INDUSTRIAL ECONOMICS II
Prof. Davide Vannoni
Handout 3
Product Differentiation
Content of lecture and objectives
Part A: preliminaries
 Motivation: relevance to (i) real world, (ii) other areas of academic IO
 key dimensions and definitions
 brief overview of the topic – main issues and development of ideas
Part B: detailed investigation of parts of the theory (a la Tirole)
 Spatial competition – lines and circles
 Monopolistic competition
 Vertical differentiation
Suggested reading
Tirole J (1988) The Theory of Industrial Organization, MIT Press, ch 7, and section 2.1 of chapter 2
Church & Ware (2000) Industrial Organization: a Strategic Approach, McGraw-Hill, ch. 11
Other sources:
Martin S (2001), Advanced Industrial Economics, Blackwell, Oxford, chapter 4
Beath J & Katsoulacos (1991), The Economic Theory of Product Differentiation, Cambridge
University Press
Cabral L (2000), Introduction to Industrial Organization, MIT, chapter 12
1
Part A Preliminaries
I
Motivation – why important?
 To introduce greater ‘realism’: in the real world, most products are not
homogeneous, they’re differentiated (variety of brands offered by firms).
Consider: beer, breakfast cereals, PCs, cars, supermarkets, newspapers; but, on
the other hand, sugar, salt, petrol, cement.
Within the academic literature, introducing differentiation into our models:
 helps resolve the Bertrand paradox
 helps our understanding of the sources of market power: are high prices due to
monopoly power & collusion, or due to very differentiated brands (with
considerable brand loyalty), or both?
 provides underpinnings for econometric estimation of demand systems
 provides insights for understanding determinants and evolution of market structure
 is essential for understanding the likely impact of mergers between firms selling
substitute brands
2
II
Key dimensions and definitions
(i) terminology: for Tirole, the industry or market is the aggregate concept, with
individual firms selling different products. I prefer to refer to individual firms selling
different brands of the same product, e.g. Stella Artois or Guiness are brands of beer
(ii) horizontal or vertical? Think of a product as a bundle of characteristics: physical
attributes, quality, location, time, availability, etc.
 In many cases, consumers have different tastes, (value characteristics
differently); if so, no objective way of saying brand A > brand B, they’re just
different. Even if both brands sell at same price, some consumers prefer A,
and some will prefer B (e.g. Brie and Parmesan): horizontal differentiation.
 In other cases, all consumers have the same ranking of brands by quality – a
small fast PC is preferred to a large slow PC; a light bulb which lasts for 2
months preferred to one which lasts for 1 month. In these cases, if all brands
sold at the same price, all consumers would buy the same one – quality can be
objectively observed. This is vertical differentiation.
(iii) do brands compete locally or globally?
In a given market, are all brands
substitutes for all others, or do they merely compete with those brands which are
‘close’ to them? Consider beer, cigarettes, newspapers, restaurants, TV
3
III
Overview of the literature
Broadly speaking, there are three types of theoretical approach:
 In one-dimensional spatial (address) models, competition is local: Hotelling
(linear); Salop (circular); Gabszewicz/Thisse (vertical). In these models, each
firm competes only with its immediate neighbours.
 In global models, deriving from Chamberlin’s Monopolistic Competition
(developed by Spence and Dixit/Stiglitz), all brands compete with each other.
 Intermediate models, based on the characteristics approach inspired by
Lancaster, in which brands compete in several different dimensions. As the
number of characteristics increase, so do the number of neighbours, and
competition becomes less local1.
Consumer Preferences: associated with any demand system, there is an underlying
model of consumer preferences. Models differ in assumptions about how many
brands consumers can purchase: tends to be only one in spatial models, giving rise
to the discrete choice approach; in global models, consumers buy more than one,
opening up an important real-world issue – consumer preferences for variety.
It can be argued that the characteristics approach is a generalisation: brands differ vertically in
their provision of any one characteristic, but horizontally in their combination of characteristics.
Consumers vary in weights they attach to different characteristics. So an encompassing approach.
1
4
Part B More detailed discussion, a la Tirole
0.
Fixed variety (non- address approach)
It allows to understand easily how differentiation helps resolving the Bertrand
Paradox.
We consider Cournot competition and Bertrand Competition in a duopoly in which
each firm manufactures a variety of a differentiated product.
Direct Demand functions:
q1 = D1(p1, p2)
q2 = D2(p1, p2)
Inverse Demand functions:
p1 = P1(q1, q2)
p2 = P2(q1, q2)
In the case of linear inverse demand functions:
p1=  - q1 - q2
and
p2=  - q2 - q1
with >0 and 2 > 2: the products are imperfect substitutes
The corresponding direct demand functions are:
q1= a - bp1 + cp2
and
q2= a - bp2 + cp1
with the following relationships between a,b,c and , , 
a = a/(+) ; b = /(2 - 2); c = /(2 - 2)
  2 / 2 can be seen as a measure of the degree of differentiation:
High differentiation (low substitutability): 0; 20 (c 0) (independent products)
Low differentiation (high substitutability): 1; 22 (cb) (homog. products)
5
Price decisions (Bertrand)
Direct demand functions: q1= a - bp1 + cp2
and
q2= a - bp2 + cp1
Cost functions:
and
C2 (q2) = k q2
C1 (q1) = k q1
Objective functions:
Max 1= Max (p1– k) q1 ; Max 2=Max (p2– k)q2
p1
p1
p2
p2
Max 1= Max (p1– k) (a - bp1 + cp2)
p1
p1
First order conditions
Firm 1:
(a - bp1 + cp2) – b(p1– k) = 0
Firm 2:
(a - bp2 + cp1) – b(p2– k) = 0
Optimal Response Functions (Reaction functions)
p1=(a + bk + cp2)/2b ; p2=(a + bk + cp1) / 2b
Price is a positive function of the rival’s price. If one firm increases the price, the
rival would react by increasing its price. Prices are thus strategic complements
(Bulow, Geneakoplos, Klemperer, 1985).
a  bK  cP2
2b
a  bK  cP1
P2 
2b
P1 
P1
R2 (P1)
R1 (P2)
P*1
a  bK
2b
a  bK
2b
P*2
P2
6
p1*= p2* = p * = (a + bk)/(2b-c)
q1*= q2* = q * = [ab - bk(b-c)]/(2b-c)
by using the parameters of the inverse demand function:
p* = k + [( - )( - k)]/(2 - )
p*>k, thus we do not have the Bertrand paradox anymore
Thus i > 0,
with p* = f- () and i =f- ()
If = (homogeneous products) Bertrand paradox and i = 0
If =0 (independent products)  p*=k+(-k)/2, as in Monopoly
Quantity Decisions (Cournot)
Inverse demand functions:
p1=  - q1 - q2
and
Cost functions:
Ci (qi) = k qi ;
I=1,2
Objective functions:
p2=  - q2 - q1
Max(-q1 - q2 )q1– kq1
yi
First order conditions
Firm 1:  - 2q1 - q2 – k = 0
Firm 2:  - 2q2 - q1 – k = 0
Optimal response functions: q1 = ( -q2 – k)/2 ;
q2 = ( -q1 – k)/2
Quantity is a negative function of the rival’s quantity. If firm 1 increases its quantity,
firm 2 reacts by reducing its output. Quantities are thus strategic substitutes.
The effect is lower with respect to the traditional Cournot model since <:
differentiation reduces rivality
q1*= q2* = q * = (-k) / (2+)
p* = [+k(+)]/(2 + )= k + (-k)/(2+)
=  Cournot and =0 Monopoly
7
q1
K
2
Y1C
Y2C
K
2
q2
Issue that has not been addressed: how firm choose the degree of differentiation ?
I.
Horizontal differentiation: the spatial analogy (section 7.12)
Checklist of insights provided:
 How the nature of competition differs from homogeneous products
 Determinants of ‘market power’, once the Bertrand paradox is avoided
 How firms choose to locate (or choice of product)
 How many firms
 How much variety
I.1
Hotelling’s ‘linear city’
(a) Basic assumptions
(i) The cost to the consumer of buying a particular brand is:
p + tx
2
See also pp. 97-9.
8
where x = distance to shop (or departure of the brand’s characteristics from the
consumer’s ideal) and t = transport cost per unit of length (or psychic costs of having
to consumer a brand which is not ideal.)3
If the consumer enjoys a surplus of S when he consumes, then his utility is
S – (p+tx)
(ii) There are two brands on offer: A and B (separate firms).
(iii) They are located at opposite ends of the city.
Define the distance between them as 1, and now think of x as the consumer’s distance
from brand A (and therefore 1-x from B). The consumer buys the brand which
generates the larger utility.
(b) Basic model, with fixed location
Assume that, in equilibrium, all consumers buy, and that both firms sell 4, then there is
a marginal consumer who is indifferent between the two brands. This is shown in
figure 1, from which we can derive:
 the demand curves for each brand
 the best response functions (from the first order conditions)
 the equilibrium
Demand:
marginal consumer, located at x
so pA + tx = pB + t(1-x)
Utility
Figure 1
S-pA
S-pB
therefore x = {(pB - pA)/2t} + 1/2
S-pA-tx
S-pB-t(1-x)
If consumers distributed uniformly with
unit density, then demand curves are:
DA = x and DB = 1 – x
0
3
4
x
1
Tirole, on pp. 279/80 goes straight to quadratic transport costs. Initially, I set the model up with linear transport costs.
But see the diagrams on p.98 for where this is not true.
9
Best responses
A = (pA – cA). DA
A = (pA – cA). {(pB - pA)/2t + ½},
f.o.c =>
pA = (pB +c +t)/2
therefore upward sloping best response functions: the brands are strategic complements.
Equilibrium pA = pB = c +t
This equilibrium yields our first two important insights:
INSIGHT 1
the brands are strategic complements (cf Cournot homogeneous)
INSIGHT 2
prices are higher the larger is t. In this sense, the degree of
differentiation increases ‘market power’
(c) More general location (i.e. not necessarily at the end of the line)
Now assume that transport costs are quadratic, rather than linear. The results are
similar, but this proves to be a more convenient way of modelling location of brands.
(What do quadratic costs imply?)
Suppose that firm A is located at point a, and that firm B is at point (1-b).
Special cases:
if a=b=0, we have maximum differentiation (as before)
if a+b=1, there is minimal differentiation (both firms locate at the same point)
Again, we can proceed to derive the demand curves, best response functions and
equilibrium price:
10
Figure 2
Demand: marginal consumer defined by:
Utility
2
S-pA-t(x-a)2
2
pA + t(x-a) = pB + t(1-b-x)
S-pB-t(1-b-x)2
therefore, solving for x:
S-pA
S-pB
DA = x = {(pB - pA)/2t(1-a-b)} + (1-a-b)/2 +a
Best response:
As before, maximise A , giving:
pA = (pB + c)/2 + t/2(1-a-b).(1+a+b)
Equilibrium
Solve for interesection of best response curves:
a
x
1-b
pA = c + t(1-a-b). {1+(a-b)/3}
Conclusion: the two basic insights still hold: the equilibrium expression confirms that
price increases with t, and the best responses show that pA is positively related to pB.
HINT: Doing Tirole’s exercise 7.1 is a useful test of whether you’ve understood this!
(d) Endogenous location
But now let’s make things even more interesting (realistic), by allowing firms to
choose their locations, so as to optimise.
This now becomes a 2 stage game, in which firms choose location in stage 1 and then
price in stage 2. (Is this sequence reasonable?) It highlights a key point: brand
positioning is often a strategic variable.
Tirole provides the algebra for you to work through (sub-section 7.1.1.2).
Summarizing (new simbols: a and b are x1 and x2, z is x, pA and pB are P1 and P2):
D1  Z  a 
1a b
P2  P1

2
2t(1  a  b)
a
0
D2  1  Z  b 
1a b
P1  P2

2
2t(1  a  b)
1-a-b
X1
Z
11
b
X2
1
Which variety will be chosen by the two firms?
Maximal (x1 = 0; x2 = 1) or Minimum (0  x1 = x2  1) differentiation?
Second stage: choice of location
Firm 1’s profits

1a b
P2  P1 

MAX P1  a 

P1
2
2t(1  a  b) 

Firm 2’s profit

1a b
P1  P2 

MAX P2  b 

P2
2
2t(1  a  b) 

From the first order conditions (first derivatives w.r.t prices), one can get the best
response functions:
t 1  a  b  1  a  b 


P1 
2



t 1  b  a  1  a  b 
P2 

2

P2
2
P1
2
Solution of the system:
ba

P* 2  t 1  a  b   1 

3 

ab

P *1  t 1  a  b   1 

3 

Intuition:
Firms try to locate at the extremes so as to reduce price competition.
First stage: choice of the variety (locations a, b)
*
*


Firm 1: MAX P*1  a  1  a  b  P 2  P 1 
a

Firm 2:
2
2t(1  a  b) 

1a b
P*1  P*2 

MAX P*2  b 

b
2
2t(1  a  b) 

 1
t 
ab
  1 
 1  3a  b   0
a
6
3 
 2
t 
ba
  1 
 1  3b  a   0
b
6
3 
12
Maximal differentiation

a
b
 
x1
x2
I want to emphasise the distinction between the demand effect and the strategic
effect. This comes about because where the firm chooses to locate (i.e. the value of a
chosen by firm 1) has two effects on its profits:
 A direct (demand) effect – the closer you are to your rival, the more of his
demand you can steal.
 A strategic effect: the closer you get, the tougher is price competition between
the two firms.
Algebraically, this is:
d1/da = (p1* - c) { D1/a + D1/pB*. pB*/a }
direct
strategic effect
effect (+)
(-)
So there’s a trade-off: the former effect makes firm 1 want to move closer to the
centre (this minimises the costs to consumers). But this will increase competition
with firm 2, and provoke a price reduction by firm 2, which thereby reduces demand
for firm 1. To avoid this latter (strategic) effect, firm 1 will want to move to the left.
Since it can be shown that the strategic effect dominates, we have:
INSIGHT 3
The two firms will locate at opposite ends of the line: MAXIMUM
DIFFERENTIATION
But is this optimal from society’s point of view?
13
INSIGHT 4
NO: optimal (in terms of minimising consumers’ transport costs)
if the firms locate at (0.25, 0.75): Therefore, the market
equilibrium involves TOO MUCH DIFFERENTIATION
P.S. Maximal or minimal differentiation?
How robust is the prediction of maximal differentiation? In reality, demand is not
uniformly distributed (shops and restaurants in historical town centres), there may
be agglomeration cost-saving effects (industrial districts, department stores), and
there may not be price competition (collusion and/or administered prices). Where
these variations occur, there may be forces moving brands to the centre.
Example: horizontal differentiation with exogenous prices (P1 = P2)
i)
Firms choose the same variety in order to maximize the demand
a


1-b


0
x1
z
x2
1
a


1-b



0
x1
z
x2
1
ii)
Which variety?
a
b



0
x1 = x2
0,5
1
If: a = 1 – b < 0,5
BOTH FIRMS TEND TO MOVE TO THE RIGHT.
14
In fact, for  > 0 small enough
a
b






0
x2
x1
Firm 1 demand is:
0,5
1
b     1  a  b     1
2
2
In the same vein, if a = 1 – b > 0,5 both firms have an incentive to move leftwards.
Thus, in equilibrium:
a
b



0
x1 = x2 = 0,5
1
Without price competition, firms offer ‘average’ varieties: political elections, TV
programs, and so on.
I.2
Salop’s circular model (section 7.1.2)
This allows us to analyse the possibility of entry and n>2. For this purpose, a circle is
better than a straight line5.
5
Because product space is now homogeneous – no location is a priori better than any other.
15
Assumptions
Mostly similar to the linear city (in terms of transport costs, distribution of consumers
etc). Crucially, however, we now assume that:
1. there are fixed costs (of say product development and marketing)
2. ‘free entry’ – as many firms are allowed into the market as are profitable
3. zero profits in equilibrium
Two stage game
Stage I
potential entrants simultaneously choose whether or not to enter (they
will be arranged equidistantly around the circle)
Stage II
actual entrants select price, given their location
Solution
Because firms are located symmetrically, we can look for an equilibrium where they
all charge the same price p.
n firms decide to enter, but each firm has only two competitors. If we define the
circumference of the circle as 1, then firms will be arrayed at intervals of 1/n.
Define the marginal consumer for firm i as located at distance x away. If he is to be
indifferent between firm i’s brand and the brand of its immediate competitor, it
follows that: pi + tx = p + t{(1/n)-x}
1/(2N)
P1
1/(2N)
X1
pN = p
p2 = p
1/N
XN
X2
X2
16
As before, this enables us to derive the demand curve for i: since demand for i’s
brand is 2x, solving for x from the above gives:
Di = 2x = {p + (t/n) – pi}/t
Inserting this, in turn, into i’s profit function gives:
Пi = (pi – c){p + (t/n) – pi}/t - F
Maximising with respect to price gives:
p = c + t/n
Notice the similarity with the linear model, except that:
INSIGHT 5:
Price is lower the larger is n: price is positively related to
concentration.
However, this is only an intermediate conclusion, in that n is, itself, endogenous.
Since this is a free entry equilibrium, firms will continue to enter until profits are
driven down to zero. Noting that each firm sells quantity 1/n, zero profits implies:
Π = (p-c) (1/n) – F = 0
and using the above expression for price:
i.e. t/n2 – F = 0
Thus n = (t/F)1/2 and p = c + (tF)1/2
INSIGHT 6
The number of firms (i.e. brands) will be higher the larger is t, and
the smaller are fixed costs
INSIGHT 7
Price will be higher the larger is t (as before), and the larger are
fixed costs. Discuss?
17
Is there too much variety?
From society’s point of view, there is
 a benefit from more variety: it benefits consumers by reducing their transport
costs, or each consumer is better able to buy a brand which suits his taste, but
 a cost from more variety: increasing the total fixed costs incurred in serving the
market.
It turns out (p. 284) that the socially optimal number of firms would be smaller than
this – there are too many firms (i.e. brands) in the market solution. This is because of
the trade diversion effect – with the entry of each extra firm, business is taken away
from rivals, but this externality is not reflected in the entry decision of each firm.
Extensions
See Tirole (p.285) on location choice, sequential entry, brand proliferation.
Or
Church & Ware on brand proliferation and brand specification.
Brand Proliferation (Schmalensee, 1978)
Entry deterrence strategy: incumbent produce different varieties in order to avoid to
leave market niches that could be profitably exploited by entrants (see lecture on
entry barriers).
The incumbent deters entry with a credible threat of continuing to sell the product
after the rival enters the market. Result: a few number of firms can divide the market,
by producing many different varieties, and avoid entry of new firms.
Examples:
Ready-to-Eat Cereals. Low economies of scale, low technology, entry should be easy
but from 1950 to 1980, four dominant firms (Kellogg, General Mills, Post, Quaker
Oats) and virtually no entry. In the 90’s, in USA: 200 different varieties of “Corn
Flakes”.
18
Office products. Supermarket chain Staples (USA) in the ’90 was trying to build a
critical mass of stores in the Northeast to shut out competitors…
“By Building these networks of stores in the big markets like New York and Boston
we have kept competitors out for a very, very long time”, Staples’ CEO, 1996.
Banking sector: The main banks open too many branches.
Restaurants: Too many fast foods in town centres.
Model: Incumbent moves first and potential entrant afterwards. There is no price
competition (only choice of location). There are fixed (and sunk) costs equal to F.
A) If the incumbent manufactures one variety only it locates at the centre, to leave
to entrant the lowest possible market share (50%):
B)
|______________|_____________|
0
½
1
If the incumbent manufactures two varieties he chooses the following locations:
|_________|__________________|_________|
0
¼
¾
1
to leave the potential entrant with the lowest market share: ¼.
Profits
In case a) i = ½ p - F and
e = ½ p – F
In case b) i = ¾ p - 2F and
e = ¼ p – F
Entrant does not enter if: (¼ p – F) < 0, that is if F > ¼ p
Is that worth to introduce two varieties in order to prevent entry?
If there is no entry: i (two varieties) = p - 2F
i (two varieties = p-2F > ½p – F = i (one variety)
The incumbent deters entry by selling two varieties if ¼ p < F < ½ p
1)
Without the entry menace, the incumbent would not introduce 2 varieties:
p – F > p-2F
19
2)
Without the presence of sunk costs, the incumbent would not credibly
threathen to impede entry (Judd, 1985)
i (one variety) = ½ p-F > i (two varieties) = ¾ p – 2F if ¼ p < F  F > ¼ p
Exercise.
Market of size M=1; Price is exogenous and equal to 1; Fixed cost F=3/8
Two stage game: in the first stage the incumbent chooses how many and which
variety to introduce; in the second stage the entrant observes the incumbents’
decisions and decides to enter or not.
1)
If the incumbent produces one variety, the entrant enters:
yi =ye = ½ and i = e = ½ p – F = ½ - 3/8 = 1/8
2) If the incumbent produces two varieties, the entrant does not enter:
yi = ¾ ; ye = ¼
e = ¼ p – F = ¼ - 3/8 = - 1/8 and i = p – 2F = 1 - 2(3/8) = ¼
3) If fixed costs are not sunk, the menace is not credible and the incumbent should
not introduce a second variety:
i (one variety) = ½ -3/8 = 1/8 > i (two varieties) = ¾ – 2(3/8) = 0
e (1) = ½ -3/8 = 1/8
II
Horizontal differentiation: Monopolistic competition
Chamberlin – each firm faces a downward sloping demand curve (as in monopoly),
but there is free entry (as in perfect competition). No strategic effects, in that a price
change by any one firm has equal (negligible) effects on the demands for all other
firms. (Global competition, as opposed to the above local competition)
SEE APPENDIX FOR QUICK RESUME OF BASIC MODEL
Tirole’s main-text comments (p.288) are addressed almost exclusively to questioning
the famous excess capacity result. This leads on to the question of whether or not the
20
market generates socially too few or too many firms (brands). In principle, there are
two opposing effects:
 Non-appropriability of social surplus – because each firm faces a downward
sloping demand curve, it sets p>MC and so the sum of consumer and producer
surplus is not maximised. In turn, this implies that some brands will not be
produced (because the firm can’t cover its fixed cost) even although it ‘should
be’ (because consumers would have received sufficient surplus to more than
offset that fixed cost, i.e. they could pay the firm to produce and still receive a
net surplus.)
 Business stealing effects: each new brand steals custom away from existing
brands – this loss of income for rivals is not taken into account by the entrant,
so the social cost > private cost.
In general, we can’t say which effect will dominate.
But see C&W p. 374:
insufficient diversity when product differentiation ‘strong’.
See also Tirole’s
Appendix, (in which he develops the analysis, using the Spence/Dixit-Stiglitz
formalisation of monopolistic competition.)
This generates a prediction for price: price is higher, the less substitutable are the
brands. The model can also be used to derive firm numbers (variety). This allows
comparisons with what would be socially optimal, using the Utility function (see pp.
299-300).
III
Vertical differentiation (pp. 96/7 and section 7.5.1, or C&W, section 11.6)
Model 1 (Based on Gabsewicz & Thisse)
For the individual consumer, if he consumes 1 unit,
U = s – p
where s measures ‘quality’ of brand and  reflects consumer’s taste for quality.
21
With only 1 brand on offer, the consumer buys if :
s > p that is  > p/s
In the market as a whole, suppose that  is uniformly distributed across consumers6
with density 1. It has upper and lower limits as follows:
U >  > L, where U = L +1 and L > 0
Competition between brands
Now suppose 2 different brands (firms), where brand B has higher quality, i.e.
sB > sA
Suppose all consumers buy 1 unit of one of the brands. The marginal consumer is
defined by:
*sA - pA = *sB - pB, i.e. * = (pA -pB)/(sA - sB)
Then demand for brand A is given by:
DA = * - L = {(pB-pA)/} - L
DB = U - * = -{(pB-pA)/} + U
where  = sB - sA , the quality differential. (High  consumers buy B)
and something similar for B.
Best responses
Substitute this expression for demand into the profit function and maximise to give:
pA = (pB+c- L)/2
pB = (pA+c+ U)/2
where c denotes the constant marginal cost
22
Solving for the equilibrium,
pA = c + {(U - 2L)/3}.
and
pB = c + {(2U - L)/3}.
A = (U - 2L)2/9
and
B = (2U - L)2/9
It can be seen (or easily shown) that:
 the brands are strategic complements
 high quality firm (B) charges higher price and earns higher profits
 price cost margins disappear as the extent of differentiation () declines
(compare with horizontal)
Brand choice/location
Now suppose that firms can choose quality. This sets up a two stage game, in which
firms first choose quality, then price.
Obviously, they will want to differentiate (not choose the same s). Initially, assume
that quality is costless for the firm. Here, they will choose the most extreme values
consistent with the market being covered.
Again therefore, we have maximum
differentiation, for the same reasons as before (to soften competition.)
In a simultaneous move game, it’s arbitrary which firm is high quality. In a
sequential game, the first mover would be high quality. But what if there is a race to
be first…? There have been a number of interesting developments to these models,
including various important insights into how market structure evolves over time in
markets where firms compete (via R&D and advertising) to increase consumers’
willingness to pay.
6
Alternatively, we can assume that consumers are distributed by income.
23
Model 2 (Based on Shaked & Sutton)
There exist n firms each with a product of quality uk (labelled so that u1>u2>…>un)
and a price pk
There exists a continuum of consumers with identical tastes but different incomes t. t
is uniformly distributed with density S (S=size of the market) on a support [a,b], with
a>0.
Consumers buy one unit of the good (the market is covered), and have utility
U(t,k)=uk (t-pk)
The game
1. Firms decide on entry (fixed cost >0)
2. They decide on quality of the good
3. They decide prices and sell (zero marginal costs)
Proposition: If b<2a, only one firm will enter the industry at equilibrium (whatever S)
(As income becomes less concentrated, more firms can enter; e.g., if 2a<b<4a, two
firms will enter at equilibrium. Generally, the number of firms which coexist
at equilibrium is finite even as S goes to infinity)
Proof of the proposition
We show that two firms cannot co-exist at equilibrium. Firms’ demand is derived by
finding the consumer indifferent between the two qualities:
From: u1 (t-p1) ≥ u2 (t-p2), we obtain:
t  t12 ( p1 , p2 , u1 , u 2 ) 
u1 p1  u 2 p2
u1  u 2
All consumers with income t ≥t12 will buy 1, all others will buy 2. Therefore:
q1 = b-t12 ; q2 = t12-a
Profits can be written as:

u p  u 2 p2 
 p1
1   b  1 1
u

u
1
2


 u p  u 2 p2

 2   1 1
 a  p2
 u1  u2

By setting dΠi/dpi=0 we obtain the best reply functions:
24
R1 : p1 
b(u1  u 2 )  u 2 p2
2u1
R2 : p1 
a(u1  u 2 )  2u 2 p2
u1
Equilibrium prices are given by:
p1 
(2b  a)(u1  u 2 )
3u1
p2 
(b  2a )(u1  u 2 )
3u 2
Therefore, if b<2a there exists no equilibrium with positive p2, and firm 2 will not
enter the industry.
Equilibrium, when b>2a
25
Generalisation
The finiteness property holds if the cost of producing a higher quality does not fall
upon variable costs. It holds across a number of different specifications (see e.g.,
Shaked-Sutton, 1987)
Sutton (1991): Endogenous Sunk costs and market structure: Advertising
Sutton (1991) puts the result to an empirical test. It shows that in advertisingintensive industries as S increases the industry does not become fragmented.
Advertising is an endogenous sunk cost:
- endogenous because, differently from set-up costs, is a variable that can
be chosen by the firm
- sunk, because, after having undertaken the investment, it cannot be
recovered
1/N
1/N
(i)
(ii)
(iii)
size
Endogenous sunk costs
size
Exogenous sunk costs
(i) high exogenous sunk costs w.r.t endogenous sunk cost
(ii) intermediate exogenous sunk costs w.r.t endogenous sunk cost
(iii) low exogenous sunk costs w.r.t endogenous sunk cost
While in free-entry models with homogenous or horizontally differentiated
products but with exogenous sunk costs concentration (1/N) has a lower bound
26
that goes down to zero as market size increases, in models with vertically
differentiated products and with endogenous sunk costs concentration has a
lower bound that does not go to zero as size increases
Intuition: there is a competitive escalation in advertising such that, if the size of
the market is sufficiently large, firms that invest aggressively gain increasing
market shares
The logic of the bound approach, that is the existence of a limit to concentration
(which can go to zero or not) as size increases clashes with the view of those who
maintain that “anything can happen in oligopoly”. We must look for some robust
results that do not depend on the specific assumptions of a model (price versus
quantity competition, homogeneous versus differentiated goods, simultaneous
versus sequential games, and so on).
Sutton (1998): Technology and market structure
Why in some high R&D industries concentration is high while in other
concentration remains low?
Entrant spend an amount K to obtain a profit equal to a Y, where Y is the amount
of sales in the previous period.
α= a/K is the escalation parameter
high α: by investing K the entrant can obtain high profits
low α: by investing K the entrant cannot obtain high profits
In high- α industries there is high R&D investment and concentration increases,
while in low- α industries concentration does not increase.
27
Examples of high- α industries: where there is high substitutability (camera tapes
after technological change, telecommunication equipment after opening to the
global market, aircraft industry)
Examples of low- α industries: low substitutability and products fill different niche
positions (flowmeters and measurement instruments, pharmaceutical industry)
Sutton (1991) puts the result to an empirical test. It shows that in advertising-
Appendix on Monopolistic Competition
Review of monopoly & perfect competition
Monopoly
Perfect competition
one seller
many sellers
many buyers
many buyers
homogeneous product (no substitutes)
homogeneous product
price setter
price takers
no entry
free entry
Outcome
Price is higher, and quantity is lower under monopoly than under perfect competition
£
Figure 1 monopoly and perfect competition revisited
MC
monopoly
perfect
competition
MR
Demand
Quantity
28
Monopolistic competition Chamberlin & Robinson pre-war.
Main assumptions

In common with monopoly, each firm produces its own differentiated product. Other firms’
products are similar, but not identical. The individual firm therefore has its own downward
sloping demand curve.

In common with perfect competition, there are a large number of firms in the market as a
whole. There is also free exit and entry.
Outcomes:

The individual firm sets MR = MC (as in monopoly). In the short-run, this may imply
P>AC, in which case the firm makes a profit (as in monopoly).

However, this profit signal will attract the entry of new firms into the market. This
will impact negatively on the firm’s demand curve (the entrants will capture some of
the firm’s existing customers.) Diagrammatically, this shifts the demand curve (&
MR) inwards until the profits are dissipated. At that point, no further entry occurs 7.
The long-run zero profit outcome has been attained (as in perfect competition).

One big difference from perfect competition is that, in long-run equilibrium, firms are
not operating at the bottom of their AC curves. They are producing sub-optimally.
The famous excess capacity result.

In terms of welfare, there is a trade-off. Since P>MC, there is allocative inefficiency consumers pay more than the social costs of production. On the other hand, this
market structure provides the variety which is lacking under perfect competition.

Modern research in this area has looked at whether monopolistic competition provides
too much or too little product variety (compared to what would be provided by a
social planner who takes into account the utility that consumers derive from variety
per se.)

7.
How does this match with real world industries in which products are differentiated?
The reverse is true if firms are making a loss in the short-run.
29
Figure 2 monopolistic competition: short-run
£
MC
AC
profits
(short-run)
MR
Demand
Quantity
Figure 3 monopolistic competition: long-run
£
MC
AC
demand
curve
shifted inwards by
new entry. Squeezes
profits out
MR
Quantity
30