Law of Equi Marginal Utility:

The law of equi marginal utility was presented in 19th century by an Australian economists H. H. Gossen. It is also known as law of maximum satisfaction or law of substitution or Gossen's second law. A consumer has number of wants. He tries to spend limited income on different things in such a way that marginal utility of all things is equal. When he buys several things with given money income he equalizes marginal utilities of all such things. The law of equi marginal utility is an extension of the law of diminishing marginal utility. The consumer can get maximum utility by allocating income among commodities in such a way that last dollar spent on each item provides the same marginal utility.

Definition:

"A person can get maximum utility with his given income when it is spent on different commodities in such a way that the marginal utility of money spent on each item is equal".

It is clear that consumer can get maximum utility from the expenditure of his limited income. He should purchase such amount of each commodity that the last unit of money spend on each item provides same marginal utility.

Assumptions of the Law of Equi Marginal Utility:

1. There is no change in the prices of the goods.
2. The income of consumer is fixed.
3. The marginal utility of money is constant.
4. Consumer has perfect knowledge of utility obtained from goods.
5. Consumer is normal person so he tries to seek maximum satisfaction.
6. The utility is measurable in cardinal terms.
7. Consumer has many wants.
8. The goods have substitutes.

Explanation With Schedule and Diagram:

The law of substitution can be explained with the help of an example. Suppose consumer has six dollars that he wants to spend on apples and bananas in order to obtain maximum total utility. The following table shows marginal utility (MU) of spending additional dollars of income on apples and bananas:

Money (Units)	MU of apples	MU of bananas
1	10	8
2	9	7
3	8	6
4	7	5
5	6	4
6	5	3

The above schedule shows that consumer can spend six dollars in different ways:

1. $1 on apples and $5 on bananas. The total utility he can get  is:
   [(10) + (8+7+6+5+4)] = 40.
2. $2 on apples and $4 on bananas. The total utility he can get is:
   [(10+9) + (8+7+6+5)] = 45.
3. $3 on apples and $3 on bananas. The total utility he can get is:
   [(10+9+8) + (8+7+6)] = 48.
4. $4 on apples and $2 on bananas. This way the total utility is:
   [(10+9+8+7) + (8+7)] = 49.
5. $5 on apples and $1 on bananas. The total utility he can get is:
   [(10+9+8+7+6) + (8)] = 48.

Total total utility for consumer is 49 utils that is the highest obtainable with expenditure of $4 on apples and $2 on bananas. Here the condition MU of apple = MU of banana i.e 7 = 7 is also satisfied. Any other allocation of the last dollar shall give less total utility to the consumer.

The same information can be used for graphical presentation of this law:

The diagram shows that consumer has income of six dollars. He wants to spend this money on apples and bananas in such a way that there is maximum satisfaction to the consumer.

Limitations:

1. The law is not applicable in case of knowledge. Reading of books provides more satisfaction and knowledge to the scholar. Different books provide variety of knowledge and satisfaction.
2. The law is not applicable in case of indivisible goods. The consumer is unable to divide the goods to adjust units of utility derived from consumption of goods.
3. There is no measurement of utility. It is psychological concept. It is not possible to express it into quantitative form.
4. The law does not hold well in case fashion and customs. The people like to spend money on birthdays, marriages and deaths.
5.  The does not hold well in case of very low income. The maximization of utility is not possible due to low income.
6. The law is not applicable in case of durable goods. The calculation of marginal utility of durable goods is impossible.
7. The law fails when goods of choice are not available. The consumer is bound to use commodity, which provides low utility due to non availability of goods having high utility.
8. There are certain lazy consumers. They do not care for maximum utility. The law fails to operate in case of laziness of consumers. They go on consuming goods with comparing utility.
9. It does not work when there are frequent prices changes. The consumer is unable to calculate utility of different commodities. Changing price levels create confusion in the minds of consumers.
10. There may be unlimited resources. The does not work due to unlimited resources. There is no need to change the direction of expenditure from one item to another when there are gifts of nature.

Importance:

1. The law of equi marginal utility is helpful in the field of production. The producer has limited resources. He uses limited resources to purchase production factors. He tries to equalize marginal utility of all factors. He wishes to get maximum output and profit.
2. National income is distributed among factors of production according to this law. An entrepreneur can pay factors of production equal to marginal product measured in money terms. He will substitute one factor for another until marginal productivity of all factors is equal to prices of their services.
3. The law is used in the field of exchange. The people like to exchange a commodity having low utility with a commodity having high utility. There is maximum benefit from exchange of commodities. The law is helpful in exchange of wealth, trade, import and export.
4. The law is applicable in consumption. A rational consumer tries to get maximum satisfaction when he spends his limited resources on various things. He tries to equalize weighted marginal utility of all the things.
5. The law is applicable in public finance. The government can spend its revenue to get maximum social advantage. The marginal utility of each dollar spent in one sector must be equal to marginal utility derived from all other sectors.
6. The law is useful for workers in allocating the time between work and rest. They can compare the marginal utility of work and the marginal utility of rest. They can decide working hours and rest hours.
7. The law holds well in case of saving and spending. The consumer can make choice between present wants and future wants. He can feel that a dollar saved has greater utility than a dollar spent, he can save more and spend less. He will substitute saving and spending till marginal utility of a dollar spent and a dollar saved are equal.
8. The law is helpful in prices. Due to scarcity of commodity its prices go up. The law tells us to use substitute commodity, which is less scarce. The result is that the price of commodity comes down.