presume most dairy cooperatives conform to the “open” model4. This fact makes the CMF quite
different to the closely related labour-managed firm since the latter commonly exists in the
“restricted” form (see Kahana (1989) and Kahana and Nitzan (1989) for a modern theoretical
treatment).
In Helmberger's framework the “open” CMF's objective is not to maximise profits but instead
seeks to maximise the average milk price paid to its supplier members5. This price is equivalent to
the maximum cooperative surplus (defined as the difference between the value of revenue less all
variable and fixed-input costs) relative to the total amount of milk supplied by its farmer members:
“We may assume that the non-cooperative firm seeks to maximise profit whereas the cooperative
seeks as an “intermediate” objective to maximise cooperative surplus for any given level of M
[level of milk supplies6]” (Helmberger (1964)).
The Helmberger framework is developed using the tools of classical comparative static analysis.
One of the contributions of this paper is to recast the classical theory of the CMF in a duality
framework. This task results in two important insights. First, it affords a ready comparison
between the theory of the CMF and the PMF and allows clear inferences to be drawn about the
relative economic behaviour of the two forms of organisation7. Second, the duality approach
provides us with a convenient template for testing the competing CMF and PMF formulations.
Using the language of modern duality theory (see for example Chambers (1988) and Brown and
Christensen (1981)), Helmberger's stated objective for the CMF can be equivalently stated as
seeking to maximise short-run restricted profit where all inputs, bar the raw material milk, is short
4 The imposition of the dairy quota system in 1984 means that new members cannot join unless through
inheritance, purchase or lease of quota. However, this development does not transform the cooperative from an
“open” to a “closed” structure since this restriction is policy driven and hence beyond the control of the cooperative.
5 Harte (1992) argues that “... the milk price paid by a cooperative to its members is more like a transfer price
between two related businesses than a market price”.
6 Our italics.
7 In the case of the labour-managed firm the failure to utilise the duality approach has led to serious errors in the
analysis of such forms of organisation (see Kahana (1989)). No such errors appear to have afflicted the analysis of
the CMF. While this may be considered a fortuitously welcome outcome it is nonetheless odd given the virtually
identical forms of organisation in both cases.