"The law of equi-marginal utility analyses the equilibrium of the consumer when he consumes more than one good. Comment.

The Law of Equi-Marginal Utility is an economic principle that states that a consumer will allocate their limited resources (such as money) in a way that equalizes the marginal utility per unit of cost across all the goods they consume. By doing so, the consumer maximizes their total utility (satisfaction) from consuming those goods.

Marginal Utility refers to the additional satisfaction a consumer gains from consuming one more unit of a good or service. As a consumer consumes more of a certain good, typically the Marginal Utility decreases, due to the Law of Diminishing Marginal Utility. This means that as more units of a good are consumed, the additional satisfaction gained from each subsequent unit will be less than the satisfaction gained from the previous unit.

A consumer is said to be in equilibrium when they have allocated their resources in such a way that they have maximized their total utility. This occurs when the consumer can no longer increase their satisfaction by reallocating their money between the goods they are consuming. The consumer's equilibrium condition can be mathematically represented as the ratio of Marginal Utility (MU) to the price (P) of a good being equal across all goods consumed, i.e., \[\frac{MU_{1}}{P_{1}} = \frac{MU_{2}}{P_{2}} = \cdots = \frac{MU_{n}}{P_{n}}\]

To achieve equilibrium, the consumer should allocate their resources such that the Marginal Utility per unit of cost is equal for all goods they consume. As the consumer increases their consumption of a good, the Marginal Utility begins to decrease due to the Law of Diminishing Marginal Utility, while the cost remains the same. As a result, the consumer will allocate their money between goods in a manner that equates the marginal utility per dollar spent on each good. When the marginal utility per dollar spent is equal across all goods, the consumer cannot increase their total utility by spending more on one good and less on another. When this equilibrium condition is met, the consumer has maximized their total utility, and the Law of Equi-Marginal Utility is satisfied.