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

The plan of the paper is as follows. Section 2 sets out a theoretical framework designed to provide
guidelines for the empirical application. We draw on the traditional and seminal analysis of
Helmberger and colleagues (1962, 1964, 1966) and recast it in a duality framework which proves
highly convenient for the empirical analysis. Section 3 outlines how the theoretical framework
could be applied to achieve the objectives established for the paper. Section 4 sets out the data
used in the empirical application and reports the econometric results. Finally in Section 5 we draw
some conclusions.

2. Theoretical framework

Suppose a dairy-marketing cooperative were classed as a profit-maximising firm (PMF) facing
given prices for all variable inputs, including its principal raw material, and its processed output.
Also let’s suppose that the capital input is short-run quasi fixed. The profit function for such a firm
is given by equation (1):

к = _k(P_y, ^w, K)                                                        (1)

where,

π k = short-run maximum restricted profits, given k.

p_y= price of processed output.

w = vector of input prices.

к = short-run quasi-fixed capital stock.

Equation (1) can be thought of as giving the maximum returns to the quasi-fixed input k.

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