1. Explain Consumers Equilibrium through Law of Equi-Marginal Utility
(Law of Equi-Marginal Utility, Law of Substitution)

Introduction

The Law of Equi-Marginal Utility is an extension to the law of diminishing marginal utility. The principle of equi-marginal utility explains the behavior of a consumer in distributing his limited income among various goods and services. This law states that how a consumer allocates his money income between various goods so as to obtain maximum satisfaction.

Assumptions

The principle of equi-marginal utility is based on the following assumptions:
(a) The wants of a consumer remain unchanged.
(b) He has a fixed income.
(c) The prices of all goods are given and known to a consumer.
(d) He is one of the many buyers in the sense that he is powerless to alter the market price.
(e) He can spend his income in small amounts.
(f) He acts rationally in the sense that he want maximum satisfaction
(g) Utility is measured cardinally. This means that utility, or use of a good, can be expressed in terms of units or utils. This utility is not only comparable but also quantifiable.

Principle

Suppose there are two goods \'x\' and \'y\' on which the consumer has to spend his given income. The consumer’s behavior is based on two factors:
(a) Marginal Utilities of goods \'x\' and \'y\'
(b) The prices of goods \'x\' and \'y\'

The consumer is in equilibrium position when marginal utility of money expenditure on each good is the same.

The Law of Equi-Marginal Utility states that the consumer will distribute his money income in such a way that the utility derived from the last rupee spent on each good is equal.

The consumer will spend his money income in such a way that marginal utility of each good is proportional to its rupee.

The consumer is in equilibrium in respect of the purchases of goods \'x\' and \'y\' when:

MUx = MUy Where MU is Marginal Utility and P equals Price

Px Py

If MUx / Px and MUy / Py are not equal and MUx / Px is greater than MUy / Py, then the consumer will substitute good \'x\' for good \'y\'. As a result the marginal utility of good \'x\' will fall.

The consumer will continue substituting good \'x\' for good \'y\' till MUx/Px = MUy/Py where the consumer will be in equilibrium. Thus this is also known as the law of substitution.

Table

Let us illustrate the law of Equi-Marginal Utility with the help of a table:

The side table shows marginal utilities of goods \'x\' and \'y\'. Let us suppose that the price of goods \'x\' and \'y\' are Rs. 2/- and Rs.3/-. Then MUx/Px & MUy/Py are as follows:

With a given income a rupee has certain utility to him. This is the Marginal Utility for him. Now the consumer will go on purchasing goods till the marginal utility of expenditure on each good becomes equal to the marginal utility of money to him. Thus the consumer will be in equilibrium at a point where:

MUx = MUy = MUm MUm refers to Marginal Utility of Money

Px Py

Let us suppose that the given income of a consumer is Rs.19/-. With the given income suppose the marginal utility of money is constant at Rs. 1 = 6 utils. By looking at the above table, it is clear that MUx/Px = 6 utils when he buys 5 units of good \'x\' and MUy/Py = 6 utils when he purchases 3 units of good \'y\'. Therefore the consumer will be in equilibrium when he is buying 5 units of good \'x\' and 3 units of good \'y\' and will be spending Rs.19/- on them.

MUx/Px = MUy/Py = MUm

12/2 = 18/3 = 6

Graph

This law can be explained with the help of the following diagram:

In the above diagram marginal utility curves of good \'x\' & \'y\' slope downwards. Marginal Utility of Money is confident at OM.

MUx/Px = OM when OK amount of good \'x\' is purchases and MUy/Py = OM when OH amount of good \'y\' is purchased.

Thus the consumer will be in equilibrium when he purchases OK amount of good \'x\' and OH amount of good \'y\' and then:

MUx/Px = MUy/Py = MUm

Limitations

This law is based on the assumption that utility can be cardinally measurable. But in actual practices it cannot be measured in such cardinal numbers. It is also assumed that marginal utility of money is constant. But this is