In this article we will discuss about:- 1. Definitions of the Law of Equi-Marginal Utility 2. Explanation of the Law of Equi-Marginal Utility 3. Scope and Importance 4. Assumptions 5. Limitations.
- Definitions of the Law of Equi-Marginal Utility
- Explanation of the Law of Equi-Marginal Utility
- Scope and Importance of the Law of Proportionality
- Assumptions of the Law of Equi-Marginal Utility
- Limitations of the Law of Equi-Marginal Utility
1. Definitions of the Law of Equi-Marginal Utility:
The law of equi-marginal utility is based on the law of diminishing marginal utility. This law operates when different units of different commodities are consumed and consumer tries to maximise his satisfaction with his given resources. The law is called the law of substitution. The consumer should allocate his resources on different units of different commodities that in the last the marginal utility of each commodity is equalised.
The law is called after the name of H.H. Gossen as the second law of Gossen. There are several names of the law, namely, the law of substitution, law of maximum satisfaction, law of economy and the law of proportionality. It is based on the law of diminishing marginal utility. It deals with the multi-commodity consumer behaviour when a consumer consumes different units of different commodities with his given income and maximises his satisfaction.
Modern economists have explained the law of equi-marginal utility in algebraic form and they call it the law of proportionality. According to them, a consumer attains the maximisation of satisfaction at the point where he equalises the marginal utility from different units of multiple commodities and their price ratios.
The consumer will attain his equilibrium at the point of equality of the ratios of the marginal utilities of the individual commodities to their prices. It will maximise his satisfaction and on the basis of such adjustment the law is also called the law of proportionality.
According to the law the modern version is expressed in algebraic form as given below:
i. Single Commodity Equilibrium Condition:
The above is the equilibrium of a consumer at the point of maximisation of satisfaction when he consumes different units of a commodity.
But in actual practice a consumer consumes multiple commodities and according to the law the different units of different commodities are consumed and the point of equilibrium can be expressed in the following way—
ii. Multiple Commodities Equilibrium Condition:
The single commodity equilibrium condition can be converted into multiple commodities equilibrium condition as expressed in algebraic form-
In the above equation MUa, MUb, MUC and so on are the marginal utilities of a, b and c commodities. MUn is marginal utility of nth commodity. Pa, Pb, and Pc are prices of a, b, c commodities. Pn is price of the nth commodity. Qa, Qb and Qc are quantities consumed of a, b and c commodities, Qn is quantity of the nth commodity.
Finally, Y is money income of the consumer. It is equal to the prices of all the units of different commodities and the multiplication of their quantities consumed by the consumer.
Hence, according to this law a consumer can maximise his satisfaction if the two conditions are met, as given below:
(1) The ratios of marginal utilities and prices of different commodities should be equal.
(2) The total expenditure made on various foods should be equal to the total income (Y) of the consumer
The law has been defined in following ways:
(1) Prof. H.H. Gossen has defined “If it is not possible to gratify all wants to the point of satisfaction, it is necessary in order to obtain maximum satisfaction, to discontinue the satisfaction of different wants at the point at which their intensity has become equal.”
(2) According to Prof. Alfred Marshall, “If a person has a thing which can be put to several uses, he will distribute it among these in such a way that it has the same marginal utility in all. For, if it has a greater marginal utility in one use than another, he would gain by taking some of it from second use and applying it to the first.”
(3) Prof. J.K. Mehta has defined, “If a commodity can satisfy many wants within a given period of time, then in order to get greatest satisfaction from a given quantity of it, its amount should be so distributed between various wants as to make its marginal utility with reference to given period of time as nearly equal in all cases as possible.”
(4) Prof. J.M. Joshi has also defined, “In case of a single commodity, which can be put to several uses, the consumer will distribute it among these uses in such a way that it has the same marginal utility in all, only then his total utility will be maximum.”
(5) According to Prof. Lipsey and Prof. Steing, “The household maximising its utility will allocate its expenditure between commodities so that the utility of the last dollar spent on each is equal.”
(6) Prof. J.R. Hicks defined, “Utility will be maximised when the marginal units of expenditure in each direction bring in the same increment of utility.”
(7) According to Prof. Samuelson, “If the consumer has arranged his consumption so that every single good is bringing his marginal utility just exactly proportional to its price, then he would be assured that he could not better himself by departing from such equilibrium.”
The above definitions of the law reveal that a consumer will attain its maximum satisfaction when the marginal utility of all goods purchased are in the proportion of their prices. Marginal utilities are equalised while maximising the satisfaction by the consumer is the expenditure setter of wealth which is called the law of equi-marginal utility.
2. Explanation of the Law of Equi-Marginal Utility:
Each consumer aims at maximisation of his satisfaction while spending his given income which has alternative uses on various goods and services, namely, food, clothing, shelter, education, sanitation and health. He arranges his wants in order of intensity and the order of satisfaction is arranged on the basis of intensity of these wants and goes on satisfying his wants till the marginal utility of all the goods is equalised in proportion to money spent on them.
In this manner he can maximise his satisfaction. He will substitute that commodity which has more utility in place of less marginal utility and he continues up to that point where the marginal utility from all goods is equalised.
The operation of the law can be understood with the example. We assume that there are Rs. 9 with a consumer and he has to allocate the amount on two commodities in such a way that in the end the marginal utility of two goods are equalised.
It can be seen from the following table:
The table reveals that the consumer has Rs. 9 which he can spend on the different commodities, namely, A and B. We also assume that the each unit of a commodity has the price of Re. 1. The various units of two commodities have been shown which gives him different marginal utilities. The MU of A and B are decreasing. He can maximise his satisfaction when he spends Rs. 5 on commodity A and Rs. 4 on commodity B.
His total utility is 32+28+24+20+16 of A and 28+24+20+16 of B which is 208 units. He cannot attain more utility by spending his given income in different way. The table can be shown in the form of diagram.
As we have seen, Rs. 5 are spent on commodity A and Rs. 4 on commodity B and the utilities he has been deriving are given:
The diagram shows that Rs. 5 have been spent on commodity A and Rs. 4 on commodity B. The bars are showing the marginal utility from different units of the commodities which are declining showing the applicability of the law of diminishing marginal utility. The last utility from the 9th and the 8th unit of money equalise the utility which is shown by equi-MU line where MUA is equal MUB (MUA = MUB) in the diagram. Thus, the consumer attains his objective.
3. Scope and Importance of the Law of Equi-Marginal Utility:
Professor Alfred Marshall has pointed out about the scope and importance of the law of equi-marginal utility stating, “The application of the principle of substitution extends over almost every field of economic enquiry.” Professor Robbins has stated, “Economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses.”
Thus the scope and importance of the law extends to all the economic areas like consumption, production, exchange, distribution and public finance:
(1) Theory of Consumer Behaviour:
Each individual consumer is faced with the problem of choice because he has unlimited wants and scarce means which have alternative uses. According to this law a consumer can maximise his satisfaction by equalising the ratio of marginal utility of different commodities and their prices with other ratios of goods and their prices.
Consumer’s equilibrium with multiple commodities can be expressed in the following equation:
(2) Theory of Production:
Every producer aims at maximisation of output at the minimisation of cost. In order to attain the objective he substitutes more productive factors of production than the less productive factors of production. He will continue to substitute the factors of production till the point where marginal productivity of factors are equalised to their prices. The law of equi-marginal utility helps producers in attaining the objective.
The producer’s behaviour will attain his equilibrium as given in the mathematical formula:
Thus, the budget of a producer will be equal to the quantities of two factors as shown in the second equation wherein QFa is the quantity of factor A, PFa is the price of factor A, QFb is the quantity of factor B and PFb price of factor B.
(3) Theory of Exchange:
The law of equi-marginal utility is also applicable to the theory of exchange. Buyers and sellers are exchanging goods for goods or goods for money and both the parties will maximise their satisfaction at the point where the marginal utility of a commodity is equalised till the sacrifice in terms of money is equalised. For example, Ram and Shyam are exchanging two commodities with each other.
Ram has commodity A and Shyam commodity B which they exchange with each other until they attain the equilibrium as given below:
This clearly shows that both Ram and Shyam will stop their exchange as they have attained the objective of equalising the marginal gain in the process of exchange.
(4) Theory of Distribution:
The law of equi-marginal utility also applies in the theory of distribution. National income is shared by various factors of production, namely, land, labour, capital, enterprise and organisation. According to marginal productivity theory of distribution, each factor of production will get the share on the basis of its marginal productivity from the national income pool.
For example, the wage rate should be equal to the marginal productivity of labour (W = MPL). If the wage rate is greater than the MP (W>MPL) the firm is incurring loss while when wage rate is lesser than the marginal productivity (W>MPL) the workers are exploited and the firm is earning profit. Hence, the law suggests that each factor of production should be paid remuneration equal to its marginal productivity.
(5) Theory of Public Finance:
Dr. Dalton has propounded the fundamental principle of public finance popularly known as the principle of maximum social advantage. It helps us in maximisation of social welfare. The law of equi-marginal utility helps us in attaining the objectives through the tools of public finance. When additional tax is levied on society it leads to sacrifice by society which is called marginal social sacrifice (MSS), while spending the public expenditure public or society is benefited.
If additional amount of public expenditure is spent, the society is benefited and it leads to marginal social benefit (MSB). Both the tools of public finance, namely, public expenditure and public revenue should be carried on that point where MSS is equalised to MSB. It will maximise the welfare of the society. It can be seen from Diagram 4.
As given in the diagram, at point E, MSS is equalised with MSB which maximises the social welfare. Before E the MSB > MSS while after E, MSS > MSB.
Thus, we can say that the law of equi-marginal utility is widely applicable law and it is important from any aspect of any economic activity.
4. Assumptions of the Law of Equi-Marginal Utility:
As pointed out by Professor Alfred Marshall, the law of equi-marginal utility operates only when other things being equal. These other things are assumptions of the law.
They are discussed below:
(1) Rationality of the Consumer:
The law is based on the assumption that all the consumers are rational human beings and they spend their given income in such a way that maximisation of satisfaction goal is attained by them.
(2) Utility is Measurable:
The law is based on the assumption that cardinal measurement of utility is possible and the measuring rod of utility is money which takes into consideration the sacrifice in terms of money and the satisfaction in terms of cardinal number of utility.
(3) Constant Marginal Utility of Money:
The law assumes that the marginal utility of money remains constant or it does not change during the process of spending by the consumers.
(4) Operation of the Law of Diminishing Marginal Utility:
The law of equi-marginal utility is based on the law of diminishing marginal utility and it assumes that the law holds good when various units of different commodities are consumed by the consumer.
(5) Taste, Preference, Fashion and Income of Consumer do not Change:
The law is based on the assumption that the income, taste, preference, fashion of the consumer do not change. During the course of consumption they are assumed as constant.
(6) No Change in the Prices of Related Goods:
The law is based on the assumption that the prices of related goods like substitutes and complementaries do not change during the process of consumption. If these variables change the law will not operate.
(7) Divisibility of Goods:
The law operates on the assumption that the goods under consumption are divisible. They can be divided into small pieces and purchased by the small units of money.
(8) The period of income and expenditure of the consumers is the same.
5. Limitations of the Law of Equi-Marginal Utility:
The law of equi-marginal utility has been criticised on various grounds.
It has the following limitations:
(1) Indivisibility of Goods:
The law is based on the assumption that the commodities under consumption are divisible into small sizes and pieces. But in actual practice we find that goods are indivisible. For example, television, car, radio and diamond cannot be divided into small pieces and if they are, they will lose their utility.
(2) Budget Period is not Definite:
The law assumes that the period of expenditure and income of the consumer is definite and the same. But in practice we see that both items do not have the same period. In case of durables, such definiteness is not possible and practical because they give utility for a long period because of their nature. Fan, watch, T.V., furniture are some of the examples.
(3) Change in the Prices of Related Goods:
The law assumes that the prices of related goods, namely, substitute and complementary do not change but in real life we find that the prices of such commodities do not remain constant. The assumption will not help in the calculation of the marginal utilities derived by the consumer.
(4) Non-Availability of Goods:
The law assumes that on the basis of marginal utility we can maximise the satisfaction by equalising the ratios of utility and prices but in practice several useful goods are not easily available. In such a case the law does not apply. For example, if the Tata salt is not available then we have to use Sambhar salt. In such a situation satisfaction cannot be maximised.
(5) Imaginary and Unrealistic Assumptions:
The law of equi-marginal utility is based on some imaginary and unrealistic assumptions like consumer’s income, taste, preferences, habits, fashion, prices of related goods, measurability of utility in cardinal number and the marginal utility of money, etc., assuming them constant. In real life we see that all these variables go under change.
(6) Psychological and Subjective Law:
The law is a psychological and subjective and does not take into consideration the objectivity while studying the economics. Hence, it is not an economic law because it is a psychological and subjective based law.
(7) Ignores Income Effect and Substitution Effect:
The law of equi-marginal utility is based on the law of demand wherein the price and quantity demanded relationship is studied but it cannot segregate the income effect and substitution effect on account of change in the price of a commodity.
(8) Ignorance and Laziness of Consumers:
The law assumes that each individual consumer is a rational human being and he tries to maximise his satisfaction by equalising the ratios of marginal utility of goods and their prices. But in actual practice all consumers are not rational. They have ignorance and are lazy as well. On account of it with the help of the law they fail to attain maximum satisfaction.
After the criticism of the law we can say that a rational human being can maximise his satisfaction with the help of this law. Professor Chapman has rightly stated, “We are not compelled to distribute our incomes according to the law of substitution or equi-marginal expenditure as a stone thrown in the air is compelled, in a sense, to fall back to the earth, but as a matter of fact we do so in a certain rough fashion because we are reasonable.”