Chapter 4
Product and Pricing Strategies
for the
Multiproduct Monopolist
Industrial Organization: Chapter 4
1
Introduction
• A monopolist can offer goods of different varieties
– multiproduct firms
• The “big” issues:
– pricing
– product variety: how many?
– product bundling:
• how to bundle
• how to price
• whether to tie the sales of one product to sales of another
• Price discrimination
Industrial Organization: Chapter 4
2
4-1
Price Discrimination
• This is a natural phenomenon with multiproduct firms
– restaurant meals: table d’hôte or à la carte
– different varieties of the same car
– airline travel
• “goods” of different quality are offered at very different prices
• Note the constraints
– arbitrage
• ensuring that consumers buy the “appropriate” good
– identification
• How to price goods of different quality?
Industrial Organization: Chapter 4
3
Price discrimination and quality
• Extract all consumer surplus from the low quality good
• Use screening devices
– Set the prices of higher quality goods
• to meet incentive compatibility constraint
• to meet the constraint that higher price is justified by higher quality
• One interesting type of screening: crimping the product
– offer a product of reasonably high quality
– produce lower quality by damaging the higher quality good
• student version of Mathematica
• different versions of Matlab
• the “slow” 486SX produced by damaging the higher speed 486DX
– why?
• for cost reasons
Industrial Organization: Chapter 4
4
A Spatial Approach to Product Variety
• Approach to product quality in Chapter 3 is an example of
vertical product differentiation
– products differ in quality
– consumers have similar attitudes to quality: value high quality
• An alternative approach
– consumers differ in their tastes
– firm has to decide how best to serve different types of consumer
– offer products with different characteristics but similar qualities
• This is horizontal product differentiation
Industrial Organization: Chapter 4
5
A Spatial Approach to Product Variety (cont.)
• The spatial model (Hotelling) is useful to consider
– pricing
– design
– variety
• Has a much richer application as a model of product
differentiation
– “location” can be thought of in
• space (geography)
• time (departure times of planes, buses, trains)
• product characteristics (design and variety)
Industrial Organization: Chapter 4
6
A Spatial Approach to Product Variety (cont.)
• Assume N consumers living equally spaced along Main
Street – 1 mile long.
• Monopolist must decide how best to supply these
consumers
• Consumers buy exactly one unit provided that price plus
transport costs is less than V.
• Consumers incur there-and-back transport costs of t per
unit
• The monopolist operates one shop
– reasonable to expect that this is located at the center of Main Street
Industrial Organization: Chapter 4
7
The spatial model
Price
Suppose that the monopolist Price
sets a price of pp11 + t.x
p1 + t.x
V
V
All consumers within
distance x1 to the left
and right of the shop
will by the product
x=0
t
t
p1
x1
1/2
What determines
x1?
x1
x=1
Shop 1
p1 + t.x1 = V, so x1 = (V – p1)/t
Industrial Organization: Chapter 4
8
The spatial model
Price
p1 + t.x
p1 + t.x
Suppose the firm
reduces the price
to p2?
V
Then all consumers
within distance x2
of the shop will buy
from the firm
x=0
Price
V
p1
p2
x2
x1
1/2
x1
x2
x=1
Shop 1
Industrial Organization: Chapter 4
9
The spatial model
• Suppose that all consumers are to be served at price p.
– The highest price is that charged to the consumers at the ends of
the market
– Their transport costs are t/2 : since they travel ½ mile to the shop
– So they pay p + t/2 which must be no greater than V.
– So p = V – t/2.
• Suppose that marginal costs are c per unit.
• Suppose also that a shop has set-up costs of F.
• Then profit is p(N, 1) = N(V – t/2 – c) – F.
Industrial Organization: Chapter 4
10
Monopoly Pricing in the Spatial Model
• What if there are two shops?
• The monopolist will coordinate prices at the two shops
• With identical costs and symmetric locations, these prices
will be equal: p1 = p2 = p
– Where should they be located?
– What is the optimal price p*?
Industrial Organization: Chapter 4
11
Location with Two Shops
Suppose that the entire market is
Price
If there are two shops
they will be located
V
symmetrically a
distance d from the
The
maximumofprice
end-points
the p(d)
the firmmarket
can charge
is determined
Now raisebythethe
price
consumers
at the
at each
shop
Start
with
a
low
center of the marketprice
at each shop
Suppose that
d < 1/4
Delivered price to
consumers
to be
servedat the
market center equals
their reservation price Price
V
p(d)
What determines
p(d)?
x=0
d
Shop 1
1/2
1-d
Shop 2
x=1
The shops should be
moved inwards
Industrial Organization: Chapter 4
12
Location with
Delivered
Twoprice
Shops
to
consumers at the
end-points equals
their reservation price
The maximum price
the firm can charge
is now determined
by the consumers
at the end-points
of the market
Price
Price
V
V
p(d)
p(d)
Now raise the price
at each shop
Start with a low price
at each shop
Now what
determines p(d)?
x=0
Now suppose that
d > 1/4
d
Shop 1
1/2
1-d
Shop 2
x=1
The shops should be
moved outwards
Industrial Organization: Chapter 4
13
It follows that
shop 1 should
be located at
1/4 and shop 2
at 3/4
Location with Two Shops
Price at each
shop is then
p* = V - t/4
Price
Price
V
V
V - t/4
V - t/4
Profit at each shop
is given by the
shaded area
c
c
x=0
1/4
Shop 1
1/2
3/4
Shop 2
x=1
Profit is now p(N, 2) = N(V - t/4 - c) – 2F
Industrial Organization: Chapter 4
14
Three Shops
What if there
are three shops?
By the same argument
they should be located
at 1/6, 1/2 and 5/6
Price
Price
V
Price at each
shop is now
V - t/6
V
V - t/6
V - t/6
x=0
1/6
Shop 1
1/2
Shop 2
5/6
x=1
Shop 3
Profit is now p(N, 3) = N(V - t/6 - c) – 3F
Industrial Organization: Chapter 4
15
Optimal Number of Shops
• A consistent pattern is emerging.
Assume that there are n shops.
They will be symmetrically located distance 1/n apart.
We have already considered n = 2 and n = 3. How many
shops should
When n = 2 we have p(N, 2) = V - t/4
there be?
When n = 3 we have p(N, 3) = V - t/6
It follows that p(N, n) = V - t/2n
Aggregate profit is then p(N, n) = N(V - t/2n - c) – n.F
Industrial Organization: Chapter 4
16
Optimal number of shops (cont.)
Profit from n shops is p(N, n) = (V - t/2n - c)N - n.F
and the profit from having n + 1 shops is:
p*(N, n+1) = (V - t/2(n + 1)-c)N - (n + 1)F
Adding the (n +1)th shop is profitable if p(N,n+1) - p(N,n) > 0
This requires tN/2n - tN/2(n + 1) > F
which requires that n(n + 1) < tN/2F.
Industrial Organization: Chapter 4
17
An example
Suppose that F = $50,000 , N = 5 million and t = $1
Then t.N/2F = 50
So we need n(n + 1) < 50. This gives n = 6
There should be no more than seven shops in this case: if
n = 6 then adding one more shop is profitable.
But if n = 7 then adding another shop is unprofitable.
Industrial Organization: Chapter 4
18
Some Intuition
• What does the condition on n tell us?
• Simply, we should expect to find greater product variety
when:
• there are many consumers.
• set-up costs of increasing product variety are low.
• consumers have strong preferences over product
characteristics and differ in these.
Industrial Organization: Chapter 4
19
How Much of the Market to Supply
• Should the whole market be served?
– Suppose not. Then each shop has a local monopoly
– Each shop sells to consumers within distance r
– How is r determined?
•
•
•
•
•
it must be that p + tr = V so r = (V – p)/t
so total demand is 2N(V – p)/t
profit to each shop is then p = 2N(p – c)(V – p)/t – F
differentiate with respect to p and set to zero:
dp/dp = 2N(V – 2p + c)/t = 0
– So the optimal price at each shop is p* = (V + c)/2
– If all consumers are to be served then price is p(N,n) = V – t/2n
• Only part of the market should be served if p(N,n) > p*
• This implies that V > c + t/n.
Industrial Organization: Chapter 4
20
Partial Market Supply
• If c + t/n > V supply only part of the market and set price
p* = (V + c)/2
• If c + t/n < V supply the whole market and set price
p(N,n) = V – t/2n
• Supply only part of the market:
– if the consumer reservation price is low relative to marginal
production costs and transport costs
– if there are very few outlets
Industrial Organization: Chapter 4
21
Are there too
many shops or
What number of shops maximizes total surplus? too few?
Social Optimum
Total surplus is consumer surplus plus profit
Consumer surplus is total willingness to pay minus total revenue
Profit is total revenue minus total cost
Total surplus is then total willingness to pay minus total costs
Total willingness to pay by consumers is N.V
Total surplus is therefore N.V - Total Cost
So what is Total Cost?
Industrial Organization: Chapter 4
22
Social optimum (cont.)
Assume that
there
are n shops
Price
Price
V
Transport cost for
each shop is the area
of these two triangles
multiplied by
consumer density
V
Consider shop
i
Total cost is
total transport
cost plus set-up
costs
t/2n
x=0
t/2n
1/2n
1/2n
Shop i
Industrial Organization: Chapter 4
x=1
This area is t/4n2
23
Social optimum (cont.)
Total cost with n shops is, therefore: C(N,n) = n(t/4n2)N + n.F
= tN/4n + n.F
If t = $1, F = $50,000,
Total cost with n + 1 shops is: C(N,n+1)
(n+1).F
There
five
shops:
N==tN/4(n+1)+
5should
millionbethen
this
with
n=4+
adding
another
tells
us
Adding another shop is socially efficient
ifcondition
C(N,n
1)
< C(N,n)
shop
is efficient
that
n(n+1)
< 25
This requires that tN/4n - tN/4(n+1) > F
which implies that n(n + 1) < tN/4F
The monopolist operates too many shops and, more
generally, provides too much product variety
Industrial Organization: Chapter 4
24
Monopoly, Product Variety and Price Discrimination
• Suppose that the monopolist delivers the product.
– then it is possible to price discriminate
• What pricing policy to adopt?
–
–
–
–
charge every consumer his reservation price V
the firm pays the transport costs
this is uniform delivered pricing
it is discriminatory because price does not reflect costs
• Should every consumer be supplied?
–
–
–
–
–
suppose that there are n shops evenly spaced on Main Street
cost to the most distant consumer is c + t/2n
supply this consumer so long as V (revenue) > c + t/2n
This is a weaker condition than without price discrimination.
Price discrimination allows more consumers to be served.
Industrial Organization: Chapter 4
25
Price Discrimination and Product Variety
• How many shops should the monopolist operate now?
Suppose that the monopolist has n shops and is supplying
the entire market.
Total revenue minus production costs is N.V – N.c
Total transport costs plus set-up costs is C(N, n)=tN/4n + n.F
So profit is p(N,n) = N.V – N.c – C(N,n)
But then maximizing profit means minimizing C(N, n)
The discriminating monopolist operates the socially
optimal number of shops.
Industrial Organization: Chapter 4
26
Bundling
• Firms sell goods as bundles
– selling two or more goods in a single package
– complete stereo systems
– fixed-price meals in restaurants
• Firms also use tie-in sales: less restrictive than bundling
– tie the sale of one good to the purchase of another
– computer printers and printer cartridges
– constraining the use of spare parts
• Why?
• Because it is profitable to do so!
Industrial Organization: Chapter 4
27
Bundling: an example
much can
• Two television stations offered two oldHow
Hollywood
films
How much can
be charged for
– Casablanca and Son of Godzilla
be charged for
If the films are sold
Godzilla?
• Arbitrage is possible between the
stations
separately total Casablanca?
• Willingness revenue
to pay is:is $19,000
$7,000
Willingness to Willingness to
pay for
pay for
Casablanca
Godzilla
Station A
$8,000
$2,500
Station B
$7,000
$3,000
Industrial Organization: Chapter 4
$2,500
28
How much can
beBundling
charged is
forprofitable
thebecause
package?
it exploits
Bundling: an example
Now suppose
aggregate willingness
that the two films are
If and
the films
Willingness
to sold
Willingness
Total
payto
bundled
sold are
as pay
a package
total pay for
for
Willingness
as a package
revenue
is $20,000Godzilla
Casablanca
to pay
Station A
$8,000
$2,500
$10,500
Station B
$7,000
$3,000
$10,000
$10,000
Industrial Organization: Chapter 4
29
Bundling (cont.)
• Extend this example to allow for
– costs
– mixed bundling: offering products in a bundle and separately
Industrial Organization: Chapter 4
30
Consumer y Each
has consumer
Bundling: another
example
reservation
price
py1
that
the
firm one
Suppose that thereAll
areconsumers inSuppose
buys
exactly
for goodsets
1 and
py2p for in
All
consumers
price
region
B
buy
1
two goods and that
unit
of
ap good
for
good
2
region
A
buy
good
1
and
price
R2
good 2
2
x hasprovided that
consumers differ inonlyConsumer
both 2goods price
for good
price px1is less than her
their reservation
pricesreservation
B
A
for good 1 and px2
for these goods
price
for good
2 reservation
yconsumers
All
in
All
consumers
in
py2
region C buy
region D buy
p2
Consumers
x
neither good
only good 1
px2
split into
four groups
D
C
px1
p1 py1
Industrial Organization: Chapter 4
R1
31
Bundling: the example (cont.)
Now consider pure
bundling
at some
All consumers in
pB E buy
Consumers in theseprice
two
regions
region
R2
can buy each good eventhe
though
bundle
their reservation price for one of
Ethe goods is less than its
Consumers
cost
All marginal
consumers
in
pB
c2
F
c1
now split into
two groups
region F do not
buy the bundle
pB
Industrial Organization: Chapter 4
R1
32
Mixed Bundling
R2
pB
p2
pB - p1
In this region
Now consider mixed
consumers
buy
Consumers
in Good
this
1 is sold bundling
either
theonly
bundle
region
buy
at price p1
or product
2
in this
good
2 Consumers
inGood
this 2Consumers
is sold
region
are willing to
region also at price
p
2
This
leaves
both
goods. They
buy the bundle buy
two
regions
buy
the bundle
Consumers
In this regionsplit
consumers
buy
Consumers in this
into
four groups:
either the bundle
region buy
nothing in this
Consumers
The
bundle is sold buy the bundle
or product 1
region
at price
pBbuy
< p1only
+ pbuy
only good 1
2
good 1
pB - p2
p1
pB
Industrial Organization: Chapter 4
R1
buy only good 2
buy nothing
33
Mixed Bundling (cont.)
Similarly, all
consumers in
this region buy
only product 2
R2
The consumer
x will buy only
product 1
Consider consumer x with
consumers
reservationAll
prices
p1x for in
Which
is
this
Consumer
surplus
from
Consumer
surplus
region
from
buy
product
1 this
and
p2x for
measure
Her
aggregate
willingness
buyingbuying
product
1 isbundle
the
only
is 1
product
2product
to
pay
for
the
bundle
is
p1x -pp1 + p - p
1x
p1x2x+ p2xB
x
pB
p2
pB - p1
p2x
pB - p2
p1
pB p1x
R1
p1x+p2x
Industrial Organization: Chapter 4
34
Mixed Bundling (cont.)
• What should a firm actually do?
• There is no simple answer
– mixed bundling is generally better than pure bundling
– but bundling is not always the best strategy
• Each case needs to be worked out on its merits
Industrial Organization: Chapter 4
35
An Example
Four consumers; two products; MC1 = $100, MC2 = $150
Consumer
Reservation
Price for
Good 1
Reservation
Price for
Good 2
Sum of
Reservation
Prices
A
$50
$450
$500
B
$250
$275
$525
C
$300
$220
$520
D
$450
$50
$500
Industrial Organization: Chapter 4
36
The example (cont.)
Price
$450
$300
$250
$50
Price
$450
$275
$220
$50
Good 1: Marginal Cost $100
Quantity
TotalConsider
revenue simple
Profit
monopoly
pricing
1
$450
$350
2
$400
$600
Good 1 should be sold
3
$750
$450
at $250 and good 2 at
4
$200
-$200
$450. Total profit
Good 2: Marginal
Cost +
$150
is $450
$300
Quantity
= Total
$750revenue
1
2
3
4
$450
$550
$660
$200
Industrial Organization: Chapter 4
Profit
$300
$200
$210
-$400
37
The example (cont.)
Now consider pure
bundling
Consumer
A
B
C
D
Reservation
Reservation
Price forThe highest
Price for
bundle
Good 1 price that
Good
2 be
can
considered
isbuy
$500
All four
consumers
will
$50
$450
the bundle and profit is
4x$500
$100)
$250- 4x($150 +
$275
= $1,000
$300
$220
$450
$50
Industrial Organization: Chapter 4
Sum of
Reservation
Prices
$500
$525
$520
$500
38
The example (cont.)
Now consider mixed
Take the monopoly prices p1 = $250; p2 = $450 and
a bundle price pB = $500
bundling
All four consumers buy
something
and profit
is
Reservation
Reservation
Sum of
Consumer
Price +
for$150x2 Price for
Reservation
Can the$250x2
seller
improve
Good
1
Good 2
Prices
=
$800
on this?
A
$50
$450
$500
B
$250
$275
$525
$500
C
$300
$250
$220
$520
D
$450
$250
$50
$500
Industrial Organization: Chapter 4
39
The example (cont.)
Try instead the prices p1 = $450; p2 = $450 and a bundle price pB = $520
This is actually
the best Reservation
that the
Reservation
All four consumers
buy
Consumer
do for
Price+forfirm can
Price
and profit is $300
Good 1
$270x2 + $350
= $1,190
A
$50
Good 2
Sum of
Reservation
Prices
$450
$450
$500
B
$250
$275
$525
$520
C
$300
$220
$520
D
$450
$450
$50
$500
Industrial Organization: Chapter 4
40
Bundling (cont.)
• Bundling does not always work
• Requires that there are reasonably large differences in
consumer valuations of the goods
• What about tie-in sales?
– “like” bundling but proportions vary
– allows the monopolist to make supernormal profits on the tied
good
– different users charged different effective prices depending upon
usage
– facilitates price discrimination by making buyers reveal their
demands
Industrial Organization: Chapter 4
41
Tie-in Sales
• Suppose that a firm offers a specialized product – a
camera? – that uses highly specialized film cartridges
• Then it has effectively tied the sales of film cartridges to
the purchase of the camera
– this is actually what has happened with computer printers and ink
cartridges
• How should it price the camera and film?
– suppose that marginal costs of the film and of making the camera
are zero (to keep things simple)
– suppose also that there are two types of consumer: high-demand
and low-demand
Industrial Organization: Chapter 4
42
Tie-In
Sales:
anthe
Example
Profit is $72 from each
Suppose
that
$
$16
type of consumer
firm
leases
the
High-Demand
Low-Demand
product for $72 perSoConsumers
this gives profit of
Consumers
Is this the best
period
$144 per pair of highthat
Demand: P = 16 - Q
Demand:
P = 12 - Q
and low-demand
the firm can do?
consumers
$
$12
High-demand
consumers buy 16
units
$128
Low-demand
consumers are
willing to buy 12
units
$72
16
Quantity
Industrial Organization: Chapter 4
12
Quantity
43
Tie-In Sales: an Example
$
$16
Profit is $70 from each
Suppose that
low-demand
consumer:
High-Demand
Low-Demand
the firm sets a
So the
firm
$50 + $20
Consumers
price
of $2
percan set a Consumers
lease
charge of $50and $78 from each
unit
Demand: P = 16 - Qto each type of Demand:
P = 12
-Q
Consumer
surplus
high-demand
consumer:
for$50
low-demand
consumer: it cannot
+ $28
$
Consumer surplus
consumers is $50
discriminate
giving
$148 per pair of
for high-demand
$12
high-demand
and lowconsumers is
$98
Low-demand
High-demand
demand
consumers buy 10
consumers buy 14
units
units
$98
$50
$2
$2
14 16
Quantity
Industrial Organization: Chapter 4
10 12
Quantity
44
Tie-In
Sales:
Suppose
that an Example
$
$16
Profit is $72 from each
the firm can
High-Demand
Low-Demand
low-demand
consumer
bundle the two
Consumers
Consumers
and
$80 from each
goods
instead
ProduceSo
a bundled
produce a second
high-demand
consumer
Demand: P = 16of- Q
Demand: P = 12
-Q
tie
them
productbundle
of camera
of camera plus
giving $150 per pair of
plus 12-shot16-shot
cartridge
cartridge
$
high-demand and lowHigh-demand
High-demand
consumers get $48
demand
consumers will$12
pay
$48
consumer surplus
$80 for this bundled
from buying it
camera ($128 - $48)
$72
Low-demand
consumers can be
sold this bundled
product for $72
$72
$8
12
Quantity
16
Industrial Organization: Chapter 4
12
Quantity
45
Complementary Goods
• Complementary goods are goods that are consumed
together
– nuts and bolts
– PC monitors and computer processors
• How should these goods be produced?
• How should they be priced?
• Take the example of nuts and bolts
– these are perfect complements: need one of each!
• Assume that demand for nut/bolt pairs is:
Q = A - (PB + PN)
Industrial Organization: Chapter 4
46
Complementary goods (cont.)
This demand curve can be written individually for nuts and bolts
For bolts: QB = A - (PB + PN)
For nuts: QN = A - (PB + PN)
These give the inverse demands: PB = (A - PN) - QB
PN = (A - PB) - QN
These allow us to calculate profit maximizing prices
Assume that nuts and bolts are produced by independent firms
Each sets MR = MC to maximize profits
MRB = (A - PN) - 2QB
MRN = (A - PB) - 2QN
Assume MCB = MCN = 0
Industrial Organization: Chapter 4
47
Complementary goods (cont.)
Therefore QB = (A - PN)/2
and PB = (A - PN) - QB = (A - PN)/2
by a symmetric argument PN = (A - PB)/2
The price set by each firm is affected by
the price set by the other firm
In equilibrium the price set by the two
firms must be consistent
Industrial Organization: Chapter 4
48
Complementary goods (cont.)
PB
A
A/2
Pricing rule for
the Nut
Equilibrium
is for
Producer:
Pricing rule
two
PN where
= (A - these
Pthe
B)/2Bolt
pricing
rules
Producer:
Pintersect
B = (A - PN)/2
A/3
A/3 A/2
A
PN
PB = (A - PN)/2
PN = (A - PB)/2
 PN = A/2 - (A - PN)/4
= A/4 + PN/4
 3PN/4 = A/4
 PN = A/3
 PB = A/3
 PB + PN = 2A/3
 Q = A - (PB+PN) = A/3
Profit of the Bolt Producer
= PBQB = A2/9
Profit of the Nut Producer
= PNQN = A2/9
Industrial Organization: Chapter 4
49
Complementary goods (cont.)
What happens if the two goods are produced by the same firm?
Merger
two firms
The firm will set a price
PNB of
forthe
a nut/bolt
pair.
Demand is now QNB =results
A - PNBinsoconsumers
that PNB = A - QNB
Why?
beingBecause
chargedthe
$
merged
firm
is the
ablefirm
to
 MRNB = A - 2QNBlower prices and
coordinate
the prices
of
making
greater
profits
MR = MC = 0
A
the two goods
 Q = A /2
NB
 PNB = A /2
Profit of the nut/bolt producer
is PNBQNB = A2/4
A/2
Demand
MR
A/2
Industrial Organization: Chapter 4
A
Quantity
50
Industrial Organization: Chapter 4
51
Product variety (cont.)
d < 1/4
We know that p(d) satisfies the following constraint:
p(d) + t(1/2 - d) = V
This gives: p(d) = V - t/2 + t.d
 p(d) = V - t/2 + t.d
Aggregate profit is then: p(d) = (p(d) - c)N
= (V - t/2 + t.d - c)N
This is increasing in d so if d < 1/4 then d should be increased.
Industrial Organization: Chapter 4
52
Product variety (cont.)
d > 1/4
We now know that p(d) satisfies the following constraint:
p(d) + t.d = V
This gives: p(d) = V - t.d
Aggregate profit is then: p(d) = (p(d) - c)N
= (V - t.d - c)N
This is decreasing in d so if d > 1/4 then d should be decreased.
Industrial Organization: Chapter 4
53