Duality Theory and Cooperatives

The adjustment of a NARP-maximising processing cooperative facing an aggregated raw agricultural supply schedule with a positive slope due to decreasing returns to scale is revisited. When the peak coordinator being responsible for the daily management of the processing cooperative is able to control members’ supplies of the raw agricultural product, unambiguous short-run qualitative comparative static results can be derived for the cooperative’s relative choice functions on the basis of the unrestricted NARP function proven to be convex in final output price and processing production factor prices. In general, no unambiguous qualitative comparative static results are forthcoming for the processing cooperative’s relative choice functions on the basis of the stable-equilibrium NARP function when the peak coordinator is unable to restrict members’ supplies of the raw agricultural product.