On Joan Robinson’s Output Symmetry Theorems with Various Taxations under Third-Degree Price Discrimination: A Generalization

Abstract

This paper incorporates more general cases with a new class of constantly adjusted concavity demand curves and includes three types of taxes. To verify the output symmetry under various forms of taxation, we simulate both linear and constant elasticity demand functions under the unit, demand ad valorem, and cost ad valorem taxes. If all the demand functions in the submarkets are linear, the total outputs are identical under both uniform pricing and third-degree price discrimination. Furthermore, if all the weak market demand curves are strictly “Robinson-concave” and all the strong market demand curves are strictly “Robinson-convex” or linear, then the total output under price discrimination exceeds that under uniform pricing, and vice versa. While different taxes lead to higher costs, the cost pass-through changes the prices of the products, and the change of total output still depends on the curvature of the demand curve. Therefore, the curvature of the demand curve remains the main determinant of changes in output. Our study provides a theoretical basis for market intervention in price discrimination.