The production function discussed previously in this chapter was deterministic. Risk was not considered in that function. A stochastic production function is a more general presentation of the same concept. Rather than a single output quantity being associated with each input quantity or set of input quantities, the stochastic production function has a probability distribution of output quantity associated with each input quantity or set of input quantities. This specification of a stochastic production function allows input quantities to affect not only the mean yield but also the probability of various degrees of loss (or gain) relative to the mean. In other words, the quantity of inputs used can affect the mean, variance, skewness, and kurtosis of the yield probability distribution. The farmer’s decision problem may be more realistically portrayed by a stochastic production function. The additional complexity introduced by the stochastic production function may also be more representative of the decision challenges faced by farmers. Not only must they consider the effects of numerous inputs on expected yield but also their effects on the probability of various degrees of yield loss or gain relative to the average yield.