[3] Suppose a monopoly seller of mineral water is able to segment its market int
ID: 1212360 • Letter: #
Question
[3] 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.
Explanation / Answer
In each group, Monopolist in order to maximize its profits will produce till it's MR = MC in each group.
Group 1 Demand: P1 = 1000 – (1/2)Q1
Total Cost = 100Q
MC = dTc/dQ = 100
Total Revenue = P*Q = (1000 - (1/2)Q1)*Q1
MR = dTR/dQ1 = 1000 - Q1
Putting MR = MC
1000 - Q1 = 100
Q1 = 900
hence P1 = 1000 - 1/2*900 = 550
Group 2 Demand: P2 = 1000 – (1/3)Q2
Total Revenue = P*Q2 = (1000 - (1/3)Q2)*Q2
MR = dTR/dQ2 = 1000 - 2/3Q2
Putting MR = MC
1000 - 2/3Q2 = 100
2/3Q2 = 900
Q2 = 1350
hence , P2 = 1000 - 1/3*1350 = 550
Group 3 Demand: P3 = 1000 – (1/5)Q3
Total Revenue = P*Q = (1000 - (1/5)Q3)*Q3
MR = dTR/dQ3 = 1000 - 2/5Q3
Putting MR = MC
1000 - 2/5Q3 = 100
2/5Q3 = 900
Q3 = 4500/2 = 2250
P3 = 1000 - 1/5*2250
P3 = 550
Firm's Profit = TR1 + TR2 + TR3 - TC
= 550*900 + 1350*550 + 2250*550 - 100*4150
= 1,867,500
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