### Law of Substitution

The law of substitution was at first pointed bout by H. H. Gossen. Hence, this law is called Gossen’s Second Law. This law is also known as law of equi-marginal utility and law of maximum satisfaction.

We know that human wants are unlimited whereas the means to satisfy those wants are limited. So a consumer tries to get maximum satisfaction out if his expenditure. For this he allocates his expenditure among several uses in such a way so as to maximize satisfaction. According to Watson and Getz –“The best, or optimum allocation is one that causes the marginal utilities in each use to be equal”. He will get maximum satisfaction only when he obtains equal marginal utilities from the consumption of different commodities. If this does not happen, the consumer can improve his satisfaction by reducing expenditure in one use and expanding in another words, he substitutes one commodity for another until the marginal utilities from all commodities are equal. This law can be illustrated by the help of a table below.

Law of Substitution
 Units MU of Orange MU of Apple 1 2 3 4 5 6 10 8 6 4 2 0 8 6 4 2 0 -2

Suppose that the consumer has \$7 to spend on orange and apple. The price of orange is \$1 per unit. The utility obtained from different units of orange and apple is presented in table. According to the law, the consumer will purchase that unit of orange and apple, which gives him maximum satisfaction. He will therefore, purchase 4 units of orange and 3 units of apple. The marginal utilities of both orange and apple are same, i.e. 4. He derives total utility = 10 + 8 + 6 + 4 = 28, 8 + 6 + 4 = 18 = 46. So, the total utility is equal to 46.

Any other combination or arrangement will not give him so much satisfaction or utility. As for example, if he purchases 3 units of orange and 4 units of apple, total utility will be equal to only 44 which is less than 46. In brief, the consumer obtains maximum satisfaction when marginal utilities from all goods purchased are equal.

The law of equi-marginal utility can be illustrated by the help of figure below. In the figures below, OX axis represents units of money and OY axis represents marginal utility. Suppose that money can be spent on commodities apple and orange. MUA and MUO curves relate to commodity apple and orange respectively. The shapes of curve MUA indicates that the desire for commodity apple is stronger. This means that the marginal utility of any quantity of money in commodity orange is greater than that of the same quantity in commodity apple. Because MUO curve is farther from the vertical axis than MUO curve. Likewise MUO curve begins from the vertical axis at a higher point than does curve MUA. Equimarginal Principle
Now suppose that the consumer has \$7 to spend on apple and oranges. In the figure, the best allocation is \$3 in commodity apple and \$4 in commodity orange. Because, with these quantities, the marginal utilities are equal in both commodities, i.e. PM = P’M’. Hence, this is the best allocation of money. Any other combination will give less total satisfaction.

If \$4 is devoted to commodity apple and \$3 to commodity orange, the gain would be the area between 3 and 4 under MU curve in commodity apple. But there would be loss of area between 3 and 4 under MU curve in commodity orange. It is clear that the loss of utility from reduced consumption of orange is greater than the gain of utility from increased consumption of apple. Hence the total utility of new combination is less. Any other allocation will make a loss in utility greater than gain in utility.

The total utility of any quantity is always the area under the marginal utility curve. When marginal utilities in two commodities are equal, total utility or the entire shaded area in the figure is at a maximum. Any change in allocation of \$7 can only reduce total utility.

The equi-marginal principle can be generalized. Any decision maker can obtain maximum return from a given quantity of a resource that has two or more uses of the allocated units of resources in such a way that the marginal returns in each use are equal.

### Limitations of the Law of Substitution

There are several limitations of this law, which can be explained as follows:
1. Increase of marginal returns: For this law to hold, marginal returns must diminish as more and more units of a resource are applied to any one of its uses. Hence, this law may not apply if the marginal utility increases instead of diminishing.
2. Custom and fashion: When people are influenced by traditions, custom and fashion, they may not behave rationally. They do not try to spend so as to maximize satisfaction. This implies that they spend more where marginal utility is less.
3. Ignorance: The ignorance of people prevents them from making good uses of money. They cannot judge where utility is higher or where utility is lower. They cannot maximize satisfaction by equalizing marginal utilities in all uses.
4. Unlimited resources: This law has no use in case of goods available in unlimited quantity. As for example, the free gift of nature like sunshine, air is found in abundance. People need not make rational use of them.
5. Indivisibility: Some durable consumer goods like motorcar, TV, refrigerator, smartphone is indivisible. For this law to hold goods should be divisible and substitutable. Hence, this law cannot be applied effectively in case of the indivisible goods.
6. Instability in prices: The consumer may be able to adjust expenditure so as to maximize satisfaction in case of the frequent changes in prices. Because, utility is always weighted in terms of prices of goods.

### Importance of the law of substitution

The resources are always limited with the people. So, they should make the best use of available resources. Due to this, the law of substitution has great practical importance. The importance of this law can be explained as follows:
• Consumption: This law is of special significance to the consumers. The consumers have limited money income. But their wants are unlimited. Hence, they should make the best use of money so as to maximize satisfaction. They should substitute the goods with low utility by goods with high utility.
• Production: This law holds goods even in production. The aim of a firm or producer is to maximize profit. For this he should select the best combinations of factors of production. He should spend more on the factors, which yield highest returns. He should substitute one factor for another till the marginal productivity of all the factors is equal.
• Exchange: This law has significance even in exchange. The exchange, in reality, is the substitution of one commodity for other. People get money by selling vegetable. They buy clothes with that money. So, clothes has greater marginal utility to them than vegetable. They have in fact, substituted clothes for vegetable.
• Distribution: One of the important theories of distribution is that factors of production should be rewarded on the basis of their marginal productivity. A firm uses each factor to the point where the marginal productivity of a factor is equal to the marginal product of other factors. This implies the substitution of one factor for other.
• Public Finance: This law is relevant even in the field of public finance. The public expenditure is made to as to maximize social welfare. Hence, the government diverts resources from less productive to the more productive sectors. The government imposes more taxes to the rich than to the poor, so that the burden of taxation is equal. Likewise, the government spends more on welfare of the poor than the rich so that benefit of expenditure is equal.

In this way, the law of substitution has wide application in all branches of economic theory. Besides, it has also practical significance. The men follow this law either consciously or unconsciously. As opined by Chapman- “We are not compelled to distribute all income according to the law of satisfaction as a stone thrown into the air is compelled to fall back to earth. But as a matter of fact, we do it in a certain rough fashion because we are reasonable.”