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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 Circular city model - PowerPoint PPT Presentation
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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
Departamento de Estructura Económica 3
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 4
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 5
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
Departamento de Estructura Económica 6
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.
Departamento de Estructura Económica 7
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 8
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
Departamento de Estructura Económica 9
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
Departamento de Estructura Económica 10
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
Departamento de Estructura Económica 11
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
Departamento de Estructura Económica 12
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
Departamento de Estructura Económica 13
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.
Departamento de Estructura Económica 14
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 15
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
Departamento de Estructura Económica 16
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
Departamento de Estructura Económica 17
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
Departamento de Estructura Económica 18
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
Departamento de Estructura Económica 19
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
Departamento de Estructura Económica 20
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
Departamento de Estructura Económica 21
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.