# Law of Equi-Marginal Utility

Contents

## Law of Equi-Marginal Utility

(Equilibrium of the Consumer Through the Law of Equi-Marginal Utility)

Other Names of this Law:

Law of Substitution OR Law of Maximum Satisfaction OR Law of Indifference OR Proportion Rule OR Gossen’s Second Law.

In the cardinal utility analysis, the principle of equal marginal utility occupies an important place.

## Definition and Statement of Law of Equi-Marginal Utility

The law of equi-marginal utility is simply an extension of the law of diminishing marginal utility to two or more than two commodities. The law of equilibrium utility is known, by various names. It is named as the Law of Substitution, the Law of Maximum Satisfaction, the Law of Indifference, the Proportionate Rule and the Gossen’s Second Law.

In cardinal utility analysis, this law is stated by Lipsey in the following words:

The household maximizing the utility will so allocate the expenditure between commodities that the utility of the last penny spent on each item is equal”.

As we know, every consumer has unlimited wants. However, the income from this disposal at any time is limited. The consumer is, therefore, faced with a choice among many commodities that he can and would like to pay. He, therefore, consciously or unconsciously compress the satisfaction which he obtains from the purchase of the commodity and the price which he pays for it. If he thinks the utility of the commodity is greater or at least equal to the loss of utility of money price, he buys that commodity.

As he buys more and more of that commodity, the utility of the successive units begins to diminish. He stops further purchase of the commodity at a point where the marginal utility of the commodity and its price are just equal. If he pushes the purchase further from his point of equilibrium, then the marginal utility of the commodity will be less than that of price and the household will be a loser. A consumer will be in equilibrium with a single commodity symbolically:

MUx = Px

A prudent consumer in order to get the maximum satisfaction from his limited means compares not only the utility of a particular commodity and the price but also the utility of the other commodities which he can buy with his scarce resources. If he finds that a particular expenditure in one use is yielding less utility than that of other, he will tie to transfer a unit of expenditure from the commodity yielding less marginal utility. The consumer will reach his equilibrium position when it will not be possible for him to increase the total utility by uses. The position of equilibrium will be reached when the marginal utility of each good is in proportion to its price and the ratio of the prices of all goods is equal to the ratio of their marginal utilities.

The consumer will maximize total utility from his income when the utility from the last rupee spent on each good is the same.  Algebraically, this is:

MUa / Pa = MUb / Pb = MUc = Pc = MUn = Pn

Here: (a), (b), (c)…. (n) are various goods consumed.

## Assumptions of Law of Equi-Marginal Utility

The main assumptions of the law of equi-marginal utility are as under.

### (i) Independent utilities

The marginal utilities of different commodities are independent of each other and diminish with more and more purchases.

### (ii) Constant marginal utility of money

The marginal utility of money remains constant to the consumer as he spends more and more of it on the purchase of goods.

## Example and Explanation of Law of Equi-Marginal Utility

The doctrine of equi-marginal utility can be explained by taking an example. Suppose a person has \$5 with him whom he wishes to spend on two commodities, tea, and cigarettes. The marginal utility derived from both these commodities is as under:

Schedule:

 Units of Money MU of Tea MU of Cigarettes 1 10 12 2 8 10 3 6 8 4 4 6 5 2 3 \$5 Total Utility = 30 Total Utility = 30

A rational consumer would like to get maximum satisfaction from \$5.00. He can spend money in three ways:

(i) \$5 may be spent on tea only.

(ii) \$5 may be utilized for the purchase of cigarettes only.

(iii) Some rupees may be spent on the purchase of tea and some on the purchase of cigarettes.

If the prudent consumer spends \$5 on the purchase of tea, he gets 30 utility. If he spends \$5 on the purchase of cigarettes, the total utility derived is 39 which are higher than tea. In order to make the best of the limited resources, he adjusts his expenditure.

(i) By spending \$4 on tea and \$1 on cigarettes, he gets 40 utility (10+8+6+4+12 = 40).

(ii) By spending \$3 on tea and \$2 on cigarettes, he derives 46 utility (10+8+6+12+10 = 46).

(iii) By spending \$2 on tea and \$3 on cigarettes, he gets 48 utility (10+8+12+10+8 = 48).

(iv) By spending \$1 on tea and \$4 on cigarettes, he gets 46 utility (10+12+10+8+6 = 46).

The sensible consumer will spend \$2 on tea and \$3 on cigarettes and will get maximum satisfaction. When he spends \$2 on tea and \$3 on cigarette, the marginal utilities derived from both these commodities is equal to 8. When the marginal utilities of the two commodities are equalized, the total utility is then maximum, i.e., 48 as is clear from the schedule given above.

## Curve/Diagram of Law of Equi-Marginal Utility

The law of equi-marginal utility can be explained with the help of diagrams.

In the figure 2.3 MU is the marginal utility curve for tea and KL of cigarettes. When a consumer spends OP amount (\$2) on tea and OC (\$3) on cigarettes, the marginal utility derived from the consumption of both the items (Tea and Cigarettes) is equal to 8 units (EP = NC). The consumer gets the maximum utility when he spends \$2 on tea and \$3 on cigarettes and by no other alternation in the expenditure.

We now assume that the consumer spends \$1 on tea (OC/ amount) and \$4 (OQ/) on cigarettes. If CQ/ more amounts are spent on cigarettes, the added utility is equal to the area CQ/ N/N. On the other hand, the expenditure on tea falls from OP amount (\$2) to OC/ amount (\$1). There is a toss of utility equal to the area C/PEE. The loss is utility (tea) is greater than that The loss in utility (tea) is maximum satisfaction except for the combination of expenditure of \$2 on tea and \$3 on cigarettes.

This law is known as the Law of maximum Satisfaction because a consumer tries to get the maximum satisfaction from his limited resources by so planning his expenditure that the marginal utility of a rupee spent in one use is the same as the marginal utility of a rupee spent on another use.

It is known as the Law of Substitution because consumer continuous substituting one good for another till he gets the maximum satisfaction.

It is called the Law of Indifference because the maximum satisfaction has been achieved by equating the marginal utility in all the uses. The consumer then becomes indifferent to readjust his expenditure unless some change takes place in his income or the prices of the commodities, etc.

## Limitations/Exceptions to Law of Equi-Marginal Utility:

### (i) Effect on fashions and customs:

The law of equi-marginal utility may become inoperative if people forced by fashions and customs spend money on the purchase of those commodities which they clearly know yield less utility but they cannot transfer the unit of money from the less advantageous uses to the more advantageous uses because they are forced by the customs of the country.

### (ii) Ignorance or carelessness:

Sometimes people due to their ignorance of price or carelessness to weigh the utility of the purchased commodity do not obtain the maximum advantage by equating the marginal utility in all the uses.

### (iii) Indivisible units:

If the unit of expenditure is not divisible, then again the law may become inoperative.

### (iv) Freedom of choice:

If there is no perfect freedom between various alternatives, the operation of law may be impeded.

## Importance of Law of Equi-Marginal Utility:

The law of equi-marginal utility is of great practical importance. The application of the principle of substitution extends over almost every field of economic inquiry. Every consumer consciously trying to get the maximum satisfaction from his limited resources acts upon this principle of substitution. Same is the case with the producer. In the field of exchange and in theory of distribution too, this law plays a vital role. In short, despite its limitation, the law of maximum satisfaction is the meaningful general statement of how consumers behave.

In addition to its application to consumption, it applies equally to the theory of production and theory of distribution. In the theory of production, it is applied on the substitution of various factors of production to the point where the marginal return from all the factors is equal. The government can also use this analysis for evaluation of its different economic prices.

The equal marginal rule also guides an individual in the spending of his saving on different types of assets. The law of equal marginal utility also guides an individual in the allocation of his time between work and leisure. In short, despite limitations, the law of substitution is applied to all problems of allocation of scarce resources.
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