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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

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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.

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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

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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

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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.

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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

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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

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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

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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
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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

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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

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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.
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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.
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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

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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

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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

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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

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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.

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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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