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

where,

= a vector of parameters.

The system in (15) implies that the cooperative firm is a “virtual” profit maximiser. In other words
the price of milk paid to suppliers is restricted in the estimation to be equivalent to the “virtual”
price implied by Hotelling’s Lemma.

To statistically test the validity of the system in (15) we can compare the log-likelihood value
obtained from estimation of this system with that yielded by estimation of a modified system which
involves replacing (15)(d) by (16):

P_m =P_m( -,P_y,w-m,k)                                              (16)

where,

≠ is a vector of parameters.

The modified system does not impose the condition that the actual milk price is got by applying
Hotelling’s Lemma. The Conrad and Unger (1987) test ascertains whether p_m systematically
differs fromp^v_m over the entire sample¹⁰.

4. Data and empirical estimation

Our empirical model is tested by estimating the systems (15)(a), (b), (c), (d) and (15)(a), (b), (c),
(16) using time-series data on the dairy-processing sector. Short-run profits were defined to be
functions of the price of processed output (p_y), the wage rate (wɪ), the price of non-milk materials

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