From: Philip Dunn (pscumnud@DIRCON.CO.UK)
Date: Mon Oct 11 2004 - 13:25:11 EDT
This problem is not easy to solve. After 20 years working on it, off and on, this is the best I have managed. Pure Joint Products: A Non-Sraffian Approach -------------------------------------------- Duménil and Lévy (1999, p.17, 2000) reach an impasse: "Each joint product is disaggregated into as many single production processes as commodities produced. The difficulty lies in allocating inputs to the various commodities. A problem of indeterminacy is posed, that the theory of value, in the strict sense, cannot solve." Let us go back to where the trouble started -- Sraffa's chapter 7 on joint production: "In Part I it has been assumed that each commodity was produced by a separate industry. We shall now suppose two of the commodities to be jointly produced by a single industry (or rather by a single process, as it will be more appropriate to call it in the present context). The conditions would no longer be sufficient to determine prices. There would be more prices to be ascertained than there are processes, and therefore equations, to determine them. In these circumstances there will be room for a second, parallel process which will produce the two commodities by a different method and, as we shall suppose at first, in different proportions." [Sraffa 1960, p.43] Sraffa later relaxes the 'second method' assumption slightly but does not exclude second methods. If we were to follow Sraffa here I think we would have already gone wrong. Firstly, we should not operate with industries or processes. We should talk about firms rather than processes. Further, we assert the principle that no two firms produce the same commodity. They may produce very similar, even practically indistinguishable, use-values but never the same commodity. There are no second methods. Sraffa's joint production processes are rigid in the sense that the joint products are produced in fixed proportions. If there is only one firm producing them we do not know how to split the constant capital transferred and the labour-power expended between the two products. Is this a problem? It would be a problem if, in this situation, the firm were producing two commodities. But is it? It produces two different types of use-value certainly. But why should we assume it is producing two different commodities? I shall argue that in rigid joint production there is only one "composite" commodity. Such composite commodities are not unknown in Sraffian treatments of joint production. Schefold (1980, p. 189) uses them to reduce the number of unknowns when considering the case of more than one machine engaged in the production of a finished good. Varri (1980, p. 86) and Baldone (1980, p. 114) do something similar. Suppose one unit of use-value A and one unit of use-value B is sold. The value of the part of the commodity produced as A or B is simply the value of the money A or B sells for. Positivity of value is assured. Inputs are split in proportion to the respective revenues. It is, after all, the same commodity. This would apply even if only one type of use-value was produced. Suppose that 3 articles are sold at prices x, y, z. Then non-labour and labour costs, and, in general, any inputs however measured are split in the proportion x:y:z. For example, suppose 3 bottles of cola, X, Y and Z, are produced in a batch and sell for $2, $3 and $5, respectively. For simplicity, let the value of money be constant in time and equal to 1 hour per dollar. Then the values of X, Y and Z are, respectively, 2, 3 and 5 hours. Say the three empty bottles cost $1 each as constant capital (or, even, cost anything whatsoever provided the total cost is $3). Use-value thinking would put the constant capital transferred at $1 per bottle in all three cases (or, alternatively, whatever the empty bottle actuallycost). However, value is not glued to use-value units. $0.60 worth of empty bottle value is transferred to X, $0.90 to Y and $1.50 to Z. The selling off of old machines or used vehicles to other firms could be treated similarly. Suppose the firm sold off its oldest vintage of vehicles once a year, then we treat the second hand vehicles as the same commodity as the firm's regular product. Rigid joint production of limited interest. Production where outputs are produced in flexible proportions presents a more challenging problem. References Duménil and Lévy (1999) http://pythie.cepremap.ens.fr/levy/dle2000a.pdf Duménil and Lévy (2000) The Conservation of Value, Review of Radical Political Economy, Vol. 32(1), pp. 119-146 Pasinetti, Luigi ed. (1980) Essays on the Theory of Joint Production, London Schefold (1980) in Pasinetti (1980) Sraffa, P. (1960) Production of Commodities by Means of Commodities, Cambridge Varri (1980) in Pasinetti (1980)
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