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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 Æ not steal all market ± Less incentives to lower prices ± Soften price competition ± Spatial (Hotelling model) ± Structural approach ± Strategic complements and substitutes
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: ² U iR -U iL =p R -p L ² 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
Linear city - continued ± Profit maximization problem for firm L: ² Max (p L -c)D(p L ,p R ) = ( p L -c ) ( a- ( p L -p R ))/ 2a ² First order conditions: ( a- ( p L -p R ))-( p L -c )=0 ² 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. • With equal costs:

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brands - Product differentiation and price competition...

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