This paper introduces an approach to the specification of non-linear cost functions in regional programming models. It can be characterised as an application of positive mathematical programming (PMP) to multiple observations. The application of PMP in policy relevant agricultural supply models as a mean for calibration has significantly increased during the last ten years. However, many modellers have not reflected the arbitrary and potentially implausible response behaviour of the resulting models implied by standard applications of the approach. Paris and Howitt (1998) interpret PMP as the estimation of a non-linear cost function and generalize the specification by employing a « Maximum Entropy (ME) » procedure. However, their approach still lacks a sufficient empirical base and involves a parameterisation to enforce correct curvature of the cost function, which induces significant problems in applications. The suggested methodology is designed to exploit information contained in a cross sectional sample to specify — regionally specific — quadratic cost functions with cross effects for crop activities. It also provides a solution to the curvature problem. The approach is applied to regional programming models for 22 regions in France. An ex-post simulation across the 1992 CAP-reform shows plausible results with respect to the simulation behaviour of the resulting models. Paths for extensions and improvements of this methodology are identified.