Product Differentiation
•Horizontal
product
differentiation:
Consumers have different preferences along
one dimension of a good.
- e.g. some consumers prefer hot salsa, some
prefer mild.
•Vertical product differentiation: Consumers
have the same ordinal preferences, but not the
same cardinal preferences.
–e.g. all consumers prefer better fuel
efficiency, but their willingness to pay will
differ.
•Firms seek to be unique along some
dimension that is valued by consumers.
–Differentiation can be based on the product
itself, the delivery system, or the marketing
approach.
•If the firm/product is unique in some respect,
the firm can command a price greater than
cost.
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Horizontal Product Differentiation
Location Models
A realistic transport cost model to replace
Cournot, Bertrand and Joint Maximising
Models
Assumes: Firms can NOT manipulate the
Intensity of Competition
Products are differentiated by t and t are
exogenously determined
Firms choose “location” along a spectrum
–Can think of this as the same product in
different location, or
–Can think of this as different products
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Hotelling (1929) Umbrellas
 Linear Market
 Consumers uniformly distributed with
density 1 along this interval
 Duopoly
 Consumers incur transport cost t per unit of
distance d traveled to the seller
Consumers choose to buy from the firm that
provides highest net value
 Each consumer located at certain point on
the spectrum
 Consumer must transport the good from firm
 Net value = V - p – td
 Will not purchase if net value < 0
 let p* = p + td
 consumers buy from the seller with lowest
p*
 let one seller be located at A, the other at B
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p*
0
A
B
1
“indifferent
consumer”
 Slope of the
(exogenous)
umbrellas
given
by
t
 Height of the umbrella stem given by p
(seller at location B has lower p than seller at
A)
 Total cost to the consumer from buying from
a particular seller = p+td
 Consumers buy from seller with lowest p+td
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 Equation of the indifferent consumer
PA+tdA = pB + tdB
 All consumers located to the left of the
indifferent consumer will buy from seller
at A (since pA+tdA < pB + tdB)
 All consumers located to the right of the
indifferent consumer will buy from seller
at B (since pA+tdA > pB + tdB)
 Finding the indifferent consumer allows us
to divide the market between firms A and
B
 Note, for a given location, higher t costs
result in higher p*
Location Models: two stage game
Stage 1
Location
Choice
(a,b)
Stage 2
NE Prices
(given location
a,b)
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Hotelling (1929) – “Simple Location Model”
No price Competition in Stage 2
Stage 1: Firms A ad B Choose location along a
Spectrum
The Principal of Minimal Differentiation –
Focus on the Catchment Area
Payoff for A(B): line segment covered
If both firms located at the end….
A
B
a
b
l
then firms have an incentive to move inwards.
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A and B are back-to-back, but not in centre:
AB
b
a
Incentive for A to jump in front of B…..
A and B are back-to-back in centre:
A
a
B
b
Neither firm has an incentive to move location,
given the location of the other
The Midpoint is a Nash Equilibrium in
Locations
Downs Theory of Modern Voting
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Hotelling (1929)
two stage game
Stage 1
Stage 2
Location
Choice
NE Prices
(given location
a,b)
(a,b)
Stage 1:
A
B
a
b
l
8
Stage 2:
A
B
“indifferent
consumer”
A
“indifferent
consumer”
B
No Nash Equilibrium in Pure Strategies
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D’Aspremont et al (1979)
Assumes Quadratic Transport Costs
Stage 2
Given locations, find a NE in prices
d1
a
<
q1 = a + d1
A
d2
Indifferent
consumer
l–a–b
and
B
b
>
q2 = b + d2
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“indifferent consumer”
p1 + td12 = p2 + td22
d1 > 0
d2 < 0
d2
d1
a
A
B
b
With quadratic costs there is a NE in prices
p1 + td12 = p2 + td22
d1 + d2 = l – a – b
solving for market share, we get
l  a  b ( p2  p1 )

2
2t (l  a  b)
l  a  b ( p1  p2 )
q2*  b  d 2  b 

2
2t (l  a  b)
q1*  a  d1  a 
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Now solve for a Nash equilibrium in prices:
Max 1  p1q1
p1
1
0
p1

Max  2  p2 q2
p2
 2
0
p2

s.t. p2
p1  R ( p2 )
s.t. p1
p2  R( p1 )
The NE in prices solves as:
a b
)
3
ba
p2*  t (l  a  b)(1 
)
3
p1*  t (l  a  b)(1 
Thus, prices depend on locations:
p1*(a,b) and p2*(a,b)
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Stage 1:
Choose locations
1(a,b) and 2(a,b)
Solve for a Nash equilibrium in locations…
Results indicate that
 1
0
a
and
 2
0
b
thus, bigger a will reduce firm 1’s profit
incentive to minimise a and move toward end
likewise for firm b
so find NE in locations occurs at a = b = 0,
where firms locate at the extreme points of the
market
trade off market coverage against increased
competition that firms face by locating near
each other
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Assumption underlying the location models:
distribution of consumers was uniform along
the line
Non-uniform distribution of consumers:
where to locate?
Trade-off: how much competition there is in a
certain niche against the available niches
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d’Aspremont et al:
1. price competition strong
2. concentration of consumers is uniform
 optimal location is at the extremes
“locate in a niche”
Hotelling:
1.no price competition
2.concentration of consumers is uniform
 optimal location is at the midpoint
“locate where the demand is”
General Predictions:
Could be anywhere along the linear city….
Optimal location trades off the intensity of
price competition with market coverage…..
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Salop (1979) Circular Road Model
1. N Sellers are located symmetrically
around the circle
2.Circumference is normalised to = 1
3.Distance between each seller is thus 1/N
Stage 1: Enter with sunk cost = 
Stage 2: given number of firms N, find NE
in prices
Solve in Backward Induction process
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p
p
p
 1/N – d 
 d   d   1/N – d
seller*
Representative
where TC = 0:
Seller*
profit
function,
 sales = 2d
 indifferent consumer:
p + td = p + t[1/N – d]
_
so
pp 1
2d 

t
N
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
_


p  p
1
  p.2d  p  

t 
N


 seller maximises it’s profit by choosing p,
given p,
_

1
pp p


 0
p
N
t
t
 S.N.E.  p = p

p* 
t
N
as t  0
 p  MC
as N 
 p  MC
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Recall, the P(N) function that links price cost
margins to a given N
P, for any given N, depends on the ‘intensity
of competition’ (Bertrand is most intense)
Horizontal Product Differentiation relaxes the
intensity of competition
SHORT RUN
p
pmonop
Differentiated
Bertrand Homogenous
Bertrand
½t
MC
1
2
N
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Bertrand under Exogenous Product
Differentiation
Stage 2:
Given N, solve for Nash Equilibrium in Prices
as
pi*
t

N
Thus, equilibrium profits solve as:
1
xi  2d 
N
s
xi  2ds 
N
i.e. where p  p
where s is market size
t s
s
 i  pi xi  .  t 2
N N
N
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Stage 2:
Enter with sunk cost ?
Last firm enters where expost entry profit = 
s
i  t 2  
N
Thus, solving for equilibrium number of firms:
N 
*
t
s

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C=1
/N
1
Homogenous
Bertrand (t=0)
Differentiated
Bertrand (t1)
Differentiated
Bertrand (t2)
s
/
t2 > t1
Greater product differentiation induces more
entry (so less concentration) for any given s/
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