The von Liebig production functions with decreasing yields

Abstract

Despite the fact that crop response to agricultural materials since a long time has been researched, there are several issues that are still waiting for answer. The importance of the issue is that a more realistic crop response model, with biological meaning, would allow a better interpretation of experimental results. The law of the minimum was stated by Justus von Liebig circa 1840. This law explains the crop response by the production factor that is most scarce to the plant. The problem associated to this law is that some researchers avoid to use it because the algebraic formulations - commonly used to express the law do not allow a decreasing yields phase. Results gotten show that von Liebig models allow to have decreasing yields. Consequences of these new von Liebig models are associated with greater plateau production levels, suggesting greater use of input to get them. The von Liebig framework using the square-root polynomial regimes and the plateau, with or without specific BP (back-plan) regime is strongly suggested. Results gotten also corroborate the idea that curvilinear response functions, which characterize marginal decreasing yields, are more suitable specifications to interpret experimental data.