The production literature has shown that inputs such as fertilizer can be defined as risk-increasing. However, farmers also consistently overapply nitrogen. A model of optimal input use under uncertainty is used to address this paradox. Using experimental data, a stochastic production relationship between yield and soil nitrate is estimated. Numerical results show that input uncertainty may cause farmers to overapply nitrogen. Survey data suggest that farmers are risk averse, but prefer small chances of high yields compared to small chances of crop failures when expected yields are equivalent. Furthermore, yield risk and yield variability are not equivalent.