An application of positive mathematical programming to the Canadian hog sector in the Canadian Regional Agricultural Model

This paper describes the Positive Mathematical Programming (PMP), a method for calibrating models of agricultural livestock production and resource use using a nonlinear marginal cost function and illustrates the application of this method in agricultural sectoral models used to study changes in policy and market signals. The Canadian Regional Agricultural Model (CRAM) is a regional, multi-sectoral, comparative static, partial equilibrium, mathematical programming model developed and maintained by Agriculture and Agri-Food Canada. The hog sector is one of the components of the CRAM. In this application, the introduction of nonlinear relationships to improve the performance of sectoral models is emphasized for the hog sector. A cubic total cost function was chosen, based on the empirical research for the hog sector in Canada. Empirical research shows that the marginal cost function is convex for the hog sector in Canada. The calibration constraints are removed and the model automatically calibrates at the base year production levels. The results indicate that the model is able to predict the impacts of changes in feed prices on the breeding herd size. Similarly, the model can predict changes in the herd size with respect to changes in pork prices.