CONSUMER CHOICE INVOLVING RISK:

The traditional theory of consumer behaviour does not include an analysis of uncertain situation. Von Neumann and Morgenstern showed that under some circumstances it is possible to construct a set of numbers for a particular consumer that can be used to predict her choices in uncertain situations. However, there is a great controversy that has centered around the question of whether the resulting utility index is ordinal or, cardinal. It will be shown that Von Neumann - Morgenstern utilities possess at least some cardinal properties. 

It has been pointed out above that consumer behaviour analysis is unrealistic in the sense that it assumes actions the consumer are followed by determinate consequences which are knowable in advance. For instance, all automobiles of the same model and produced in the same factory will not always have the same performance characteristics. As a result of random accidents in the production process, some substandard  automobiles could be occasionally produced and sold. The consumer has no way of knowing ahead of time whether the particular automobile, which she purchased, is of standard quality or not.

Let A represent the situation in which the consumer possesses a standard quality automobile and B be a situation in which she does not. Again, let there be C, in which she possesses a substandard automobile. Assume that the consumer prefers A to B and B to C. That is, not having a car is assumed preferable to owning a substandard one because of the nuisance and expense involved in its uptake. Present her with a choice between two alternatives: (1) She can maintain the status quo and have no car at all. This is a choice with certain outcome i.e., the probability of the outcome equals unity. (2) She can obtain a lottery ticket with a chance of winning either a satisfactory automobile (alternative A) or an unsatisfactory one (alternative C). The consumer may prefer to retain her income (or money) with certainty, or she may prefer the lottery ticket with dubious outcome, or she may be indifferent between them. Her decision will depend upon the chances of winning or losing in this particular lottery. If the probability of C is very high, she might prefer to retain her money with certainty; if the probability of A is very high, she might prefer the lottery ticket. The triplet of numbers (P, A, B) is used to denote a lottery offering outcome A with probability 0

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