The paper introduces a general methodological approach for the estimation of constrained optimisation models in agricultural supply analysis. It is based on optimality conditions of the desired programming model and shows a conceptual advantage compared to Positive Mathematical Programming in the context of well posed estimation problems. Moreover, it closes the empirical and methodological gap between programming models and duality based functional models with explicit allocation of fixed factors. Monte Carlo simulations are performed with a maximum entropy estimator to evaluate the functionality of the approach as well as the impact of empirically relevant prior information in small sample situations.