The Effect of Uncertainty in Input Quantities on the Optimal Expected Input Combination

The problem faced here by a firm whose input quantities are fluctuating is to choose the optimal combination of average input quantities so as to maximize expected revenue under a cost constraint. We show that for the prevailing production functions, the firm might find it optimal to increase the average use of the stochastic factor (even when such an increase will further increase uncertainty) at the expense of other, possibly certain factors. This holds even when increased uncertainty in input reduces total expected revenue. The solution is shown to depend on characteristics of the production function which are generally ignored in the classical theory of the firm. The model may be used in general maximization problems with underlying stochastic variables.