Testing a von Liebig Crop Response Function against Polynomial Specifications

Abstract

Crop responses to fertilizers traditionally have been specified as polynomial functions. Recently, criticisms were raised against such specifications because they force substitution between nutrients and overestimate the optimal fertilizer quantity. With those criticisms, an alternative crop response function was presented in the form of a minimum function which equates the realized output to the production potential associated with a limiting input. In this paper a non nested test is performed to discriminate between the two rival specifications. The results of this test reject the hypothesis that a crop response is of the polynomial type, while they do not reject the hypothesis that it is of the minimum and plateau type.