Duality theorems summarising some unambiguous qualitative comparative static results for processing cooperatives - The restricted profit function applied

Cooperatives can broadly be divided into processing and marketing cooperatives on the one hand, and purchasing and supplying cooperatives on the other. In the early economic cooperative literature it is suggested that a processing cooperative may pursue either one of the following four objectives: a) Maximisation of the net average revenue product, b) Maximisation of the dividend, c) Maximisation of the processing cooperative’s profit, and d) Maximisation of members’ producer surplus plus the cooperative’s profit. The corresponding objectives for purchasing and supplying cooperatives are: e) Minimisation of the purchasing price, f) Maximisation of the dividend, g) Maximisation of the purchasing cooperative’s profit, and h) Maximisation of members’ consumer surplus plus the cooperative’s profit. This article analyses processing cooperative behaviour within a duality framework based on the restricted profit function. The five derived duality theorems concisely summarise the unambiguous qualitative comparative static results for a cooperative’s ordinary or relative choice functions, depending on which objective the daily manager is assumed to pursue.