The parameters of yield response functions can vary by year. Past studies
usually assume yield functions are nonstochastic or “limited” stochastic. In
this study, we estimate rye–ryegrass yield functions in which all parameters
are random. The three functional forms considered are the linear response
plateau, the quadratic, and the Spillman-Mitscherlich. Nonstochastic yield
models are rejected in favor of stochastic parameter models. Quadratic
functional forms fit the data poorly. Optimal nitrogen application
recommendations are calculated for the linear response plateau and
Spillman-Mitscherlich. The stochastic models lead to smaller recommended
levels of nitrogen, but the economic benefits of using fully stochastic crop
yield functions are small because expected profit functions are relatively
flat for the stochastic yield functions. Stochastic crop yield functions
provide a way of incorporating production, uncertainty into input
decisions.