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):
Pm =Pm( -,Py,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 pm systematically
differs frompvm 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 (py), the wage rate (wɪ), the price of non-milk materials
13
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