Some alternative functional forms for estimating economically optimal nitrogen fertilizer rates

Abstract

Estimation of economically optimal nitrogen (N) fertilizer rates involves fitting some production functions to crop yield data obtained at different N fertilizer rates. Most common production functions that have been used in previous N fertilizer response studies are quadratic and square root. In this paper, we employ two alternative production functions, namely Cobb‐Douglas and transcendental, for estimating economically optimal N fertilizer rates. Although these production functions are quite popular in production economics literature, they have not been used in N fertilizer response studies. The two functions were used to estimate economically efficient N fertilizer rates for corn (Zea mays L.). Estimation involves corn yield data obtained from six site‐years in New Jersey during the period 1992–1995. Each site‐year had 10 rates of fertilizer N applied as sidedress. The results obtained by the two functions were compared with those obtained for quadratic and square root models. Economically optimal mean rate for each model was computed assuming that average profits are maximized over observed site‐years. Mean economically optimal N rates for the four models at a common fertilizer‐to‐corn price ratio ranged from 184 kg N ha^‐1 for the transcendental to 344 kg N ha^‐1 for the Cobb‐Douglas functions. Statistical analyses indicate that the transcendental model is a better predictor of economically optimal N fertilizer rates than the other three models.