A Simple Agro-Economic Model for Optimal Farm Nitrogen Application under Yield Uncertainty

Abstract

Farmers in the developed world tend to over-apply fertilizer, and we explore a model for decision-making under uncertainty in yields. This article proposes an agro-economic model for farmer decision-making based on subjective expected yield and crop response to fertilization. The model explores subjective yield probability distributions that are both better suited to subjective crop yields than the previously proposed probability distribution and is easier to extract from farmers. The model allows the analysis of the impact of changes in fertilizer price and variance of expected yields. The model result is consistent with observed farmer behavior based on the rule of “fertilizing for the good years” that appears, according to our model, as rational and consistent with expected profit maximization under yield uncertainty since the cost of over-application is lower than that of the opportunity cost of under-application. The goal of increasing the efficiency of nitrogen use requires both technical innovation and an expansion of the knowledge on the socioeconomic factors underlying excessive crop fertilization that must be improved both to meet future food demands and to prevent environmental degradation and climate change.