Lecture%2026%20-%20Macroeconomics%20I

Lecture%2026%20-%20Macroeconomics%20I - FIN 501 Financial...

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    1 FIN 501 Financial Economics Lecture 26: Macroeconomics I Professor Nolan Miller
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    2 Announcements Problem Set #8 is Due December 7.  Will be available on Compass  soon. Final exam is December 15, 1:30 – 4:30. No class next week (Thanksgiving break). No office hours next week.
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    3 Stackelberg The standard Cournot game has both players moving simultaneously. What happens when one of the players moves before the other? The version of the Cournot game where player 1 moves first and player 2  moves second (after seeing Player 1’s quantity) is called the “Stackelberg  Duopoly” game. Player 1 is called the “Stackelberg Leader.” Is there a “first mover advantage” in this game? If so, why?
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    4 Stackelberg Duopoly Stay with the same model: P = 150 – Q MC 1  = MC 2  = 30. Timing of Game: Player 1 chooses Q 1 . Player 2 observes Q 1  and then chooses Q 2 . Total quantity determines the price. Analysis: this is a game of sequential moves. Start at the end and work back to the beginning.
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    5 Stackelberg Follower’s Problem Consider Player 2. Player 2 first observes Q 1 And then chooses Q 2  to maximize profit. Optimal strategy is a function Q 2 (Q 1 ) that gives the Q 2  that maximizes profit  for the observed Q 1 . Profit = (150 – Q 1  – Q 2 )Q 2  – 30Q 2 . Notice: this is the same expression for profit as in the simultaneous version  of the game. Player 2 chooses Q 2  = (120-Q 1 )/2. Now, consider Player 1. Player 1 anticipates that Player 2 will choose Q 2  = (120-Q 1 )/2 units of output  if Player 1 chooses Q 1 . Substitute this into Player 1’s profit function and find the optimal Q 1 .
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    6 Stackelberg Leader’s Problem Player 1’s Profit: (150 – Q 1  – Q 2 * )Q 1  – 30Q 1 Where Q 2 *  is 2’s optimal reaction after seeing Q 1 . Substituting in 2’s reaction function: (120 – Q 1  – (120-Q 1 )/2))Q 1 (60-Q 1 /2)Q 1 To find optimal Q 1 , take derivative with respect to Q 1 , set = 0: 60 – Q 1  = 0 Q 1  = 60. From 2’s reaction function: Q 2  = (120-Q 1 )/2 = 30.
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    7 Stackelberg Game: Outcome In the Stackelberg game: Q 1  = 60, Q 2  = 30. P = 150 – 90 = 60. Firm 1’s profit = (60-30)60 = 1800 Firm 2’s profit = (60-30)30 = 900 In the Cournot game, each firm made profit 1600. So, the first mover does better than in the simultaneous-move  game, and the second mover does worse.
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This note was uploaded on 01/18/2011 for the course FIN fin580 taught by Professor Miller during the Spring '10 term at University of Illinois, Urbana Champaign.

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Lecture%2026%20-%20Macroeconomics%20I - FIN 501 Financial...

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