A monopolist sells in two geographically divided markets that has different pric
ID: 1123090 • Letter: A
Question
A monopolist sells in two geographically divided markets that has different price elasticities, 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) In this case profit is maximized when MRE = MC and MRW = MC
In East market,
PE = 450 - 0.5QE
Total revenue (TRE) = PE x QE = 450QE - 0.5QE2
Marginal revenue (MRE) = dTRE/dE = 450 - QE
Equating MRE & MC,
450 - QE = 50
QE = 400
PE = 450 - (0.5 x 400) = 450 - 200 = 250
Profit = QE x (PE - MC) = 400 x (250 - 50) = 400 x 200 = 80,000
In West market,
PW = 700 - QW
TRW = 700QW - QW2
MRW = dTRW/dQW = 700 - 2QW
Equating MR & MC,
700 - 2QW = 50
2QW = 650
QW = 325
PW = 700 - 325 = 375
Profit = QW x (PW - MC) = 325 x (375 - 50) = 325 x 325 = 105,625
Total profit = 80,000 + 105,625 = 185,625
(b) With price discrimination, higher (lower) price is charged in the market with inelastic (elastic) demand. Since price is lower in East market, demnd is more elastic in this market.
(c) If same price is charged, PE = PW = P.
otal market demand (Q) = QE + QW
PE = 450 - 0.5QE
0.5QE = 450 - PE
QE = 900 - 2PE
PW = 700 - QW
QW = 700 - PW
Q = 900 - 2PE + 700 - PW = 900 - 2P + 700 - P
Q = 1,600 - 3P
3P = 1,600 - Q
P = (1,600 - Q) / 3
TR = P x Q = (1,600Q - Q2) / 3
MR = dTR/dQ = (1,600 - 2Q) / 3
Equating with MC,
(1,600 - 2Q) / 3 = 50
1,600 - 2Q = 150
2Q = 1,450
Q = 725
P = (1,600 - 725) / 3 = 875 / 3 = 291.67
Profit = Q x (P - MC) = 725 x (291.67 - 50) = 725 x 241.67 = 175,210.75
Decrease in profit (Compared to price discrimination) = 185,625 - 175,210.75 = 10,414.25