## Law of Equi-marginal Utility Explained with 2 Case Studies

Let us illustrate this law with help of an arithmetic example. Suppose our imaginary consumer is consuming two commodities such as apple and grapes. He has only seven rupees income at his disposal.

He will try to spend it in such a way that he will get maximum satisfactions. Suppose one kilogram of apples and grapes is equal to one rupee each in the market.

If he spends seven rupees on apple he can buy 7 kilograms of it and will get 175 units of satisfaction. Similarly, if he spends all the seven rupees on grapes he will get 140 units of satisfaction.

Only, when he spends 4 rupees on apples and 3 rupees on grapes he gets {(40 + 35 + 30 + 25) + (35 + 30 + 25)} = (130 + 90) = 220 units of satisfaction. If he spends 3 rupees on apples and 4 rupees on grapes he gets {(40 + 35 + 30) + (35 + 30 + 25 + 20)} = (105 + 110) = 215 units of satisfaction. So 4 kg of apples and 3 kg of grapes will give him the highest satisfaction, i.e., 220 units.

Now, we explain the law of Equi-marginal utility with respect to Case-1 andTable-3 with the help of diagrams given below.

The above diagram indicates that MUA curve is the marginal utility curve for apple and MUA is the marginal utility curve for grapes. The consumer will attain equilibrium when he purchases 4 kg of apples and 3 kg of grapes, so that marginal utilities will be equal i.e., HD = MR. Any other alternative way of spending money income will result in the greater loss than gain to the consumer.

Suppose he spends Rs. 3 on apples and Rs. 4 on grapes. Thus his loss of utility would be CDHG and his gain of utility would be RSNM. Here CDHG > RSNM. Therefore, the only combination Rs. 4 on apples and Rs. 3 on grapes gives him maximum satisfaction than any other combinations.

We can also diagrammatically represent the arithmetic Table-3, which is taken to explain the law of equimarginal utility, in another alternative way as given below.

In the above diagram 3(b) MUA and MUG are the marginal utility of apple and marginal utility of grapes respectively. Both intersect at point S, where MUA = MUC and at that point consumer maximise his satisfaction by spending Rs.4 on apples and Rs. 3 on grapes.

If he will increase 1 unit of grapes his gain would be CDSK and if he will decrease one unit of apple the loss would be CDSR. Here CDSR (Loss) > CDSK (gain) CDSR – CDSK = RSK (net loss).

So it is not wise on the part of the consumer to do so. Therefore, the only combination Rs. 4 on apple and 3 on grapes gives him maximum possible satisfaction.

#### (b) Case-II: When the prices of different commodities are unequal:

In reality, we find that the prices of different commodities the consumer wants to purchase are unequal or different. In this situation, how a consumer attains equilibrium should be explained here.

Let us illustrate the above mentioned aspect of law of equi-marginal utility or consumer’s equilibrium with the aid of an arithmetic example and diagrams.

Let the price of good X and Y be Rs. 2 and Rs. 3 respectively. Reconstructing the above table by dividing marginal utilities of X (MUX) by Rs. 2 and marginal utilities of Y (MUy) by Rs. 3 we get,

With Rs. 19 as the income of the consumer. Suppose his marginal utility of money is constant at Re. 1 = 6 utils. By looking at the table it is clear that MUX / PY is equal to 6 utils when the consumer purchases 5 units of good X and MUY / PY is equal to 6 utils when he buys 3 units of good Y.

Therefore, consumer will be in equilibrium when he is buying 5 units of good X and 3 units of good Y and will be in spending (Rs. (2 x 5) + (3 x 3) = Rs. 19) on them.

The above phenomenon can be graphically portrayed in Fig-4.

Since marginal utility curves of goods slopes downwards, curves depicting MUX / PX and will also scope downward.

Taking the income of a consumer as given, let his marginal utility of money be constant at OM utils. MUX / PX is equal to OM (the marginal utility of money) when OH amount of good X is purchased.MUY / PY is equal to OM when OK quantity of good Y is purchased. Thus, when the consumer is buying OH of X and OK of Y, then MUX / PX = MUY /PY = MUM.

Therefore, the consumer is in equilibrium when he is buying OH of X and OK of Y. No other allocation of money expenditure will yield greater utility than when he is buying OH of X and OK of Y.

If now the Money income of the consumer increases, his marginal utility of money will fall. Suppose, the new marginal utility of money is equal to OM’ then the consumer will increase the purchases of good X and Y to OH’ and OK’ respectively.