An economic analysis of water priority rights and their effect on farm planning in the San Carlos Irrigation and Drainage District

The farmer within the San Carlos Irrigation and Drainage District, Coolidge, Arizona, is faced with an uncertain water supply. The decisionmaker must make decisions regarding the planting of crops without advanced knowledge of the total amount of water which will be available. The farmer can have definite expectations only if he has definite knowledge of his environment and the uncertainties which are involved. This study attempts to add to the stock of knowledge about the farmer’s environment and uncertainties associated with the water supply. An analytical method of applying Game Theory to empirical data gathered from stream flow records is presented. This procedure was developed to formulate a method whereby the farm manager can utilize these stream flow records to reduce the uncertainty of crop planning. The stream flow data were converted into frequencies of natural flow water priority right fulfillment which were taken to be the probabilities with which priority rights would be filled in future periods. Probability formulae were applied to combine the probability associated with each period into the probability of receiving water in at least r periods and of not receiving water in k periods for related priorities. The resultant probabilities were multiplied by the net return above variable costs (gain) and pre-harvest variable costs (loss) associated with the planting of a particular crop strategy. These values were placed in a game payoff matrix with the farmer as one player and nature as the other. To account for differences in resources and psychologies of farmers, several criteria were then employed to resolve the decision problem.hydrology collectio