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8

C

h

a Suppose the firm

pt The spatial model 2

er reduces the price

Price Price

7: to p2?

p1 + t.x p1 + t.x

P V V

o

d

u Then all consumers p1

ct within distance x2

V p2

of the shop will buy

ar

e from the firm

y

a z = 0 x2 x1 x1 x2 z = 1

1/2

n Shop 1

d

Q

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9

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a

pt The spatial model 3

er

7: • Suppose that all consumers are to be served at price p.

P – The highest price is that charged to the consumers at the ends of

o the market

d – Their transport costs are t/2 : since they travel ½ mile to the shop

u – So they pay p + t/2 which must be no greater than V.

ct

V – So p = V – t/2.

ar • Suppose that marginal costs are c per unit.

e • Suppose also that a shop has set-up costs of F.

y π(N,

• Then profit is 1) = N(V – t/2 – c) – F.

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10

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pt Monopoly pricing in the spatial model

er

7: • What if there are two shops?

P • The monopolist will coordinate prices at the two shops

o • With identical costs and symmetric locations, these prices

d

u will be equal: p1 = p2 = p

ct – Where should they be located?

V – What is the optimal price p*?

ar

e

y

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11

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pt Location with two shops

Delivered price to

er consumers at the

7: Suppose that the entire market is to be served

market center equals

P their reservation price

Price Price

If there are two shops

o they will be located

d V V

u symmetrically a

ct distance d from the p(d)

p(d)

V The maximum price

end-points of the

ar the firm can charge

market What determines

e is determined by the p(d)?

Now raise the price

consumers at the

at each shop

y Start with a low price

center of the market

a at each shop d 1/2 1 - d

z = 0 z = 1

n Shop 1 Shop 2

d Suppose that

Q The shops should be

u d < 1/4 moved inwards

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12

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a

pt Delivered price to

Location with two shops 2

er consumers at the

7: end-points equals

The maximum price

P their reservation price

the firm can charge Price Price

is now determined

o by the consumers

d V V

at the end-points

u of the market

ct p(d)

p(d)

V

ar Now what

e determines p(d)?

Now raise the price

at each shop

y Start with a low price

a at each shop d 1/2 -

z = 0 1 d z = 1

n Shop 1 Shop 2

d Now suppose that

Q The shops should be

u d > 1/4 moved outwards

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t

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13

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a

pt Location with two shops 3

It follows that

er shop 1 should Price at each

7: be located at shop is then

P Price Price

1/4 and shop 2 p* = V - t/4

o at 3/4

d V V

u

ct V - t/4

V - t/4

V Profit at each shop

ar is given by the

e c

c

shaded area

y

a z = 0 1/4 1/2 3/4 z = 1

n Shop 2

Shop 1

d

Q π(N,

Profit is now 2) = N(V - t/4 - c) – 2F

u

al

t

y

14

C

h

a By the same argument

pt Three shops they should be located

er What if there at 1/6, 1/2 and 5/6

7: are three shops?

P Price Price

o

d V V

u Price at each V - t/6 V - t/6

ct shop is now

V

ar V - t/6

e

y

a z = 0 1/6 1/2 5/6 z = 1

n Shop 1 Shop 2 Shop 3

d

Q π(N,

Profit is now 3) = N(V - t/6 - c) – 3F

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15

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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

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16

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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.

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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.

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18

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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

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d

Q

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19

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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

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20

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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

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d

Q

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21

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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

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22

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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

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23

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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

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y

24

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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

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25

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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

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26

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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

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d

Q

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27

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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

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28

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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

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29

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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

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30

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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

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31

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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

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32

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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

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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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