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Law of Equi Marginal Utility With Explanation And Example

The Law of Equi-Marginal Utility was first explained by Hermann Heinrich Gossen. Later on Alfred Marshall refined and developed it. This law is also known as the Proportionality Rule, the Law of Substitution, the Law of indifference, the Law of Equi-marginal Returns and Gossen’s Second Law or Consumption.

The Law of Equi-Marginal Utility is described as the Proportionality Rule because the consumer substitutes one commodity for the other until the marginal utility of each commodity is in proportion to its price. Since the consumer goes on substituting the more useful thing for the less useful one, it is described as the Law of substitution. It is also called as the Law Of Indifference because the consumer, when he reaches the point of maximum satisfaction, becomes indifferent about any other combination of the commodities bought.

It is also described as the Law Of economy of expenditure as it analyses the expenditure behavior of the consumer whose aim is to save his money. Since the marginal returns derived by a consumer from different commodities is equal, it is called as the Law of Equi-Marginal Returns. Marshall’s Definition : Marshall defined this The Law of Equi-Marginal Utility as follows : “If a person has a thing which he can put to several uses, he will distribute it among these uses in such a way that it has the same marginal utility”

Explanation of The Law of Equi-Marginal Utility:

The Law of Equi-Marginal Utility explains that a consumer spends his income on different goods in such a way to get maximum satisfaction. A consumer continues his purchases until the marginal utilities derived from all commodities remain equal. He, while purchasing commodities, compares. the marginal utilities of different commodities. He substitutes those commodities which yield high marginal utilities in place of those commodities which yield low marginal utilities. Suppose he has to make a choice between three commodities. At the point of margin, he compares the marginal utilities of three commodities.

Example of The Law of Equi-Marginal Utility:

If commodity X gives higher marginal utility than the other two commodities, he substitutes more of commodity X in place of Y and Z, in this way, he goes on buying high marginal utility commodities instead of low marginal commodities by distributing his limited income in an economical way.

Weighted Marginal Utilities : This law may be explained by the following equation:

MUx / Px= MUy / Py=MUz /Pz Where MUx MUy MUz denote marginal utilities and Px, Py and Pz represent prices of the commodities respectively.

A consumer attains equilibrium when he gets maximum satisfaction from his expenditure on different commodities. As shown in the above equation, a consumer spends in such a way that the marginal utilities and Prices of the commodities are equal. The Marginal utility of a commodity when divided by its price, is known as weighted marginal utility. A wise consumer attains maximum satisfaction when the weighted marginal utilities of the three commodities are equal.

This law may be explained with the help of the following table.

Money Spent Marginal Utility
Of Coffee (Utils)
Marginal Utility
Of Bananas (Utils)
1st Dollar 10 8
2nd Dollars 8 6
3rd Dollars 8 4
4th Dollars 4 2
5th Dollars 3 1

Suppose a consumer desires to buy different quantities of coffees and bananas with a money of 5 Dollars. If he spends 3 dollars on coffee and 2 dollars on bananas, his marginal utility between the two commodities remain equal. When marginal utilities of coffee and bananas are equal, the consumer attains maximum satisfaction. The consumer gets a total utility of 24 utils (10+8+6) =24 utils from the consumption of coffee and 14 utils (8+6=14 utils) from the consumption of bananas. Altogether, he derives a total utility of 38 utils from the consumption of the two commodities. It may be noted that this combination of coffee and bananas alone yield maximum satisfaction to the consumer. At other combinations, the consumer’s satisfaction is not maximum. Hence, two things are clear from the above table. They are- 1) A consumer goes on consuming different quantities of commodities until the marginal utilities derived from them are equal. 2) A consumer tries to maximize his satisfaction by substituting one commodity for the other.

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