This study uses a Cox parametric bootstrap test to select between two specifications of the von Liebig hypothesis, a switching regression model and a non-linear mixed stochastic plateau function. The selected production function was used to determine optimal stocking density for dual-purpose winter wheat, under production and output price uncertainty. The switching regression approach was rejected in favor of the non-linear mixed stochastic plateau function. The relatively small difference in optimal stocking density between risk aversion and risk neutrality suggests that risk-aversion is much less important in explaining producer response to uncertainty than is nonlinearity in the production function.