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On the analysis of joint production

Published online by Cambridge University Press:  17 February 2009

J. E. Woods
J. E. Woods
Affiliation:
Department of Economics, Queen Mary College, University of London, Mile End Road, London E1 4N5England.
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Abstract

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It is well known that n-process, n-commodity (or square), models of productive single-product industries have positive solutions to their price and quantity systems if the rates of profit and growth lie in appropriate non-negative intervals. On the other hand, negative prices and quantities can occur in formal solutions of models of square, productive, multiple-product industries even when the rates of profit and growth are less than their respective maximum positive values. It is shown in this paper that these differences can be attributed to the presence in joint production of dominance, in either row or column versions. Results on positive solutions to the price (respectively, quantity) system are derived in terms of the absence of column (respectively, row) dominance of the net output matrix. As the concepts of row and column dominance are defined in terms of linear inequalities, the basic mathematical results to be applied are theorems of the alternative.

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 1 , July 1987 , pp. 59 - 78
Copyright
Copyright © Australian Mathematical Society 1987

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