PSEUDOMONOTONE VARIATIONAL INEQUALITY IN ACTION: CASE OF THE FRENCH DAIRY INDUSTRIAL NETWORK DYNAMICS

A pseudomonotone operator serves to study the dynamic network equilibrium of the French dairy industry. Using a modified variational inequality model, which is based on the price variations, we reverse the typical problem formulation and claim that the absence of synchronization between the variations, which also need to be proportionate, is what causes the network disequilibrium. Provided the pseudomonotonicity of the mapping, the solution of the variational inequality problem also happens to be a fixed point. The model outputs show that the economic viability of the upstream agents is in conflict with the overall network equilibrium. The results further suggest that increasing the threshold of resale-below-cost should enlarge the asynchronicity between the upstream and instream price adjustments, which is problematic because the price variations are already asymmetric at the levels of upstream and downstream layers. The best path toward the network equilibrium would go by carrying out a further integration of the upstream layer.