Chapter 2: Product Selection and Quality Relax A1. The goods - - PDF document

Chapter 2: Product Selection and Quality

Relax A1. The goods produced by the monopolist are not given.

• A2. No price discrimination.
• Choice of quality and pricing behavior by a

monopolist.

• Consumers can learn the quality before purchasing

(search goods), – too low of too high quality relative to social

• ptimum?

– too much or too little product variety?

• Consumers can learn the quality after purchasing

(experience goods), – what are the incentives of the monopolist to supply quality? – How to provide information to consumers? 1

1 Product Space

• Goods are always differentiated by some charac-

teristics.

• There are always interactions between groups of

goods.

• What is the differentiation between the goods within

an industry? Hotelling (1929), Chamberlin (1952, 1962)

• A good is a bundle of characteristics: quality,

location, availability, consumer’s information about its existence, its quality..... 2 types of differentiation:

• 1. vertically differentiated product space = quality;
• 2. horizontally differentiated product space = location.

2

1.1 Vertical Differentiation

• All consumers agree over the most preferred mix of

characteristics.

• Higher quality is preferred to lower quality (BMW

is preferred to Subaru). Model of vertical differentiation

• single quality/good monopolist.
• Each consumer consumes 0 or 1 unit of a good.
• N consumers.
• s: quality index (service), s > 0.
• A consumer has the following preferences

u = ( θs − p if he buys the good of quality s at price p

if he does not buy where θ > 0 is a taste parameter.

• θ, density f(θ), a cumulative distribution F(θ) ∈

[0, 1] and F(0) = 0 and F(∞) = 1.

• F(θ): fraction of consumers with a taste parameter

< θ.

3

What are the demand functions?

• 1. If 1 quality s at price p, the demand is

D(p) = N[1 − F(p s)]

• 2. If 2 qualities: s1 < s2 and that prices are p1 < p2,

different cases:

• if s2

p2 ≥ s1 p1, then demands are

D2(p1, p2) = N[1 − F(p2 s2 )] D1(p1, p2) = 0

• If low quality good is not dominated. e

θ = p2−p1

s2−s1:

indifferent consumer. – Consumers with θ ≥ e

θ buy quality 2.1−F(p2−p1

s2−s1):

proportion of consumers who buy quality 2. – Consumers with θ < e

θ and θ ≥ p1

s1 buy quality 1.

Thus F(p2−p1

s2−s1) − F(p1 s1): proportion of consumers

who buy quality 1. – if θ < p1

s1 no purchase.

D2(p1, p2) = N[1 − F(p2 − p1 s2 − s1 )] D1(p1, p2) = N[F(p2 − p1 s2 − s1 ) − F(p1 s1 )]

4

1.2 Horizontal Differentiation

• Spatial differentiation: location.

Model of Hotelling (1929)

• Linear city of length 1.
• N consumers are distributed uniformly along the

city.

• 2 shops are located at the 2 ends of the city, shop 1

is at x = 0 and of shop 2 is at x = 1.

• Both sell the same physical good.
• Consumers have transportation costs t per unit of

length.

• They consume either 0 or 1 unit of the good.
• p1 and p2 are the prices charged by the 2 shops.
• Price of going to shop 1 for a consumer at x is

p1 + tx.

• Price of going to shop 2 for a consumer at x

p2 + t(1 − x).

• The utility of a consumer located at x is

5

U = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ s − p1 − tx

if he buys from shop 1

s − p2 − t(1 − x) if he buys from shop 2

• therwise

What are the demands?

• 1. If p2 − p1 < t, and prices are not too high

– There exists an indifferent consumer located at

e x(p1, p2) = p2−p1+t

2t

. Thus demands are

D1(p1, p2) = Ne x(p1, p2) D2(p1, p2) = N(1 − e x(p1, p2))

– See graph

• 2. If p2 − p1 > t, shop 2 has no demand.

D1(p1, p2) = N

if p1 < s − t

D1(p1, p2) = N s−p1

t

if p1 > s − t – See graph

• 3. If p1 and p2 belong to [s − t, s],

– 2 local monopolies 6

– the indifferent consumer does not consume

D1(p1, p2) = N s − p1 t D2(p1, p2) = N s − p2 t

– See graph

• Residual demand for good 1, as price of good is

given has a kink (see graph). Remark 1 Endogenous transportation costs: Dos San- tos Ferreira and Thisse (1996), IJIO. 7

2 Product Selection

• Spence (1975, 1976)

2.1 Single-product Monopolist

• Monopolist chooses p and s.
• p = P(q, s): inverse demand function, ∂P(.)

∂s > 0,

• C(q, s): cost function, ∂C(.)

∂s > 0.

• 1. Social planner maximizes the gross consumers

surplus minus cost, W(q, s)

Max

q,s

Z q P(x, s)dx − C(q, s) FOCq P(q, s) = ∂C(q,s)

∂q

(price=MC)

FOCs R q

∂P(x,s) ∂s

dx = ∂C(q,s)

∂s

⇒ q

R q

∂P(x,s) ∂s

dx q

= ∂C(q,s)

∂s R q

∂P(x,s) ∂s

dx q

average marginal valuation of quality. 8

• 2. Monopolist maximizes his profit function Πm(q, s)

Max

q,s

qP(q, s) − C(q, s) FOCq q∂P(q,s)

∂q

+ P(q, s) = ∂C(q,s)

∂q

(MR=MC)

FOCs q∂P(q,s)

∂s

= ∂C(q,s)

∂s

(MR=MC)

• 3. Comparison:
• Quantities and prices: usual inefficiencies, pm >

MC.

• Quality:

– the social planner is concerned about the average marginal value of quality, – the monopolist is concerned with the marginal (consumer) marginal (quality) valuation.

• Why?

– The social planner looks at the effect of an increase in quality on all consumers. – The monopolist considers the effect of an increase

• f quality on the marginal consumer.

9

Summary The incentive to provide quality is related to the marginal willingness to pay for quality for the marginal consumer in the case of the monopolist, and for the average consumer in the case of the social planner. Result 1 For a given output level, the monopolist undersupplies quality relative to the optimum when

R q

∂P(x,s) ∂s

dx q

> ∂P(q,s)

∂s

and conversely. 2.1.1 Example of underprovision of quality

• Vertical differentiation model
• Utility is

u = ( θs − p if he buys the good of quality s at price p

if he does not buy

• θ, f(θ), F(θ) ∈ [0, 1] and F(0) = 0 and F(∞) = 1.
• Normalization: N = 1.
• If only one quality s at price p, the demand is

D(p) = [1 − F(p

s)] and the inverse demand function

10

is

p = P(q, s) = sF −1(1 − q) F −1(.) (increasing) inverse function of F.

• Average marginal valuation for quality (social

planner)

1 q

R q

∂P(x,s) ∂s

dx = 1

q

R q

0 F −1(1 − x)dx

• Marginal marginal valuation for quality (monopolist)

∂P(q,s) ∂s

= F −1(1 − q)

• As x ≤ q, ⇒ F −1(1 − x) > F −1(1 − q) and thus

R q

0 F −1(1 − x)dx > qF −1(1 − q)

⇒ Average valuation for quality > marginal

valuation.

• For a given q, the monopolist undersupplies quality.
• But it is not clear that the quality of the monopoly is

lower, because quantities and prices are different!

• See exercise 22 page 104: θ ∼ U[0,1] and the cost

function is C(q, s) = cs2

2 q

11

2.2 Multi-product Monopolist

• Too many or too few products?

2.2.1 Single-product monopolist and underprovi- sion

• f fixed cost of introducing (or producing) the good.
• Monopolist introduces the good only if Πm > f.
• Social planner introduces the good if W > f.
• As W > Πm, there exit values of f such that

W > f > Πm

and thus – the monopolist does not introduces the good – the social planner would do it. Result 2 With only one potential product, a monopoly situation may imply too few products. Why?

• In general a monopolist cannot appropriate all the

social surplus.

• Except if he can price-discriminate (Chapter 3).

12

2.2.2 Multi-product monopolist and overprovision

• 2 goods are substitutes, ∂Dj

∂pi > 0, i 6= j and i = 1, 2.

• The monopolist sets p1 > MC1, thus demand for

good 2 increases.

• It is thus profitable to produce good 2 which would

not be profitable if p1 = MC1. Exercise 2.3

• Horizontal differentiation model
• linear city of length 1; consumers are uniformly
• distributed. N = 1.
• transportation cost: t.
• Unit demands.
• Product diversity: monopolist can sell at: x = 0 and

x = 1.

• f fixed set-up cost of establishing one store.
• MC = 0.
• What is the benefit to open a second shop?

– If the monopolist opens 1 shop, he sets the price

p = s − t, and profit is s − t − f

13

– If he opens 2 shops, the price increases to s − 1

2t,

and profit is s − 1

2t − 2f

– Thus the increase in profit of adding one shop is

∆Π = 1 2t − f

– Social planner: minimizes costs (transportation costs and set-up costs) – If 1 shop, the cost is R 1

0 txdx + f

– If 2 shops, the cost is 2

R 1

2

0 txdx + 2f

– Thus the gain of adding one shop is

∆W = 1 4t − f

• Comparison:

– for 1

4t < f < 1 2t the monopolist opens the second

shop whereas it is not socially optimal to do so.

2.3 Product Selection and Discrimina- tion

• Monopolist can discriminate: sell at a higher price

to consumers with high valuation.

• Cons. have no incentive to reveal high valuation.

14

3 Quality and Information

3 kinds of goods:

• 1. Search goods - quality can be learned before a

purchase (example: dress)

• 2. Experience goods - quality can be learned after a

purchase (example: food)

• 3. Credence goods - quality can never be learned

(example: doctor intervention) Main issues for

• 1. Search goods - product selection (quality and

product diversity)

• 2. Experience goods - information:

– How do consumers learn the quality? – What incentives do firms have to supply quality?

• 3. Credence goods - information; requires government

intervention. 15

Warranty goods

• full warranty ⇔ search goods: if buyers are fully

compensated - no need to learn before.

• Firms have incentive to give full warranty to signal

quality.

• But in general, the warranty system does not exist or

is imperfect.

• if quality = durability, and depends also on con-

sumers, problem of moral hazard on the consumer side.

• Limited warranty.

16

3.1 One-shot Relationship

• No warranty
• experience goods

3.1.1 Moral Hazard on the producer side

• one-shot purchasing
• Example: food in restaurants in some tourist areas....

Model

• consumers are all identical; N = 1
• demand is 0 or 1
• Utility is

u = ( θs − p if they buy the good

if they do not buy

• Monopolist chooses p and s.
• Unit cost of production is cs for quality s

– high quality, s = 1, c1 > 0; – low quality, s = 0, c0 ∈ [0, c1].

• Assumption: θ > c1.

17

• Monopolist profit is

Πm = ( p − cs if he sells quality s at price p

• therwise
• 1. Consumers do not observe quality before purchas-

ing. – What is the equilibrium?

∗ The monopolist chooses s = 0 and p0 = 0 if c0 = 0. This is an equilibrium. ∗ If c0 > 0, the market disappears.

• 2. Some consumers learn information related to quality

(Example: they read consumers reports).

• α: fraction of informed consumers. They are willing

to pay θ for s = 1, and 0 otherwise.

• (1 − α) observe the quality only after they purchase.
• The monopolist charges a price p ∈ [0, θ].
• Informed consumers

– buy if quality is high, – don’t buy otherwise.

• Profit of the monopolist α(p − c1) if informed

18

consumers buy.

• Behavior of non-informed consumers?
• a. Suppose they do not buy.

– Demand comes from the informed consumers. Thus, monopolist chooses s = 1 as long as

p ≥ c1.

– But non informed consumers should expect high quality, and thus buy. CONTRADICTION

• b. Suppose they buy. Profit of monopolist

p − c1

if high quality

(1 − α)(p − c0) if low quality

– Monopolist chooses s = 1 if

p − c1 > (1 − α)(p − c0) ⇒ αp > c1 − (1 − α)c0

– Thus monopolist supplies high quality if

∗ high price; signal of good quality ∗ high fraction of informed consumers.

Result The informed consumers exert a positive externality on the uninformed consumers. 19

3.1.2 The Lemons Problem (Akerlof (1970))

• Quality is given.

Model

• Robinson Crusoe: monopoly owner of a goat,
• Friday: potential purchaser.
• s quality of the goat (amount of milk produce daily);

private information.

• Trade of the goat (not the milk)
• Surplus of Robinson

θ1s if he keeps the goat p

if he sells it

• Surplus of Friday

θ2s if he buys the goat

• therwise
• Assume: θ2 > θ1, i.e. Friday’s marginal valuation

for quality exceeds Robinson’s.

• Thus trading is Pareto optimal regardless of s.
• Friday has only prior beliefs: s ∼ U[0,smax]

20

• Friday is risk neutral, this his objective function is

θ2sa − p

where sa= expected quality if offered for sale.

• Suppose there a price p < θ1smax such that trade

takes place.

• If Robinson is willing to sell his goat at price p, the

quality must be p > θ1s ⇒ s < p

θ1.

• The average expected quality is

sa(p) = 1 2 p θ1

• Thus sa(p) < 1
• 2smax. Adverse selection problem, or

lemons problem.

• Friday accepts to buy only if

θ2sa(p) > p ⇒ θ2 > 2θ1

• If tastes do not differ that much (θ2 < 2θ1) ⇒ the

market disappears!

• Only if tastes are such that θ2 > 2θ1, there exists an

equilibrium price.

• How to attenuate this problem?

– repeat purchasing 21

– warranty – multidimentional contracts 22

3.2 Repeat Purchases

• The quality of the good may remain the same over

time. – Past consumption brings direct information on quality. – High quality producer gets consumers to try the product; – Low price in first period can signal high quality.

• The quality may change over time.

– The repeated purchases mechanism must operate in an indirect way. – Model of reputation.

• Sketch of important ideas for unalterable quality:

– a high quality producer is more willing to sacrifice current profits (charge a low price) to attract consumers. – a low quality product for a given price yields high profit due to low production cost. 23

3.3 Quality, information and public policy

• What the government can do?
• subsidize information;
• information requirements (labelling);
• minimum health and safety requirements.

24

4 Conclusion

• Search goods

– a monopolist chooses the characteristics of the good in a suboptimal way (consider marginal rather than average consumer). – Product quality can be oversupplied or under- supplied (model dependent). – Product diversity: – if one product: the monopolist does not introduce it even thought it is socially efficient to do so. – if more than one product: too many products can be introduced.

• Experience goods

– quality tends to be undersupplied (moral hazard problem). – Consumers information may alleviate the infor- mation problem. 25