This paper presents an innovative quantitative approach to modelling milk and beef supply, which is then applied to Hungary and Poland. Utilising generalised maximum entropy estimation, we provide an empirical basis for treating ill-posed and -conditioned problems by reconciling sample and non-sample information. Adjustments in quasi-fixed factors are explicitly taken into account in order to capture dynamics. Inelastic milk supply responses were found both for Hungary and for Poland. Milk and beef outputs behave as complements in the medium run, but not in the short run for Poland. The empirical estimates found generally support the assumed parameters used in calibrated models.