Improvement of a Bio-Economic Mathematical Programming Model in the Case of On-Farm Source Inputs and Outputs

We present a two-step process for solving nonlinear farm activity models inside a linear framework under the assumption that market prices approximate the shadow prices of the model’s constraints. In the event of market imperfections or missing prices (for example non-marketed outputs), the previous assumption is not justified and the derived solution is not optimal. To circumvent this problem and to avoid nonlinear algorithms that may prove unwieldy for large models, we propose an iterative computation method, based on the re-estimation of shadow prices in each step until a converging solution is found. The method is applied to the bio-economic model AROPAj, which consists of a number of linear programming (LP) farm sub-models representing different farming systems across the European Union. For most of LPs producing non-marketed outputs a converging solution is obtained in two iterations, while the remaining LPs lead to periodic solutions of very low amplitude.