On the Productivity Criteria of Leontief Matrices and the Conceptual Validity of Labor Values

Zalai, E. (1983). On the Productivity Criteria of Leontief Matrices and the Conceptual Validity of Labor Values. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-83-056

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Abstract

This paper generalizes some well-known productivity (nonnegative L-invertibility) criteria defined for nonnegative quadratic input-output coefficient matrices. The new economic criteria cover both the reducible and irreducible cases, treated separately until now, and are based on the absence of self-serving production and/or complete automation, which can be viewed as dual concepts. Detailed investigation of these concepts also reveals that their presence is incompatible with the idea of pure market commodity production. In particular, it is shown that the fundamental assumptions of the pure market economy and the indispensability of labor are sufficient to rigorously prove the existence, uniqueness, and strict positivity of labor values.

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