L9-oligopoly3_post

# L9-oligopoly3_post - Economics Economics100C OligopolyIII I...

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onomics 100C ligopoly III Economics 100C Oligopoly III rice competition I. Price competition II. Comparing oligopoly solutions for omogenous goods homogenous goods III. Oligopolies with product differentiation 1

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Price competition I. Price competition Firms choose the price and then produce the quantity that consumers demand at that price No capacity constraints Whether this is the “right” model depends on the nature of the production process 2
ertrand model I. Bertrand model Assumptions There are a small number of firms in the market All firms have constant marginal costs Firms produce a homogenous good Firms choose price simultaneously and independently Quantity Q(p) is determined by the demand function There is no repeated interaction between firms 3

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ertrand model I. Bertrand model Bertrand solution No price p i > MC can be a Nash equilibrium because other firms always have an incentive to underbid 4
uopoly example I. Duopoly example Bertrand price competitors Q ( p ) = a – bp, where p = Min( p 1 , p 2 ) Assume firm 1 offers a price p 1 = k , where c < k < a/b Firm 2 has the following options: Set p 2 > k : Sells nothing Set p 2 = k : Set p 2 = k– ε : q 2 = (a–bk)/2 π 2 = (k–c) × (a–bk)/2 q 2 a–bk π 2 (k–c) × (a–bk) 5

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ertrand reaction functions I. Bertrand reaction functions 2 p 1 R 21 p p m p 2 R c m 6 1 p c p
ertrand model I. Bertrand model Nash equilibrium with two firms with identical (constant) marginal costs Both firms set p = c q 1 = q 2 = 0.5 × Q ( c ) Bertrand paradox : With only two firms, competition drives price down to marginal cost 7

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ertrand model I. Bertrand model If firms can collude, their price will equal the monopoly price But the incentive to cheat is even stronger than under the cartel model If one firm lowers its price by \$0.01 it will capture the entire arket and make approximately the monopoly profit market and make approximately the monopoly profit 8
. Comparing oligopoly solutions II. Comparing oligopoly solutions

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## This note was uploaded on 10/21/2010 for the course ECON 1530 taught by Professor Ohly during the Spring '10 term at Dartmouth.

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L9-oligopoly3_post - Economics Economics100C OligopolyIII I...

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