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The economics of deficit irrigation are examined. The concepts developed in the heuristic discussion are developed into a set of rigorous mathematical expressions for determination of optimum water use under deficit irrigation. These expressions also can be used to estimate the range of water use within which deficit irrigation would be more profitable than full irrigation. The expressions are completely general in the sense that they can be used with any crop production function and cost function that the analyst chooses. The general expressions are used to derive a set of specific expressions for a particular case study involving a quadratic production function and linear cost function.
Marshall English (1990) studied this question.