The Weak Axiom of Revealed Preference. Assume that a consumer has strictly convex preferences so that the optimal choice is unique for every set of prices. Let X and Y be two different consumption bundles, and assume that a consumer chooses X over Y when both are affordable, that is, X is directly revealed preferred to Y. WARP states that in this case Y is never directly revealed preferred to X. If the revealed preference violates WARP, it is inconsistent with the consumer having preferences that can be described by a utility function. The Strong Axiom of Revealed Preference (SARP) extends this property to a chain of choices. Let {X₁, …, X_n } be different consumption bundles, and let X₁ be directly revealed preferred to X₂, X₂ be directly revealed preferred to X₃, etc., and X_n-1 be directly revealed preferred to X_n; then X₁ is said to be (indirectly) revealed preferred to X_n. SARP states that when X and Y are different and X is revealed preferred to Y, then Y cannot be revealed preferred to X. The Generalized Axiom of Revealed Preference (GARP) further extends this property to the case when more than one consumption bundle maximizes utility for a given set of prices. Let X and Y be two different consumption bundles, and assume that a consumer chooses X over Y given the set of prices p when pX >pY; then X is said to be strictly directly revealed preferred to Y. GARP states that when X is directly or indirectly revealed preferred to Y, Y cannot be strictly directly revealed preferred to X. GARP is never violated if an optimizing consumer has complete and transitive preferences.