Marginal Productivity Theory versus the Labor Theory of Property: An analysis using vectorial marginal products

TL;DR

This paper compares scalar and vectorial formulations of marginal productivity theory, revealing conflicts with traditional distributive shares and providing a modern perspective on the labor theory of property through vectorial analysis.

Contribution

It introduces a vectorial formulation of marginal productivity theory that clarifies its relation to the labor theory of property and challenges conventional distributive share interpretations.

Findings

Vectorial MP theory conflicts with the distributive shares picture.

Modern treatment of labor theory of property uses vectorial marginal products.

Labor theory of property aligns with juridical norm of imputation.

Abstract

Neoclassical economic theory presents marginal productivity (MP) theory using the scalar notion of marginal products, and takes pains, implicitly or explicitly, to show that competitive equilibrium satisfies the supposedly ethical principle: ``To each what he and the instruments he owns produces.'' This paper shows that MP theory can also be formulated in a mathematically equivalent way using vectorial marginal products--which however conflicts with the above-mentioned ``distributive shares'' picture. Vectorial MP theory also facilitates the presentation of modern treatment of the labor theory of property which on the descriptive side is based on the fact that, contrary to the distributive shares picture, one legal party gets the production vector consisting of 100 percent of the liabilities for the used-up inputs and 100 percent of the produced outputs in a productive opportunity. On the normative side, the labor theory of property is just the application of the usual juridical norm of imputation to the question of property appropriation. Keywords: marginal productivity theory, property theory, imputation of responsibility, vectorial marginal products JEL Classification]{D2, D3, D63, P14