Output and welfare implications of monopolistic third-degree price discrimination

Abstract

A number of Joan Robinson's classic results on third-degree monopolistic price discrimination are generalized and extended. The relation between demand function curvature and the impact of monopolistic discrimination on total output is clarified in the general N-market case. It is shown that unless total output is increased sufficiently, monopolistic discrimination produces a net (Marshallian) efficiency loss. Qualifications necessary if discrimination allows new markets to be served are discussed. Under pure Pigouvian third-degree price discrimination, a monopolist maximizes profits by charging different prices to different markets or classes of customers, with no (second-degree discriminatory) bulk discounts or other nonlinear pricing allowed. The standard comparison of such conduct with that of a single-price monopoly remains that presented by Joan Robinson (Book V) almost a half-century ago. Using an algebraic approach, this note generalizes and extends some of her main results. Robinson (pp. 190-2) shows geometrically that if a single-price monop-oly selling in two markets under constant costs is allowed to discriminate between them, total output is unchanged if both markets have linear demand 1 curves. This result is easily extended to the N-market case below. If demand curves are not linear, she argues (pp. 192-5) that a comparison of their "adjusted concavities " at the nondiscriminating monopoly price deter-mines whether total output rises or falls. Her formal argument depends critically on the assumption that the discriminating monopoly's prices are nearly equal, however, and Melvin Greenhut and H. Ohta show by (non-pathological) example that her proposed test does not work when those prices differ substantially. The general relation between curvature of demand functions and total output changes due to monopolistic discrimination is analyzed below, Robinson's discussion of the welfare implications of discrimination (ch. 16) is very brief and informal, and it emphasizes equity as much as efficiency. Perhaps because of this, much of the subsequent literature seems to equate the efficiency effects of discrimination with its impact on total output. Basil Yamey uses a rather special example to argue that this equation is invalid; he asserts that in general the usual