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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

References

[1]Berman, A. and Plemmons, R. J., Nonnegative matrices in the mathematical sciences (Academic Press, London, 1979).Google Scholar
[2]Burmeister, E. and Dobell, A. R., Mathematical theories of economic growth (Collier-Macmillan, London, 1970).Google Scholar
[3]Dumenil, G. and Levy, D., “Valeurs et prix de production”, Revue Economique 33 (1982), 30–70.CrossRefGoogle Scholar
[4]Filippini, C., “Positivita dei prezzi e produzione congiunta”, Giornale degli Economisti e Annali di Economia 36 (1977), 91–99.Google Scholar
[5]Filippini, L. and Filippini, C., “La relazione tra saggio di salario a saggio di profitto in produzione congiunta”, Rivista Internazionale di Scienze Sociale 87 (1979), 425–441.Google Scholar
[6]Filippini, L. and Filippini, C., “Two theorems on joint production”, Economic Journal 92 (1982), 386–390.CrossRefGoogle Scholar
[7]Fujimori, Y., Modern analysis of value theory (Springer-Verlag, Berlin, 1983).Google Scholar
[8]Gale, D., The theory of linear economic models (McGraw-Hill, London, 1960).Google Scholar
[9]Levy, D., “La formalisme unificateur du surclassement”, in La Production Jointe (ed. Bidard, C.), (Economica, Paris, 1985).Google Scholar
[10]Mangasarian, O. L., Nonlinear programming (McGrw-Hill, London, 1969).Google Scholar
[11]Pasinetti, L. L., “The notion of vertical integration in economic analysis”, Metroeconomica 25 (1973), 1–29.CrossRefGoogle Scholar
[12]Pasinetti, L. L., Lectures on the theory of production (Macmillan, London, 1977).CrossRefGoogle Scholar
[13]Sraffa, P., Production of commodities by means of commodities (Cambridge University Press, Cambridge, 1960).Google Scholar
[14]Steedman, I., “Positive profits with negative surplus value”, Economic Journal 85 (1975), 114–123.CrossRefGoogle Scholar
[15]Steedman, I., “Positive profits with negative surplus value: a reply to Wolfstetter”, Economic Journal 86 (1976), 873–876.CrossRefGoogle Scholar
[16]Toker, M. A., “A note on ‘negative’ quantities of embodied labour”, Economic Journal 94 (1984), 149–154.CrossRefGoogle Scholar
[17]Woods, J. E., Mathematical economics (Longmans, London, 1978).Google Scholar