Questions: Revealed Preference and Consumer Rationality

Question 1

A consumer chose bundle A when both A and B were affordable. Later, when only B was affordable (A was outside the budget), the consumer chose B. Does this violate WARP?

• A. Yes — once A is revealed preferred to B, choosing B under any circumstances violates WARP
• B. No — WARP is only violated if the consumer chooses B when A is also affordable in the second situation
• C. Yes — the consumer must always choose A over B to satisfy revealed preference
• D. No — the consumer may change preferences between observations

Answer: (B)

WARP says: if A is revealed preferred to B, then B cannot be revealed preferred to A. B is only 'revealed preferred to A' when the consumer chooses B in a situation where A was also affordable. If A is outside the budget constraint in the second situation, the consumer has no choice but to select from the affordable set — choosing B doesn't reveal B is preferred to A. The consumer is simply choosing the best available option within their budget. No violation occurs.

Question 2

A consumer's choices across multiple budget sets satisfy SARP (the Strong Axiom of Revealed Preference). What can an economist conclude?

• A. The consumer has a unique utility function, and we can identify its exact form from the choice data
• B. The consumer's choices can be rationalized by some stable, well-behaved utility function, even though we don't know its exact form
• C. The consumer maximizes a linear utility function, since SARP implies linearity
• D. The consumer never violates their budget constraint, which confirms SARP

Answer: (B)

SARP satisfaction is equivalent to the existence of a utility function that rationalizes the choices — but it doesn't tell us which utility function. Many different utility functions could generate the same SARP-consistent choice data; we can only say the behavior is consistent with utility maximization. The revealed preference approach deliberately avoids specifying the functional form — its power is that it tests rationality without assuming any particular utility function.

Question 3

Revealed preference theory makes no assumptions about consumer behavior — it simply observes choices and reads off preferences directly.

• T. True
• F. False

Answer: False

Revealed preference theory does make strong assumptions — it assumes that preferences are consistent and transitive (captured by WARP and SARP). These are not trivially satisfied: behavioral economics documents many systematic violations. The theory assumes choices reflect stable underlying preferences, not context-dependent or time-inconsistent behavior. 'No assumptions' is precisely the misconception the topic warns against. The advantage over utility theory is that the assumptions are testable from observed choice data rather than unobservable utility values.

Question 4

If a consumer's choices violate SARP, this proves the consumer has no preferences at most.

• T. True
• F. False

Answer: False

SARP violation means the choices cannot be rationalized by any single, stable, transitive preference ordering — but this does not mean the consumer has no preferences. It means their choices are inconsistent with the rational consumer model. Behavioral economists document that real people violate SARP due to framing effects, reference dependence, fatigue, and context sensitivity. These are not random; they are systematic patterns. Violating SARP means the neoclassical model is an inadequate description of behavior, not that behavior is unintelligible.

Question 5

Explain what it means for a consumer to 'reveal a preference' for bundle A over bundle B, and why this only counts when both bundles were affordable.

Model answer: A consumer reveals a preference for A over B when they choose A from a budget set that also contained B (i.e., B was affordable but not chosen). The choice of A when B was available and affordable is evidence that A is at least as good as B in the consumer's ranking. If B were outside the budget, choosing A tells us nothing about the A vs. B comparison — the consumer simply couldn't afford B. Affordability is the key condition because it establishes that the consumer genuinely had a choice.

This is the core logic of revealed preference: we can only infer preferences from choices where the unchosen option was genuinely available. Choices made under binding constraints reveal only that the chosen option was feasible, not that it was preferred to the constrained alternatives. The 'revealed' in revealed preference refers specifically to the information content of choosing A from an affordable set containing B.