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Core assumption firms choose assuming quantities of

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Core assumption: firms choose assuming quantities of rivals as given (Cournot conjecture) Result: Firms price above the marginal cost ¾ For our numbers: p=5, MC=c=1 Easy to show ¾ More firms Æ price closer to MC + less profits ¾ As N Æ infinity, p=MC; competitive market in the limit Main criticisms of the Cournot model 1. Timing seems off: Decisions of firm are not simultaneous. Æ Stackelberg model of oligopoly 2. Firms choose prices (not quantities) Æ Bertrand model Chapter 13 –Oligopoly Slide 12 Continuous Strategies - Stackelberg Sequential Cournot Game An industry leader (first mover) chooses her quantity A follower (second mover) then chooses her quantity The market price is determined (as in the Cournot game) by p=a-b(Q 1 +Q 2 ) Marginal cost of production: c
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Chapter 13 –Oligopoly Slide 13 The Stackelberg Game Representation Leader Follower 2 11 2 12 (( ) ) , ) ) qab qa bq q c qq c + + 1 0 q 2 0 q Chapter 13 –Oligopoly Slide 14 Solving Dynamic Games with Infinite Space Use backward Induction Determine the best response function of the last player (follower) The previous player can also compute that (complete information) and thus incorporate the best response function in his decision rule • The leader solves her problem with the best response function of the follower substituted into her objective function!
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Chapter 13 –Oligopoly Slide 15 The follower’s problem [( )] 20 2 f ff l q lf l f Maxq a q q c FOC acq q acq q + ∈ℜ −+− −− − = −− = The Follower’s Best Response Function (Same as in Cournot) This is the follower’s best response strategy . Produce the quantity q f once q l is observed. Chapter 13 –Oligopoly Slide 16 The Leader’s problem * 2 :0 2 l l ll f q l q l Maxq a q q c aq c q c ac FOC q + + −+ −= * 2 l q = The Leader can anticipate the player 2’s move and will take that in consideration when choosing her own quantity. She does that by directly incorporating the follower’s response in her own profit calculations. This way, she can take into consideration how the follower’s response will ultimately affect her profits.
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Chapter 13 –Oligopoly Slide 17 The Equilibrium The Equilibrium is given by () * * 2 ,, 2 l l f aq ac q c q = −− ⎛⎞ ⎜⎟ ⎝⎠ Which solves for , 4 2 For a=13 and c=1, the quantities are (6,3) Chapter 13 –Oligopoly Slide 18 Cournot vs. Stackelberg Contrast Quantities: , 4 2 , 33 acac Vs.
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Core assumption firms choose assuming quantities of rivals...

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