# Concept of utility pdf

This article is about the economic concept. It was recognized that utility could not be measured concept of utility pdf observed directly, so instead economists devised a way to infer underlying relative utilities from observed choice. Utility is taken to be correlative to Desire or Want.

It has been already argued that desires cannot be measured directly, but only indirectly, by the outward phenomena to which they give rise: and that in those cases with which economics is chiefly concerned the measure is found in the price which a person is willing to pay for the fulfillment or satisfaction of his desire. At one time, it was assumed that the consumer was able to say exactly how much utility he got from the commodity. The economists who made this assumption belonged to the ‘cardinalist school’ of economics. When cardinal utility is used, the magnitude of utility differences is treated as an ethically or behaviorally significant quantity. For example, suppose a cup of orange juice has utility of 120 utils, a cup of tea has a utility of 80 utils, and a cup of water has a utility of 40 utils. With cardinal utility, it can be concluded that the cup of orange juice is better than the cup of tea by exactly the same amount by which the cup of tea is better than the cup of water.

One cannot conclude, however, that the cup of tea is two thirds as good as the cup of juice, because this conclusion would depend not only on magnitudes of utility differences, but also on the “zero” of utility. For example, if the “zero” of utility was located at -40, then a cup of orange juice would be 160 utils more than zero, a cup of tea 120 utils more than zero. In the above example, it would only be possible to say that juice is preferred to tea to water, but no more. Then this consumer prefers 1 orange to 1 apple, but prefers one of each to 2 oranges.

In micro-economic models, there are usually a finite set of L commodities, and a consumer may consume an arbitrary amount of each commodity. In the previous example, we might say there are two commodities: apples and oranges. They are usually monotonic and quasi-concave. However, it is possible for preferences not to be representable by a utility function. Von Neumann and Morgenstern addressed situations in which the outcomes of choices are not known with certainty, but have probabilities attached to them.

By making some reasonable assumptions about the way choices behave, von Neumann and Morgenstern showed that if an agent can choose between the lotteries, then this agent has a utility function such that the desirability of an arbitrary lottery can be calculated as a linear combination of the utilities of its parts, with the weights being their probabilities of occurring. Axioms 3 and 4 enable us to decide about the relative utilities of two assets or lotteries. Of all the axioms, independence is the most often discarded. Von Neumann and Morgenstern’s theory. Specifically for any utility function, there exists a hypothetical reference lottery with the expected utility of an arbitrary lottery being its probability of performing no worse than the reference lottery. Suppose success is defined as getting an outcome no worse than the outcome of the reference lottery. Then this mathematical equivalence means that maximizing expected utility is equivalent to maximizing the probability of success.

In many contexts, this makes the concept of utility easier to justify and to apply. For example, a firm’s utility might be the probability of meeting uncertain future customer expectations. An indirect utility function gives the optimal attainable value of a given utility function, which depends on the prices of the goods and the income or wealth level that the individual possesses. One use of the indirect utility concept is the notion of the utility of money. The boundedness reflects the fact that beyond a certain point money ceases being useful at all, as the size of any economy at any point in time is itself bounded.

The asymmetry about the origin reflects the fact that gaining and losing money can have radically different implications both for individuals and businesses. The non-linearity of the utility function for money has profound implications in decision making processes: in situations where outcomes of choices influence utility through gains or losses of money, which are the norm in most business settings, the optimal choice for a given decision depends on the possible outcomes of all other decisions in the same time-period. Robinson also pointed out that because the theory assumes that preferences are fixed this means that utility is not a testable assumption. This is so because if we take changes in peoples’ behavior in relation to a change in prices or a change in the underlying budget constraint we can never be sure to what extent the change in behavior was due to the change in price or budget constraint and how much was due to a change in preferences. Another criticism comes from the assertion that neither cardinal nor ordinal utility is empirically observable in the real world.