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# Revealed Preference

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Consider a situation in which you can afford to buy anything in the world. That would be fantastic, wouldn't it? That is not the case in the actual world, as we are all restricted by budget constraints. We usually choose diverse combinations of products that optimize our utility while on a budget. And, while choosing our combination of products, we tend to reveal our preferences. Isn't it fascinating? Let us jump right into the revealed preference article to discover more about its theory, methods, and properties!

## Revealed Preference Theory

Before jumping directly into the revealed preference theory, let's have a quick refresher on budget constraints. We all have the desire to buy luxury goods or go on long vacations, but we are restricted by the limited amount of budget for such expenditures. Hence, budget constraint is a phenomenon that consumers face due to their limited amount of income.

Revealed preference theory states that the consumer's product or service choice under different income and price levels provides information about their preferences. For example, if there were two combinations of goods (A and B) and if the consumer chooses A (which is expensive) over B, then the consumer reveals their preference for A over B.

The theory is based on the premise that consumers are rational thinkers who compare many options before making a decision. As a result, when a consumer selects one choice over another, it must be the one they prefer.

Paul Samuelson developed the theory of revealed preference in 1938, which argues that what people buy at different income and price levels can reveal their preferences.

Budget constraints are the restrictions caused by the limited income of consumers.

- Budget Constraint;

- Consumer Choice.

## Revealed Preference Diagram

Now let us understand the concept of revealed preference by using the budget line diagram of an individual. Let us assume Max has a limited budget (L) of $200 for food and beverages, which can be spent on Coca-Cola and Pizza. Fig. 1 - Revealed preference theory In Figure 1, the budget line (L) helps us illustrate the combinations of Coca-Cola and Pizza that Max can buy with his budget of$200. Among various combinations, if max chooses bundle B, then it can be said that Max prefers to have 20 cans of coke and 40 pizzas. Similarly, Max could have also chosen other alternative bundles (A and C) in the same budget line, but he decided to choose B. This reveals Max's preference for bundle B over bundles A and C.

When a consumer's consumption pattern is determined by observing the bundle of goods they choose over other alternatives, when all of them are within the budget is known as revealed preference.

A budget line is a diagram that depicts the combination of products that a consumer can purchase at a certain income and price level.

You have come this far in learning. Great job! If you are interested in finding out more about the budget constraint, then click here:

- Budget Constraint Graph.

## Revealed Preference Properties

Now, let us comprehend the concept of the revealed preference properties.

• There are three axioms of revealed preference which are listed as follows:
1. Weak axiom of revealed preference;
2. Strong axiom of revealed preference;
3. Generalized axiom of revealed preference.

Fig. 2 - Revealed Preference Properties

In Figure 2, we can see that there are 4 bundles (A, B, C, and D) of consumer goods. Bundles A and B are on the budget line of the consumer, whereas bundles C and D are inside and outside the budget line, respectively.

As bundle D is outside of the budget line, the consumer will not be able to afford it. Bundles A and B are both on the budget line, which means that both bundles can be afforded by the consumer. If a consumer chooses bundle A (that satisfies their needs) over bundle B, which is on the same budget line, then it is known as a weak axiom of revealed preference.

When a consumer chooses one bundle over other alternatives on the same budget line, it is known as the weak axiom of revealed preference.

Further, bundles A and C can both be afforded by the consumer. As bundle C is inside the budget line, it is cheaper than bundle A which is on the budget line. If a consumer chooses bundle A (an expensive alternative that satisfies their needs) over bundle C, it is known as a strong axiom of revealed preference.

When a consumer chooses an expensive alternative between several bundles, it is known as the strong axiom of revealed preference.

If bundles A and B both satisfy consumer needs equally and one of them cannot be chosen, then it is known as the generalized axiom of revealed preference.

When a customer cannot choose one specific bundle as more than one bundle satisfies their needs is known as the generalized axiom of revealed preference.

The theory of revealed preference is based on several assumptions, which are listed below.

1. Consumer Rationality: The first assumption of the theory is that consumers are rational, and they try to maximize their utility within their budget.
2. Transitivity: The theory also assumes that if a consumer chooses bundle A over bundle B and bundle B over bundle C, the consumer will also choose bundle A over bundle C.
3. Consistency: Another assumption is that if the consumer chooses bundle A over bundle B, then they will always choose bundle A over bundle B.

## Revealed Preference Method

Now, let's learn about the revealed preference method. If a buyer consistently chooses an expensive option over two alternatives, it is easier to determine their preferences. Using the budget lines, we can evaluate the preferences that the consumer 'reveals.'

• The two revealed preference methods are:
1. Using two budget lines;
2. Using four budget lines.

### Revealed Preference Method: Two Budget Lines

Let us have a look at the revealed preference method using two budget lines.

Fig. 3 - Revealed preference method with two budget lines

In Figure 3, let us suppose that a consumer chooses bundle A over B on budget line L2. The consumer could have purchased bundle B and all of the bundles below budget L2, but he chose bundle A. This means the consumer prefers bundle A over B.

Now, let us suppose that the relative price of food and clothing changes, forming a new budget line L1. Here, the consumer chooses bundle B over bundle C. The consumer could have chosen bundle C and all of the bundles below budget line L1 but decided to choose bundle B. This means the consumer prefers bundle B over C. As bundle A is preferred over B and B is preferred over C, we can infer that A is preferred over C even when the relative price levels of food and clothing change. Likewise, as food and clothes are consumer goods, all of the bundles to the right of A in the pink-shaded area are preferred to A.

### Revealed Preference Method: Four Budget Lines

Let's further look at the revealed preference method using four budget lines.

Fig. 4 - Revealed preference method with four budget lines

In Figure 4, bundle A is located on the budget line L2. Two additional budget lines (L3 and L4) are drawn that pass through consumption bundle A.

In the case of budget line L3, let us suppose that the consumer chooses bundle E over A. As E was chosen even though A was equally expensive, we can say that the consumption bundle E is preferred to A, as well as all of the bundles to the right of E in the pink-shaded area.

Similarly, In the case of budget line L4, let us suppose that the consumer chooses bundle D over A. As D was chosen even though A was equally expensive, we can say that the consumption bundle D is preferred to A, as well as all of the bundles to the right of D in the pink-shaded area.

To further ace your understanding of revealed preferences, check out our article: Indifference Curve.

## Revealed Preference vs. Stated Preference

Let us have a look at revealed preference vs. stated preference.

Stated preference is a phenomenon where we tend to state our answers through different mediums. For example, if someone asks what your favorite color of the jacket is, you might state your preference is green. But not everything we tell is the truth. You might like the color blue, but you stated your preference as green, whether done intentionally or unintentionally.

However, in the case of revealed preference, if someone wants to know what your favorite color is, they might observe your consumption pattern. For example, if you wear a blue colored jacket more often, it might be perceived that you prefer the color blue.

## Revealed Preference - Key Takeaways

• Budget constraints are the restrictions caused by the limited income of consumers.
• When a consumer's consumption pattern is determined by observing the bundle of goods they choose over other alternatives, when all of them are within the budget is known as revealed preference.
• A budget line is a diagram that depicts the combination of products that a consumer can purchase at a certain income and price level.
• Three axioms of revealed preferences are:- Weak axiom- Strong axiom- Generalized axiom
• The theory of revealed preference is based on the assumption of consumer rationality, transitivity, and consistency.

When a consumer's consumption pattern is determined by observing the bundle of goods they choose over other alternatives when all of them are within the budget is known as revealed preference.

Preference is when we tend to state our answers through different mediums whereas, when a consumer's consumption pattern is determined by observing the bundle of goods they choose over other alternatives when all of them are within the budget is known as revealed preference.

The theory of revealed preference is based on the assumption of consumer rationality, transitivity, and consistency.

The limitation of the revealed preference theory is that it is based on many assumptions which are not ideal in the real-world scenario.

The three main properties of the theory of revealed preference are consumer rationality, transitivity, and consistency.

## Revealed Preference Quiz - Teste dein Wissen

Question

What does the revealed preference theory state?

Revealed preference theory states that the consumer's product or service choice under different income and price levels provides information about their preferences.

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Question

Explain revealed preference with the help of an example.

If there were two combinations of goods (A and B) and if the consumer chooses A (which is expensive) over B, then the consumer reveals their preference for A over B.

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Question

What are budget constraints?

Budget constraints are the restrictions caused by the limited income of consumers.

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Question

Who developed the theory of revealed preference?

Paul Samuelson.

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Question

What is a budget line?

A budget line is a diagram that depicts the combination of products that a consumer can purchase at a certain income and price level.

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Question

What is a revealed preference?

When a consumer's consumption pattern is determined by observing the bundle of goods they choose over other alternatives when all of them are within the budget.

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Question

What is a weak axiom of revealed preference?

When a consumer chooses one bundle over other alternatives on the same budget line, it is known as the weak axiom of revealed preference.

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Question

What is a strong axiom of revealed preference?

When a consumer chooses an expensive alternative between several bundles, it is known as the strong axiom of revealed preference.

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Question

What is a generalized axiom of revealed preference?

When a consumer cannot choose one specific bundle as more than one bundle satisfies their needs is known as the generalized axiom of revealed preference.

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Question

What are the assumptions under which the theory of revealed preference is formulated?

The assumptions under which the theory of revealed preferences is stated are consumer rationality, transitivity, and consistency.

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Question

What is the difference between stated preference and revealed preference?

Stated preference is when we tend to state our answers through different mediums whereas, when a consumer's consumption pattern is determined by observing the bundle of goods they choose over other alternatives when all of them are within the budget is known as revealed preference.

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Question

One of the assumptions of the revealed preference theory is that consumers are rational.

True.

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