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 = 1000 - (1/2)Q1
Group 2 Demand: P2 = 1000 - (1/3)Q2
Group 3 Demand: P3 = 1000 - (1/5)Q3
The total cost faced by the monopolist is: TC = 100Q, where the quantity produced (Q) is distributed across the 3 groups such that Q1 + 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.