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15

C

h

a

pt Optimal number of shops

er

7: • A consistent pattern is emerging.

P • Assume that there are n

o shops.

• They will be symmetrically located distance 1/n apart.

d

u How many

• We have already considered n = 2 and n = 3.

ct shops should

V • When n = 2 we have p(N, 2) = V - t/4 there be?

ar • When n = 3 we have p(N, 3) = V - t/6

e • It follows that p(N, n) = V - t/2n

y

a π(N,

• Aggregate profit is then n) = N(V - t/2n - c) – nF

n

d

Q

u

al

t

y

16

C

h

a

pt Optimal number of shops 2

er

7:

P π(N,

Profit from n shops is n) = (V - t/2n - c)N - nF

o and the profit from having n + 1 shops is:

d π*(N, n+1) = (V - t/2(n + 1)-c)N - (n + 1)F

u

ct Adding the (n +1)th shop is profitable

V π(N,n+1) π(N,n)

ar if - > 0

e This requires tN/2n - tN/2(n + 1) > F

y which requires that n(n + 1) < tN/2F.

a

n

d

Q

u

al

t

y

17

C

h

a

pt An example

er

7:

P Suppose that F = $50,000 , N = 5 million and t = $1

o Then tN/2F = 50

d

u For an additional shop to be profitable we need n(n + 1) < 50.

ct This is true for n < 6

V

ar There should be no more than seven shops in this case: if

e n = 6 then adding one more shop is profitable.

y But if n = 7 then adding another shop is unprofitable.

a

n

d

Q

u

al

t

y

18

C

h

a

pt Some intuition

er

7: • What does the condition on n tell us?

P • Simply, we should expect to find greater product variety

o when:

d – there are many consumers.

u

ct – set-up costs of increasing product variety are low.

V – consumers have strong preferences over product characteristics

ar and differ in these

e • consumers are unwilling to buy a product if it is not “very close”

to their most preferred product

y

a

n

d

Q

u

al

t

y

19

C

h

a

pt How much of the market to supply

er • Should the whole market be served?

7:

P – Suppose not. Then each shop has a local monopoly

– Each shop sells to consumers within distance r

o – How is r determined?

d • it must be that p + tr = V so r = (V – p)/t

u • so total demand is 2N(V – p)/t

ct π

• profit to each shop is then = 2N(p – c)(V – p)/t – F

V • differentiate with respect to p and set to zero:

ar • dπ/dp = 2N(V – 2p + c)/t = 0

e • So the optimal price at each shop is p* = (V + c)/2

• If all consumers are served price is p(N,n) = V – t/2n

y – Only part of the market should be served if p(N,n)< p*

a – This implies that V < c + t/n.

n

d

Q

u

al

t

y

20

C

h

a

pt Partial market supply

er

7: • If c + t/n > V supply only part of the market and set

P price p* = (V + c)/2

o • If c + t/n < V supply the whole market and set price

d p(N,n) = V – t/2n

u

ct • Supply only part of the market:

V – if the consumer reservation price is low relative to marginal

ar

e production costs and transport costs

– if there are very few outlets

y

a

n

d

Q

u

al

t

y

21

C

h

a Are there too

pt Social optimum many shops or

er too few?

7: What number of shops maximizes total surplus?

P Total surplus is consumer surplus plus profit

o

d Consumer surplus is total willingness to pay minus total revenue

u Profit is total revenue minus total cost

ct

V Total surplus is then total willingness to pay minus total costs

ar

e Total willingness to pay by consumers is N.V

y

a Total surplus is therefore NV - Total Cost

n

d So what is Total Cost?

Q

u

al

t

y

22

C

h

a

pt Social optimum 2

Assume that

er

7: there

P are n shops Price

Price Transport cost for

o each shop is the area

d V V

u of these two triangles

Consider shop

ct multiplied by

i

V consumer density

ar

e Total cost is t/2n t/2n

total transport

y

a cost plus set-up 1/2n 1/2n z = 1

z = 0

n costs Shop i

d

Q This area is t/4n2

u

al

t

y

23

C

h

a

pt Social optimum 3

er

7: Total cost with n shops is, therefore: C(N,n) = n(t/4n2)N + nF

P = tN/4n + nF

If t = $1, F = $50,000,

o

d N = 5 million then this

Total cost with n + 1 shops is: C(N,n+1) = tN/4(n+1)+ (n+1)F

u condition tells us

There should be five

ct Adding another shop is socially efficient if C(N,n + 1) < C(N,n)

that n(n+1) < 25

V shops: with n = 4 adding

ar another shop is efficient

This requires that tN/4n - tN/4(n+1) > F

e which implies that n(n + 1) < tN/4F

y

a

n The monopolist operates too many shops and, more

d generally, provides too much product variety

Q

u

al

t

y

24

C

h

a

pt Product variety and price discrimination

er

7: .

• Suppose that the monopolist delivers the product

P – then it is possible to price discriminate

o • What pricing policy to adopt?

d

u – charge every consumer his reservation price V

ct – the firm pays the transport costs

V

ar – this is uniform delivered pricing

e – it is discriminatory because price does not reflect costs

y

a

n

d

Q

u

al

t

y

25

C

h

a

pt Product variety and price discrimination

er

7: • Suppose that the monopolist delivers the product.

P – then it is possible to price discriminate

o • What pricing policy to adopt?

d

u – charge every consumer his reservation price V

ct

V – the firm pays the transport costs

ar – this is uniform delivered pricing

e – it is discriminatory because price does not reflect costs

y

a

n

d

Q

u

al

t

y

26

C

h

a

pt Product variety and price discrimination 2

er

7: • Should every consumer be supplied?

P – suppose that there are n shops evenly spaced on Main Street

o – cost to the most distant consumer is c + t/2n

d – supply this consumer so long as V (revenue) > c + t/2n

u

ct • This is a weaker condition than without price

V discrimination.

ar • Price discrimination allows more consumers to be

e served.

y

a

n

d

Q

u

al

t

y

27

C

h

a

pt Product variety & price discrimination 3

er

7: • How many shops should the monopolist operate now?

P — Suppose that the monopolist has n shops and is supplying

o the entire market.

d — Total revenue minus production costs is NV – Nc

u — Total transport costs plus set-up costs is C(N, n)=tN/4n + nF

ct π(N,n)

— So profit is = NV – Nc – C(N,n)

V — But then maximizing profit means minimizing C(N, n)

ar

e — The discriminating monopolist operates the socially

optimal number of shops.

y

a

n

d

Q

u

al

t

y

28

C

h

a

pt Monopoly and product quality

er

7: • Firms can, and do, produce goods of different qualities

P • Quality then is an important strategic variable

o • The choice of product quality determined by its ability to

d generate profit; attitude of consumers to q uality

u • Consider a monopolist producing a single good

ct –

V what quality should it have?

ar – determined by consumer attitudes to quality

e • prefer high to low quality

• willing to pay more for high quality

y • but this requires that the consumer recognizes quality

a • also some are willing to pay more than others for quality

n

d

Q

u

al

t

y

29

C

h

a

pt Demand and quality

er

7: • We might think of individual demand as being of the form

P – Qi = 1 if Pi < Ri(Z) and = 0 otherwise for each consumer i

o – Each consumer buys exactly one unit so long as price is less

d than her reservation price

u – the reservation price is affected by product quality Z

ct

V • Assume that consumers vary in their reservation prices

ar • Then aggregate demand is of the form P = P(Q, Z)

e • An increase in product quality increases demand

y

a

n

d

Q

u

al

t

y

30

C

h

a

pt Demand and quality 2

er

7: Begin with a particular demand curve

P for a good of quality Z1

Price Then an increase in product

o R1(Z2 Suppose that an increase in

quality from Z1 to Z2 rotates

P(Q, Z2)

d ) quality increases the

the demand curve around

u If the price is P1 and the product quality

willingness to pay of

the quantity axis as follows

ct is Z1 then all consumers with reservation

inframarginal consumers more

P2

V prices greater than P1 will buy the good

than that of the marginal

R1(Z1)

ar Quantity Q1 can now be

consumer

e This is the

These are the

P1 sold for the higher

marginal

inframarginal

y price P2

consumer

consumers

a

n P(Q, Z1)

d

Q Q1 Quantity

u

al

t

y

31

C

h

a

pt Demand and quality 3

er

7:

P Suppose instead that an

Price Then an increase in product

increase in

o quality from Z1 to Z2 rotates

quality increases the

d the demand curve around

willingness to pay of marginal

u the price axis as follows

consumers more

ct than that of the inframarginal

V R1(Z1) consumers

ar Once again quantity Q1

e P P1 can now be sold for a

2

y higher price P2

a P(Q, Z2)

n P(Q, Z1)

d

Q Q1 Quantity

u

al

t

y

32

C

h

a

pt Demand and quality 4

er

7: • The monopolist must choose both

P – price (or quantity)

– quality

o

d • Two profit-maximizing rules

u – marginal revenue equals marginal cost on the last unit sold for

ct a given quality

V – marginal revenue from increased quality equals marginal cost

ar of increased quality for a given quantity

e • This can be illustrated with a simple example:

y P = Z(θ - Q) where Z is an index of quality

a

n

d

Q

u

al

t

y

33

C

h

a

pt Demand and quality 5

er

7: P = Z(θ - Q)

P Assume that marginal cost of output is zero: MC(Q) = 0

o αZ2

Cost of quality is C(Z) =

d

u Marginal cost of quality = dC(Z)/d(Z)

ct = 2αZ This means that quality

V costly and becomes

ar The firm’s profit is:

e increasingly costly

π(Q, αZ2

Z) =PQ - C(Z) = Z(θ - Q)Q -

y

a

n

d

Q

u

al

t

y

34

C

h

a

pt Demand and quality 6

er

7: Again, profit is:

P π(Q, αZ2

Z) =PQ - C(Z) = Z(θ - Q)Q -

o

d The firm chooses Q and Z to maximize profit.

u Take the choice of quantity first: this is easiest.

ct

V Marginal revenue = MR = Zθ -

ar 2ZQ

e ⇒ ⇒ θ/2

MR = MC Zθ - 2ZQ = 0 Q* =

y ∴ P* = Zθ/2

a

n

d

Q

u

al

t

y

35

C

h

a

pt Demand and quality 7

er

7: Total revenue = P*Q* = (Zθ/2)x(θ/2) = Zθ2/4

P So marginal revenue from increased quality is

o θ2/4

MR(Z) =

d Marginal cost of quality is

u

ct MC(Z) = 2αZ

V Equating MR(Z) = MC(Z) then gives

ar

e θ2/8α

Z* =

y Does the monopolist produce too high or too low quality?

a

n

d

Q

u

al

t

y

36

C

h

a

pt Demand and quality: multiple products

er

7: • What if the firm chooses to offer more than one

P product?

o – what qualities should be offered?

d

u – how should they be priced?

ct • Determined by costs and consumer demand

V

ar

e

y

a

n

d

Q

u

al

t

y

37

C

h

a

pt Demand and quality: multiple products 2

er

7: • An example:

P – two types of consumer

o – each buys exactly one unit provided that consumer surplus is

d nonnegative

u – if there is a choice, buy the product offering the larger

ct consumer surplus

V

ar – types of consumer distinguished by willingness to pay for

e quality

• This is vertical product differentiation

y

a

n

d

Q

u

al

t

y

38

C

h

a

pt Vertical differentiation

er

7: • Indirect utility to a consumer of type i from consuming a

P θi(z

product of quality z at price p is Vi = – zi) – p

θi

– where measures willingness to pay for quality;

o – zi is the lower bound on quality below which consumer type i

d will not buy

u θ1 θ2:

– assume > type 1 consumers value quality more than type

ct 2

V – assume z1 > z2 = 0: type 1 consumers only buy if quality is

ar greater than z1:

e • never fly in coach

• never shop in Wal-Mart

y • only eat in “good” restaurants

– type 2 consumers will buy any quality so long as consumer

a surplus is nonnegative

n

d

Q

u

al

t

y

39

C

h

a Vertical differentiation 2

pt

er • Firm cannot distinguish consumer types

7:

P • Must implement a strategy that causes consumers to self-

select

o – persuade type 1 consumers to buy a high quality product z1 at a

d

u high price

ct – and type 2 consumers to buy a low quality product z2 at a lower

V price, which equals their maximum willingness to pay

ar z, z

e • Firm can produce any product in the

range

y • MC = 0 for either quality type

a

n

d

Q

u

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t

y


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DESCRIZIONE DISPENSA

Materiale didattico per il corso di Impresa, management e mercati della prof.ssa Ornella Tarola. Trattasi di slides aventi ad oggetto il tema della qualità e della varietà dei prodotti venduti in regime di monopolio ed in particolare: la differenziazione orizzontale e la differenziazione verticale, la discriminazione in base al prezzo, e la competizione imperfetta.


DETTAGLI
Corso di laurea: Corso di laurea magistrale in scienze delle pubbliche amministrazioni
SSD:
A.A.: 2011-2012

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher Atreyu di informazioni apprese con la frequenza delle lezioni di Impresa management e mercati e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università La Sapienza - Uniroma1 o del prof Tarola Ornella.

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