Pricing organic nitrogen under the weak disposability assumption: An application to the French pig sector

The authors are grateful to the two anonymous referees for helpful comments on an earlier draft of this paper. The nonparametric approach Data Envelopment Analysis is used in order to measure individual technical inefficiency. Different models are evaluated using a 1991 FADN data set of French pig farms. Organic nitrogen is considered as a by-product of animal breeding. Used as plant nutrient, organic manure becomes an input in crop production which is pollutant when excessive amounts enter surface and groundwater. In the latter case, the usual hypothesis of strong disposability of organic nitrogen is refuted because the elimination of pollution is costly. In this paper, we introduce a hypothesis of weak disposability of organic nitrogen and compare the technical efficiency measures obtained with and without this assumption. Then, using the duality between the restricted cost function and the input-output distance function and following Färe and Primont (1995), we derive a shadow price of organic nitrogen which can be compared to the unit cost of different existing manure treatments.