A consumer is in equilibrium position when he/she achieves maximum satisfaction out of the available resources. A consumer in an equilibrium position when he/she distributes expenditure on purchase of different goods in such a way that marginal utility of a different good is equal to that of the good. This behaviour of customers is called the law of equal marginal utility. Based on the mention assumption the consumer will maximize this utility if he allocates his income in such a way that a shilling spent on one good yield as much satisfaction as a shilling spent to any other goods. The marginal utility per shilling spent on good X equals to the marginal utility spent on good Y hence consumer equilibrium is obtained when
Marginal utility x = Marginal Utility of Y
Price of X Price of Y
Mux =Muy
PX PY

The law of diminishing marginal utility is also based on the assumption that the consumer is rational. An economic agent is said to be rational when the agent exhibits behaviour which is consistent with a set of rules governing preferences. In the context of consumer behavior this would imply the following assumption or axioms;

• The axiom of dominance which implies that consumers will always prefer more goods or less. This is also known as the axiom of non- satiation
•  The axiom of selection which relates to the idea that the consumer aims for his or her most preferred state.
• The axiom of completeness states that the consumer is able to order al the available combinations of goods according to his or her preferences.
• The axiom of transivity states that if in some combination of goods; A is preferred to B and B is preferred to C then (by transivity) A is preferred to C.

Importance of Law of Equal Marginal Utility
1) It is application in consumption .A consumer can achieve maximum satisfaction when utility of different commodities is equal since the objective is to achieve maximum satisfaction.
2) Application in production. Objective of the firm is to maximize profit achieved when cost of production is minimal and when marginal productivity of all factors is equal.
3) Application is distribution. When share of different factors of production are determine, they are determined according to the principal of marginal utility
4) Application in saving and spending. A special part of the income is spent on purchase of consumer good and the remaining saved for future use.

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