The Law of Equi-Marginal Utility: Definitions and Core Principles

The Law of Equi-Marginal Utility addresses the competitive nature of human wants and the necessity of choosing between more urgent and less urgent needs. When a consumer decides to buy a little more or a little less of a commodity, they are attempting to balance the marginal utility of the commodity against the marginal utility of money. The law posits that a consumer will adjust the quantity of different goods by changing their purchasing plan in such a way that the marginal utilities of all goods purchased become equal. This law applies specifically when a consumer purchases two or more goods. A consumer is said to be in equilibrium when they spend their income on various goods in such a way that the marginal utility of money in every direction of purchase is the same. Alternatively, it can be defined as a state where the marginal utility ($MU$) of every Rupee spent on each good is equal. The law states that maximum total utility will be achieved only if the consumer divides their expenditure such that the marginal utility of the last unit of money spent on various goods remains the same.

Numerical Illustration of Consumer Equilibrium

Consider a consumer with 5 units of money to spend on two goods: flour and ghee. In this example, one unit of money is defined as $100\,Rs$. The marginal utilities for these goods fluctuate based on the amount of money units spent. If all 5 units are spent on flour, the marginal utilities derived from each successive unit are $24$, $20$, $16$, $12$, and $8$, resulting in a total utility ($TU$) of $80$. If all 5 units are spent on ghee, the marginal utilities are $20$, $16$, $12$, $8$, and $4$, resulting in a total utility of $60$. To maximize satisfaction, the consumer seeks an arrangement where marginal utilities are equal. By spending three units of money on flour and two units on ghee, the marginal utility of the third unit of flour is $16$, and the marginal utility of the second unit of ghee is also $16$. Under this arrangement ($16 = 16$), the total budget is exhausted, and satisfaction is maximized. The total utility from flour is $24 + 20 + 16 = 60$, and the total utility from ghee is $20 + 16 = 36$. The aggregate utility of both goods combined is $60 + 36 = 96$. This aggregate utility of $96$ is higher than the total utility achieved by spending all money on either flour ($80$) or ghee ($60$).

Comparative Analysis of Utility Allocation

If the consumer chooses any combination where marginal utilities are not equal, their total satisfaction will fall. For example, if the consumer spends one additional unit of money on flour (making it 4 units total), the total utility for flour becomes $24 + 20 + 16 + 12 = 72$. However, the consumer is then left with only one unit of money to spend on ghee, where the marginal utility is $20$. The new aggregate utility would be $72 + 20 = 92$, which is less than the optimal $96$. Diagrammatic analysis shows that when the consumer spends the 4th unit of money on flour, the addition in marginal utility is $12$. Because they must sacrifice the 2nd unit of ghee to do so, the decrease in marginal utility from ghee is $16$. Since the decrease ($16$) is greater than the addition ($12$), there is a net loss of $4$ units of utility. This confirms that the consumer cannot maximize satisfaction without equalizing marginal utilities.

General Equilibrium and Commodity Prices

In scenarios involving commodity prices, the consumer reaches equilibrium by equating the price of a good with its marginal utility, represented as $MU_x = P_x$. If a consumer is purchasing more than two goods, they will equate the marginal utilities to their respective prices such that $MU_x = P_x$, $MU_y = P_y$, and $MU_n = P_n$. Dividing both sides by the prices yields the normalized equilibrium condition: $\frac{MU_x}{P_x} = \frac{MU_y}{P_y} = \dots = \frac{MU_n}{P_n}$. Consequently, a consumer is said to be in equilibrium when the ratio of the marginal utility and the price for all goods becomes equal.