Utility function Kinds of utility functions
Currently, there is no doubt about the special role of consumers in the economy. They act as key actors in market relations. The concept of utility is used to analyze consumer preferences. It implies the ability of the product to meet the needs of the buyer. Let us consider in more detail what the utility function of consumption is.
For the first time the concept of "utility" was introduced into circulation by I. Bentham. This English sociologist and philosopher considered the key principle of human behavior to maximize the ability to meet their needs. The rational individual manages his costs for the purchase of services and products so as to obtain the greatest possible utility from them. In other words, using goods, he seeks to satisfy the maximum number of needs.
It should be noted that the concept of "utility" is not always identical to the term "benefit". An example is treatment.Therapy can bring undoubted benefits to a person. However, it will not always be a pleasure for him. The usefulness of a service or product is related to its quality characteristics. At the same time, such properties are taken into account, with the help of which certain human desires will be satisfied. These qualities include the following:
- Ease of use.
- Design, aesthetic beauty.
- Taste and aroma.
- Individuality, etc.
The presence in the utility of objective and subjective qualities makes it relativity.
Different people purchase products for different purposes and for one reason or another. For example, live fish bought at a store can be used to make dinner, to feed a cat, or to move into an aquarium. In any of the above cases, the product will have one or another utility. This property may vary depending on the place and time. For example, the usefulness of soft drinks will be different in summer and winter.
The subjective character possessed by utility allows one to compare the amount of satisfaction a person receives when consuming services and goods.The desire of economists to compare the ability to realize certain desires of people led to the emergence of two key areas of analysis and, accordingly, two theories. A quantitative approach was developed at the beginning of the 19th c. Menger, Jevons and Walras. Within their cardinal theory, a hypothesis was put forward about the possibility of quantitatively measuring the usefulness of a good. The utility function was declared by researchers as an integral element of the analysis.
The ordinal theory and the ordinal approach were proposed at the end of the 19th - beginning of the 20th c. in the writings of Edgeworth, Pareto and Fisher. Scientists refused to quantify and focused on the possibility of ranking existing utilities: from the highest to the lowest and from the best to the worst. The basis of the analysis was a certain set of a number of hypotheses. On their basis, indifference curves were formed and the optimum of the buyer was studied. Today, the neoclassical synthesis of the ideas of the ordinal and quantitative approaches is widespread, in which the utility function is used in the analysis.
It is known that in the market a person is faced with a huge amount of services and products.To better understand what constitutes a utility function of a consumer, it is advisable to simplify the analysis and assume the existence of two products. Suppose a person chooses the first product in the amount of q1, the second, respectively, in the amount of q2. A set of two products will determine the consumer basket. It will include one or another number of both products. The basket has a certain measurable quality. If the sets are food, then the main indicator can be caloric, the amount of sugar, vitamins and so on. If the products are metals, then melting point, strength, or another similar characteristic can become qualities. Of course, not all properties can be measured by number. For example, the quality of clothes is characterized not only by the length of the period of socks (which can be calculated), but also by the conformity to modern fashion (this indicator cannot be quantified).
General utility function
Suppose that each basket (q1, q2) corresponds to a certain number of TUs. It acts as an aggregate satisfaction that a person gets when using a given volume of goods or services for a specific time.The utility function is influenced not only by the physical characteristics, but also by the psychological characteristics of the person, his personal experience, cultural and social environment. Despite the fact that these factors are in the field of view of economists, in practice they focus exclusively on quantitative indicators. These include, in particular, sales, the number of units of goods purchased, and so on. All other factors (non-quantitative) are analysts to constant values that affect human behavior. The assumption "with other things being equal" makes it possible to simplify the evaluation of the conditions for maximizing satisfaction without serious harm to the model. In the mathematical sense, this means that a certain equation is given. The utility function is
TU = U (q1, q2 ... qn).
The indicator is set from the use of the product / service in the amount of n for a certain time period.
The utility function reflects a quantitative relationship between the volume of use of each product / service for a given time period and the cumulative satisfaction, expressing individual preferences of a person.In addition to the equation, it can be presented in the form of a graph or table. If you do not take special cases in which there is a utility function, for most products and services there will be a single pattern. It consists in the fact that the greater the volume of use of the goods, the higher the total satisfaction received by the person.
When using an additional product per unit of time, marginal utility arises. Mathematically, it is derived from cumulative satisfaction. It is calculated using the following equation:
MU = TU (q) = d (TU) / dq, where:
- increment of aggregate satisfaction - d (TU);
- increase in the amount of product / service - dq.
There are various kinds of utility functions. However, the simplest and most used option is the expression of satisfaction using a cubic equation:
TU = a + bq + cq2 - dq3, where:
- quantity of the used goods - q;
- positive constants - a, b, c, d.
If with consistent consumption of a certain product a person reaches saturation, then the additional utility when using a new unit of goods will decrease. This pattern has a universal character.It is called the principle of decreasing marginal satisfaction, or the law of Gossen. At a certain point, the additional utility from the new unit of good decreases as the volume of use increases. In mathematical form, this means that the second derivative of aggregate satisfaction in terms of the quantity of a given product is a negative quantity.
Explained by Marshall
The law of decreasing maximum utility was used to explain the paradox of water and diamonds. The essence of the dilemma was as follows. The market price of diamonds is disproportionately higher than the price of water. At the same time, it is obvious to all that without the first people it will be able to live. Water is necessary for people, without it they will die.
Marshall’s explanations were as follows. The value of a product is not determined by its overall utility for the individual, but by the maximum satisfaction that it will extract from the last sip. In other words, the price of water will be measured by the amount that the individual wants to give for additional volume. Due to the fact that the marginal value will decrease as the amount already drunk increases, and the planet has much more moisture reserves than diamond deposits, the latter will have a significantly higher value on the market.This explains the difference in price.