 # Equimarginal Principle

## Statement

The equimarginal principle states that by keeping other things constant, if a consumer spends his income on different commodities, he or she will get maximum satisfaction when marginal utility per unit of money is the same for each commodity.

This principle is also known as the law of substitution or the law of maximum satisfaction.

This principle is used to find consumer equilibrium when a consumer consumes multiple commodities.

## Origin

The equimarginal principle is explained by many economists and given due importance. This concept was first introduced by H. H. Gossen, a Prussian Civil Servant (1810–1858), and was further popularised by British economist Alferd Marshall. This principle is basically an extension of the law of diminishing marginal utility in managerial economics.

## Equation

Assuming that a consumer is consuming two goods, A and B, the equation or formula for consumer equilibrium is as follows:

The consumer will be in equilibrium, and his or her total utility will be maximised, when the above equation is satisfied. MU/price is called the marginal utility of expenditure on each unit of good.

## Assumptions

The equimarginal principle has the following assumptions:

### Multiple Commodities

The consumer is consuming two goods, A and B.

### Cardinality

Utility can be measured numerically.

### Rationality

The consumer is a rational decision maker.

### Prices

The prices of goods A and B are constant.

### Income

The money income of the consumer is constant.

### Marginal Utility of Money

The marginal utility of money is constant.

### Taste and Fashion

Taste and fashion remain constant during the period of consumption.

### Size of Commodity

The units of goods A and B are of reasonable size.

### Objective

The objective of the consumer is to maximise total utility.

## Basic Terms

### Utility

The power of a commodity to satisfy a human want is called utility.

### Marginal Utility (MU)

The extra satisfaction gained by a consumer from the consumption of an extra unit of a commodity is called its marginal utility.

### Total Utility (TU)

Total satisfaction gained by a consumer from the consumption of a given quantity of a commodity is called total utility.

### Cardinal Utility

The utility that can be measured numerically is called cardinal utility. Its unit of measurement is called `Util’.

### Consumer Equilibrium

A consumer is said to be in equilibrium when he/she allocates income in such a way that total satisfaction is maximised and there is no tendency to change that state.

## Understanding the Equimarginal Principle with a Data Example

Suppose that the consumer has a constant money income of \$5 and the price of each of goods A and P is \$1. The following data is also assumed:

 Quantity of A MU of A Quantity of B MU of B 0 --- 0 --- 1 12 1 14 2 10 2 12 3 8 3 10 4 6 4 8 5 4 5 6

Now let’s calculate the marginal utility per unit of money for each commodity.

 Quantity of A MU of A/Price of A Quantity of B MU of B/Price of B 0 --- 0 --- 1 12 1 14 2 10 2 12 3 8 3 10 4 6 4 8 5 4 5 6

The equation of the marginal utility principle is satisfied for 2 units of good A and 3 units of good B. Also, all of the consumer income (\$5) is spent on this combination. Hence, the consumer should consume 2 units of A and 3 units of B to maximise total utility (TU).

## Application of the Marginal Utility Principle

### Case 1: When MU of A/Price of A > MU of B/Price of B

In this situation, the consumer is not in equilibrium. The consumer is getting a higher MU from the last \$ spent on good A than from good B. So, the consumer will reallocate his spending by increasing the quantity of good A and decreasing the quantity of good B. In this way, consumer equilibrium will be achieved.

### Case 2: When MU of A/Price of A = MU of B/Price of B

In this situation, the consumer is in equilibrium, and there is no tendency to change that state. The consumer is getting the same MU from the last \$ spent on good A and on good B. So, the consumer is getting the maximum TU.

### Case 3: When MU of A/Price of A < MU of B/Price of B

In this situation, the consumer is not in equilibrium. The consumer is getting a higher MU from the last \$ spent on good B than from good A. So, the consumer will reallocate his spending by increasing the quantity of good B and decreasing the quantity of good A. In this way, consumer equilibrium will be achieved.

## Derivation of Demand Curve

The consumer equilibrium, according to the law of equimarginal utility, is where

MU of A/Price of A = MU of B/Price of B.

If the price of good A is decreased, then MU of A/Price of A will be greater than MU of B/Price of B.

In this situation, the consumer is getting a higher MU from the last \$ spent on good A than from good B. So, the consumer will reallocate his spending by increasing the quantity of good A and decreasing the quantity of good B.

Hence, the quantity of good A will increase as a result of a decrease in its price. This explains the inverse relationship between the price of good A and its quantity demanded, which can also be represented by the following downward-sloping demand curve. The quantity demanded of good A is taken on the horizontal axis (X-axis), and the price of good A is taken on the vertical axis (Y-axis). A graph of downward-sloping demand curve derived by using the equimarginal principle.

## Limitations of Equimarginal Principle

Despite its merits, the equimarginal principle has a few limitations:

### Cardinality

The equimarginal principle assumes that the utility is cardinal and it can be numerically. In reality, this is not true. There is no device invented so far which can measure utility.

### Rationality

The equimarginal principle assumes that the consumer is a rational decision maker with perfect information, which may not always be the case in the real world. The consumer may consume goods out of a habit or may purchase them under the influence of adverting or impulse.

### Prices

The prices of goods A and P may not be constant.

### Size of the Commodity

The equimarginal principle assumes that the units of goods A and B are of reasonable size. Yet, in real life, goods may be of a larger size, for example, a car.

## Conclusion

The equimarginal principle is a key concept in economics, and it serves as a powerful tool for optimising resource allocation. By equalising the marginal utility across different products, consumers can make rational decisions to maximise their total satisfaction. While the principle has its limitations, its application can lead to better allocation of resources and improved decision-making.