# Cardinal Utility Analysis and its Assumptions

Contents

### Concept of Cardinal Utility Analysis

In this article, we will know the concept of cardinal utility analysis and its fundamental assumptions. The cardinal utility analysis or the marginal approach to utility states that utility or the satisfaction derived from the consumption of a commodity or service is measurable and can be expressed in quantitative terms. This approach or method of utility analysis is also known as marginal analysis or neoclassical approach because it was developed and explained by neoclassical economists.

The British social scientist Jeremy Bentham (1748-1832) had employed the concept of cardinal measurement for the first time in his attempt to develop a rational system of civil and criminal law.  According to George J. Stigler, Bentham in his book ‘Introduction to the Principles of Morals and Legislation (1789), suggested the measurement of quantities of ‘pleasure’ and ‘pain’ to make a more rational system of civil and criminal law.  In this article, we will discuss the concept of the cardinal utility analysis, its basic concepts, and terminologies, and its major assumptions (cardinal analysis and its assumptions).

The German economist Hermann Heinrich Gossen (1854), English economist William Stanley Jevons (1871), and French mathematical economist Leon Walras (1874) made the concept of cardinally measurable utility theory generally accepted in economic analysis.  They believed utility is measurable and additive so that ‘utils’ (units of utility) obtained from one good are not affected by the rate of consumption of other goods. It means that they believed the utility derived from the consumption of a product is independent of the consumption of other products.

The theory of cardinal utility was made more advanced by neoclassical economists (Alfred Marshall, A.C. Pigou, etc.) With their marginal revolution of the 1870s. Neoclassical economists enlarged the utility theory with their assumption of measurability. Their units of measurement are random; they are ‘utils’. For example, they believed in the measurement of utility like if a consumer consumes 3 units of orange, he would say that he got 10 utils from the first unit, 8 utils from the second unit, and 6 utils from the third unit.

With the passes of time and tackling so many problems relating to practical life the cardinal utility theory had faced so many criticisms and as a result some alternative theories like ordinal utility analysis or Hicks-Allen’s indifference curve analysis, Samuelson’s revealed preference theory, and Hick’s logical weal ordering theory have been advanced. The issues and problems associated with the cardinal approach have shifted the microeconomic theories from cardinal to ordinal utility or ranked preference.

### Basic Concepts and Terminologies

The basic concepts and terminologies developed by cardinal utility analysis are briefly explained as below;

### Concept of Total Utility

It is the whole satisfaction that an individual obtains by consuming a specified quantity of a commodity per unit of time. According to Richard G. Lipsey and K. Alec Chrystal, ‘Total utility refers to the total satisfaction derived from all the units of that product consumed’.

For instance, suppose a consumer consumes five units of a commodity T. Suppose, he obtains 7 utils from the first unit of the commodity, 6 utils from the second unit, 5 utils from the third unit, 4 units from the fourth unit, and 3 utils from the fifth units. Then total utility obtained by this hypothetical consumer from the five units of the commodity consumed is 25 (=7+6+5+4+3) utils. The total utility he receives from the first 2 units of X is 13(=7+6) utils. Similarly, the total utility derived from the first three units is 18 (=7+6+5) utils and the total utility derived from the first four units is 22 (7+6+5+4) utils.

Therefore, due to the additive property and independence of utility in the cardinal approach of utility, we can write the total utility (TU) as;

TU= U1(X1) +U2(X2) +…. +Un (Xn)

Where, Ui (i=1, 2… n) is the utility derived from unit ‘i’ of good X.

Putting alternatively, if we add the utilities obtained all the units of a commodity during the given time we get the value of total utility (TU). Thus the mathematical formula to measure total utility can also be expressed as;

TU= MU1+MU2+MU3+……..+MUn

Where TU is total utility; MU1+MU2+MU3+……..+MUn is a marginal utility from 1 to n units of a given commodity. Therefore, total utility is the function of the quantity consumed by a consumer.

### Concept of Marginal Utility

It can be defined as the change in total utility concerning a change in per unit consumption of a commodity at a given time. According to economists Richard G. Lipsey and K. Alec Chrystal, ‘Marginal utility refers to the change in satisfaction resulting from consuming one unit more or one unit less of a product’. Similarly, economists P.A. Samuelson and W.D. Nordhaus sate, ‘The expression ‘marginal’ is a key term in economics and always means ‘additional’ or ‘extra’. Marginal utility denotes the additional utility you get from the consumption of an additional unit of a commodity.

For instance, consider our example of total utility, the total utility from the consumption of the first four units is 22 utils and from all five units is 25 utils; so the marginal utility of the fifth unit is 3 (=25-22) utils. The marginal utility of the fifth unit of the commodity consumed is the addition to the total utility provided by consuming that extra unit of commodity. Thus, marginal utility is a change in total utility as a result of the change in the unit of a commodity consumed.

Mathematically, marginal utility is the slope of the total utility curve. It can be expressed as;

MUn= ΔTU/ΔQ or, MU= dTU/dQ

Where ΔTU=change in total utility; and ΔQ= change in quantity consumed

Donald Stevenson Watson and Malcolm Getz express that the marginal utility (MU) of any amount ‘j’ of a product is the total utility (TU) of that product minus the TU of one fewer (j-1) units. Thus,

MUj=TUj-TUj-1

### Assumptions of Cardinal Utility Analysis

Cardinal utility analysis of demand relies on certain important assumptions. The fact is that the cardinal utility analysis is being criticized due to its unrealistic assumptions, so we need to know the basic assumptions of cardinal utility analysis. The following are those major assumptions on which the whole utility analysis rests.

Rationality

All the consumers are rational in the sense that they attempt to maximize their utilities from their given money income. They obtain all the relevant information needed to maximize their satisfaction.

Cardinal Measurement of Utility

The system of cardinal utility analysis holds that utility is a measurable and quantifiable entity. Cardinal utility analysis advocates that an individual can state utility or satisfaction he gets from the goods in arithmetic terms. So, an individual can say that he derives utility equals 25 units from the consumption of a unit of Good J, and 35 units from the consumption of Good S. Furthermore the cardinal account of utility assumes that an individual can compare utilities obtained from merchandise in respect of size. That is in the form of how much one level of satisfaction is greater than another.

Marshall believed that marginal utility is quantifiable in terms of money. It means, the amount of money that a person is prepared to pay for a unit of a good rather than go without it, is a measure of utility he derives from that good. Thus, money is the measuring rod of utility, according to Marshall.  Some other economists belonging to the cardinal school measure utility in imaginary units called utils. Accordingly, a consumer can say that one orange for example provides him satisfaction equal to5 utils.

Independent Utilities

The cardinal school of utility analysis assumes that the utility derived by consumers by consuming any goods or services is independent of the quantity consumed of other goods and services. Thus, the satisfaction from consumption of any particular good depends only on the quantities of that particular good. For instance, if there are n commodities in the basket with quantities J1, J2, J3,….Jn, then total utility is a function of all goods and expressed as;

U=f (J1, J2, J3… Jn)

According to Anna Koutsoyiannis, total utility is additive as;

U= U1 (J1) +U2 (J2) +…… +Un (Jn)

In the later versions of the cardinal utility analysis, the assumption of additivity was removed. They then assumed that the total utility that a person derives from the whole collection of goods purchased by him is simply the total sum of the separate satisfaction of the goods. Thus, the cardinal method of utility analysis regards utility as an additive.

Constant Marginal Utility of Money

This assumption is entirely related to measuring rod use of money in the analysis of utility. Unit this analysis marginal utility of money should remain constant to use as a measuring rod of utility. The necessary quantity of a standard unit of measurement is that the utility remains constant throughout the analysis. If the marginal utility of money changes the measuring rod for utility becomes unrealistic. Marshall measured marginal utilities derived from any good or service in terms of money. By holding constant marginal utility of money even with the change in the price of the commodity Marshall ignored the income effect of change.

Diminishing Marginal Utility

The cardinal utility analysis assumes that the marginal utility of a commodity diminishes as the consumer purchases larger quantities of it. It means if a consumer consumes the successive units of the commodity one after another, the satisfaction that is derived from the additional units of the commodity goes diminishing.

Introspection

It is the method of judging the behavior of the consumers. In this method, it is possible to conclude another person from one’s own experience. It means, by looking into ourselves we see inside the heads of other individuals. We can know from our experience that as we have more things, the less satisfaction we derive forms an extra unit of it. Thus, we can conclude from it that other person’s minds will work similarly.

### Conclusion

The article has described the matter related to the concept of cardinal utility analysis and its assumptions. The Cardinal utility approach believes that utility can be measured and compared to each other in terms of mathematical numbers like 1, 2, 3,…, n. It was initially developed by H.H. Gossen and further developed by the leader of neoclassical economics Alfred Marshall. It is thus well-known as Marshallian Utility Analysis. They define the utility as a cardinal measurement phenomenon.  Cardinal school also believes that an individual can express his satisfaction derives from the consumption of a good in cardinal number and he can make comparisons too. The basic assumptions of cardinal utility analysis are the foundation of cardinal utility analysis and play a key role in economic theories like the law of diminishing marginal utility, and the law of equi-marginal utility.