. It is meant to be used for making predictions about two or more alternatives relating to gambling, lottery tickets, etc. and out of them which one a person may prefer.

The N-M index is based on the expected values of utilities. It provides a method to measure cardinally the marginal utility of money. This method of measuring utility analyses the actions of a person making risky choices.

The Neumann-Morgenstern method is based on the expected values of utilities. It does not refer to whether the marginal utility of money diminishes or increases. In this respect, this method of measuring utility is incomplete. The answer of this problem has been provided by the Friedman-Savage

Hypothesis’.

Economists like Dorman, Samuelson and Solow have derived the Paretian indices of utility from the N-M formula. And when the N-M Index based on individual ranking is constructed, it conveys information about his preferences.