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Topic 7. Product differentiation (II): Market Structure Applied Industrial Economics Juan Antonio Máñez Castillejo Departamento de Estructura Económica Universidad de Valencia Index Topic 8: Product differentiation (II): market structure 1. Circular city model 2. Product proliferation strategies: breakfast cereal market Departamento de Estructura Económica 2 1. Circular city model (Salop, 1979): aim Aim: analyzing the influence of product differentiation in the equilibrium number of firms in a free entry market. Departamento de Estructura Económica 3 1. Circular city model (Salop, 1979): assumptions Assumptions: • Consumers are located with unit density around a circle. The corresponding circumference measures L • Firms are locates around the possible • Consumer only can travel around the circel • Each consumer buys a unit of the product that is identical except for the location of the firm • Per unit of distance transport cost is linear and equal to t • Marginal costs are identical for all firms, ci=c • Firms incur a cost F to enter the market • Firm i profits are – (pi - c)di-F if firm i enters the market – 0 if firm i does not enter the market Departamento de Estructura Económica 4 1. Circular city model (Salop, 1979): utility function Ejemplos: • City located around a lake with an inefficient system of ships • Supermarkets located in the outbound of a city with a citycenter permanently congested The utility that a consumer i located in X obtains from purchasing the good from a firm j is given by: U ij r p j tx ij Departamento de Estructura Económica 5 1. Circular city model: structure of the game Salop considers a two-stage game: • Stage 1: potential entrants simultaneously choose whether or not to enter the market. We exogenously impose maximum product differentiation firms do not choose their location but rather they are located equistant fron one another in the circle LN LN LN LN • LN LN LN LN Stage 2: firms compete in prices given these locations. Departamento de Estructura Económica 6 1. Circular city model Main assumption: free entry • Equilibrium profit of entering firms is zero We are interested in: • Determination of the Nash equilibrium in prices for any number of firms (N) • Factors determining the equilibrium number of firms (N) determine the Nash equilibrium in the entry game Departamento de Estructura Económica 7 1. Circular city model: demands determination Salop’s model is a model of localized competition, in practice each of firm has only two real competitors the two firms surrounding it: L/N I I-1 L/N A B I+1 We determine the demands using the indifferent consumer condition: • A consumer indifferent between purchasing from I or I-1 • B consumer indifferent between purchasing from I or I+1 Departamento de Estructura Económica 8 1. Circular city model: demands determination A p I tx 1 p I 1 t L N x 1 x 1 p I 1 t L N x B p I tx 2 p I 1 t L N x 2 x 2 p I 1 t L N x pI tx pI 1 LN pI pI tx pI 1 LN x1 x2 L N x1 I-1 A L N x2 I+1 B dI x1 x 2 I p pI pI 1 pI L d I x 1 x 2 I 1 2t N Departamento de Estructura Económica 9 1. Circular city model: obtaining the Nash equilibrium in prices We solve by backwards induction: Step 2: Determination of the Nash equilibrium in prices for any N Step 1: Determination of the equilibrium number of firms 1. Step 2: Determination of the Nash equilibrium in prices for any N: p p I p I 1 p I L max i d 1 p1 c F I 1 pI c F p I Firm I reaction function N p p I 1 2c tL p I* p I 1 , p I 1 I 1 4 2N 2t As we have exogenously imposed symmetric locations The Nash eq. in prices for any N pI p i p tL c N 10 Departamento de Estructura Económica 1. Circular city model: properties of the Nash equilibrium in prices Which are the properties of this equilibrium? p tL c N • With product differentiation price is higher than marginal cos • The difference between price and costs: – Decreases when the number of firms increases. – Increases when the transport cost increases – In the limit, when the transport cost is zero, the price is equal to the marginal cost Departamento de Estructura Económica 11 1. Circular city model: determination of the number of firms 2. Stage 1: Determination of the equilibrium number of firms. We use: • Equilibrium price for any N • Zero-profits condition (free-entry equilibrium) 0 p c d F 0 Ne L t F tL L tL2 F 2 F 0 N N N p e tF c Departamento de Estructura Económica 12 1. Circular city model: determination of the number of firms Ne L t F p e tF c Which are the properties of this equilibrium? Reduction of F increase N reduces L/N less product differentiation reduction of market power (ability to set a price p, p > c) When F 0: N y L N 0 no product differentiation price competition with homogeneous products p =c When t increases price increase (p-c) raises reduction of the demand that is needed to compensate F increase of the number of firms. Departamento de Estructura Económica 13 2. Product proliferation: market characteristics Schmalensee (1978) product proliferation in the US breakfast cereals market between 1950 and 1970. Characteristics of the breakfast cereals market: • Relatively small minimum efficient scale • Low technological requirements From the technological viewpoint: entry is relatively easy • The four incumbent firms (Kellogs, General Mills, General Foods, Quaker Oats) were obtaining large profits Attractive entry What do we observe between 1950 and 1970? • Entrance did not happen • The established firms increased the number of brands from 25 to 180. Departamento de Estructura Económica 14 2. Product proliferation: assumptions Suppose that breakfast cereals are differentiated in just one characteristic sweetness: 0 a 1 • The least sweet: cornflakes • The sweetest: chococrispies • • Two firms: • Firm 1: incumbent firm • Firm 2: potential entrant There is no price competition: p1 p 2 p Departamento de Estructura Económica 15 2. Proliferación de productos: juego secuencial Sequential game 1. Incumbent firm (F1) chooses variant (location) 2. Poetential entrant (F2) chooses variant Two versions of the game versiones del juego: 1. Firms can introduce only one variant 2. Firms can introduce only two variants Additional assumption: • The cost of introducing a new variant is F p 4 F p 2 Departamento de Estructura Económica 16 2. Product proliferation: sequential game with only one variant Optimal location for firm 1: 1/2 0 12 F1 1 If it locates at the left of 1/2 0 d1 F2 12 F1 F2 d2 d2 1 If it locates at the right 1/2 0 1 E1 d1 17 12 Departamento de Estructura Económica 2. Product proliferation: sequential game with only one variant IF F1 locates at ½, will fimr 2 enter the market producing a breakfast cereal variant? 0 F2 12 F1 1 d1 d 2 1 2 1 2 1 p F 0 2 F2 enters the market producing a breakfast cereal variant Departamento de Estructura Económica 18 2. Product proliferation: sequential game with only more than one variant Suppose that firm 1 introduces two variants ¼ and ¾: Is firm 2 interested in introducing a new cereal variant? 0 14 38 18 F1 12 5 8 3/4 1 18 F1 F2 14 d2 1 4 2 1 p p p F 0 because F 4 2 4 F2 does not introduce any new cereal variant in the market Departamento de Estructura Económica 19 2. Product proliferation: sequential game with only more than one variant Is firm 1 interested in introducing two cereal variants instead of just one? • When F1 introduces a unique variant, F2 introduces also a variant F 2 • When firm 1 introduces two variants E2 does not introduce any variant 2 1 p 2F 1 1 p p p p 2 1 1 1 p 2F F F 0 porque F 2 2 2 F1 introduces two variants to avoid the entrance of F2. Departamento de Estructura Económica 20 2. Product proliferation: concluding remarks Product proliferation strategy in the breakfast cereals market: : • Before any other firm enters the market, the incumbent firm introduces a variant in the location that could choose the potential entrant: the aim is to remove any incentive to enter the market If the potential entrant enters the market, the demand it obtains is not enough to compensate entry costs Proliferation is rational only if the aim is deterring entrance, in any other case the incumbent firm is better off producing just one variant. Other example: banks, home-delivery pizzas higher density of locations. Departamento de Estructura Económica 21

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