Transcript Economics of Management Strategy BEE3027

Economics of Management Strategy
BEE3027
Lecture 6
07/03/2008
Recap
• In the last couple of weeks we looked at some
sophisticated strategies firms may employ to
extract surplus from consumers.
– Non-linear pricing;
– Seasonal or peak-load pricing.
• Sometimes these pricing tactics are harmful to
consumers, but sometimes they are beneficial,
as they allow low-valuation consumers to be
served.
Quality
• This week we look at the concepts of product
differentiation and quality.
• We will look at how we can model product
differentiation through a “location” decision.
• We will look a particular aspect of quality,
durability;
Product Differentiation
• One of the most obvious ways a firm can gain
market power is to differentiate itself from its
competitors.
• This can be done via:
– Different type of technology: Windows vs. Mac
– Brand loyalty;
– Target demographics
Product Differentiation
• We will focus today on modelling such
decisions through a model of location.
• Consider the case of set of consumers whose
preferences can be described as different
points on a line.
Product Differentiation
• Consider two firms, A and B which can pick
where they want to settle on the line:
• Consumers must consider two things:
– The price each firm charges;
– The cost of “travelling” to each firm.
Product Differentiation
• Consumers to the left of A will only purchase
from A;
• Consumers to the right of B will only purchase
from B.
Product Differentiation
• Let’s consider some consumer who is located
between A and B:
• Assume he is indifferent between the two firms.
– Let his location be given by
• This means:
Product Differentiation
• Solving for x^ gives the demand for firm A:
• The demand for firm B is given by L – x^:
Product Differentiation
• Firms will maximise profits given their choice of
location and demand functions:
Product Differentiation
• Solving for the equilibrium price and quantity
gives:
• If a = b, firms split the market between them, as
well as profits. Firm A’s profit is then equal to:
Product Differentiation
• Prices and profits increase with:
– The distance between the two firms (a-b);
– The consumers’ cost of “travelling”, T
• In fact, firms have an explicit incentive to make
these costs as high as possible.
Product Differentiation
• What if we allow for firms to pick their locations
in addition to their prices?
• The answer to this problem is rather technical;
– In particular, it hinges on how costly it is for
consumers to “travel”.
• Hotelling (1929) assumed consumers have
linear costs of travel.
Product Differentiation
• In this case, firms have an incentive to move
towards each other;
– Since they share the consumers lying between
them, moving to the centre makes their exclusive
section of the market bigger.
• However, once they are together in the centre,
a=b;
– Hence, Pa = Pb = 0!
– Therefore, both firms have an incentive to deviate!
– As a result, there is no equilibrium in pure strategies
Product Differentiation
• D’Aspremont et al (1979) showed that if costs
of “travelling” are quadratic, firms have the
opposite incentive.
– Now firms wish to be as far away as possible from
each other.
– Hence, in the two player case, firms would locate at
the two ends of the line.
– With more than two players equilibria become more
difficult to compute.
Product Differentiation
Durability
• So far, when we dealt with models of oligopoly,
we haven’t worried too much about the goods
themselves.
• Implicitly we assumed that their consumption is
immediate, hence demand is constant.
• However, a lot of goods we purchase have a
long shelf-life, such that we don’t need to buy
the good again for a while.
Durability
• A question is then, what is the optimal durability
of a given good? Does it depend on market
structure?
• Early economists argue that a monopolist would
be willing to reduce the durability of the good if
demand was sufficiently inelastic.
Durability
• However, Swan (1970) showed that the choice of
durability of a particular product is completely
independent of market structure.
• His argument is as follows:
• Consider a firm which produces 2 types of light bulbs:
long-duration (2 periods) and short-duration (1 period).
• Also consider a consumer who values light at $V per
period.
Durability
• The cost of producing a short-duration light bulb
is Cs;
• The cost of producing a short-duration light bulb
is Cl;
• Assume that for production to be profitable the
following hold:
– 0 < Cs < V, 0 < Cl < 2V, Cs < Cl
Durability
• What type of bulb should a monopolist sell?
• If the monopolist chooses short-lasting bulbs,
the maximum price it can set is p = V.
• In this case, it will sell two units, one in each
period.
• Hence, its profits will be equal to:
–Πs = 2 (V - Cs)
Durability
• If the monopolist chooses long-lasting bulbs,
the maximum price it can set is p = 2V.
• In this case, it will sell one units, which will last
two periods.
• Hence, its profits will be equal to:
–Πl = 2V - Cl
Durability
• Clearly, the monopolist will only produce shortlasting bulbs if it is more profitable to do so:
–Πs > Πl → 2(V – Cs) > 2V – Cl
– 2 Cs > Cl
Durability
• What would happen in a competitive market?
• In that case, P=MC for both types of bulbs:
– Pl = Cl and Ps = Cs
• The consumer will buy the short-lived bulbs as
long as it is a better deal:
– 2 (V – Ps) > 2V - Pl → 2 Ps > Pl ↔ 2 Cs > Cl !!!
Durability
• In other words, this model states that the
durability of a product will ultimately depend on
production costs, rather than any market
factors.
– However, note the consumer here only cares about
length of service and not durability per se.
– Hence, he’d be indifferent between pay £3 for a
light bulb that lasts 30 days and buying 30 bulbs
that last one day! Is this realistic?