Standard definitions of the cost function do not admit risk. Standard
(ex post) approaches to cost function estimation yield biased and inco
nsistent estimates when production is stochastic. Recently an (ex ante
) approach to cost function estimation with stochastic production has
been developed by imbedding the distance function in the cost function
estimation problem. We generalize the approach to consider risk avers
ion in decision making. Only two empirical studies have considered sto
chastic production in cost function estimation. Both have required con
stant returns to scale. We demonstrate a methodology sufficiently gene
ral to consider nonconstant returns to scale.