Competitive Market Achieves the Greatest Happiness of the Minimum Number

Abstract

This note studies homogenous good markets, assuming that each buyer/seller has a unit demand/supply and that side payments beyond buyer-seller pairs are prohibited. We show that the quantity of good traded under the competitive market equilibrium is minimum among all Pareto efficient and individually rational allocations, provided that the definition of Pareto efficiency incorporates the presumption of no side payment. Our finding may suggest that the competitive market results in the most unequal allocation, since the number of buyers or sellers left-behind from profitable trades is maximized. Conversely, unless a demand or supply curve is completely flat, there always exists a Pareto efficient allocation that entails strictly larger number of profitable trades than the equilibrium quantity. Implications to positive analysis are also discussed.

Keywords: competitive market, equality, market design

JEL Classification: B12, B21, D40, D63