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The Law of Equi-Marginal Utility/ The Law of Substitution
The law of equi-marginal utility was propounded by the German economist Hermann Heinrich Gossen. Therefore, this law is also known as 'Gossen's Second Law'.
According to this law, a consumer spends their limited resources on two or more goods in such a way that they obtain maximum utility or satisfaction. Hence, this law is also known as the 'Law of Maximum Satisfaction'.
Consumers have limited resources to spend on goods. As a consumer consumes more of a good, the utility derived from it decreases. Therefore, according to this law, to maximize satisfaction from the consumption of goods, a consumer will substitute units of a good that provide less utility with units of a good that provide more utility and continue consumption.
Hence, this law is also known as the 'Law of Substitution'. This law is based on the assumption that a consumer consumes two or more goods or services, not just one.
According to economist Alfred Marshall, "If a person has a thing which he can put to several uses, he will distribute it between these uses in such a way that it has the same marginal utility in all."
In this way, a consumer takes away some resources from a good that yields less marginal utility and uses them on a good that yields more marginal utility and finally makes the marginal utility derived from all goods equal to each other. In this state, the utility derived by the consumer is maximum.
Assumptions of the Law of Equi-Marginal Utility
(a) The consumer is rational, meaning they spend their limited income on goods in such a way as to obtain maximum satisfaction.
(b) The consumer consumes only two goods (apples and oranges).
(c) The units of each good consumed are homogeneous.
(d) The units of the goods consumed are appropriate, standard, and defined, and the period of consumption is fixed.
(e) There should be no change in the consumer's habits, interests, tastes, and preferences during the consumption process.
(f) The prices of the goods consumed and the consumer's income are given, i.e., fixed.
(g) The utility derived from the consumption of units of the good can be measured numerically.
(h) The law of diminishing marginal utility applies during the consumption of goods.
Based on the assumptions mentioned above, the law of equi-marginal utility is clarified in the table below.
Let's assume a consumer has resources or income of Rs. 5. They spend this Rs. 5 on two goods, say, apples and oranges. The price per unit of apples and oranges is Rs. 1, i.e., the same. According to the law of equi-marginal utility, the consumer spends the Rs. 5 they have on goods in such a way that the total utility or satisfaction they derive is maximum.
The consumer's total utility or satisfaction is maximum only when they spend their entire amount on the two goods, i.e., apples and oranges, in such a way that the marginal utility derived from the last unit of each good is equal.
Table of the Law of Equi-Marginal Utility
| Units of Goods | Marginal Utility of Apples (in Utils) | Marginal Utility of Oranges (in Utils) |
|---|---|---|
| First | 12 (First Rupee) | 9 (Third Rupee) |
| Second | 10 (Second Rupee) | 8 (Fourth Rupee) |
| Third | 8 (Fifth Rupee) | 7 |
| Fourth | 6 | 6 |
| Fifth | 4 | 5 |
| Total | 40 | 35 |
The consumer compares the marginal utility derived from different units of the two goods given in the table. They spend the first rupee on purchasing the first unit of apples because it gives them the highest utility or marginal utility of 12 utils.
Now they spend the second rupee on purchasing the second unit of apples because the second unit of apples gives utility or marginal utility of 10 utils. But the consumer now spends the third rupee on oranges because the first unit of oranges gives them utility or marginal utility of 9 utils.
Similarly, they spend the fourth rupee on the second unit of oranges, from which they derive utility or marginal utility of 8 utils. Now the consumer spends the fifth rupee on apples instead of oranges because the third unit of apples gives them more marginal utility than the third unit of oranges.
Therefore, when the consumer's monetary income is Rs. 5 and the price per unit of both goods is Rs. 1, i.e., the same, they obtain maximum satisfaction by consuming 3 units of apples and 2 units of oranges, or they obtain a total utility of 12 + 10 + 9 + 8 + 8 = 47 utils.
This is their state of maximum total utility or equilibrium. In this state, the consumer has spent all the money they had on the consumption of the two goods. Also, the utility or marginal utility derived from the last unit of both goods is equal. Any other situation besides this cannot be their state of maximum satisfaction.
Here, if the consumer spends all the Rs. 5 they have on purchasing apples, they can buy 5 units of apples, from which they will only get a total utility of 40 utils. Similarly, if they spend all the Rs. 5 they have on purchasing oranges, they can buy 5 units of oranges, from which they will only get a total utility of 35 utils.
If the consumer purchases and consumes 2 units of apples and 3 units of oranges instead of 3 units of apples and 2 units of oranges with the Rs. 5 they have, they will only get a total utility of 12 + 10 + 9 + 8 + 7 = 46 utils.
Therefore, the only option for the consumer to achieve maximum satisfaction is the consumption of 3 units of apples and 2 units of oranges. Any other option besides this cannot give them maximum satisfaction or maximum total utility.
Explanation of the law of Equi-marginal utility with Example
Lest us suppose that a consumer who has 7 rupees to spend on apples and oranges, with the marginal utilities (MU) of each unit given in the table below. The consumer initially spends 3 rupees on oranges and 4 rupees on apples.
The MU of the 3rd orange is 6, whereas the MU of the 4th apple is only 2. As the marginal utility of oranges is higher, the consumer should buy more oranges and lesser apples.
By substituting one orange for one apple, the consumer ends up purchasing 4 oranges and 3 apples. Now, the MU of both goods becomes equal (4 utils each), getting maximum satisfaction. The total utility is:
4 oranges: 10 + 8 + 6 + 4 = 28 utils
3 apples: 8 + 6 + 4 = 18 utils
Total Utility: 46 utils (higher than any other combination)
Table of Marginal Utility
| Units | Marginal Utility of Oranges | Marginal Utility of Apples |
|---|---|---|
| 1 | 10 | 8 |
| 2 | 8 | 6 |
| 3 | 6 | 4 |
| 4 | 4 | 2 |
| 5 | 2 | 0 |
| 6 | -2 | -2 |
| 7 | -4 | -4 |
| 8 | -6 | -6 |
Graphical Representation of the law of Equi-marginal utility
In the diagram, the X-axis represents the units of money spent on apples and oranges, while the Y-axis represents marginal utility. The AP curve represents the marginal utility of apples, and the OR curve represents the marginal utility of oranges.
The consumer reaches equilibrium at point M (3 rupees spent on apples) and M’ (4 rupees spent on oranges), where PM = P'M'. Any other allocation would result in lower total satisfaction.
If the consumer reallocates MN money (1 rupee) from oranges to apples, they lose the utility represented by LN'M'P' (from reduced orange consumption) and gain utility PMNE (from increased apple consumption). However, since LN'M'P' > PMNE, the total utility decreases. Hence, the consumer attains maximum satisfaction when MU of both goods is equal.
Limitations or Exceptions of the Law of Equi-Marginal Utility
The situations where the law of equi-marginal utility does not apply or is not effective are the limitations or exceptions of this law. These limitations or exceptions are as follows:
(a) If the consumer is not rational: A consumer is considered rational if they spend their limited resources on purchasing goods in such a way as to obtain maximum satisfaction. This law does not apply if the consumer is not rational.
(b) If the law of diminishing marginal utility does not apply: The law of equi-marginal utility is based on the law of diminishing marginal utility. Therefore, this law does not apply in situations where the law of diminishing marginal utility does not apply.
(c) If the marginal utility of money is not constant: This law is based on the assumption that the utility derived from the consumption of goods can be measured numerically in terms of money or in hypothetical units called utils. Therefore, this law assumes that the marginal utility of money is constant. However, this law does not work if the marginal utility of money is not constant but variable or if utility cannot be measured numerically.
(d) If the consumer's income and the prices of goods change during the consumption period: If the consumer's income or the price of goods changes during the consumption period, the utility derived from that good changes, and the consumer's equilibrium state also changes, meaning the law of equi-marginal utility does not apply.
(e) If the consumer's habits, interests, preferences, fashion, etc., change: If the consumer's habits, interests, preferences, fashion, etc., change during the consumption period, the law of equi-marginal utility does not apply in this situation, meaning the consumer's equilibrium state changes.
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