Product Differentiation
Sample Response
The following response sets out in note-form what I consider to be the key points of the activity –
you may have presented your answers differently, focused on other aspects of the problem or
included relevant material not presented below.
Introduction
• Much microeconomic theory is concerned with homogenous goods
o Homogenous goods are goods that differ only by their price
 Their characteristics are identical
 Their availability etc is identical
o Homogenous goods are excellent for theoretical analysis because we can
abstract from other differences and focus only on the price
o Examples of real-world markets with homogenous goods are, however,
few:
 Markets for raw commodities
 Markets for financial instruments
o Microeconomic theories with homogenous goods include the theory of
perfect competition / Bertrand duopoly
 A Bertrand Duopoly is when two firms compete on price alone – the
sole equilibrium is when both firms charge marginal cost
 In this sense, the result is identical to the outcome in perfect
competition despite the fact that there are only two firms
 In practice, we rarely see this outcome – where there are few firms
prices tend to be higher than marginal cost
o In practice, we are often concerned with goods for which the cross-price
elasticity of demand is positive but not infinite (imperfect substitutes)
 This means that changes in the price of one alter the other
 Note, if A is an imperfect substitute to B and B is an imperfect
substitute to C it does not follow that C and A are substitutes – this
may be due to variation of consumers on a continuum
• Some consume only A
• Some might choose between A or B but not C
• Some consume only B
• Etc
o This is what the theory of product differentiation seeks to explain
• Imperfect substitutes are modelled as being differentiated along two axis – which
correspond to how consumers respond to different products.
• Differentiation between goods creates market power
o Firms with market power are able to set prices higher than marginal cost
and, thereby, extract rents but their ability to do so is constrained by the
behaviour of other firms – this is what contrasts it with a true monopoly
o Differentiation reduces price competition
1
•
A model with product differentiation with which AS students may be familiar is
monopolistic competition – here firms make no excess profits because of free
entry.
Horizontal Product Differentiation
• Different consumers have different tastes
o People prefer different types of clothes
o Some people prefer more salt in their food / some less
• This is the realm of Horizontal Product Differentiation – goods differ not because
some are inherently superior / inferior but because they satisfy the preferences of
different consumers – they are a response to variation amongst consumers.
• Note that this variation is not to do with ability to pay but with tastes / preferences.
• Under Horizontal Product Differentiation,
o When a consumer is offered two goods A and B such that A matches his
preferences better than B,
 The consumer will always choose A over B when the price of A is
less than or equal to the price of B
 The consumer may choose A over B even when B is cheaper
 There will typically be a limit to the willingness of the consumer to
pay extra for A, this is because paying more for A reduces the
quantity of goods that the consumer can consume – this is an
income effect
o It is this willingness to pay more for goods that match preferences that
gives firms market power; it is limited by
 The extent of that willingness to pay;
 The number of similar goods offered on the market.
• In considering horizontal differentiation we are interested in:
o What are the prices that we observe in equilibrium?
o What makes firms choose the variation in products we see?
o Is this variation socially efficient – is there too much or too little variation?
• To some extent the answers we get to these questions depend on the model we
use – in many cases done to the actual preference relationships we embody.
Vertical Product Differentiation
• Some characteristics of a product are universally desired
o Consider an aspect of a product denoted θ and two products 1 and 2 such
that θ1 > θ2
 If the price of 1 is less than or equal to the price of 2, all consumers
will buy 1 over 2
 If the price of 1 is greater than or equal to the price of 1, some
consumers will still buy 1 over 2 but some either
• Will not be able to afford to; or
• Will not carry enough about θ to justify the difference
o Examples of such characteristics of products include
 Quality
 Fuel Efficiency (ceteris paribus)
 Hard drive size (ceteris paribus)
• Products that differ by such characteristics are said to be Vertically Differentiated.
o Here different products are on the market not to satisfy the preferences of
different circumstances – but to satisfy their ability / willingness to pay
2
•
o Examples:
 Supermarkets often sell goods of differing quality to different groups
of consumers
 Airlines sell different qualities of service on their planes
o In many cases, quality differentiation is a form of price discrimination
In considering vertical product differentiation, we are interested in similar things to
when we consider vertical product differentiation.
Models of Product Differentiation
• Spatial Models of Horizontal Product Differentiation
o Spatial location models are presented by the following metaphor
 Consumers and Firms are located in a city of a certain shape
• The location of a consumer in the city represents his tastes
as regards a certain aspect of the firm – eg amount of pepper
in chips
• The location of a firm represents the type of product they
offer along the same dimension as the consumers’
preferences are distributed
 There is a cost to consumers of ‘travelling’ to firms which is
proportional to the distance along the city they must travel
• The higher the cost the more adverse consumers are to
consuming goods which are different from their ideal
preference
• If cost = 0, the consumer does not mind consuming goods
which are different from their ideal preference.
 Typically consumption is fixed in that each consumer is assumed a
surplus from consumption that is assumed to be higher than the
maximum possible cost – consumers always consume;
• If this assumption was not made then calculating the social
effects of the model would be more difficult;
• If this assumption is made then the socially optimal location
is the location which minimises aggregate costs;
o Spatial models are solved into stages –
 First the locations are treated as exogenous and the equilibrium
prices are derived; and
 Second the locations are treated as endogenous and given the
equilibrium prices from stage 1 –locations are derived
• Either the number of firms is fixed; or
• There is free entry until supernormal profits are driven to zero
o Where there are no fixed costs, this is equivalent to
price = marginal cost where marginal costs are
homogenous amongst firms
•
Hotelling’s Linear Model of Horizontal Product Differentiation
o Hotelling’s model has a linear city:
3
It is typically solved with costs linear in the distance or quadratic (i.e.
where t is the cost and d is the distance and c some constant t=cd
or t=cd2);
 More general cost formulations are not always solvable;
o When firms are forced to charge the same price – typically the marginal
cost, there is no incentive for firms to differentiate
 This is the Principal of Minimal Differentiation – with duopolists it
leads to back-to-back locations in the centre
• The left-firm takes the entire left half;
• The right-firm takes the entire right half;
 If the linear city is thought to represent the spread between right
and left wing voters, it explains why political parties tend to have
similar views – each located so as to capture half the market;
 With three firms, this model is not stable – there is no equilibrium –
since firms will always have an incentive to move;
 With four or more firms, the model has equilibria;
o When price competition is introduced, firms will tend to
differentiate themselves from each other – to reduce price competition
 This is the Principal of Maximum Differentiation – with duopolists it
leads to firms being located at the two ends of the city;
 In the typical case, this leads to more differentiation then is optimal
– the optimum for duopolists can be shown to be at the ¼ and ¾
position;
 The intuition is that greater differentiation reduces price competition
so suits the firms but reduces consumer surplus (because it
increases transport costs as well as prices);
o Hotelling’s model can only be solved when the number of firms is fixed;
Models of Vertical Product Differentiation under Monopoly
o A monopolist – or, more generally, a firm with market power – has an
incentive to try to discover a consumers’ willingness to pay;
 If a monopolist could know every individuals’ willingness to pay, he
could
• Provide products of optimal quality;
• Charge each individual his maximum price;
• Eliminate all consumer surplus;
 This outcome would be socially efficient – since surplus would be
maximised although it would all be in the hands of the monopolist;
 There may still be vertical product differentiation since some
consumers may not be willing to pay the average cost of goods of a
certain quality so may instead be provided lower quality goods
which cost less to produce;
 The vertical product differentiation would be socially optimal;
o Consumers, however, have an incentive to conceal their willingness to pay
in order to increase their consumer surplus;
 An example where this is not possible is cinema tickets;
 The cinema would like to charge more to people with jobs than
students and pensioners –
• Students and pensioners are assumed to have lower
willingness to pay – owing to their reduced means;
• It uses official identity papers for this purpose;

•
4
Its surplus is increased since it is able to charge a different price to
different groups. If it did not then it would have to charge an
average price which may lead to either:
• Working adults being charged too low a price (from the
cinema’s point of view); or
• Students and pensioners not attending the cinema because
of high prices. The cinema would lose their revenue.
 Which of these effects dominates would depend on which source of
revenue (higher prices/students and pensioners) was more
important.
o Owing to this problem of asymmetric information, the monopolist must,
accordingly, design a scheme whereby consumers choose to reveal their
willingness to pay. One way to achieve this result is through quality
discrimination and price discrimination
 The firm will offer a menu of different goods each having a different
quality – these are vertically differentiated from each other;
 The prices will be set so that:
• Consumers with low(er) willingness to pay will choose the
low(er) quality goods; and
• Consumers with high(er) willingness to pay will choose the
high(er) quality goods.
 Note the difference in price will normally be greater than is justified
by the difference in the marginal price of the different qualities;
o From the firm’s point of view, the optimal menu will have the following
characteristic:
 The lower quality goods will have their quality kept unnecessarily
low;
 In this sense, unnecessary means lower than would be justified
without asymmetric information.
• The marginal cost of improving the goods slightly will be less
than the extra marginal revenue that would be gained from
the consumers with the lower willingness to pay;
• This increase in marginal revenue would come from the extra
price that lower quality consumers would pay for the better
goods or the extra consumers that would buy the goods;
 Even though the firm could improve the quality of the lower quality
goods – it will not do so for the following reason:
• Better quality goods would lead to some consumers of the
higher quality goods ‘jumping ship’ to the lower quality goods
– i.e. they would say that the reduced difference in quality
between the two types of goods could no longer justify the
difference in price;
• To stop this the firm would have to reduce the price of the
higher quality goods – losing more revenue;
 The optimal menu accordingly has a socially suboptimal difference
in quality so as to maintain a greater difference in prices;
o A real-world example of this is air travel:
 Economy class is very uncomfortable;
 It could be made better for relatively low cost;

5
But by making it better some business class customers would ‘jump
ship’ to economy class1 thereby causing a serious loss of revenue;
 Hence economy class is uncomfortable in order to charge higher
prices to business class customers than would otherwise be
possible;
o In the case where the firm is not actually a monopolist, this effect is
attenuated by product/price competition which tends to undermine the
‘screening’ menu described above and create an incentive for firms to
introduce better services. In air travel, there is evidence that competition
has led to an improvement in quality of service and lower prices.
Models of Vertical Product Differentiation under Competition/Oligopoly
o As with Horizontal Product Differentiation, firms introduce Vertically
Differentiated Goods in order to avoid reducing price competition;
o Location models in Vertical Differentiation differ from those in Horizontal
Product Differentiation in the following way:
 Each consumer is located in a linear city with a parameter θ such
that their gross surplus in consuming a good of quality s is θs
 A consumer will consume the quality for which θs-ps (their net
surplus) is maximised where ps is the price of a good of quality s
 Hence, θ is the willingness to pay
o It is possible to obtain a Maximum Differentiation result even when cost is
costless
 Duopolists will locate at opposite ends of the quality spectrum in
order to avoid price differentiation;
 One firm will serve consumers with lower willingness to pay and the
other consumers with higher willingness to pay;
o The Maximum Differentiation result is dependent on willingness to pay
being sufficiently heterogeneous in the consumer population
 If this is not the case even with costless entry and constant returns
to scale, only one firm (the higher quality firm) will serve the entire
market and make supernormal profits;
 Hence, higher quality will drive low quality out when consumers are
not heterogeneous enough to support the number of firms;
o More generally, there will be a finite number of firms in a market with
Vertical Product Differentiation – even under these assumptions:
 Price competition amongst high quality firms will drive out the lowquality firms;
 This contrasts with the horizontal product differentiation models
where with zero-entry costs, the number of firms tends to infinity
(see the circular model below for an example of this phenomenon);

•
Social Efficiency of Product Differentiation
• The Social Optimum where aggregate Surplus is maximised. Aggregate Surplus
is the sum of:
1
Perhaps because they have more space now for their laptop
6
•
•
•
•
o Consumer Surplus; and
o Producer Surplus
Introducing new goods into the market affects aggregate surplus in three ways:
o The Surplus of the Producer making the entry is affected;
o Consumer Surplus is affected; and
o The Surplus of all other Producers is affected.
A rational firm will enter the market (or introduce a new product) if and only if it
does not make a loss – ie if its surplus either increases or remains the same.
o Hence we can assume that this effect is always nonnegative
The remaining two effects are externalities because the firm’s entry condition
(described above) does not care about consumers or other producers.
Introducing new products will typically have a nonnegative effect on consumer
surplus
o Consumers will then have a choice between the existing products and the
new products. Their surplus will remain the same if they consume the
existing products and may increase if they prefer the new goods (because
they prefer the new goods to the old goods for instance);
o In most realistic models of competition, introducing new goods will reduce
the price of other goods – this will also increase consumer surplus;
o Consumer surplus will only go down if the entry of new goods drives out
existing products to a sufficient extent by driving other firms into loss – this
is typically thought not to occur to a sufficient extent but may arise in some
borderline cases;
o Because firms do not care about consumer surplus when entering the
market, there is a positive externality to entry due to the nonapproproability of social surplus – this will lead to less entry than is socially
optimal;
o When there is only one producer introducing multiple products (ie a
multiproduct monopolist), this means that there will be fewer products than
is socially optimal;
•
Introducing new products will typically have a nonpositive effect on the surplus
of other producers
o Some consumers will switch from existing products to the new product;
o Prices may fall because of increased competition;
o This will reduce the profits of existing producers;
o Because firms do not care about the profits of their rivals, there is a
negative externality to entry due to business stealing or trade diversion;
o This will lead to over-entry;
•
In general, it is impossible to say which effect will dominate. Models of
monopolistic competition can be constructed in which either effect dominates.
Circular models of horizontal product differentiation
o A circular model of horizontal product differentiation is similar to Hotelling’s
model only the end points are removed by creating a circular city;
o In a circular model, each firm competes only with the firm to its left and the
firm to its right – i.e. the nearest two firms;
o An application of the circular model is to study the question of over-entry –
it answers the question Are there too many restaurants in a town?
•
7
o To answer this question, we no longer assume that the number of firms is
fixed but that entry continues until the zero-profit condition is satisfied;
 We typically assume that firms are located symmetrically;
 We assume that firms have fixed costs of entry – without this
assumption it is trivial to show that:
• There is marginal-cost pricing;
• Zero super-normal profits;
• Zero aggregate transport costs;
• Each consumer effectively has his own firm – this is not quite
the same as infinite entry but is pretty close;
• The number of firms is trivially shown to be optimal;
 Where there are fixed costs:
• There is not marginal-cost pricing – marginal-cost pricing
would lead to negative profits as the fixed costs would not be
covered – prices are higher than marginal costs;
• Prices lower until each firm covers its marginal-cost + the
fixed cost – hence this is a case (like in monopolistic
competition of non marginal-cost pricing with zero
supernormal profits);
• Each consumer has some transport cost – remember these
represent the degree to which the consumer must suffer for
having a less than perfect good – but these decrease as the
number of firms increase;
• The optimal number of firms depends on the fixed costs;
 Under linear or quadratic costs, too many firms will enter. This is
because increases in consumer surplus due to greater product
diversity (lower transport costs) occur more slowly than aggregate
fixed costs rise – trade diversion dominates.
8