Duality of weakly disposable technology

The axiom of weak disposability is frequently imposed in data envelopment analysis (DEA) models involving undesirable outputs such as pollution. This paper sheds new light on the economic interpretation of weak disposability by developing dual formulations of the weakly disposable DEA technology. We find that the economic implications of weak disposability on the multiplier DEA problem are two-fold: (1) the shadow prices of the undesirable outputs can be positive or negative, and (2) the economic loss of the benchmark cannot exceed the suck cost of the inputs. We interpret the second implications as a limited liability condition. The dual formulations developed in this paper enable one to estimate shadow prices of the undesirable outputs using the weakly disposable technology. The insights gained are illustrated by a numerical example and an empirical application to the US power plants.