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

run variable and the firm faces given prices for its output and all other inputs, bar milk. Short-run
restricted profits are simply, p_mrn, where, p_m is the price of milk and m is the level of milk supplied
by members. If the CMF maximises p_mrn, then p_m is also maximised.

Thus the firm must process all the milk its suppliers deliver for processing. The level of raw
material processed or demanded by the cooperative is a given for the “open” cooperative firm but
the price paid for the raw material is a choice variable.

Let’s now characterise the dairy cooperative as an “open” entity but unlike, Helmberger and Hoos,
let’s retain the assumption, as a maintained hypothesis, that capital is a short-run quasi-fixed input.
The behavioural objective of such a firm will be to maximise short-run restricted profits
conditional on a given level of raw material (m) and capital stock (k). This can be thought of as
maximising the returns to capital and raw materials. The profit function of the dairy-processing
firm will now be given by equation (3):

^c_k,_m = ^c_k,Λp_y,^w,^m,^k)                                                        (ʒ)

where,

^c_{k m} = maximum short-run profit for the cooperative firm.

m = level of raw material (milk) which the cooperative must process.

w = vector of variable input prices such that w < w.

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