Economic: Microeconomic |Law of substitution or Equi-marginal utility

Law of Substitutions 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 a famous economist HH Gossen in 1854 AD. Therefore it is also called as Gossen’s second law. Finally this law was fully developed by Alfred Marshall.
                           Human wants are unlimited but resources are limited. Every rational consumer want to gain maximum satisfication or utility by purchasing goods from him/her limited budget. For the purpose he/she has to spend limited budget for the purchasing of more than one commodity in such a way so thathe/she could obtain equal marginal utility from all commodity consumer is able to gain maximum satisfication when marginal utility derived from all commodity becomes equal.
                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."

Mathematically, a consumer is at maximum satisfaction when:

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

Where,

Mu_x = Marginal Utility of X goods

P_x = Price of X goods

MU_y = Marginal Utility of Y goods

P_y = Price of Y goods

MU_n = Marginal Utility of n^th goods

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.

Assumption:

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.
• No change in the price of goods.
• It is based on two commodity.

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 2^nd rupee and snickers with his 3^rd 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

• Cardinal Utility:

Law of substitution is based on the assumption cardinal measurement of utility but in reality utility is psychological phenomenon which cannot be measured in cardinal term. Therefore, this law is based on wrong assumption of cardinal utility.

• Irrational Consumer:
  

 According to the assumption of these law, consumer must be ratrional. Therefore, this law is not applicable for the irrational consumer because irrational consumer can't judge utility of satisfaction properly.

• Custom & Tradition:

The law of substitution is influenced by the different custom & tradition. For the fulfillment of different requirement of custom & tradition. For the fulfillment of different requirement of custom & tradition consumer may spent without considering equal marginal utility of different commodity. As a result, this law may not be applied during custom & tradition.

• Indivisible Goods:

According to assumption of the law of substitution different goods must be divisible in different units. Therefore, this law is not applicable in the context of indivisible goods. It means this law may not be applied in the case of indivsible goods like T.V, motorcar, washing machine, etc.

• Shortage of Goods:

This theory is not applied when there is shortage of goods. If goods are shortage in market, hoe consumer equalizes marginal utility of one commodity with another commodity.

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 MP_c=MP_k) 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.