lecture22 - Economics 101A (Lecture 22) Stefano DellaVigna...

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Economics 101A (Lecture 22) Stefano DellaVigna April 16, 2009
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Outline 1. Oligopoly: Cournot 2. Oligopoly: Bertrand 3. Second-price Auction 4. Auctions: eBay Evidence
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1 Oligopoly: Cournot Nicholson, Ch. 14, pp. 524-530 ( better than Ch. 14, pp. 418—419, 421—422, 9th) Back to oligopoly maximization problem Assume 2 f rms, cost c i ( y i )= cy i ,i =1 , 2 Firms choose simultaneously quantity y i Firm i maximizes: max y i p ( y i + y i ) y i cy i . First order condition with respect to y i : p 0 Y ³ y i + y i ´ y i + p c =0 ,i =1 , 2 .
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Nash equilibrium: y 1 optimal given y 2 ; y 2 optimal given y 1 . Solve equations: p 0 Y ( y 1 + y 2 ) y 1 + p c =0 and p 0 Y ( y 2 + y 1 ) y 2 + p c =0 . Cournot - > Pricing above marginal cost
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2 Oligopoly: Bertrand Cournot oligopoly: f rms choose quantities Bertrand oligolpoly: f rms f rst choose prices, and then produce quantity demanded by market Market demand function Y ( p ) 2 f rms Pro f ts: π i ( p i ,p i )= ( p i c ) Y ( p i ) if p i <p i ( p i c ) Y ( p i ) / 2 if p i = p i 0 if p i >p i
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First show that p 1 = c = p 2 is Nash Equilibrium Does any f rm have a (strict) incentive to deviate? Check pro
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lecture22 - Economics 101A (Lecture 22) Stefano DellaVigna...

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