The utility function examples

Jump to navigation Jump to search This article is the utility function examples the economic concept. Within economics the concept of utility is used to model worth or value, but its usage has evolved significantly over time. Consider a set of alternatives facing an individual, and over which the individual has a preference ordering. A utility function is able to represent those preferences if it is possible to assign a real number to each alternative, in such a way that alternative a is assigned a number greater than alternative b if, and only if, the individual prefers alternative a to alternative b.

Gérard Debreu precisely defined the conditions required for a preference ordering to be representable by a utility function. Utility is usually applied by economists in such constructs as the indifference curve, which plot the combination of commodities that an individual or a society would accept to maintain a given level of satisfaction. Individual utility and social utility can be construed as the value of a utility function and a social welfare function respectively. In finance, utility is applied to generate an individual’s price for an asset called the indifference price. It was recognized that utility could not be measured or observed directly, so instead economists devised a way to infer underlying relative utilities from observed choice.

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These ‘revealed preferences’, as they were named by Paul Samuelson, were revealed e. 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. There has been some controversy over the question whether the utility of a commodity can be measured or not. 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. Neoclassical economics has largely retreated from using cardinal utility functions as the basis of economic behavior. Sometimes cardinal utility is used to aggregate utilities across persons, to create a social welfare function.

In the above example, it would only be possible to say that juice is preferred to tea to water, but no more. Although preferences are the conventional foundation of microeconomics, it is often convenient to represent preferences with a utility function and analyze human behavior indirectly with utility functions. 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. Note that for u to be a utility function on X, it must be defined for every package in X.