Risk and irrigation water use decisions in Arizona : an economic analysis

Abstract

This thesis considers economic optimization of irrigation water use in Arizona. Attention is given to both the questions of risk resulting from stochastic climatic conditions in the production of field crops and farmers' behavior under risk. The risk attitudes of any particular farmer are assumed to be characterized by either a quadratic or an exponential utility function for profit. This assumption permits a simplified analysis of the decision problem in terms of maximizing expected utility on an efficiency frontier in expectation and variance of profit. The methodology is applied to a case study involving four hypothetical farmers facing water price increases. Efficiency frontiers corresponding to different water prices are derived using a quadratic programming algorithm. The exponential formulation is used to represent the individual utility functions due to the failure of the quadratic formulation to satisfy positive marginal utility. For each farmer, an optimal irrigation water use plan, specifying crop mix, water applications, and fallow land, is determined at each water price. Case study results indicate that an approach to irrigation water use optimization that considers risk often leads to optimal plans that differ substantially from those plans selected without this consideration.