A Duality Approach to Testing the Economic Behaviour of Dairy-Marketing Co-operatives: The Case of Ireland

retaining majority dairy farmer ownership. A second objective of the paper was to examine how
these firms responded to the imposition of the dairy quota by way of their output supply and input
demand decisions.

The traditional theory of the cooperative managed firm (CMF) developed by Helmberger and
others was recast in a duality framework. The CMF firm differs from the profit maximising firm
(PMF) in (a) having as its objective the maximisation of the price paid to its members for the raw
material they supply and (b) being obliged to process all the raw material supplied by its members.
The CMF in practice differs from its close relative - the labour managed firm - in usually having an
“open” rather than a “restricted” membership policy. This means that the only requirement in being
a member of a typical dairy cooperative is that one produces and supplies milk.

The duality framework assisted in clarifying the behavioural objective of the CMF and in particular
in drawing out its relationship with the PMF. In the duality framework the CMF’s objective can be
stated as one of maximising short-run restricted profits, where the main restriction is the amount of
raw material (milk) supplied by its membership which it is obliged to process. The CMF thus
maximises the product of the milk price and the given amount of raw material processed which is
equivalent to maximising the milk price paid to its membership. Expressed in this way the principal
difference between the CMF and the PMF (assuming price-taking behaviour in input and output
markets) is that in the former case the milk price is the choice variable and the amount of raw
material processed is a given variable while the opposite situation holds for the PMF.

The key to testing the equivalence of the competing behavioural objectives is thus to establish
whether the CMF behaves “as if” it were a PMF, or, in our terminology, is a virtual profit
maximiser. At the margin the PMF will only demand additional units of the raw material, given its
price, if short-run profits are enhanced whereas at the margin the CMF will only increase the price
it’s prepared to pay for the raw material, given the amount supplied to it for processing, if short-
run profits are increased at the margin. The equivalence between these two approaches was
formally tested for the Irish dairy-processing sector over the period 1961 to 1987 using a
procedure suggested by Conrad and Unger (1987).

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