A Mathematical Interpretation of Marxian Unproductive Labour

Abstract

Marx's theory of unproductive labour is incomprehensible without a proper understanding of his dual theory of value. Hence, the mathematical analysis of his model of value and growth is a useful and instructive investigation. Up to now, however, no attempt has been made to grasp the basic distinction between productive and unproductive labour in terms of matrix algebra. We hope this paper will fill this gap. It will be shown that Marx's distinction between productive and unproductive labour follows from his dual theory of labour value and use-value. Once this theory is formulated in terms of matrix algebra, it will be shown that Marx's results are confirmed without any further ideological digression. We will also consider the rate of profit formula developed by Morishima and Seton (1961) in the light of our previous results. In a last section some hints will be given for a less abstract mathematical analysis of unproductive labour today.