CRIEFF Discussion Paper Number 0208
Competitive Firm Behaviour With Simultaneous Price and Output Uncertainty
Ardeshir J. Dalal and Moavia Alghalith
download this paper
Abstract
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
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 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.
Key Words
Multiplicative output uncertainty, price uncertainty, comparative
statics, Ross increasing relative risk aversion, quadratic utility, Stein's
Lemma.
JEL Classifications
D21, D81
Ardeshir J. Dalal
Northern Illinois University
Moavia Alghalith
University of St Andrews
Back
to CRIEFF Discussion Papers list