1. Topic 7. Product differentiation (II): Market Structure
Applied Industrial Economics
Juan Antonio Máñez Castillejo
Departamento de Estructura Económica
Universidad de Valencia

2. Departamento de Estructura Económica
Index
Topic 8: Product differentiation (II): market structure
Circular city model
Product proliferation strategies: breakfast cereal market
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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.
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4. 1. Circular city model (Salop, 1979): 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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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:
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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
Stage 2: firms compete in prices given these locations.
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7. 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
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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: I
I+1
I-1
L/N A B
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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9. 1. Circular city model: demands determinationB
I-1
I+1 I
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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 N
Step 1: Determination of the equilibrium number of firms
Step 2: Determination of the Nash equilibrium in prices for any N:
Firm I reaction function
As we have exogenously imposed symmetric locations
The Nash eq. in prices for any N
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11. 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
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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)
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13. 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:
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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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.
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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:
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16. 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
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17. 2. Product proliferation: sequential game with only one variant
Optimal location for firm 1: 1/2 1 F1
If it locates at the left of 1/2 F2 1 F1 d1 d2
If it locates at the right 1/2 F2 1 E1 d2 d1
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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 1 F1
 F2 enters the market producing a breakfast cereal variant
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19. Departamento de Estructura Económica
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? 1 F1 F2
F2 does not introduce any new cereal variant in the market
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20. 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.
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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.
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