Question

A monopolist sells in two adjacent countriesand has a constant marginal cost of 20. The demand in country 1 is Q1= 90 –P1, and the demand in country 2 is Q2= 150 –P2. Resale is not prohibited so the monopolist must deal with the two countries as one market.a. What is the equilibrium quantity, price,and profit?b. What is the price elasticity at the equilibrium price?c. Suppose resale is now prohibited so the monopolist can now practice price discrimination. What is the equilibrium quantity, price,and profitin each country?d. What is the price elasticity at the equilibrium price in each of the two countries?

Answer 1

a. Total demand, Q = Q1 + Q2 = 90 - P + 150 - P = 240 - 2P (P1 = P2 = P)
So, Q = 240 - 2P
2P = 240 - Q
So, P = (240/2) - (Q/2)
So, P = 120 - 0.5Q
Total Revenue, TR = P*Q = (120 - 0.5Q)*Q = 120Q - 0.5Q²
So, Marginal Revenue, MR = d(TR)/dQ = 120 - 2(0.5Q) = 120 - Q
Monopolist maximizes profit according to the rule: MR = MC
So, 120 - Q = 20
So, Q = 120 - 20
So, Q = 100

P = 120 - 0.5(100) = 120 - 50
So, P = 70

Profit = TR - TC = P*Q - MC*Q = (P - MC)*Q = (70-20)*100 = 5000
So, Profit = 5,000

b. Price elasticity, e = (dQ/dP)*(P/Q) = (-2)*(70/100) = -1.4

c. Monopolist maximizes profit in each market according to the rule: Mr = MC

Q1= 90 –P1
So, P1 = 90 - Q1
TR1 = P1*Q1 = (90-Q1)*Q1 = 90Q1 - Q1²
So, MR1 = d(TR1)/dQ1 = 90 - 2Q1
Now, MR1 = MC gives,
90 - 2Q1 = 20
So, 2Q1 = 90 - 20 = 70
So, Q1 = 70/2
So, Q1 = 35
P1 = 90 - 35
So, P1 = 55
Profit = TR1 - TC1 = P1*Q1 - MC*Q1 = (P1 - MC)*Q1 = (55-20)*35 = 1,225

Q2 = 150 –P2
So, P2 = 150 - Q2
So, TR2 = P2*Q2 = (150 - Q2)*Q2 = 150Q2 - Q2²
MR2 = d(TR2)/dQ2 = 150 - 2Q2
Now, Mr2 = MC gives
150 - 2Q2 = 20
So, 2Q2 = 150 - 20 = 130
So, Q2 = 130/2
So, Q2 = 65
P2 = 150 - 65 = 85
So, P2 = 85
Profit = TR2 - TC = P2*Q 2- MC*Q2 = (P2 - MC)*Q2 = (85-20)*65 = 4,225

d. In country 1,
Price elasticity, e1 = (dQ1/dP1)*(P1/Q1) = (-1)*(55/35) = -1.57

In country 2,
Price elasticity, e2 = (dQ2/dP2)*(P2/Q2) = (-1)*(85/65) = -1.31