Conceptual Foundations of Risk Theory. Technical Bulletin No. 1731.

Understanding the way farmers respond to risk is a prerequisite for sound agricultural policymaking. Clarifying established agricultural economic theory to describe how individuals make choices among risky alternatives and providing a more precise set of concepts for studying behavior under risk contributes to such an understanding. A mathematically rigorous approach ensures that concepts are defined unambiguously and results are established decisively, and finds that individuals' preferences over an important class of risky alternatives are independent of preferences among certainties. Economic behavior under this type of risk cannot generally be predicted from behavior under certainty. Farmers' aversion to risk, or lack thereof, cannot invariably be determined from the shape of their utility curve of income. Farmers' profit-maximizing choices of production inputs may differ from those traditionally thought to be dictated by classical theory, even when preferences satisfy the explicit assumptions of that theory. Separate sections examine lotteries; the existence, uniqueness, invariance, continuity, and decomposition of measurable utility functions; aspects of measurable utility on the real line; definitions of risk aversion and its relation to concavity; and economic applications to optimal production levels under price uncertainty and optimal saving rates under uncertainty. (NEC)