GARP: Generalized Axiom of Revealed Preference

The Generalized Axiom of Revealed Preference (GARP) is a fundamental concept in consumer theory that helps to determine if a set of choices is consistent with the theory of utility maximization.

The Generalized Axiom of Revealed Preference (GARP) is a fundamental concept in consumer theory that helps to determine if a set of choices is consistent with the theory of utility maximization.

Historical Context

The Axiom of Revealed Preference (ARP) was introduced by economist Paul Samuelson in 1938. The idea was to provide a way to empirically test whether a consumer’s behavior is consistent with utility maximization, without directly knowing the utility function. The concept was later extended to its generalized form, GARP, allowing for a broader set of consumer choice situations.

Types/Categories

• Weak Axiom of Revealed Preference (WARP): Asserts that if a consumer prefers bundle A over bundle B in one instance, they should not prefer B over A in another instance.
• Strong Axiom of Revealed Preference (SARP): A stricter version of WARP, taking into account all indirect preference comparisons.
• Generalized Axiom of Revealed Preference (GARP): A further extension that allows for a broader range of consumer behaviors to be tested for consistency with utility maximization.

Key Events

• 1938: Paul Samuelson introduced the Axiom of Revealed Preference.
• 1970s: The GARP concept was further developed to address limitations of the original ARP.

Detailed Explanations

GARP states that if a consumer chooses a bundle A over bundle B given their budget constraint, then A is revealed preferred to B. If over time, their choices consistently reveal preferences that do not contradict each other, their behavior can be said to be consistent with utility maximization.

Mathematical Formulas/Models

Mathematically, GARP can be represented as:

• Suppose p_i is the price vector and x_i is the consumption bundle chosen at these prices. GARP requires that if p_i * x_j ≥ p_i * x_i and p_j * x_k ≥ p_j * x_j then p_k * x_i cannot be greater than p_k * x_k.

Charts and Diagrams

    graph LR
	  A[Bundle A] -->|Revealed Preferred To| B[Bundle B]
	  B -->|Revealed Preferred To| C[Bundle C]
	  C -.->|Cannot be Revealed Preferred Back To| A

Importance

Understanding GARP helps in testing the rationality of consumer behavior without knowing their utility function. This is particularly useful in empirical economic analysis and behavioral economics.

Applicability

GARP is applied in:

• Consumer Behavior Analysis: To test if observed consumer choices are rational.
• Market Research: To understand preference consistency.
• Policy Formulation: For predicting responses to policy changes.

Examples

Suppose a consumer has the following choices:

1. Chooses Bundle A when Bundle B is affordable.
2. Chooses Bundle B when Bundle C is affordable.

Using GARP, we can test if these choices are consistent with utility maximization.

Considerations

While GARP provides a robust framework for analyzing consumer choices, it assumes that preferences are consistent and transitive over time, which might not always be the case in real-world scenarios.

Related Terms with Definitions

• Revealed Preference: An economic concept indicating that the preferences of consumers can be revealed by their purchasing habits.
• Utility Maximization: The principle that consumers choose combinations of goods to maximize their utility.

Comparisons

• GARP vs WARP: GARP is a more generalized and less restrictive version compared to WARP.
• GARP vs SARP: GARP allows for some degree of inconsistency in consumer choice compared to SARP.

Interesting Facts

• GARP is used extensively in modern economic research to empirically validate consumer behavior theories.
• Despite its theoretical nature, GARP has practical applications in developing economic models.

Inspirational Stories

The development of GARP and its predecessors has significantly influenced modern economic theory, showcasing the power of mathematical rigor in understanding human behavior.

Famous Quotes

• “The ultimate test of an economic theory is the ability to deduce facts that can be independently tested by empirical evidence.” – Paul Samuelson

Proverbs and Clichés

• “Actions speak louder than words,” which is akin to the idea behind revealed preferences.

Expressions, Jargon, and Slang

• “Revealed Preference” in economics often refers to what consumers’ choices imply about their preferences.

FAQs

What is the purpose of GARP?

To determine if a consumer’s choice behavior is consistent with utility maximization.

How is GARP different from WARP?

GARP generalizes the restrictions imposed by WARP, allowing for a broader analysis of consumer behavior.

Can GARP be applied in real-world scenarios?

Yes, GARP is extensively used in empirical research to analyze and predict consumer behavior.

References

• Varian, H. R. (1982). “The Nonparametric Approach to Demand Analysis.” Econometrica.
• Samuelson, P. A. (1938). “A Note on the Pure Theory of Consumer’s Behavior.” Economica.

Summary

The Generalized Axiom of Revealed Preference (GARP) is a pivotal concept in consumer theory, enabling economists to test the rationality of consumer choices. Developed from the foundational work of Paul Samuelson, GARP is an invaluable tool in modern economics, providing deep insights into consumer behavior without requiring direct knowledge of their utility functions.

By understanding and applying GARP, one can better analyze and predict how consumers make choices, ensuring consistency with utility maximization and contributing to the broader field of economic research.