Topic 7. Product differentiation (II): Market Structure

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 • Circular city model • Product proliferation strategies: breakfast cereal market Departamento de Estructura Económica

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

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

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 city-center permanently congested • The utility that a consumer i located in X obtains from purchasing the good from a firm j is given by: Departamento de Estructura Económica

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 • Stage 2: firms compete in prices given these locations. Departamento de Estructura Económica

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

I L/N L/N I-1 I+1 B A 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: • 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

I+1 I-1 B A I 1. Circular city model: demands determination Departamento de Estructura Económica

Firm I reaction function As we have exogenously imposed symmetric locations The Nash eq. in prices for any N 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 • Step 2: Determination of the Nash equilibrium in prices for any N: Departamento de Estructura Económica

1. Circular city model: properties of the Nash equilibrium in prices • Which are the properties of this equilibrium? • 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

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) Departamento de Estructura Económica

no product differentiation  price competition with homogeneous products p =c 1. Circular city model: determination of the number of firms • 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: • 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

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

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: Departamento de Estructura Económica

2. Proliferación de productos: juego secuencial • Sequential game • Incumbent firm (F1) chooses variant (location) • Poetential entrant (F2) chooses variant • Two versions of the game versiones del juego: • Firms can introduce only one variant • Firms can introduce only two variants • Additional assumption: • The cost of introducing a new variant is F Departamento de Estructura Económica

0 1 F1 F2 0 1 d2 d1 F1 F2 0 1 d2 d1 E1 2. Product proliferation: sequential game with only one variant • Optimal location for firm 1: 1/2 • If it locates at the left of 1/2 • If it locates at the right 1/2 Departamento de Estructura Económica

F2 0 1 F1 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?  F2 enters the market producing a breakfast cereal variant Departamento de Estructura Económica

0 1 F1 F1 F2 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? F2 does not introduce any new cereal variant in the market Departamento de Estructura Económica

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 • When firm 1 introduces two variants E2 does not introduce any variant F1 introduces two variants to avoid the entrance of F2. Departamento de Estructura Económica

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

Topic 7. Product differentiation (II): Market Structure