ABSTRACT
The response o f profit-m axim izing producers to uncertainty about the level o f nitrates present in the soil is developed in this section .3 L et Na be the level o f applied nitrogen fertilizer and let Ns be the level o f nitrogen already present in the soil. Let both be m easured in equivalent units so that yield, y, is a function o f total nitrogen: y = F(Na + Ns). A ssum e for now that F is continuous with FN> 0 and Fm < 0 , where the subscripts on F denote partial derivatives. L et g(Ns) be the relevant density function o f soil nitrogen at the tim e Na is applied. Throughout this article, g(Ns) will be interpreted as representing a producer’s beliefs, based on year-to-year variations in soil nitrogen loss and gain rates, about the single nitrogen level in a field. It is im plicitly assum ed that there is no spatial variation in soil nitrate levels in the field. The risk-neutral producer’s problem is to choose Na to m axim ize the expected value o f profits, * with the expectation, E, being taken with respect to Ns:
nitrogen fertilizer typically is applied just before or at planting in early spring or with fall fieldwork. T raditional soil tests in the fall o r early spring could give an indication o f soil nitrate levels at the tim e o f application, but they are not widely used. Potentially large, and random , nitrate gains and losses through leaching and denitrification between the tim e o f testing and plant use m ake such tests unreliable predictors o f nitrate levels when plants start rapid uptake in late spring and early sum m er.2
