Explain The Principle Of Equimarginal Utility?

In economics it is known as law of Equi-marginal Utility. It basically shows the behavior of a consumer in allocating his limited earnings among different goods and services. In short this law tells that how a consumer distributes his earnings between set of goods so as to get maximum satisfaction.

The Principle of euqmarginal utility states that a rational consumer will always try to maximise his satisfaction by buying a combination of two or more goods which give him maximum marginal utility per dollar for each good, until the budget is used up completely.

Mathematically, it means:

MU of good A/ Price of A = MU of good B/ Price of B

In any case when the Marginal Utilities of the goods A and B are unequal, the consumer will purchase a combination that will give him highest Marginal Utility per dollar value of each good, in such a way that the entire budget amount is spent.

We will use the utility theory to explain consumer demand and to understand the nature of demand curves. For this purpose, we need to know the condition under which I, as a consumer, am most satisfied with my market basket of consumption goods. We say that a consumer attempts to maximize his or her utility, which means that the consumer chooses the most preferred of goods from what is available.
Can we see what a rule for such an optimal decision would be? Certainly I would not expect that the last egg I am buying bring exactly the same marginal utility as the last pair of shoes I am buying, for shoes cost much more per unit than eggs. A more sensible rule would be: If good A costs twice as much as good B, then buy good A only when its marginal utility is at least twice as great as good B's marginal utility.
This leads to the equimarginal principle that I should arrange my consumption so that every single good is bringing me the same marginal utility per dollar of expenditure. In such a situation, I am attaining maximum satisfaction or utility from my purchases. This is clear concept of equimarginal principle.

This theory is propounded by H.H Gossen and called second law of Gossen. It was developed by Alfered Marshall and all the credits are given to Alfred Maeshall.
This theory states that a rational consumer spent his total budget between or among the goods he will derived marginal utility from the last money purchased of goods.