Topic 7. Product differentiation (II): Market Structure

1
Topic 7. Product differentiation (II) Market
Structure

• Applied Industrial Economics
• Juan Antonio Máñez Castillejo
• Departamento de Estructura Económica
• Universidad de Valencia

2
Index

• Topic 8 Product differentiation (II) market
  structure
• Circular city model
• Product proliferation strategies breakfast
  cereal market

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.

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, cic
• 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

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

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.

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

8
1. Circular city model demands determination

• Salops 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 I1

9
1. Circular city model demands determination
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

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

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)

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 gt c)
• When F ? 0

• When t increases ? price increase ? (p-c) raises?
  reduction of the demand that is needed to
  compensate F ? increase of the number of firms.

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.

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

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

17
2. Product proliferation sequential game with
only one variant

• Optimal location for firm 1 1/2

• If it locates at the left of 1/2

• If it locates at the right 1/2

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
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?

F2 does not introduce any new cereal variant in
the market
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

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

F1 introduces two variants to avoid the entrance
of F2.
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.