Explanation of the law:

Assume that there are two goods X and Y on which a consumer has to expend a specified income. The consumer being rational, he will attempt to spend his inadequate income on goods X and Y to maximize his total utility or fulfillment. Only at that point the consumer will be in symmetry.

According to the law of equi-marginal utility, the consumer will be in balance at the point where the utility derived from last income spent on each is equivalent.

Representatively the consumer will be in equilibrium if,

MU_x/P_x = MU_y/P_y = MU_m

Here,

MU_x = Marginal utility of commodity X
MU_y = Marginal utility of commodity Y
P_x = Price of commodity X
P_y = Price of commodity Y
MU_m = Marginal utility of money.

MU_x/P_x and MU_y/P_y are termed as marginal utility of money expenditure. They elucidate the marginal utility of one rupee used up on commodity X and the marginal utility of one rupee used up on commodity Y.

Let us exemplify the law of equi marginal utility with the help of the table shown below:

Table: Marginal utility of Goods X and Y

 

Table: Marginal utility of money expenditure

Assume that the marginal utility of money is steady at $ 1 = 5 units, then the consumer will purchase 6 units of commodity ‘x’ and 5 units of commodity ‘y’. His net expenditure will be ($ 5 x 6) + ($ 4 x 5) = $ 50/- on both commodities. At this position of expenditure his satisfaction is maximized and hence he will be in balance.

Figure: Consumer’s Equilibrium

Consumer’s equilibrium is graphically illustrated in figure shown above as marginal utility curves of goods slope down, curves depicting MUx/Px and MUy/Py will also slope downward. Taking the income of a consumer as specified, let his marginal utility of money be steady at OM utils in figure shown above. MUx/Px is equivalent to OM (i.e., the marginal utility of money) whenever OH amount of good x is bought; MUy/Py is equivalent to OM whenever OK quantity of good Y is purchased. Therefore, when the consumer is purchasing OH of X and OK of Y, then,

MU_x/P_x = MU_y/P_y = MU_m

Thus, the consumer will be in equilibrium whenever he purchases OH of X and OK of Y. No other allotment of money expenditure wills outcome greater utility than whenever he buys OH of X and OK of Y. Assume that the money income of the consumer falls. Then the new marginal utility of money will be equivalent to OM; then the consumer will raise the purchases of good X and Y to OH and OK correspondingly.

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