Derived Estimation of Willingness-to-Pay to Avoid Probabilistic Shortage

A mathematical programming approach is developed for deriving estimates of the willingness-to-pay of water customers for improvements in water supply reliability. Reliability is represented as a probability distribution of different shortage levels, allowing the valuation of different profiles of water supply reliability. The approach is examined analytically and a two-stage linear programming variant is developed for applied problems. The approach can be applied to estimate the willingness-to-pay for improved reliability of different classes of customers and for suggesting promising water conservation programs for different customer classes. An example application is presented to illustrate the approach. Introduction While much effort has been devoted to estimating the reliability of urban water supplies, little effort has been expended in developing methods to value different reliability profiles. Most recent attempts to value urban water supply reliability have been empirical, through the use of direct contingent valuation studies and have examined only one shortage level and frequency combination at a time (CUWA, 1994; Howe and Smith, 1993, 1994; Howe, et al., 1990). The approach taken here provides somewhat more derived estimates of willingness-to-pay. Two-stage mathematical programming is used to estimate a customer's willingness-to-pay to avoid a particular and complete shortage probability distribution, given estimates of consumer willingness-to-pay to avoid implementing specific shortand long-term water conservation measures and estimates of the water conserving effectiveness of those measures. The method assumes expected value costminimizing behavior by the consumer, where the costs of specific conservation activities can be merely financial or include perceived costs (and benefits) as estimated by more focused contingent valuation studies. Additional limitations of these estimates of the willingness-to-pay to avoid a set of probabilistic shortages are discussed. In addition to providing an estimate of customer willingness-to-pay to avoid a given shortage probability distribution, the method also suggests the least-cost mix of longand short-term water conservation measures for customers to implement in response to such a shortage profile. This derived approach should have uses for a) estimating customer willingness-topay to avoid a set of probabilistic water shortages without the expense of situation-specific contingent valuation surveys of probabilistic situations, b) providing a check on the results of direct contingent valuation estimates of willingness-to-pay to avoid shortages, and c) suggesting promising designs for longand short-term water conservation programs suitable to local conditions. However, implementation of the proposed approach often