Economics of Management StrategyBEE3027

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 short-lasting 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?