A model for the global optimization of water prices and usage for the case of spatially distributed sources and consumers

Different problems addressed to the efficiency of the water use and allocation are of great importance in numerous regions including Middle East. Water scarcity is the foremost problem for which solutions are urgently needed. Water prices can be considered as an instrument for satisfactory water allocation and must be justified in a satisfactory way. The significant water losses in distribution also must be taken into consideration. In this paper, an extended model of the water allocation for urban, agricultural and other secondary users is presented. The spatial system of conveyance channels is considered. These channels are of two kind: channels for fresh water and channels for treated water. Each user is assumed to have an efficiency function for all kinds of the consumed water. For this purpose the model of Chakravorty et al. (CHZ model) [J. Environ. Econ. Manage. 29 (1995) 25] is modified. Use of desalinated water and re-use of the treated waste water are also considered. A global optimization method is applied provided with conditions of optimality (transversality conditions). Both water allocation and shadow prices could be found from these conditions.