The Law of Equi-Marginal Utility or Gossen's Second Law - Owlcation - Education
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# The Law of Equi-Marginal Utility or Gossen's Second Law

## Introduction

The fundamental problem in an economy is that there are unlimited human wants. However, there are no adequate resources to satisfy all human wants. Hence, a rational individual tries to optimize the available scarce resources in order to attain maximum satisfaction. An individual’s attempt to optimize the available scare resources is known as consumer’s behavior. The law of equi-marginal utility explains such consumer’s behavior when the consumer has limited resources and unlimited wants. Because of this reason, the law of equi-marginal utility is further referred to as the law of maximum satisfaction, the principle of income allocation, the law of economy in expenditure or the law of substitution.

## What does the law say?

Suppose that a person possesses \$200 (limited resources). However, his wants are unlimited. The law explains how the person allocates the \$200 among his or her various wants in order to maximize the satisfaction. The point at which the consumer’s satisfaction is maximum with the given resources is known as consumer’s equilibrium. Hence, we can say that the law explains how the consumer’s equilibrium is attained. The law is basically a cardinal utility approach.

Concept of Equi-marginal Utility

Now let us see how an individual maximizes his or her satisfaction with the help of equi-marginal utility. The law says that in order to attain maximum satisfaction, an individual allocates the resources in such a way that he or she derives equal marginal utility from all things on which the resources are spent. For instance, you have \$100 and you spend the money to buy 10 different things. What the law says is that you spend money on each thing in such a way that all the 10 things provide you with the same amount of marginal utility. According to the law of equi-marginal this is the way to attain maximum satisfaction.

## Assumptions of the Law of Equi-Marginal Utility

The following explicit assumptions are necessary for the law of equi-marginal utility to hold good:

1. Consumer’s income is given (limited resources).
2. The law operates based on the law of diminishing marginal utility.
3. The consumer is a rational economic individual. This means that the consumer wants to gain maximum satisfaction with limited resources.
4. The marginal utility of money is constant.
5. Another important assumption is that the utility of each commodity is measurable in cardinal numbers (1, 2, 3 and so on).
6. The prices of the commodities are constant.
7. There prevails perfect competition in the market.

## Explanation of the Law of Equi-Marginal Utility

Let us look at a simple illustration to understand the law of equi-marginal utility. Suppose there are two commodities X and Y. The consumer’s income is \$8. The price of a unit of commodity X is \$1. The price of a unit of commodity Y is \$1.

Assume that the consumer spends all his \$8 to purchase commodity X. Since the price of a unit of commodity X is \$1, he can buy 8 units. Table1 shows the marginal utility derived from each unit of commodity X. since the law is based on the concept of diminishing marginal utility, the marginal utility derived from the subsequent unit diminishes.

## Table 1

Units of Commodity XMarginal Utility of X

1st unit (1st dollar)

20

2nd unit (2nd dollar)

18

3rd unit (3rd dollar)

16

4th unit (4th dollar)

14

5th unit (5th dollar)

12

6th unit (6th dollar)

10

7th unit (7th dollar)

8

8th unit (8th dollar)

6

Consider that the consumer spends all his \$8 to purchase commodity Y. Since the price of a unit of commodity Y is \$1, he can buy 8 units. Table2 shows the marginal utility derived from each unit of commodity Y. since the law is based on the concept of diminishing marginal utility, the marginal utility derived from the subsequent unit diminishes.

## Table 2

Units of Commodity YMarginal Utility of Y

1st unit (1st dollar)

16

2nd unit (2nd dollar)

14

3rd unit (3rd dollar)

12

4th unit (4th dollar)

10

5th unit (5th dollar)

8

6th unit (6th dollar)

6

7th unit (7th dollar)

4

8th unit (8th dollar)

2

Now the consumer plans to allocate his \$8 between commodity X and Y. Let us see how much money he spends on each commodity. Table 3 shows how the consumer spends his income on both the commodities.

## Table 3

Units of Commodities (X and Y)Marginal Utility of XMarginal Utility of Y

1

20 (1st dollar)

16 (3rd dollar)

2

18 (2nd dollar)

14 (5th dollar)

3

16 (4th dollar)

12 (7th dollar)

4

14 (6th dollar)

10

5

12 (8th dollar)

8

6

10

6

7

8

4

8

6

2

Since the first unit of commodity X gives the highest utility (20 utils), he spends the first dollar on X. Second dollar also goes to commodity X as it gives 18 utils (the second highest). Both the first unit of commodity Y and the third unit of commodity X give the same amount of utility. However, the consumer prefers to buy commodity Y because has already spent two dollars on commodity X. Similarly, the fourth dollar is spent on X, fifth dollar on Y, sixth dollar on X, seventh dollar on Y and eighth dollar on X.

In this manner, the consumer consumes 5 units of commodity X and 3 units of commodity Y. In other words, 5 units of commodity X and 3 units of commodity Y leave him with the same amount of marginal utility. Therefore, according to the law of equi-marginal utility, the consumer is at equilibrium at this point. Furthermore, this is point at which the consumer experiences maximum satisfaction. Let us calculate the total utility of commodities consumed to understand this.

Total utility = TUX + Y = TUX + TUY = (20 + 18 + 16 + 14 + 12) + (16 + 14 + 12) = 122

Any other combinations of commodities would have left the customer with less total utility. This is a simple hypothetical illustration to explain how consumer’s equilibrium is attained with the concept of equi-marginal utility.

## Graphical Illustration

Figure 1 details the above explanation graphically. In figure 1, X-axis measures units of money spent on commodity X and Y, or units of commodities (X and Y) consumed. Y-axis measures marginal utility derived from each unit of commodity X and Y.

Condition for Equilibrium

The law states that the consumer is said to be at equilibrium, when the following condition is met:

(MUX/PX) = (MUY/PY) or

(MUx/MUY) = (Px/PY)

In our example, the consumer reaches equilibrium when he consumes the fifth unit of commodity X and third unit of commodity Y ((12/1) = (12/1)).

## Limitations of the Law of Equi-Marginal Utility

Though the law of equi-marginal utility appears to be very convincing, the following arguments are advanced against it:

Firstly, the utility derived from commodities is not measurable in cardinal numbers.

Secondly, the marginal utility of money cannot be constant. As the money you possess depletes, the marginal utility of money increases.

Thirdly, even a rational economic individual does not allocate his or her income according to the law. Usually, people tend to spend in a certain rough fashion. Therefore, the applicability of the law is doubtful.

Finally, the law assumes that commodities and their marginal utilities are independent. However, in real life, we see many substitutes and complements. In this case, the law loses its credibility.

Moon on December 02, 2019:

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hussain on October 18, 2019:

Thank you very much sir it helps me alot rather than other websites

Palak on March 24, 2019:

ndago ngaiyaye on August 09, 2018:

the law may not be accurately applied in every day life. in fact its not practical at all. thank you for explaining in a way that i have understood

M Naseem Nasar on May 16, 2018:

I clearly understand even before.tried do more for us because learning is from one another.

K Subhash on November 06, 2017:

Really very good explanation

subhalaxmi sahoo on October 07, 2017:

nicely describe the topic...i like it

sazar rajbanshi on September 15, 2017:

interesting very good to understand

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Imran Khan on December 07, 2016:

My Topic project is Law of Equi -marginal utility

jazz brar on August 22, 2015:

easy nd understandable..

jazz brar on August 22, 2015:

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rahul on August 20, 2015:

Really gud explaination

david vinay on March 05, 2015:

Nice to understand

shivani on January 16, 2015:

A very gud work.