Suppose a monopoly seller of mineral water is able to segment its market into three consumer groups: 1, 2, and 3. The (inverse) demand for mineral water on the part of each group is given by: Group 1 Demand:P1=1000â(1/2)Q1Group 2 Demand:P2=1000â(1/3)Q2Group 3 Demand:P3=1000â(1/5)Q3The total cost faced by the monopolist is:TC=100Q, where the quantity produced (Q) is distributed across the 3 groups such thatQ1+Q2+Q3=Q. Having the ability to charge each group a unique price, determine the profit-maximizing price and quantity the monopolist should set for each group, as well as the firm's profit.
