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 What is Utility Function?

The most preferred choices of the goods and services by the consumers underlie a demand function. There are two approaches to the utility analysis. Initially the economists thought utility as a measurable and comparable physical property. This is called cardinal utility in its extreme form. However, later on it was understood that utility is not easily measurable and comparable across consumers by the marginalists. Then it was suggested that the utility could  be given meaningful numbers for the consumption of different goods. 

Based on the consumption of ordinal utility, there exists a bundle of consumption goods, which denotes the combination of different consumption goods. There can be given only a rank ordering of the consumption goods, under the concept of ordinal utility. A number is assigned to every consumption bundle, under the concept of the ordinal utility. Preference will be given to a bundle with a higher utility number to a bundle with a lower utility number. Thus, there is no meaning for the magnitude of the utility numbers, while the ranking of the utility numbers has only the meaning. Ordinal properties of the utility function are considered more important since  the most preferred affordable bundle is chosen by the consumer. Thus, all the combinations of the consumed goods by a consumer are specified by the utility function. The welfare and the preferences of the consumer are represented by the utility function. 

The utility function can be represented as U = U(X, Y), where there are only two consumption goods X and Y. The slope of the utility curve is the marginal utility. The utility function can be used to describe the consumer preferences in different circumstances provided the preferences about consumption are reasonable for the consumers. The valuation of consumption by a person in comparison to the other depends on the probability that the state in question occurs actually. Thus, there are two factors upon which the utility function depends namely the probabilities and the consumption levels. The utility function of perfect substitutes is given by U (Cl, C2, π1 , π 2 ) = π1Cl + π 2C2. This is known as expected value under uncertainty. This represents the average consumption level obtained by a consumer. Another form of the utility function is given by U(Cl,C2, π1 , π 2 ) = π1ν(Cl) + π 2 ν (C2). Here utility is represented as the weighted sum of some consumption function in each state ν(Cl)  and ν (C2).

In the utility curve below, the x-axis represents the quantity of good consumed and Y axis represents the total utility from consuming that good.

 

Utility Curve

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