Comparative statics of production when there are multiple sources of risk

Abstract

Economists have analyzed exhaustively the impact of uncertainty on producers' decisions when there is a single source of risk [Sandmo, 1971; Batra and Ullah, 1974; Leland, 1972]. The case where there are multiple sources of risk, however, remains largely unexplored. In its general form, the multiple sources of risk problem is untractable. Only by imposing a fairly rigid structure on the problem can the nut be cracked. Fooladi [ 1985] investigates the production problem when there is uncertainty in both output price and input price. The effect of covariance between price and multiplicative output risk has been examined in a series of papers [Rolfo, 1980; Fraser, 1984; Newbery and Stiglitz, 1981]. This paper extends this literature to examine the comparative statics of production decisions when there are three sources of risk: output price, yield, and input price. As with the papers cited, some strong assumptions are made in order to get tractability. A recent paper by Meyer [1987] provides the foundation for a simplified derivation of some commonly used results about the decisions of a competitive producer in the presence of output price uncertainty. The derivation of comparative statics results is based on a mean-standard deviation model. As Meyer [1987] demonstrates, use of this model does not require any special assumptions about the form of the utility function or the distribution of error terms. (However, derivation of comparative statics of changes in months of the random variable requires special assumptions about the interrelationships of the random variables.) We show that many of the results of single source models carry through to the case in which there are multiple sources of risk. For example, partial stabilization of the output price will cause a risk averse producer to increase output. How-