Most production activities undertaken involve a certain degree of risk. Agricultural production is particularly risky since it is susceptible to the physical vagaries of nature and all economic and social variations. For most countries, agriculture is an important and vital sector where production decisions are made under risk. Hence, decision making under risk requires careful analysis and represents an important area of study. The present research has been directed to advance our knowledge about the consequences of risk, and the behavior toward risk in the organization of production, particularly agricultural production. This objective is achieved by a review of risk theory, duality and the use of applied econometrics in order to develop some empirical production structures capable of assessing the impacts of risk, particularly increasing risk, on producer's behavior. The concept of increasing risk as incorporated into production structures is then applied to a livestock example in Utah. A stochastic production function for ranch operations in Utah is estimated in order to derive information about the impacts of increasing risk on the output and input choices of ranchers. The results of the estimation and tests suggest that ranchers in Utah produce with inflexible production technology and are subject to significant production risk. Any policy affecting the use of inputs such as feed and pasture may exacerbate the risk condition which the ranchers face, since choices to employ alternative input combination to modify the condition of risk are limited.