Note on Law of Substitutions Or Equi-Marginal Utility

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Law of substitution or Equi-marginal utility

Law of substitution is an important law in economics. It is equally applicable in all parts of economics. This law was propounded by HH Gossen in 1854 AD. Therefore it is also called as Gossen’s second law. However scientific and analytical explanation of this law was made by Prof. Dr. Alfred Marshall.

According to Marshall "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 in all."

Thus this law state that a consumer is in maximum satisfaction when the utility obtained from the last rupee spent on each commodity is same. Therefore this law is also known as the law of equi-marginal utility and law of maximum satisfaction.

Mathematically, a consumer is at maximum satisfaction when:

\(\frac{MU_x}{P_x}\) = \(\frac{MU_y}{P_y}\) = MUm


Mux = Marginal Utility of X goods

Px = Price of X goods

MUy = Marginal Utility of Y goods

Py = Price of Y goods

MUm = Marginal Utility of money

So, in order to maximize utility, an individual consumer compares the marginal utilities obtained from the different commodities. If the marginal utility obtained from the different commodities is not equal, the consumer goes on substituting one commodity with higher marginal utility for the commodity with lower marginal utility till the marginal utility obtained from the both commodities are equal. Therefore, this law is called a law of substitution.


This law is based on the following assumption:

  • The consumer is rational.
  • The utility can be measured in cardinal numbers.
  • The marginal utility of money remains constant.
  • Commodities are perfectly divisible.
  • Income of consumer and prices of commodity remains constant.

Based on the above assumption this law can be explained further with the help of table and diagram. For simplicity, let us assume that there are only two commodities choco fun and snickers available for an individual for consumption. The consumer has only Rs. 5 to spend on choco fun and snickers. Price per unit of both choco fun and snickers be Re. 1. Under this condition, the following table shows MU derived from choco fun and snickers.


In the adjoining table, the marginal utility of both choco fun and snickers are tabulated. An individual has limited resource ie. Rs 5 for the consumption of choco fun and snickers. Thus he takes into an account of marginal utilities of both choco fun and snickers in order to maximize satisfaction. As such the highest MU is of choco fun ie. 10 so he spent first Re.1 for purchasing choco fun. Then the second highest MU is 8 which can be obtained either by consuming choco fun or snickers. So at this point, an individual is indifferent about which one to purchase as both the commodity gives same MU. Let’s suppose an individual purchase choco fun with his 2nd rupee and snickers with his 3rd rupee. This process will continue till the resource allocated by an individual for the consumption of both commodities finishes ending up with equal marginal utility obtained from the last rupee spent on the both commodity. Thus the consumer will be at maximum satisfaction with Total utility (10+8+8+6+6=38 utils) by consuming 3 units of choco fun and 2 units of snickers than any other combination of choco fun and snickers.


In the above figure, units of consumption and MU of respective commodities are measured along X-axis and Y-axis respectively. For each combination of units of consumption and their respective MU, we plot points in a graph. Joining the points we derive two different marginal utility curves for choco fun and snickers. There is a line of equi-marginal utility parallel to X-axis at MU Rs 6 with a combination of 3 units of choco fun and 2 units of snickers. The consumer is at maximum satisfaction at this combination with total utility (Rs 10+8+8+6+6) equals to Rs 38. Any deviation from this combination of consumption will lower the total utility of an individual. Suppose, opposing the law of substitution if a consumer purchases 2 units of choco fun and 3 units of snickers rather than 3 units of choco fun and 2 units of snickers then the consumer will only have total utility (Rs 10+8+8+6+4) equals to Rs 36. This fact is clearly visualized in the above diagram.The red shaded area is greater than green shaded area.The red shaded portion is the loss of marginal utility and green shaded portion is a gain of marginal utility. Therefore in aggregate loss exceeds the gain of MU and thus decreases the total utility of a consumer.

Limitation of Law of substitution

  • Ignorance of the consumer:

The consumers ignore the law of substitution and blindly follow custom or fashion and are thus making wrong use of money. Thus the ignorance by the consumer has made no use of the existence of this law.

  • Commodities indivisible:

The law is based on the assumption that commodities are divisible and substitutable. But this is an unrealistic assumption because all commodities are not possible to divide or split into small units. Even if their utility will be destroyed. For instance, commodities like buffalo, fridge, bus etc cannot be split. Therefore this law fails in these circumstances.

  • Utility measurement:

The law of substitution is based on the unrealistic assumption that utility is measurable in cardinal number. However, critics are with a view that utility is a subjective concept and cannot be quantified exactly. For instance, if we consume momo then we can say it is tasty or salty but we never say it is 15 tasty or 20 salty.

  • Unlimited resources:

The law of substitution has no use when the resource is unlimited as in the case of a free gift of nature. In such cases, there is no need to re-arrange expenditure because no price is to be paid for whatever be the quantity consumed or used.

  • Choice uncertain:

This law assumes alternatives available to the consumer must be certain to allocate available resource to consume them. But consumers’ choices are uncertain and even risky.

  • Impact of custom, tradition, and fashion:

Sometimes an individual is compelled to purchase a product that has lower marginal utility for a close substitute product with higher marginal utility due to an influence of custom, tradition, and fashion. In such cases, this law does not hold true.For instance, in our culture traveler is served with curd before a journey. But some individuals might not enjoy drinking curd or may not have any interest in having curd. Rather they may love much to have milk. Thus in this case because of the culture an individual is not able to maximize his/her satisfaction.

Importance of law of substitution
  • In consumption:

We know that the major objectives of the rational consumer is utility maximization given his income and prices of his goods. The law of substation guides the consumers to select the best combination of good by equalizing the marginal utility obtained from various commodities.

  • In production:

The major objective of all the producers is producing a maximum amount of goods of minimum possible costs. The producer always wants to maximize their profit by selecting the best combinations of factor input which provide the maximum possible output for that, the producer substitutes one factor for another till their marginal productivities become equal (i.e MPc=MPk) and at that point total point, total product becomes maximum.

  • In exchange:

Law of substitution also guides in exchange as it is related to purchase of goods by spending money till marginal utility of goods become equal to price. In other words,the law of substitution also guides to determine the price.

  • In distribution:

Distribution is the process of determining the rewards of a factor of production land, labor, capital and organization in the form of rent, wages, interest, and profit. Such factor payments are determined according to the marginal productivity.

  • In public finance:

Law of substitution is also equally important in the field of public finance regarding the revenue and expenditure pattern of government. Government by imposing progressive tax system enhances the welfare of all as the burden of taxation falls equally to all.


Adhikari, D. R., Dahal, G. D., Acharya, K. R., Lamichhane, B., & Shrestha, P. P. (2011). Economics II. Kathmandu: Asmita.

Jha, P.K., et al. Economics II. Kalimati, Kathmandu: Dreamland Publication, 2011.

Karna, Dr.Surendra Labh, Bhawani Prasad Khanal and Neelam Prasad Chaulagain. Economics. Kathmandu: Jupiter Publisher and Distributors Pvt. Ltd, 2070.

Khanal, Dr. Rajesh Keshar, et al. Economics II. Kathmandu: Januka Publication Pvt. Ltd., 2013.

According to Marshall "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 in all."

Limitation of Law of substitution

  1. Ignorance of the consumer
  2. Commodities indivisible
  3. Utility measurement
  4. Unlimited resources
  5. Choice uncertain 
  6. Impact of custom, tradition, and fashion

Importance of law of substitution

  1. In consumption
  2. In production
  3. In distribution
  4. In public finance

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