The Flexible Cubic Polynomial and Plateau Production Functions

Abstract

The S-shaped three-stage production function, popular in teaching economics and farm management, is often motivated in the context of yield response to fertilization and illustrated using a third degree polynomial specification (cubic). Indeed, the cubic model is used as basis for fertilization recommendations and norm setting in Denmark. Yet, contemporary agricultural economic and agronomic knowledge favors non-linear response with plateau (NLRP) specifications. An analysis, based on fitting the cubic to yield/nitrogen data sets from 40 Danish winter wheat field trials, did not in a single case reveal a three-stage response pattern. It is interesting, however, that in the majority of 40 estimations, the cubic exhibited or strongly suggested an NLRP-like pattern within the domain of measured nitrogen application. Thus, the flexible cubic often works well for the purpose of norm setting when care is taken to avoid extrapolation outside the data domain.