Negative values in pure joint production

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

DumÚnil and LÚvy (1999, p.17, 2000) reach an impasse:

"Each joint product is disaggregated into as many single production processes
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

"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

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"

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

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
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.  


DumÚnil and LÚvy (1999)

DumÚnil and LÚvy (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)

This archive was generated by hypermail 2.1.5 : Wed Oct 13 2004 - 00:00:01 EDT