brands-1 - pricecompetition Product differentiation and...

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Product differentiation and  price competition
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ECO 171 Product differentiation and price competition Rarely do firms sell same product Undercutting not steal all market Less incentives to lower prices Soften price competition Spatial (Hotelling model) Structural approach Strategic complements and substitutes
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ECO 171 Linear city model There are 2 firms: { L,R } Everybody buys one unit, but chooses which firm to buy from. Let d i denote the relative preference for firm R. Suppose d i is distributed uniformly between [- a , a ] Representation: The person with d i =0 will buy from lowest priced firm If d i >0, will buy from R unless p R -p L >d i If d i <0, will buy from L unless p L -p R >|d i | -a 0 a 1/2a
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ECO 171 Linear city - continued Market is split into demand for firm L and firm R. Indifferent consumer: U iR -U iL =p R -p L So d * = p R -p l D R ( p L ,p R ) = ( a- ( p R -p L ))/2a D L ( p L ,p R ) = ( a- ( p L -p R ))/2a -a 0 a 1/2a d * Demand for L = 1 - D R Demand for R = ( a-d * )/2a
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ECO 171 Linear city - continued Profit maximization problem for firm L: Max (p L -c)D(p L ,p R ) = ( p L -c ) ( a- ( p L -p R ))/ 2a First order conditions: ( a- ( p L -p R ))-( p L -c )=0 So p L = ( a+c )/2 + p R /2 and p R = ( a+c )/2 + p L /2 p L p R ( a+c )/2 ( a+c )/2 BR R BR L equilibrium • Equilibrium solves both reaction functions.
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