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Engel Curves Leading to the Weak Axiom in the Aggregate

Xavier Freixas
Andreu Mas-Colell

Abstract

For every range of admissible incomes we characterize the class of Engel curves with the property that if an economy has, first, a price independent distribution of income and, second, preferences which are identical across consumers and generate Engel curves in the class, then the corresponding aggregate demand function satisfies the Weak Axiom of Revealed Preference. This class is defined by two simple conditions. The no torsion condition says that, in the relevant range of income, the Engel curve is contained in a plane through the origin (which may depend on the price vector). The uniform curvature condition says that in addition, the Engel curve is either convex or concave to the origin. We also study the nonidentical preferences case and give a sufficient condition on Engel curves (called positive association) for the Weak Axiom to be satisfied in the aggregate.