Edward Oczkowski develops the generalised Nash bargaining solution for a bargaining co-operative selling its raw output to a single processor. Three assumptions for co-operative member behaviour are examined: profit maximisation, co-operative surplus maximisation and maximising members' price. Solutions are compared and comparative statics presented for these alternative assumptions and two model types, price bargaining with a given quantity and simultaneous price and quantity bargaining.
The most striking feature of the results is that the objective of maximising members' price does not necessarily lead to the highest members' price. Even in the exogenous quantity model, reducing output does not necessarily increase members' price. These findings question the relevance of co-operative members seeking to maximise members' price when trading with a single processor.