Flexible quota constraints in positive mathematical programming models

Traditional deterministic programming models do not simulate any change of quota-limited decision variables as long as the quota have positive quota rents. However, in practice a quota constraint is rarely exactly binding because the decision variables are stochastic. This papers presents a simple model extension to integrate quota flexibility in mathematical programming models to simulate the observed over- and underuse of quota. The theory is confirmed by three different cases of quota systems in the EU agriculture: dairy quota, sugar quota and manure emission rights. The dairy quota flexibility model is applied to simulate the impact of the soft landing of the EU dairy quota system