Reexamination of the Marxian Exploitation Theory

In this paper, we reexamine the mathematical analysis of Marxian exploitation theory. First, we reexamine the validity of the two types of Marxian labor exploitation, Morishima's (1974) type and Roemer's type (1982), in the argument of Fundamental Marxian Theorem (FMT). We show that the FMT does not hold true if we adopt the Roemer exploitation, and equilibrium notions are the reproducible solution [Roemer (1980)]. Also, we show that the FMT does not hold true for the Morishima exploitation if there exist heterogeneous demand functions among workers. Second, we reexamine the Class-Exploitation Correspondence Principle (CECP) [Roemer (1982)]. We show that the CECP does not hold true in the general convex cone economy even if we adopt the Roemer exploitation. Finally, we propose a new definition of Marxian labor exploitation, and show that all of the above difficulties can be resolved under this new definition.