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

The cooperative firm seeks to maximise the price paid to its members for a given raw material
supply:

P_m=(         p_m∕ m) = (α_m-l)( ∕m²)                         (12)

The profit-maximising firm chooses the price that maximises profits for a given level of raw
material supply:

P^v_m=^a_nS. ∕∞)=>( P^v_m∣ m) = a_m(a_m-V)( ∕m²)                     (13)

The partial derivatives (12) and (13) will vanish if:

( log( ) / log(m)) = a_m = 1                                               (14)

3. Applying the theoretical framework

The theoretical framework set out above can be exploited to address the issues raised in our
introduction. The first issue was whether Irish dairy cooperatives could be classified as “virtual”
profit maximisers. For instance, if cooperative firms were under pressure to maximise the milk
price paid to its members at the expense of adequately remunerating its capital stock this would
imply p_m> p^v_m. Whether this outcome is consistent with the empirical evidence can be tested
using the framework suggested by Conrad and Unger (1987). This approach involves estimating a
system given in (15):

⅛= ⅛( -,P_y,w,m,k) (a)

У^С = У^С( -,P_y,w-m,k) (b)

-x^c = X^c( ,p_y,w,m,k) (c)

P^v_m = P^v_m(. -,p_y,w-m,k) (d)

12

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