A Bayesian approach is used to provide a framework for optimal input allocation for a stochastic production function with uncertain parameters. The chosen production function is a single-input version of a function which can exhibit positive or negative marginal risk. The sensitivity of optimal input allocation to the degree of risk aversion, the marginal risk parameter, and the assumed level of uncertainty about the parameters is examined. Using an example problem it is shown that parameter uncertainty will not always lead to a lower input level when a producer is risk averse. Some problems with the production function specification are uncovered, as is the incompatibility of some expected utility and stochastic assumptions.