Abstract
AbstractConsider a water supplier who determines sales rates with the goals of maximizing profits, protecting consumer welfare, and ensuring adequate future water supplies. Buyers are differentiated and can use the water for domestic, agricultural, and industrial purposes. We propose a leader-follower finite-horizon differential game. The leader (the water supplier) determines the selling price and the followers (consumers) react by requesting their optimal amount of water. We calculate a feedback Stackelberg equilibrium assuming that all user demand is satisfied (interior equilibrium). We compare two different tariff schemes: linear tariffs (the price paid is a multiple of the volume of water purchased), and increasing block tariffs (the unit price is lower for quantities of water that do not exceed a fixed threshold). We show that block pricing is never optimal and linear pricing is always preferred.
Publisher
Springer Science and Business Media LLC
Subject
Management Science and Operations Research,General Decision Sciences