What is Law of equi marginal utility?

Lawof Equi-Marginal Utilitystates that a consumer allocates his expenditure on various commodities in such a manner that the utility derived from each additional unit of the rupee spent on each of the commodities is equal. Algebraically, this is represented the following equality.

Numerical Example

Let us understand the concept of Consumer's Equilibrium in case of two commodities with the help of the following numerical example. Let us suppose that for a consumer the Marginal Utility of Money (MU_m) is 5 utils and the price of commodityx(P_x) is Rs 5, while, the price of another commodityy, (P_y) is also Rs 5

Consider the following Marginal Utility Schedule for commodityx(MU_x) and commodityy(MU_y)

Units ofx

(units)

MU_x

(utils)

MU_y

(utils)

1

2

3

4

5

6

7

30

28

25

20

10

2

5

35

32

28

25

12

3

1

As per the schedule, the consumer strikes equilibrium when he is consuming 3 units of commodityxand 4 units of commodityy. At such a consumption combination, the Marginal Utility of a Rupee spent on the commodityxis equal to the Marginal Utility of a Rupee spent on the commodityy, which in turn is equal to the Marginal Utility of Money (MU_m).

That is,

Marginal Utility of a Rupee spent on commodityx= Marginal Utility of a Rupee spent on commodityy =Marginal Utility of Money

Diagrammatically, the consumer's equilibrium in case of two commodities is represented as:

In the above figure, OO₁represents the total income of a consumer.MU_xandMU_yrepresent the Marginal Utility curves of commodityxand commodityy, respectively. The pointErepresents the point of consumer's equilibrium, where:

At this point,OMamount of income is spent on commodityxand the remaining amount of incomeMO₁is spent on commodityy.

Suppose, instead of pointM, the consumer is at pointS, where he spendsOSamount of income oncommodityxandSO₁amount of income on commodityy. At pointS,however;

Thus, the consumer would increase his consumption of commodityxtill the equality is achieved. That is, in other words, when he reaches pointE, where the equilibrium is restored by the equality between the marginal Utilities of each commodities.