In: Economics

# Law Equi-Marginal Utility in Economics.

Give an analysis of Law Equi-Marginal Utility with suitable example?

## Solutions

##### Expert Solution

LAW OF EQUI-MARGINAL UTILITY -

In real life our consumption is not confined to a single commodity. This problem of choosing between different goods is solved by the law of equi-marginal utility.

If we are using more than one commodity, then the law of equi-marginal utility tells us that how should we distribute our consumption on different commodities in order to get maximum satisfaction. According to this law.

"If a consumer is taking more than one commodity then he should decide the quantities in such a way that the marginal utility derived from different commodities is the same, and his total income is also spent."

This law of equi-marginal utility can be explained by the following example. Suppose, a person is using two commodeties 'x' and 'y'. The price of both of them being $1 per unit and he has an income of$10. The marginal utility derived from different units of consumption of these goods is given in the following table.

Table -1

(Equi-Marginal Utility)

 Units of               Consumption MU of 'x' MU of 'y' 1 20 (1) 16 (4) 2 18 (2) 14 (6) 3 17 (3) 13 (7) 4 15 (5) 10 (10) 5 12 (8) 9 6 10 (9) 8 7 8 6 8 7 4 9 5 2 10 4 1

In the above table we are showing the marginal utilities of the two commodities received from different units of consumption. Under the given situation, the consumer would like to spend his $10 in the following manner, which has been shown in brackets in the above table. The first$ he would like to spend on the 1 unit of 'X' commodity because that gives, him a satisfaction higher than the 1 unit of 'y' commodity. For the same reason, he would spend the second and third $on the 2 and 3 units of x commodity respectively. The fourth$, he would spend on the 1 unit of 'y' commodity because it gives a utility of 16 as against the 4 unit of x commodity which gives a utility of 15 only. By the same logic he would spend the fifth $on the 4th unit of x commodity, sixth and seventh$ on 2 and 3 units of y commodity, eighth $on 5 unit of x commodity and ninth and tenth$ on 6 unit of x and 4 unit of y respectively: In this way his entire income of $10 is spent. Thus, the consumer has 6 units of x and 4 units of y, where the marginal utility of both commodities is equal i.e. 10. For the consumer this will be his equilibrium position where he gets maximum utility which is 145. From 6 x he gets 20 + 18 + 17 + 15 + 12 + 10 = 92 From 4 y he gets 16 + 14 + 13 + 10 = 53 Hence, Total Utility is = 145 This is the maximum utility that he can get for$10 on the two commodities. If we take any other combination the total utility will be less than 145. For example, if we take 5 units of x and 5 units of y, Then total utility would be 144 units only.

In this table, if we look at the marginal utilities we find hat 'x' appears to be more useful because at every level its utility is greater than y. But it does not mean that he should spend his entire money on x, because, even if he does so the total utility received would be 116 only, which is less than what he can get by properly distributing his income on two commodities. Thus, this law of equi-marginal utility tells us that it is not wise to spend our entire income on any single commodity, even if it appears to be more useful. We should wisely distribute our income on different commodities to get maximum utility.

On the basis of the above analysis we can say that consumer's equilibrium is reached where,

MUx   =   MUy

or

Marginal Utility of x is equal to Marginal Utility of y.

However, if the price of the two commodities are not equal, then the above equation needs to be modified as follows.

MUx / Px   =    MUy / Py

Where,

Px and Py represent the price of x and y respectively.

or

MUx / MUy  =  Px / Py

In other words, equilibrium is reached where the ratio of marginal utilities is equal to the ratio of prices of x and y.

The law of equi-marginal is a very important tool of econimic analysis. It provides us with the best tool of allocation. It is used not only in utility maximisation but also in cost minimisation, revenue maximisation etc.

In real life our consumption is not confined to a single commodity. This problem of choosing between different goods is solved by the law of equi-marginal utility.