Topic 7. Product differentiation (II): Market Structure

Topic 7. Product differentiation (II): Market Structure

Applied Industrial EconomicsJuan Antonio Máñez CastillejoDepartamento de Estructura

EconómicaUniversidad de Valencia

Departamento de Estructura Económica 2

Index

Topic 8: Product differentiation (II): market structure1. Circular city model2. Product proliferation strategies: breakfast cereal

market


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.


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


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:

ij j ijU r p tx


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

L N

L N

L N

L N L N

L N

L N

L N

• Stage 2: firms compete in prices given these locations.


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


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

I

I+1I-1L/N L/N

A B


1. Circular city model: demands determination

A

1x 1L N x

I-1 I+1

I

L N L N

Ip

Ip tx Ip tx

1Ip

1Ip t L N x

B

2x 2L N x

1Ip

1Ip t L N x

1 2Id x x

1 1 1 1I IA p tx p t L N x x 2 1 2 2I IB p tx p t L N x x

1 1

1 2 2I I I I

I

p p p p Ld x x

t 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 NStep 1: Determination of the equilibrium number of firms

1. Step 2: Determination of the Nash equilibrium in prices for any N:

1 11 1max

2I

I I I Ii I

p

p p p p Ld p c F p c F

t N

* 1 1

1 12

,4 2

I II I I

p p c tLp p p

NFirm I reaction

function

As we have exogenously imposed symmetric locations Ip p i

The Nash eq. in prices for any N tL

p cN


1. Circular city model: properties of the Nash equilibrium in prices

Which are the properties of this equilibrium?

tL

p cN

• 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


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)

2

2

0

0

0

p c d F

tL L tLF F

N N N

e

e

tN L

F

p tF c


1. Circular city model: determination of the number of firms

e

e

tN L

F

p 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: y 0N L N

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.


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.


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:

1 2p p p


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 variant2. Firms can introduce only two variants

Additional assumption:• The cost of introducing a new variant is F

4 2p p

F


2. Product proliferation: sequential game with only one variant

Optimal location for firm 1: 1/2

0 11 2

F1

0 11 2

F1

F2

d1 d2

0 1

1 2E1

F2

d1d2

If it locates at the left of 1/2

If it locates at the right 1/2


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

0 11 2

F1

F2

1 2

12

d d

1 2

10

2p F


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?

F1 F1

1 4 3/ 4

F2

10 1 25 8

1 4

3 8

1 8 1 8

2

14

d 2

1 p p0 because

4 2 4p F F

F2 does not introduce any new cereal variant in the market


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

F1 introduces two variants to avoid the entrance of F2.

11 2

pF

• When firm 1 introduces two variants E2 does not introduce any variant

21 2p F

2 11 1 2 0 porque

2 2 2p p p

p F F F F


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.

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Topic 7. Product differentiation (II): Market Structure