A monopolist sells in two geographically divided markets, the East and the West.
ID: 1204987 • Letter: A
Question
A monopolist sells in two geographically divided markets, the East and the West. Marginal cost is constant at $50 in both markets (marginal cost is also equal to average total cost). The inverse demand curve in each market is as follows:
PE=450-.5QE
PW=700-QW
a) Find the profit-maximizing quantity, price and profit in each market.
b) In which market is demand more elastic?
c) Show what will happen to the monopolist's profit if it is to charge the same price in both markets (That is, profit if the monopolist treats the markets as if they are the same).
Explanation / Answer
a. Market-East:
Pe = 450 – 5Qe
Marginal revenue = 450 – 10Qe
Setting MC = MR, we get
450 – 10Q = $50
450 – 50 = 10Q
Q(E) = 40.
P = 450 – (5x40)
P(E) = $250.
Market-West:
Pw = 700 – Qw
Marginal revenue = 700 – 2Qw
Setting MC = MR, we get
700 – 2Q = $50
700 – 50 = 2Q
Qw = 325
P = 700 – 325
Pw = $375.
b. The demand is more elastic in Market-East.
c. Profit in Market-East when price is $250
Total revenue = $250x40 = $10,000
Total cost = $50x40 = $2,000
Profit in Market-East= $10,000 - $2,000 = $8,000.
Profit in Market-West when price is $250
Total revenue = $250x325 = $81,250.
Total cost = $50x325 = $16,250
Profit in Market-West = $81,250 - $16,250 = $65,000.
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