# Marginal Utility Formula

## Introduction

Understanding complex human behaviour is at the core of economics. Economists use utility analysis to understand consumer behaviour. In this article, we will explain the concept of utility and its types in detail so that we can develop the foundation of the topic of utility analysis in understanding consumer behaviour. Let’s begin with the definitions of some basic terms.

## Utility

Utility refers to the satisfaction gained by a consumer from the consumption of a commodity. For example, a footballer may feel thirsty after playing a football match. When he/she drinks water, his or her need of thirst is satisfied. We say that the footballer is deriving utility from the consumption of water.

Utility is different from usefulness because consumers get satisfaction from the consumption of harmful products as well, such as alcohol. Utility varies from one person to another because two different people may derive different satisfaction from the consumption of the same product. Many factors, like the intensity of need, personal preferences, taste, and fashion, affect utility.

## Approaches to Utility

There are two approaches to utility in economics, which are explained as follows:

### Cardinal Approach

The cardinal approach to utility assumes that the utility can be measured numerically. The unit of measurement is called ‘Util’. This school of thought assumes that there is a hypothetical device in the human mind, that measures utility. This device is called the ‘Utilometer’. When discussing the formulas of utility, we assume utility to be cardinal.

### Ordinal Approach

The ordinal approach to utility assumes that the utility cannot be measured numerically. However, consumers can differentiate between high and low utility. This school of thought uses utility along with indifference curves and budget line to study consumer behaviour.

## Types of Utility

There are two main types of utility, which are explained below:

### Total Utility (TU)

Total utility refers to the total satisfaction gained by a consumer from the consumption of a given quantity of a commodity. Total utility is the collective form of utility that is derived by consumer from consuming a given number of units of a good or service. For example, a person has eaten five units of chocolate bar. His total utility will be the satisfaction he has gained from all five units of chocolate.

Total utility is calculated by adding the marginal utilities of all the units consumed.

Total Utility = Sum of Marginal Utilities

TU = MU1+MU2+ - - - +MUn

TU = ∑MU

Let’s understand this formula by taking an example for calculations. Suppose that a consumer has consumed five units of product X and the marginal utilities from all five units of consumption are given in the table below.

The total utility derived by consumer from the consumption of all five units of product X will be calculated as follows:.

TUx = MU1 + MU2 + MU3 + MU4 + MU5 = 10 + 8 + 6 + 4 + 2 = 30 utils

It is obvious from the table that the total utility is increasing with the increase in the quantity consumed. For example, the total utility derived from the consumption of three units is greater than the total utility from two units. This is because the marginal utility is positive, and with each additional unit consumed, a positive value is added to calculate the total amount of utility. So total utility increases with the increase in the number of units consumed. However, the total utility increases at a decreasing rate because the consumption of additional units give a lower satisfaction to consumer as the previous units have partially satisfied the need to some extent.

### Marginal Utility (MU)

Marginal utility refers to the additional satisfaction gained by a consumer from the consumption of an additional unit of a commodity. Marginal utility is the one that measures the change in total utility when consuming an additional unit of something or when the amount of something consumed is increased by one unit. Generally, marginal utility is used to measure the extra level of satisfaction by consuming an additional unit.

### Marginal Utility Formula

Marginal utility is calculated from total utility by using the following marginal utility formula.

Marginal Utility = Change in Total Utility / Change in Quantity Consumed

MU = ∆TU / ∆Q = (TU2 – TU1) / (Q2 – Q1)

Let’s understand this formula by taking the following marginal utility example.

In the above table, the consumer has obtained 10 utils of satisfaction from the first unit of product X and 18 units of satisfaction from the first and the second units. The marginal utility of the second unit is calculated as follows:

MU2 = (TU2 – TU1) / Q2 – Q1 = (18 – 10) / 2 – 1 = 8 utils

This shows that the consumer has obtained 8 utils of satisfaction from the consumption of the second unit.

Economists assume that the economic agents make decisions by using marginal values. This is called marginal analysis or decision making at margin. Different marginal values are calculated in economics in order to understand decision making by economic agents. Some examples of marginal values are marginal utility, marginal cost, marginal revenue, marginal propensity to consume and so on. Marginal utility is an important figure in understanding the consumption decisions of consumers.

## Historical Background of Marginal Utility

In the 18th century, the famous economist, Adam Smith, explained the diamond-water paradox or the paradox of value. This paradox states that water is essential for life and human beings cannot live without water, however its price is low in the market. On the other hand, diamonds command a higher price in the market even though they are not essential for living. This paradox was explained by using the concept of marginal utility. In the 19th century, some other economists, like William Stanley Jevons, Carl Menger, and Leon Walras, used the concept of marginal utility to study consumer behaviour.

## Types of Marginal Utility

The following are some main types of marginal utility:

### Positive Marginal Utility

A type of marginal utility that occurs when additional consumption of a good or service increases the total level of satisfaction is called positive marginal utility.

### Zero Marginal Utility

A type of marginal utility that occurs when additional consumption of a good or service does not change the total level of satisfaction is called zero marginal utility.

### Negative Marginal Utility

A type of marginal utility that occurs when additional consumption of a good or service decreases the total level of satisfaction is called positive marginal utility.

## Factors affecting Marginal Utility

The following are some factors that affect the marginal utility:

### Level of Consumption

The level of consumption affects the marginal utility. The marginal utility decreases with an increase in the consumption units of a good or service, referring to the law of diminishing marginal utility.

### Individual Preferences

Individual preferences also affect marginal utility because they vary from person to person. These preferences directly affect the level of satisfaction derived by consumers.

### Taste or Fashion

Tate or fashion affects the marginal utility derived by a consumer. A product which is liked by a consumer or is in fashion may give a higher marginal utility when consumer as compared to a product which is not liked or is out of fashion.

## Difference between Marginal Utility and Total Utility

The following table summarises the main points of difference between marginal utility and total utility.

## Importance of Marginal Utility

The following points explain the importance of marginal utility:

### Consumer Behaviour

Consumer behaviour means the choices made by consumers for consumption when they are constrained by limited income. Rational consumers make decisions about consumption by using marginal utility. That is why marginal utility has a great importance in the study of the choices made by consumers. The law of diminishing marginal utility and the law of equi-marginal utility are used to study consumer behaviour.

### Pricing and Demand

According to the law of diminishing marginal utility, price, demand, and marginal utility are all related to each other. The price which a consumer is willing to pay depends on the marginal utility which he/she is expecting to get from the consumption of the product. A higher marginal utility means the consumer will be willing to pay a higher price.

The demand curve for an individual consumer as well as the market demand curve is derived from utility analysis. The normal demand curve is downward sloping because of diminishing marginal utility.

### Resource Allocation

The best possible allocation of resources by consumers is an important point of marginal utility. With limited resources, consumer aim to maximise total utility (utility maximization). When the total utility is maximized, the resource allocation is considered good and desirable.

## Steps to Calculate Marginal Utility

The following steps are used to calculate marginal utility in a simple and easy way:

### Step 1: Total Utility

First, we must have the values of total utility for different quantities of the product before and after the additional unit consumed.

### Step 2: Total Units Consumed

Second, we must have the total number of units consumed before and after the additional unit consumed.

### Step 3: Change in Total Utility

By using the values from step 1, we calculate the change in total utility by subtracting the value of the initial total utility from the value of the final total utility.

### Step 4: Change in the Quantity Consumed

By using the values from step 2, we calculate the change in the total quantity consumed by subtracting the value of the initial quantity from the value of the final quantity.

### Step 5: Divide Values

Lastly, we divide the change in total utility by the change in quantity consumed by using the values from step 3 and step 4. This will give us the value of marginal utility.

## Conclusion

In conclusion, marginal utility is the additional satisfaction gained by a consumer from consuming an additional unit of a product. The marginal utility formula gives us the measure of marginal utility by using the values of total utilities. In microeconomics, marginal utility is considered an important topic in understanding consumer behaviour.

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