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Implications of the Weak Ordering Axioms
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assume assumption batch binary relation bought budget commodity compensating variation construction consumer consumer's behaviour consumer's choice contradicts convex set Corollary defined definition demand functions denoted differential equation economic equilibrium equivalent establish the following following Theorem given Hence hyperplane hypothesis implies Xj income effect indifference curve indifference direction indifference varieties inequality inferior income sequence integrability conditions integral variety introduce the following Lemma locus marginal utility marginal valuation N-l N-l ordering axioms ordinal preference Pareto plaisir position preference field price set price-ratio Proof PsXs Q. E. D. Theorem relation revealed preference rewrite Samuelson's semitransitivity Slutsky strong ordering substitution effect superior income sequence supporting hyperplane theory of consumer's tion total utility transitivity utility function utility theory VILFREDO PARETO Walras weak ordering postulates welfare economics Xk imply xlt x2 xu x2