Cost and Pricing in a Regime of Sustainable Water Resources

The article offers a mathematical and numerical programming analysis of cost and pricing of freshwater and effluent in a sustainable regime. Since demand in the urban sector is inelastic, the program focuses on agriculture. Sustainability is maintained by limiting withdrawal from natural sources to “safe yield” and by removing all salts added annually to the aquifers. Consistently, the mathematical model is formulated in terms of a steady state. The model yields marginal cost of fresh and recycled water and corresponding prices that incorporate both conventional cost items and the cost of removing salts. The withdrawal of water and its conveyance, sewage disposal, irrigation with freshwater and effluent—all interfere in the natural water cycle and influence the quantity and quality of the resources. A sustainable regime will maintain acceptable quantity and quality of water. This may entail constraining of withdrawals to safe yields (water is not mined) and costly artificial removal of contaminations. In the article we identify the implied cost of water from its sources and the corresponding pricing of fresh and recycled water. Since the demand for water to be used in the urban sector is inelastic, the sector is a price taker. Consequently, the major questions of allocation and pricing pertain to agriculture, and they are discussed in the paper in two parts. The first is a mathematical analysis of cost and pricing; the second part is an illustrative application to a regional water economy in Israel. The mathematical model is also presented in the terms of the illustration. The analysis is preceded by a short review of the water economy in Israel and the region (for a detailed survey, see Kislev, 2006). The water economy Israel is a small and narrow country; half of its area is desert. Precipitation, only in the winter, averages more than 700 mm per year in the north and less than 35 mm in the southern tip of the country. The core functions of the water sector have been to store water from winter to summer and from rainy to dry years and to carry water from the north to the center and the south. With expanding population and growing urbanization, sewage treatment and recycled water are growing in importance and seawater desalination is being introduced. Fresh water is stored in Lake Kinneret (Sea of Galilee) and in several groundwater reservoirs; the largest two are the Mountain and the Coastal aquifers, both stretching from north to south in parallel to the coast of the Mediterranean Sea. The discussion in the paper is presented in terms of the Coastal region, the area above the Coastal aquifer. The country’s largest urban centers, including Tel Aviv, are located along the coast and they draw water locally from the region’s aquifer.