Abstract

The “marginality principle” states that the share of joint output atrributable to any single factor of production should depend only on that factor's own contribution to output. This property, together with symmetry and efficiency, uniquely determines the Shapley value. A similar result characterizes Aumann—Shapley pricing for smooth production functions with variable input levels.

Introduction

In a perfectly competitive market, the wage of a laborer equals his marginal product. No ethical judgment need be made as to whether marginal productivity is a “just” rule of compensation so long as competitive markets are accepted as the correct form of economic organization. Nevertheless, the idea that rewards should be in proportion to contributions has considerable ethical appeal in itself, and appears to reflect widely held views about what constitutes “just compensation” without any reference to the theory of perfect competition.

In this paper we shall ask what “compensation in accordance with contribution” means in the absence of competition. How does the marginality principle translate into a rule of distributive justice when cooperation rather than competition is the mode of economic organization?

Unfortunately, if we attempt to translate marginalism directly into a cooperative sharing rule, difficulties arise. For, except in very special cases, the sum of individuals' marginal contributions to output will not equal total output.