Progressivity, Inequality Reduction, and Merging-Proofness in Taxation

Progressivity, inequality reduction and merging-proofness are three well-known axioms in taxation. We investigate implications of each of the three axioms through characterizations of several families of taxation rules and their logical relations. We also study the preservation of these axioms under two operators on taxation rules, the so-called convexity operator and minimal-burden operator, which give intuitive procedures of determining a tax schedules.