A monopolist sells in two geographically divided markets that has different pric
ID: 1124581 • Letter: A
Question
A monopolist sells in two geographically divided markets that has different price elasticitics, 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. (12 pts) b) In which market is demand more elastic? (2 pts) Show what will happen to the monopolist's profit if it is to charge the same price in both mark (That is, profit if the monopolist treats the markets as if they are the same). c) (6 pts)Explanation / Answer
a) Find the marginal revenues and keep them equal to marginal costs
MRE = MC MRW = MC
450 - QE = 50 700 - 2QW = 50
QE = 400 QW = 325
PE = 250 PW = 375
Profit E = (250 - 50)*400 = $80,000
Profit W = (375 - 50)*325 = $105,625
Total profit = $185,625
b) Demand is more elastic where price is low. This implies that market in the East is more elastic. Confirm this by finding the elasticity = P/(P - MC)
e(West) = 375/325 = 1.15
e(East) = 250/200 = 1.25
Hence elasticity of demand is more in the East
c) In that case, it treats the demand as market demand
QE = 900 - 2PE and QW = 700 - PE
Market demand is Q = 1600 - 3PE
Inverse demand is P = 1600/3 - (1/3)Q
Marginal revenue = 1600/3 - (2/3)Q
MR = MC
1600/3 - (2/3)Q = 50
This gives Q = 725 and P = 291.67
Profits are (291.67 - 50)*725 = $175,211
Total profit falls from $185,625 to $175,211