The State-Contingent Properties of Stochastic Production Functions

The state-contingent properties of the most frequently used representations of stochastic production in the agricultural-economics literature are examined. Particular attention is paid to the cases of multiplicative uncertainty, additive uncertainty, and the Just-Pope production function, State-contingent technologies and their associated cost functions are reviewed, and that theory is applied to the stochastic production function. A generalization of the Just-Pope technology that has desirable state-contingent characteristics is proposed. Cost functions based upon state-contingent technologies are compared with cost functions based on a parametrized distribution representation of production uncertainty.