In order to respond to the current pressures on agriculture in the EU, the industry will have to go through fundamental structural change. Economic modelling provides the framework for understanding such changes. Mathematical programming is probably the most robust of all the modelling approaches notwithstanding several criticisms of the technique. Economists have long understood that profit maximisation is not the only objective of farmers. Although there are techniques to incorporate other objectives there does not exist a statistically rigorous method for estimating an appropriate objective functions. This problem also occurs at national and international levels of aggregation. This paper presents a new approach to modelling national and international production and trade through partial equilibrium and the use of a new development called positivistic mathematical programming. The nonlinear element of the objective function representing the partial equilibrium is estimated using past observations on supply, consumption and prices. Further, the paper also presents an original parameterisation of the demand curve that allows perfect competition to be simulated within the framework of a single mathematical model. Such a methodology is an advancement over methods that are currently in use.