# Equimarginal Principle

The equimarginal principle states that consumers allocate their money such that the marginal utility per dollar of each good is the same because this is how they maximize their total utility.

Marginal utility is the additional satisfaction derived by a consumer by consuming one additional unit of a good. The law of diminishing marginal utility dictates that the marginal utility decreases with each additional unit consumed. Because different goods have different prices, their marginal utilities can’t be compared directly. This is where the concept of marginal utility of income becomes relevant. Marginal utility of income is the marginal utility of a good per dollar.

Consumers adjust their choices in the descending order of the marginal utility of income (i.e. marginal utility per dollar) of different products. They prefer a good that offer higher marginal utility per dollar over any other good with lower marginal utility per dollar. They consume more of a good whose marginal utility of income is higher than the average marginal utility of income and vice versa. This dynamically leads to a situation in which the marginal utility per dollar of all goods is the same.

$$\frac{{\rm \text{MU}} _ \text{A}}{\text{P} _ \text{A}}=\frac{{\rm \text{MU}} _ \text{B}}{\text{P} _ \text{B}}=\frac{{\rm \text{MU}} _ \text{C}}{\text{P} _ \text{C}}=\text{...}=\frac{\text{MU}}{\text{\}}$$

Where MUs stands for marginal utility and Ps represents the prices.

## Example

Let’s consider a consumer who has allocated $250 per month for dine-outs. Meals at Restaurant A and Restaurant B cost$30 and $35 respectively. The following table shows their marginal utilities (MU)and marginal utilities of income (MU/$):

Units MU(A) MU(A)/$MU(B) MU(B)/$
1 200 6.67 300 7.50
2 180 6.00 270 6.75
3 160 5.33 240 6.00
4 140 4.67 210 5.25
5 120 4.00 180 4.50
6 100 3.33 150 3.75
7 80 2.67 120 3.00
8 60 2.00 90 2.25

The first meal at Restaurant B yield the highest marginal utility per dollar i.e. 7.50, so a rational consumer should decide to spend the first $35 dollars at Restaurant B. The second meal also yields the highest satisfaction per dollar at Restaurant because it has a marginal utility per dollar of 6.75 as compared to marginal utility per dollar of 6.67 offered by a meal at Restaurant A. For the third meal, the consumer should go to Restaurant B because it gives a MU/$ of 6.67. For the fourth meal, there is a tie between Restaurant A and Restaurant B. The consumer will switch between these two choices by looking at the marginal utility of income per unit consumed.

The above example is a simplification. In real life, consumers must choose between a range of different choices and the calculus becomes more complex. Equimarginal principle of utility dictates that consumers will allocate their dollars such that marginal utility of income i.e. MU/$derived from consumption of all goods is the same. The quimarginal principle and the law of diminishing marginal utility can explain the law of demand i.e. why a demand curve slopes downward. Because consumers attempt to equate the marginal utility of income of all goods, if price of a good rises, in accordance with law of diminishing marginal utility, consumers reduce the quantity demanded to increase the marginal utilty and rebalance its MU/$ to the equilibrium MU/\$.