The Law of Equi-Marginal Utility

The Law of Equi-Marginal Utility

This law explains the consumer's equilibrium in a multi-commodity model. This law was first mentioned by H.H.Gossen, that is why it is called Gossen's second law. Further, this law was refined by Alfred Marshall. It is also known as the law of ''Maximum Satisfaction" or the law of substitution.

This law states that a consumer consumes various goods in such a way that the marginal utility derived per unit of expenditure on each good is the same.

According to Marshall, "If a person has a thing which can be put to several uses, he will distribute it among these uses in such a way that it has the same marginal utility in all."

There are limited resources to fulfill unlimited wants. Every consumer wants maximum satisfaction with the minimum income. For this purpose, he substitutes the more useful for the less useful thing. He spends his income in such a manner that marginal utility in each direction of his purchases has been equalized.

This law is an extension of the law of Diminishing Marginal Utility. The law of Diminishing Marginal Utility is applicable only on a single good while the law of equi-marginal utility is applicable to various goods.

Conditions of this Law

• It is applicable on two or more goods.
• He should get equal marginal utility from both goods.
• He must spend all his income.

Example: Suppose a consumer is having Rs.50 and he wants to purchase apples and oranges with the given income. The price of an apple is Rs.10 and that of orange is Rs.5.

The consumer is said to be in equilibrium at a point at which the marginal utility per rupee of both the goods is equal in symbolic terms.

MUX / PX = MUY / PY

Where x = apple and y = orange.

Income = Rs 50

Px = Rs 10 

Py = Rs 5

There are four combinations  according to this table:

1. One unit of good X and two units of good Y

2. Two units of good X and three units of good Y

3. Three units of good X and four units of good Y

4. Four units of good X and five units of good Y

Now in these four combinations, in which he will be in equilibrium.

Formula:        Income = Px X Qx + Py X Qy

1. 50 = 10 X 1 + 5 X 2

    50 = 10 + 10 

    50  > 20 (Condition not satisfying)

2. 50 = 10 X 2 + 5 X 3

    50 = 20 + 15

    50 >  35 (Condition not satisfying)

3. 50 = 10 X 3 + 5 X 4

    50 = 30 + 20

    50 = 50 (Condition satisfying)

4. 50 = 10 X 4 + 5 X 5

    50 = 40 + 25

    50 < 65 (Condition not satisfying)

From the given table and explanation it is clear that the consumer will be in equilibrium where he is buying three units of good X (apple) and four units of good Y (orange) and getting maximum satisfaction from the given income.

In the above diagram units of goods and MU of respective goods are measured along X-axis and Y-axis respectively. For each combination of units of goods and their respective MU, we derive two different MU curves for good X and Y. There is a line of euqi-marginal utility parallel to the X-axis at MU 6 with a combination of three units of good X and four units of good Y. The consumer is at maximum satisfaction at this combination.

Assumptions of this law:

Cardinal Measurement of Utility: It is assumed that utility is a quantifiable entity and can be measured by assigning definite numbers such as 1, 2, 3, etc.

Constant marginal utility of money: It is assumed that the marginal utility of a commodity varies with the quantity of the commodity purchased, but the marginal utility of the money remains constant. This assumption becomes necessary because we measure the marginal utility of a commodity in terms of money.

Rationality: Consumer should be rational in behavior so that he/she can maximize total satisfaction  from the given  income and prices of goods

  

Taste, Preference, and Income of Consumers should not be changed: The income, taste, preference of the consumer should not change during the course of consumption.

No Change in the Prices of Related Goods: The prices of related goods like substitutes and complementary should not change during the process of consumption otherwise this law will not operate.

Divisibility of Goods: Goods can be divided into various units and purchased by the small units of money.

Limitations of the law:

1. Not measurable in cardinal numbers: Utility is a subjective matter and can not be expressed in cardinal numbers.

2. Ignorance of consumers: Consumers may not be aware of other more useful alternatives. Hence, no substitution takes place and this law does not operate.

3. Irrational consumer: For the application of this law, the consumer has to calculate the marginal utilities of different commodities that he wants to purchase and compare them. In real life, the consumer does not behave so rationally.

4. Customs and habits: Sometimes a consumer is restricted with the custom, habit, and advertisement and is the least concerned about maximum satisfaction.

 5. Indivisible commodities: In the case of indivisible commodities, this law is not applicable. Durable goods are not divisible into small units to enable consumers to equalize marginal utilities.

Importance of this law:

This law is applicable to the utilization of time, distribution of assets, and the allocation of resources among various usages.

In the field of consumption:  Every consumer wants to get maximum satisfaction with the minimum income. With the help of this law, he can achieve this.

In the field of production: The manufacturer and the businessman will substitute one factor for another till their marginal productivities are made the same and able to maximize their profit

Price determination: In case of scarcity of the commodity this law comes to release. We start substituting the less scarce goods for the more scarce ones. The scarcity of the latter will be eased and its price will come down.

In the field of exchange: This law also works in all our exchanges. The substitution character of our exchange plays great importance in this basic economics principle. 

In the field of distribution: It is also useful in the determination of the rewards of the various factors of production such as rent, wages, interest, and profit. These shares are determined according to the principle of marginal productivity.

Public finance:  This law is important in the field of public finance for the revenue and expenditure pattern of government. Govt must try to maximize the welfare of the community by cutting down all unnecessary expenditure

Thus this law applies in all branches of economics theory.

Dr. Swati Gupta

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