Transcript Product differentiation: 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
1. Circular city model
2. Product proliferation strategies: breakfast cereal market
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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:

I-1

I
L/N
A
L/N
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  pI  tx 1  p I 1  t L N  x 1   x 1
B  pI  tx 2  p I 1  t L N  x 2   x 2
pI 1  t L N  x 
pI 1  t L N  x 
p I  tx
p I  tx
pI 1
pI 1
pI
LN
L N  x1
I-1
LN
x1
x2
L N x2
B
dI  x1  x 2
I
 p  pI    pI 1  pI   L
d I  x 1  x 2  I 1
2t
N
A
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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
2t
N
p  p I 1  2c tL
p I*  p I 1 , p I 1   I 1

4
2N
As we have exogenously imposed symmetric locations
The Nash eq. in prices for any N
p 
pI  p i
tL
c
N
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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
tL L
tL2
F  2 F  0
N N
N
Ne L
t
F
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  yL 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  p2  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
12
0
1
F1
 If it locates at the left of 1/2
F2
12
0
d1
1
d2
F1
 If it locates at the right 1/2
F2
0
d2
12
1
E1
d1
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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
1
12
F1
d1  d 2 
1
2
1
p F  0
2
 F2 enters the market producing a breakfast cereal variant
1   2 
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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
12
14 38
18
F1
d2 
1
4
2 
5 8 3/4
1
18
F2
14
F1
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
p
F
2
• When firm 1 introduces two variants E2 does not introduce any
variant
12  p  2F
11 
p
p
 p
12  11   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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