Book cover for Intermediate Microeconomics: A Modern Approach

Intermediate Microeconomics: A Modern Approach

Hal R. Varian

ISBN #9780393927023

7th Edition

224 Questions

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Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter on Revealed Preference provides a framework for understanding how consumers' choices serve as indicators of their underlying preferences. It highlights important axioms such as WARP and SARP, which maintain internal consistency in decision-making, and discusses the practical application of these ideas through the use of index numbers and price indices in economic policy, such as adjusting social security payments. Overall, the chapter underscores the significance of observed behaviors in economic analysis and decision-making.

Learning Objectives

1

Explain the concept of revealed preference and its significance in economic analysis.

2

Describe and differentiate between the Weak Axiom of Revealed Preference (WARP) and the Strong Axiom of Revealed Preference (SARP).

3

Analyze how observed consumer choices can be used to infer underlying preferences.

4

Illustrate the practical applications of index numbers and price indices in economic decision-making.

Key Concepts

CONCEPT

DEFINITION

Revealed Preference

A method of inferring consumer preferences based on observed choices rather than stated opinions.

WARP (Weak Axiom of Revealed Preference)

An axiom stating that if a consumer chooses bundle A over bundle B when both are affordable, then the consumer should not choose B over A under any circumstances, ensuring consistency in consumer choice.

SARP (Strong Axiom of Revealed Preference)

An extended axiom that not only incorporates the ideas of WARP but also requires transitivity across multiple choice scenarios to maintain consistency in revealed preferences.

Index Numbers and Price Indices

Statistical measures (often summarized in index numbers) that track changes in the price level of a basket of goods over time, used in applications like adjusting social security payments for inflation.

Example Problems

Example 1

When prices are $\left(p_{1}, p_{2}\right)=(1,2)$ a consumer demands $\left(x_{1}, x_{2}\right)=(1,2)$ and when prices are $\left(q_{1}, q_{2}\right)=(2,1)$ the consumer demands $\left(y_{1}, y_{2}\right)=(2,1)$ Is this behavior consistent with the model of maximizing behavior?

Example 2

When prices are $\left(p_{1}, p_{2}\right)=(2,1)$ a consumer demands $\left(x_{1}, x_{2}\right)=(1,2)$ and when prices are $\left(q_{1}, q_{2}\right)=(1,2)$ the consumer demands $\left(y_{1}, y_{2}\right)=(2,1)$ Is this behavior consistent with the model of maximizing behavior?

Example 3

In the preceding exercise, which bundle is preferred by the eonsumer, the $x$ -bundle or the $y$ -bundle?

Example 4

We saw that the Social Security adjustment for changing prices would typically make recipients at least as well-off as they were at the base year. What kind of price changes would leave them just as well-off, no matter what kind of preferences they had?

Example 5

In the same framework as the above question, what kind of preferences would leave the consumer just as well-off as he was in the base year, for all price changes?
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Step-by-Step Explanations

QUESTION

If a consumer chooses bundle A over bundle B when both are affordable, what does the concept of revealed preference imply about the consumer's underlying preferences?

STEP-BY-STEP ANSWER:

Step 1: Observe that the consumer selected bundle A when both A and B were within the affordable set.
Step 2: Infer that the consumer prefers bundle A to bundle B based on that choice.
Step 3: Conclude that this observed choice reveals the consumer's underlying preference, even if they express no formal ranking.
Final Answer: The consumer’s choice implies that they value bundle A more than bundle B according to the principle of revealed preference.

Revealed Preference

QUESTION

How does WARP (the Weak Axiom of Revealed Preference) ensure consistency in consumer decision-making?

STEP-BY-STEP ANSWER:

Step 1: Understand that WARP posits if a consumer chooses bundle A over bundle B when both are affordable, then there should not be any situation where the consumer reverses this preference by choosing B over A when A is still available.
Step 2: Observe that this consistency prevents cyclical or contradictory choices.
Step 3: Apply this axiom to ensure that each observed choice reflects a consistent and rational underlying preference structure.
Final Answer: WARP ensures consistency by disallowing any reversal of a previously revealed preference from one choice set to another.

WARP

QUESTION

What distinguishes the Strong Axiom of Revealed Preference (SARP) from WARP?

STEP-BY-STEP ANSWER:

Step 1: Recognize that while WARP focuses on pairwise comparisons to prevent direct contradictions, SARP extends this idea to a broader range by addressing transitivity among multiple choices.
Step 2: Understand that SARP ensures that if a consumer prefers A to B and B to C, then the consumer must also prefer A to C.
Step 3: Analyze how this transitivity requirement further solidifies the internal consistency of the consumer’s choice behavior.
Final Answer: SARP is more robust than WARP by enforcing transitive consistency across all choice scenarios, thereby preventing indirect preference reversals.

SARP

QUESTION

How are index numbers and price indices used in practical applications such as adjusting social security payments?

STEP-BY-STEP ANSWER:

Step 1: Note that index numbers are statistical measures that capture changes in the prices of a specified basket of goods over time.
Step 2: Understand that price indices derived from these numbers track inflation or changes in cost of living.
Step 3: Recognize that government and economic institutions use these indices to adjust social security payments so that benefits keep pace with the cost of living.
Final Answer: Index numbers and price indices are vital tools for adjusting economic payments, ensuring that benefits are consistent with current price levels.

Index Numbers and Price Indices

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Common Mistakes

  • Confusing revealed preference with stated preferences, leading to misinterpretation of consumer behavior.
  • Overlooking the importance of consistency axioms like WARP and SARP in ensuring rational choice.
  • Neglecting the role of practical applications, such as the use of index numbers and price indices, thereby underestimating their impact on economic policies.