Problem 3: Suppose that the market for air travel between Chicago and Dallas is

Question

Problem 3: Suppose that the market for air travel between Chicago and Dallas is seeved by just two airlines, United and American the demand curves for round-trip tickets for each airline are as follows An economist has studied this market and has estimated that = 10,000-100h, +99Pa (United's Demand) Q' 10,000-100Pa + 99h (Arnerican's Demand) where Pu is the price charged by United, and PA is the price charged by American. Suppose that both United and American charge a price of $300 each for a round-trip ticket between Chicago and Dllas. What is the price elasticity of demand for United flights between Chicago and Dallas? ·What is the market-level price elasticity of demand for air travel between Chicago and Dllas when both airlines charge a price of $300. [Hint: Because United and Emerican are the only two airlines serving the Chicago-Dallas market, what is the equation for the total demand for air travel between Chicago and Dallas, assuming that the airlines charge the same price?]

Explanation / Answer

(a) PU = PA = $300

QdU = 10,000 - (100 x 300) + (99 x 300) = 10,000 - 300 = 9,700

Price elasticity of demand (United) = (dQdU / dPU) x (PU / dQdU) = - 100 x (300 / 9,700) = - 3.09

(b) Let PA = PU = P (= $300)

QdU = 10,000 - 100P + 99P = 10,000 - P

QdA = 10,000 - 100P + 99P = 10,000 - P

Market demand, Q = QdU + QdA = 10,000 - P + 10,000 - P

Q = 20,000 - 2P

When P = 300, Q = 20,000 - (2 x 300) = 20,000 - 600 = 19,400

Market price elasticity of demand = (dQ / dP) x (P / Q) = - 2 x (300 / 19,400) = - 0.03

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