The investigation reported in this dissertation is a portion of a larger effort to determine how allocation of water resources affects economic and social development in an arid environment. The study focuses on irrigated crop agriculture in Western Yuma County, Arizona, where irrigation water supplies are obtained from diversions from the Colorado River. Irrigated agriculture accounts for nearly 95 percent of total water use in this area. Linear programming techniques are used to determine optimum farm output and resource use patterns for five different farm models representing different farm size groups. The farm models were synthesized from data collected in a survey of 102 farms within the study area in 1964. This sample represented about one-fourth of the total universe. The linear programming analysis proceeds in four phases. In the first phase solutions are obtained for each model under the assumption that the size structure of agricultural firms and the resource base is fixed at current levels. In the second phase additional activities are added to permit land acquisition or disposal by each model farm. In the third phase the original formulation is modified to permit reclamation of new lands under the assumption that existing water rights will be perfected. The fourth phase combines the individual models analyzed in phase two into an integrated general model in which resource disposals by one farm size model must be balanced by acquisition in another. The final stage of the analysis includes estimates of crop output, and resource use under conditions specified in each phase. The marginal value product of selected resources is discussed and demand schedule for additional water is estimated. Land transfer price ranges are also discussed.