• Collective Utility: A Systems Approach for the Utilization of Water Resources

      Dupnick, Edwin; Duckstein, Lucien; Systems Engineering Department, University of Arizona (Arizona-Nevada Academy of Science, 1971-04-23)
      In the semiarid southwestern U.S. where competition for water is fierce between competing users, no regional agency controls water allocation, and as a result, much court litigation ensues. This paper attempts to develop a model for optimal allocation of water resources and to apply the model to a specific case study. In November 1969, the largest farming interest in the Sahuarita-continental area near Tucson filed a court suit seeking first to reduce the amount of groundwater used by 4 nearby copper mines, and then to allocate the water more evenly among various interests in the area. The farming interest maintained that the mines' drawdown on the groundwater table would soon deplete the supply to the point where agriculture would become impossible. The model utilizes the concept of collective utility which postulates the existence of an economic decision maker (edp). To get around the problem of determination of net revenue functions, the theory compares the relative desirability of neighboring economic states. The edp has the power to impose groundwater-use taxes in such a way as to maximize overall growth of collective utility in the Sahuarita-continental area, taking into account the externalities of the resource consumption. The mathematical analysis is presented in detail.
    • Comparison of Water Pricing Structures from a Collective Utility Viewpoint

      Metler, Bill; Duckstein, Lucien; Systems Engineering Department, University of Arizona, Tucson, Arizona 85721 (Arizona-Nevada Academy of Science, 1971-04-23)
      As a result of continually lowering water tables in the arid regions of the west, many people are beginning to realize that water should be treated like any other rare resource, letting supply and demand factors regulate its distribution. Three types of price structures are used by water agencies: (1) the flat rate system (2) the step rate system and (3) the block rate system. Each of these structures may be progressive or regressive. At present, Tucson's only source of water lies underground and will presumably decrease as the population increases. To optimize the benefits to the community, it may be necessary to decrease not only average consumption but also summertime peak consumption for swimming pools, evaporative coolers and lawn sprinkling. Currently, Tucson uses a regressive block rate pricing structure. Using the theory of collective utility, a model is developed for use in comparing 2 price structures in an effort to define a monetary value for water conservation. It is concluded that the change in collective utility, du, which is a measure of the worth of change from economic state 1 to 2, is the best measure of price changes in arid areas. The model shows that Tucson water consumption would be lowered and money would be lost with either price structure, but with the permanent change, monetary flow of goods would be greater than under the seasonal structure.