Production decisions under joint price and production uncertainty

While production decisions in the presence of price uncertainty have been extensively studied, this is not so for the case in which the level of production is itself uncertain. In this paper,we provide a decision analysis under multiplicative production uncertainty, both with and without price uncertainty. We depict equilibrium and obtain comparative statics results with the aid of a diagram based on the difference between expected price and marginal cost. Comparative statics results are obtained for the model with production uncertainty alone and also for simultaneous price and production uncertainty (including two special cases). We first derive results based on the Arrow-Pratt coefficients of risk aversion, and then supplement these with the Ross measure of relative risk aversion, since this proves useful in the presence of multiple sources of uncertainty. We find that increases in risk (both price and production) or input prices reduce expected output. However, expected output supply is an increasing function of (expected) price only for "low" levels of risk aversion, and in general the relationship is ambiguous.