A consumer buys bundle A = (3 apples, 2 oranges) when bundle B = (2 apples, 4 oranges) is also affordable. Later, at different prices, bundle B is chosen when bundle A is also affordable. Which axiom is violated?
ASARP but not WARP — this is an indirect cycle, not a direct reversal
BWARP (and therefore SARP) — A was directly revealed preferred to B, yet B was then directly revealed preferred to A
CNeither axiom — preferences are allowed to change when relative prices change
DSARP only — WARP permits reversals when prices are sufficiently different
WARP says: if A is directly revealed preferred to B (chosen when B was affordable), then B must never be directly revealed preferred to A (chosen when A is affordable). Both observations show direct choices when the alternative was affordable — making this a direct pairwise reversal, which violates WARP. Since SARP extends WARP to chains, SARP is also violated.
Question 2 Multiple Choice
What is the key methodological advantage of revealed preference analysis over classical demand analysis that assumes a specific utility function?
ARevealed preference allows utility functions to be estimated with less data
BRevealed preference is nonparametric — it tests rationality and recovers preference information without imposing a functional form on the utility function
CRevealed preference can predict behavior in markets that have not yet been observed
DRevealed preference eliminates the need for budget constraints in the analysis
Classical analysis assumes a utility form (Cobb-Douglas, CES, etc.) and estimates parameters. Revealed preference imposes no functional form. It tests only whether observed choices are consistent with SOME rational preference ordering. If the data satisfy SARP, a well-behaved utility function must exist — but you never need to specify what it looks like. This makes the approach more general and more empirically honest.
Question 3 True / False
If a consumer's choices satisfy the Weak Axiom of Revealed Preference (WARP), their behavior can typically be rationalized by a well-behaved utility function.
TTrue
FFalse
Answer: False
WARP is necessary but not sufficient for rationalizability. It only rules out direct pairwise preference reversals, but longer cycles (A preferred to B, B preferred to C, C preferred to A through a chain of direct choices) are still possible. The Strong Axiom of Revealed Preference (SARP) — which rules out all preference cycles through any chain of comparisons — is necessary and sufficient for the existence of a well-behaved utility function.
Question 4 True / False
Revealed preference theory starts with observed choices and infers what the consumer's preferences must be, without needing to assume the form of the utility function.
TTrue
FFalse
Answer: True
This is the defining methodological feature of revealed preference theory. Samuelson's insight was that consumer behavior is observable but preferences are not — so theory should be grounded in observations. By checking whether choice data satisfy SARP, one can determine if a rational preference ordering exists without ever writing down a utility function.
Question 5 Short Answer
How does revealed preference theory 'flip' the logic of standard consumer theory, and what makes this reversal powerful?
Think about your answer, then reveal below.
Model answer: Standard consumer theory assumes preferences (specifies a utility function) and deduces what choices the consumer will make. Revealed preference inverts this: it starts from observed price-quantity choices and asks whether those choices are consistent with some rational preference ordering. The power is methodological — you can test rationality directly from market data without assuming a functional form. If the data satisfy SARP, you know a well-behaved utility function must exist that rationalizes the behavior; if not, you can measure the severity of violations.
The reversal matters because utility functions are unobservable mental constructs, while choices are directly measurable. Grounding consumer theory in observable behavior rather than assumed preferences makes it testable and falsifiable — a significant step toward empirical economics.