Questions: Revealed Preference Theory: Preference Recovery from Choices

Question 1

An economist observes that a consumer chose bundle A when bundle B was affordable, and later chose bundle B when bundle A was also affordable. What does this violate?

• A. The law of demand, because prices must have changed to cause different choices
• B. The Weak Axiom of Revealed Preference, because A is revealed preferred to B but B is also revealed preferred to A — a contradiction
• C. The income effect, because the consumer's budget must have changed
• D. The Slutsky symmetry condition, which requires consistent substitution effects

Answer: (B)

WARP requires one-directional consistency: if A is revealed preferred to B (chosen when B was affordable), then B must never be revealed preferred to A in any subsequent observation. When both are observed, the consumer's choices contradict each other — no stable preference ordering could generate both observations. WARP is a consistency condition on observable choices, not a statement about why prices or income changed.

Question 2

What does it mean to say that a dataset of consumer choices 'satisfies SARP'?

• A. The consumer spends the same amount in every observation period
• B. The consumer's choices can be rationalized by some utility function — there exists a consistent preference ordering generating all observed choices
• C. The consumer only buys goods they previously preferred, never switching brands
• D. The consumer maximizes the same Cobb-Douglas utility function in every period

Answer: (B)

SARP (Strong Axiom of Revealed Preference) is the necessary and sufficient condition for rationalizability: if choices satisfy SARP (no cycles in the revealed-preference relation), then some utility function exists that is consistent with all observed choices. Crucially, satisfying SARP doesn't identify *which* utility function — it only guarantees one exists. Option D is far too specific — rationalizability requires only some consistent ordering, not any particular functional form.

Question 3

Revealed preference theory requires the analyst to first specify a utility function, then verify it against observed choices.

• T. True
• F. False

Answer: False

This gets the theory exactly backward. Revealed preference theory's entire point is to *avoid* assuming any utility function. Starting from observed choices, it asks what preferences are implied by behavior — inferring preferences from choices, not verifying choices against assumed preferences. If choices satisfy SARP, we know some utility function rationalizes them, but we need not specify which one. This assumption-lean approach is what makes the theory powerful for empirical welfare analysis.

Question 4

A consumer who consistently chooses the cheapest available option has choices that are consistent with revealed preference theory.

• T. True
• F. False

Answer: True

Revealed preference theory only requires consistency of choices — the same preference ordering must generate all observations. If a consumer consistently minimizes expenditure, this is a consistent preference ordering (preferring less spending). The theory does not require the consumer to maximize any particular objective — only that choices do not cycle (violate WARP/SARP). Consistent cheapest-option purchasing trivially satisfies WARP: if the cheap option A was chosen over B, the consumer would never choose B over A when both are available at the same prices.

Question 5

Explain why revealed preference theory is described as 'assumption-lean' compared to standard consumer theory, and what empirical advantage this provides.

Model answer: Standard consumer theory assumes consumers maximize a specific utility function (Cobb-Douglas, CES, etc.) and derives demand predictions from that assumption. Revealed preference theory makes no assumption about functional form — it only requires that observed choices be consistent (satisfy SARP). The empirical advantage is that SARP can be tested directly on price and quantity data without specifying utility: if choices cycle, the data violate SARP and reject rational consumer theory without any functional form assumption. Conversely, if SARP holds, welfare bounds like compensating variation can be computed nonparametrically — without specifying what utility function the consumer has.

This is what Samuelson meant by 'operationalizing' consumer theory: replacing unobservable psychological preferences with observable choice behavior. The revealed preference approach underlies nonparametric demand estimation and welfare analysis methods that remain valid across a wide class of utility functions.