Econ 4010 Lecture 27

Econ 4010 Lecture 27 - <Lecture 27> 12. Oligopoly...

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Cournot Model, Stackelberg Model, and Bertrand Model Q1. Two firms have constant marginal costs MC 1 = 1/2 and MC 2 = 2. If they choose outputs, they face inverse demand functions P 1 = 5 – Q 1 – (1/2)Q 2 and P 2 = 5 – Q 2 – (1/2)Q 1 . If they set prices, they face demand functions Q 1 = 2(5 – 2P 1 + P 2 ) / 3, Q 2 = 2(5 – 2P 2 + P 1 ) / 3. a. Find the Cournot equilibrium. Reaction curve 1: MR 1 = MC 1 => Q 1 = 9/4 – (1/4)Q 2 Reaction curve 2: MR 2 = MC 2 => Q 2 = 3/2 – (1/4)Q 1 Equilibrium: Q 1 = 2, Q 2 = 1, Q T = 3, P 1 = 2.5, P 2 = 3. b. Find the Stackelberg equilibrium, with firm 1 as the leader. Reaction curve 2: Q 2 = 3/2 – (1/4)Q 1 Firm 1: Max. π 1 => Q 1 = 15/7 Equilibrium: Q 1 = 15/7, Q 2 = 27/28, Q T = 87/28, P 1 = 133/56, P 2 = 83/28. c. Find the Bertrand equilibrium. Reaction curve 1: 1 / dP 1 = 0 => P 1 = 3/2 + (1/4)P 2 Reaction curve 2: 2 / dP 2 = 0 => P 2 = 9/4 + (1/4)P 1 Equilibrium: P 1 = 33/15, P 2 = 42/15, Q 1 = 34/15, Q
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Econ 4010 Lecture 27 - <Lecture 27> 12. Oligopoly...

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