micro-fall-2007-22

# micro-fall-2007-22 - 1 x 2 x 1& c 1 x 1 = = a& b x 1...

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Duopoly Bertrand-Duopoly Identical products. Firms set prices. p 1 < a b ) D 1 ( p 1 ; p 2 ) = 8 < : 0 for p 1 > p 2 1 2 ( a bp 1 ) for p 1 = p 2 a bp 1 for p 1 < p 2 p 1 < a b ) π 1 ( p 1 ; p 2 ) = 8 < : 0 for p 1 > p 2 1 2 ( a bp 1 ) ( p 1 c ) for p 1 = p 2 ( a bp 1 ) ( p 1 c ) for p 1 < p 2 Ani Guerdjikova ECON 313 Fall 2007 226 / 235

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Duopoly Bertrand Equilibrium Prices: p B 1 = p B 2 = c Quantities: x B 1 = x B 2 = a bc 2 π B 1 = π B 2 = 0 Ani Guerdjikova ECON 313 Fall 2007 227 / 235
Duopoly Cournot Duopoly Identical products. Firms set quantities. Inverse demand function: d ( x ) = a bx , a , b > 0. i = 1 , 2 c i ( x i ) = cx i , c > 0. Ani Guerdjikova ECON 313 Fall 2007 228 / 235

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Duopoly max x 1 π 1 ( x 1 ; x 2 ) = d ( x
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Unformatted text preview: 1 + x 2 ) x 1 & c 1 ( x 1 ) = = [ a & b ( x 1 + x 2 )] x 1 & cx 1 Reaction function of &rm 1: x ± 1 = a & c 2 b & 1 2 x 2 : = r 1 ( x 2 ) Reaction function of &rm 2: x ± 2 = a & c 2 b & 1 2 x 1 : = r 2 ( x 1 ) Ani Guerdjikova ECON 313 Fall 2007 229 / 235 Duopoly Cournot Equilibrium Quantities: x C 1 = x C 2 = a & c 3 b Price: p C = a + 2 c 3 Pro&ts: π C 1 = π C 2 = ( a & c ) 2 9 b Ani Guerdjikova ECON 313 Fall 2007 230 / 235...
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## This note was uploaded on 04/30/2008 for the course ECON 3130 taught by Professor Masson during the Fall '06 term at Cornell.

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micro-fall-2007-22 - 1 x 2 x 1& c 1 x 1 = = a& b x 1...

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