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# Utility Theory

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Let’s say you just started to study something new. You feel excited after you have completed your one-hour lesson and learned something. The following hour, you study more and you learn further. Another hour passes by, and you add to your knowledge. However, after studying for six to eight hours, you feel exhausted because during the first hours you put your brain under a lot of pressure to learn and memorise.

This is what utility theory is all about: the degree of satisfaction or usefulness derived from consuming a product or service.

## What is utility?

Utility is the level of satisfaction a person derives from consuming a good or service. When the product or service is useful to the consumer’s needs or wants, they can achieve a certain level of utility from consuming it. In economics, there are two different types of utility: expected utility and subjective utility.

### Expected utility

Expected utility is the utility that an economic agent is expected to reach in the future given several probable outcomes. Expected utility value is a probability concept used when several future outcomes are possible. It is calculated by multiplying each possible utility outcome by the probability of its occurrence and then adding them up. Expected utility theory deals with decision-making under uncertainty.

### Subjective utility

Subjective utility is utility based on an individual's perceived level of satisfaction from consuming a good or service. Subjective utility is not based on market judgment. It is based on how attractive an individual perceives the benefit of using a good or service.

### Utility theory

Students choose to study because they want to pass their exams. We eat something because we're hungry. We drive a car to reach a certain destination. We sleep to give our bodies some rest. Utility is involved in everything we do and we get satisfaction from consuming or using goods or services. This is what utility theory is concerned with: explaining individuals’ choices and measuring the satisfaction level from consuming a good or service.

The level of satisfaction is measured in units called ‘utils.’

## Total utility and marginal utility

There are two different types of utility:

### Marginal utility (MU)

Marginal utility is the satisfaction that a person receives from consuming an additional unit of the same good or service.

If John is drinking his first glass of water and gets 10 units of satisfaction, the marginal utility he derives from the first glass is 10 units. He then has a second glass of water and gets 8 units of satisfaction. The marginal utility he derives from the second glass is 8 units. With the third glass, he gets only 7 units of satisfaction. Thus, the marginal utility he derives from the third glass is 7 units.

### Total utility (TU)

Total utility is the aggregate satisfaction a person receives from the consumption of all the units of the same good or service.

Total utility is derived from adding every marginal utility from each additional unit.

Continuing with our previous example, where John derived 10, 8, and 7 units of utility from the glasses of water, the total utility that John would derive is 10 + 8 + 7 = 25 units.

The equation for total utility (TU) is:

Where MU-N is the marginal utility from consuming the N-th unit of a good.

 Number of glasses of water Marginal utility Total utility 1 10 10 2 8 18 3 7 25 4 4 29 5 0 29 6 -2 27

Table 1. Relationship between marginal utility and total utility - StudySmarter.

As the table shows, the marginal utility decreases with the addition of further units, whereas the total utility increases until a certain point. At that point, which is 5 glasses of water, the total utility reaches its maximum and starts declining.

Figure 1 shows the relationship between marginal utility and total utility:

Figure 1. Relationship between marginal and total utility, StudySmarter Originals

We can conclude the following relationship between MU and TU:

• As the number of units increases, MU decreases, and TU increases.
• When TU reaches its maximum level, MU is 0. At that unit, the marginal utility is 0.
• MU starts to get negative and TU starts decreasing.

## The law of diminishing marginal utility

Economists believe that the utility reduces as the consumption of the same product or service increases.

The Law of diminishing marginal utility states that the level of satisfaction for an individual diminishes as the use of the same product increases. Eventually, the consumer either looks for an alternative or stops consuming the product.

According to the law of diminishing marginal utility, the consumption of the first unit gives the consumer maximum utility. Then, the level of satisfaction starts reducing as the units increase. The consumer starts getting negative utility after a particular unit of consumption, which may vary from consumer to consumer.

Suppose Alan is very hungry and decides to eat a hamburger. The first burger satisfies his hunger. However, he is still hungry, so he buys another burger. This further satisfies his hunger. However, not as much as the first burger. He goes on to have a third burger to fill the little hunger he still has and gets fully satisfied. Any further burger will not satisfy Alan's hunger and might be a bit too much for him to eat. It may make him feel too full and may also result in him feeling sick. Thus, the fourth burger may not give any satisfaction to Alan and instead give him a negative utility.

## Utility maximisation

Utility maximisation means that a consumer will try to get the highest level of satisfaction for consuming something they paid for. The utility may be different for every individual and cannot be stated as a single total unit.

Imagine you are paying a tutor to help you with maths five days per week. However, the tutor isn't available at least two or three times per week as initially agreed. Would you be happy with that? Would you be satisfied with the tutor and willing to pay the same price? The answer is generally no. If someone is paying for five days a week tuition fee, they will expect to receive the tutoring hours they paid for. This is utility maximisation.

However, even though consumers wish to have the maximum utility from the consumption of a product or service, sometimes they may have to make other choices due to constraints. Let's explore them:

### Limited income

Even though someone may fancy having the best of all products because it gives them the highest satisfaction, limited income may stop them from buying it.

Richard wishes to have a Ferrari car. However, his income just covers his basic needs of food, clothing, shelter, and a comparatively cheaper car. He has no budget for a Ferrari. In his case, limited income stops him from having the car that will satisfy him the most.

### A given set of prices

Some individuals like some products or services more than others. However, they may opt for a substitute or a similar product due to the set of prices. Although they will get the maximum utility from consuming the high-priced goods, they may not be willing to pay the given set of prices. Thus, they will look for alternatives.

Many people like McVities digestive biscuits. However, some decide not to buy them because they have a high price. They may opt for cheaper available alternatives like a supermarket's own brand of digestive biscuits.

### Budget constraints

Consumers’ choices are subject to their budget constraints. Budget refers to the total amount of money an individual is willing to spend, save, and borrow. Budget constraints can also be understood as limited income.

If Richard, the man who wants a Ferrari, has limited savings and is not willing to borrow money, his budget constraint will restrain him from buying the luxury car. His budget constraints don't allow him to make the choice that would maximise his utility.

### Limited time

Another constraint consumers may face while making choices is the availability of time.

Suppose an individual is willing to get the goods currently on sale. However, they could not go to the store to buy the goods on time for the sale. They will not enjoy the maximum utility they would have gained if they purchased the good when the price was affordable for them.

## The importance of margin when making choices

Economists say that most choices are made at the margin. The margin is the current state at which an individual is making choices. Margin helps the consumers decide how much they will gain or lose with the extra unit of a good or service. Hence, the consumer’s buying decision is on the margin.

Margin is important for these reasons:

• It is the point at which an individual decides whether to consume more or less.
• The margin determines the benefit that a consumer may receive by consuming an additional unit of a good or service. Therefore, it helps in deciding whether to consume additional units.
• Understanding consumers’ total marginal utility also lets the supplier decide whether the consumer will buy further goods or services.

## Utility Theory - Key takeaways

• Utility is the level of satisfaction a person derives from consuming a good or service.

• Utility theory explains individuals’ choices and measures their level of satisfaction from consuming a good or service. The level of satisfaction is measured in units called ‘utils.’

• Marginal utility is the satisfaction that a person receives from consuming an additional unit of the same good or service.

• Total utility is the aggregate satisfaction a person receives from consuming all the units of the same good or service.

• As the number of units increases, marginal utility decreases, and total utility increases. When the total utility reaches its maximum level, the marginal utility is zero. After that point, marginal utility starts to get negative and total utility starts decreasing.

• The Law of diminishing marginal utility states that an individual’s level of satisfaction diminishes as the use of the same product increases. Eventually, the consumer either looks for an alternative or stops consuming the product.

• Utility maximisation is the highest level of satisfaction a consumer is able to derive from the decision they made in return for the cost they paid.

• Individual choices when trying to maximise utility may be limited by income, prices, time, and budget constraints.

Utility theory explains individuals' choices and measures the level of satisfaction they obtain from consuming a good or service.

The standard utility theory says that the level of satisfaction is measured in units called ‘utils.’

Expected utility, subjective utility, marginal utility, and total utility.

Marginal utility is the satisfaction that a person receives from consuming an additional unit of the same good or service.

Expected utility is the utility that an economic agent is expected to reach in the future given several probable outcomes. Expected utility value is a probability concept that is used when several future outcomes are possible.

## Final Utility Theory Quiz

Question

What is utility?

Utility is the level of satisfaction a person derives from the consumption of goods or services.

Show question

Question

What are the units of measuring utility called?

Utils

Show question

Question

Total utility decreases as the units of consumption increases.

False

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Question

Marginal utility and total utility have the same curve.

False

Show question

Question

Marginal utility decreases as the units of consumption increase.

True

Show question

Question

What is marginal utility?

Marginal utility is the satisfaction that a person receives from consuming an additional unit of the same good or service.

Show question

Question

What is total utility?

Total utility is the aggregate satisfaction a person receives from the consumption of all the units of the same good or service.

Show question

Question

When TU reaches its maximum level, MU is zero.

True

Show question

Question

As the number of units increases, MU increases and TU reduces.

False

Show question

Question

As the number of units increases, MU reduces, and TU Increases.

True

Show question

Question

What is expected utillity?

Expected utility in simple terms is the utility that an economic agent is expected to reach in the future given several probable outcomes.

Show question

Question

What is Subjective utility?

The subjective utility is utility based on an individual's perceived personal level of satisfaction that they obtain from consuming a good or service.

Show question

Question

How is expected utility calculated?

It is calculated by multiplying each possible utility outcome by the probability of its occurrence and then adding them up.

Show question

Question

What does the law of diminishing marginal utility explain?

The Law of diminishing marginal utility states that the level of satisfaction for an individual diminishes as the use of the same product increases and eventually the consumer either looks for an alternative or stops consuming the product.

Show question

Question

The consumer starts getting negative utility after a particular unit of consumption, which is the same for all individuals.

False

Show question

Question

The utility that an economic agent is expected to reach in the future given several probable outcomes is called

expected utility.

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Question

________ is based on how attractive an individual perceives the benefit of using a good or service.

Subjective utility

Show question

Question

Subjective utility is based on market judgment.

False

Show question

Question

The satisfaction a person receives from consuming an additional unit of the same good or service is called __________.

marginal utility

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Question

____________ is derived from adding every marginal utility from each additional unit.

Total utility

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Question

Fill in the blanks:

 Number of glasses of water Marginal utility Total utility 1 10 10 2 __ 18 3 __ 25 4 4 __ 5 0 __ 6 __ 27

 Number of glasses of water Marginal utility Total utility 1 10 10 2 8 18 3 7 25 4 4 29 5 0 29 6 -2 27

Show question

Question

As the number of units increases, MU _________, and TU _________.

decreases, increases

Show question

Question

When MU starts to get negative and TU starts __________.

decreasing

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Question

Tu is at the maximum when MU is ___.

0

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Question

According to the law of diminishing marginal utility, the consumption of the first unit gives the consumer maximum utility.

True

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Question

The utility of a good is universal.

False

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Question

Factors restricting utility maximization are ______, ______, time, and budget constraints

income, prices

Show question

Question

___________ states that the level of satisfaction for an individual diminishes as the use of the same product increases.

The Law of diminishing marginal utility

Show question

Question

Can time be a factor of utility maximisation?

Yes

Show question

Question

How can prices affect utility maximisation?

They may not be willing to pay the given set of prices. This will prompt them to look for alternatives.

Show question

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