micro-fall-2007-22 - 1 + x 2 ) x 1 & c 1 ( 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
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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 &amp; c 1 ( x 1 ) = = [ a &amp; b ( x 1 + x 2 )] x 1 &amp; cx 1 Reaction function of &amp;rm 1: x 1 = a &amp; c 2 b &amp; 1 2 x 2 : = r 1 ( x 2 ) Reaction function of &amp;rm 2: x 2 = a &amp; c 2 b &amp; 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 &amp; c 3 b Price: p C = a + 2 c 3 Pro&amp;ts: C 1 = C 2 = ( a &amp; c ) 2 9 b Ani Guerdjikova ECON 313 Fall 2007 230 / 235...
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micro-fall-2007-22 - 1 + x 2 ) x 1 &amp;amp;amp; c 1 ( x 1...

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