# Use of Economic Optimization to Assess the Value of Water Marketing

*by*Richard Howitt,

Jay Lund,

**Document Type:**Proceeding Paper

**Part of:**WRPMD'99: Preparing for the 21st Century

**Abstract:**

(No paper) There is an increasing interest and implementation of water markets as an allocation mechanism for water in the Western U.S. However, the importance of the timing and location of water supplies offered to the market requires a similar level of disaggregation of the measures of water value. An optimization model of Californian agriculture is used to simulate monthly marginal value product functions for water. The value functions are calculated for twenty-one regions in the state that differ by water institutions or growing conditions. The regional model is calibrated to a four-year database on cropping patterns, cost, returns and water use. The driving force is a calibrated output cost function based on the PMP method ( Howitt 1995). In this model the approach is generalized to incorporate a full matrix of direct and indirect costs from the combination of crop output observed in the base data set. Given the limited data set available, the full cost matrix results in an ill-posed calibration problem. A Maximum Entropy estimation procedure is used to reconstruct a cost matrix that calibrates the model. The agricultural production model is calibrated to an annual profit and cropping pattern. Monthly water values are embedded in the annual optimization by use of monthly crop and regionally specific water requirements and a constraint that restricts stress irrigation in any given month. The potential for substituting improved water application technologies is modeled using a Constant Elasticity of Substitution production function whose elasticity of substitution determines the rate of technological adoption. The value functions are defined as step functions that are used to drive an optimizing network flow model.

**Subject Headings:**Optimization models | Calibration | Hydrologic models | Matrix (mathematics) | Economic factors | Water management | Marketing | Crops | California | United States

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