Competitive Firm Behaviour With Simultaneous Price and Output Uncertainty

While a competitive firm facing price uncertainty has been extensively studied, this is not so for output uncertainty. This paper analyzes the behavior of a competitive firm facing multiplicative output uncertainty, either with or without price uncertainty. We depict equilibrium and obtain comparative statics results with the aid of a diagram which exploits the properties of a covariance term present in the first order conditions. Comparative statics results are obtained for the model with output uncertainty and price certainty and for simultaneous price and output uncertainty (including two simple, specific cases). We first derive results based on the Arrow-Pratt coe?cients 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 are able to obtain the intuitively appealing inverse relationship between increases in risk (both price and output) or input prices, and the optimal 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.