Download EC 170: Industrial Organization

Product Variety and Quality
under Monopoly
1
Introduction
• Most firms sell more than one product
• Products are differentiated in different ways
– horizontally
• goods of similar quality targeted at consumers of
different types
– how is variety determined?
– is there too much variety
– vertically
• consumers agree on quality
• differ on willingness to pay for quality
– how is quality of goods being offered determined?
2
Horizontal product differentiation
• Suppose that 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
– firm designs products that appeal to different types of
consumer
– products are of (roughly) similar quality
• Questions:
– how many products?
– of what type?
– how do we model this problem?
3
A spatial approach to product variety
• 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)
– consumers prefer products that are “close” to their
preferred types in space, or time or characteristics
4
A Spatial approach to product variety 2
• 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 mile
• The monopolist operates one shop
– reasonable to expect that this is located at the center of Main
Street
5
Suppose that the monopolist
The spatial model
Price
sets a price ofPrice
p1
p1 + tx
p1 + t.x
V
V
All consumers within
distance x1 to the left
and right of the shop
will by the product
z=0
t
t
p1
x1
1/2
What determines
x1?
x1
z=1
Shop 1
p1 + tx1 = V, so x1 = (V – p1)/t
6
The spatial model
Price
p1 + t.x
Suppose the firm
2reduces the price
Price
p1 +tot.xp2?
V
V
Then all consumers
within distance x2
of the shop will buy
from the firm
z=0
p1
p2
x2
x1
1/2
x1
x2
z=1
Shop 1
7
The spatial model 3
• 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.
8
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*?
9
Location with two shops
Delivered price to
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
z=0
consumers at the
tomarket
be served
center equals
their reservation price Price
V
p(d)
What determines
p(d)?
d
Shop 1
1/2
1-d
Shop 2
z=1
The shops should be
moved inwards
10
Delivered price to
consumers at the
end-points equals
their reservation price
Location with two shops 2
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 suppose that
d > 1/4
Now what
determines p(d)?
z=0
d
Shop 1
1/2
1-d
Shop 2
z=1
The shops should be
moved outwards
11
It follows that Location
shop 1 should
be located at
Price
1/4 and shop 2
at 3/4
with two shops 3
Price at each
shop is then
p* = V - t/4
Price
V
V
V - t/4
V - t/4
Profit at each shop
is given by the
shaded area
c
c
z=0
1/4
Shop 1
1/2
3/4
Shop 2
z=1
Profit is now p(N, 2) = N(V - t/4 - c) – 2F
12
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
z=0
V - t/6
1/6
Shop 1
1/2
Shop 2
5/6
z=1
Shop 3
Profit is now p(N, 3) = N(V - t/6 - c) – 3F
13
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) – nF
14
Optimal number of shops 2
Profit from n shops is p(N, n) = (V - t/2n - c)N - nF
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.
15
An example
Suppose that F = $50,000 , N = 5 million and t = $1
Then tN/2F = 50
For an additional shop to be profitable we need n(n + 1) < 50.
This is true for 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.
16
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
• consumers are unwilling to buy a product if it is not “very close”
to their most preferred product
17
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 served 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.
18
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
19
Are there too
Social optimum many shops or
What number of shops maximizes total surplus? too few?
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 NV - Total Cost
So what is Total Cost?
20
Assume that
there
are n shops
Social optimum 2
Price
Price
Transport cost for
each shop is the area
V
of these two triangles
multiplied by
consumer density
V
Consider shop
i
Total cost is
total transport
cost plus set-up
costs
t/2n
z=0
t/2n
1/2n
1/2n
z=1
Shop i
This area is t/4n2
21
Social optimum 3
Total cost with n shops is, therefore: C(N,n) = n(t/4n2)N + nF
If =
t =tN/4n
$1, F+=nF
$50,000,
5 million then
this
Total cost with n + 1 shops is: C(N,n+1)N==tN/4(n+1)+
(n+1)F
condition
tells
There
should
beusfive shops:
Adding another shop is socially efficient if that
C(N,n
+ 1) << C(N,n)
n(n+1)
25 another
with n = 4 adding
This requires that tN/4n - tN/4(n+1) > F
shop is efficient
which implies that n(n + 1) < tN/4F
The monopolist operates too many shops and, more
generally, provides too much product variety
22
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
23
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
24
Product variety and price discrimination 2
• 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.
25
Product variety & price discrimination 3
• 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 NV – Nc
—Total transport costs plus set-up costs is C(N, n)=tN/4n + nF
—So profit is p(N,n) = NV – Nc – C(N,n)
—But then maximizing profit means minimizing C(N, n)
—The discriminating monopolist operates the socially
optimal number of shops.
26
Monopoly and product quality
• Firms can, and do, produce goods of different qualities
• Quality then is an important strategic variable
• The choice of product quality determined by its ability to
generate profit; attitude of consumers to q uality
• Consider a monopolist producing a single good
– what quality should it have?
– determined by consumer attitudes to quality
•
•
•
•
prefer high to low quality
willing to pay more for high quality
but this requires that the consumer recognizes quality
also some are willing to pay more than others for quality
27
Demand and quality
• We might think of individual demand as being of the form
– Qi = 1 if Pi < Ri(Z) and = 0 otherwise for each consumer i
– Each consumer buys exactly one unit so long as price is less
than her reservation price
– the reservation price is affected by product quality Z
• Assume that consumers vary in their reservation prices
• Then aggregate demand is of the form P = P(Q, Z)
• An increase in product quality increases demand
28
Demand and quality 2
Begin with a particular demand curve
for a good of quality Z1
Price
Then an increase in product
R1(Z2)
Suppose that
an from
increase
quality
Z1 toinZ2 rotates
P(Q, Z2)
quality the
increases
demandthe
curve around
If the price is P1willingness
and the product
quality
to pay of
the quantity
axis as follows
is
Z
then
all
consumers
with
reservation
1
inframarginal consumers more
P2
prices greater than
than P
the good
1 will
that
of buy
the marginal
R1(Z1)
Quantity Q1 can now be
consumer
This
is
the
These are the
P1
sold for the higher
marginal
inframarginal
price P2
consumer
consumers
P(Q, Z1)
Q1
Quantity
29
Demand and quality 3
Price
R1(Z1)
P2
P1
P(Q, Z1)
Q1
Suppose instead that an
Then anin
increase in product
increase
fromthe
Z1 to Z2 rotates
qualityquality
increases
thepay
demand
curve around
willingness to
of marginal
the price
axis as follows
consumers
more
than that of the inframarginal
consumers
Once again quantity Q1
can now be sold for a
higher price P2
P(Q, Z2)
Quantity
30
Demand and quality 4
• The monopolist must choose both
– price (or quantity)
– quality
• Two profit-maximizing rules
– marginal revenue equals marginal cost on the last unit sold for
a given quality
– marginal revenue from increased quality equals marginal cost
of increased quality for a given quantity
• This can be illustrated with a simple example:
P = Z( - Q) where Z is an index of quality
31
Demand and quality 5
P = Z( - Q)
Assume that marginal cost of output is zero: MC(Q) = 0
Cost of quality is C(Z) = aZ2
Marginal cost of quality = dC(Z)/d(Z)
= 2aZ
The firm’s profit is:
This means that quality
costly and becomes
increasingly costly
p(Q, Z) =PQ - C(Z) = Z( - Q)Q - aZ2
32
Demand and quality 6
Again, profit is:
p(Q, Z) =PQ - C(Z) = Z( - Q)Q - aZ2
The firm chooses Q and Z to maximize profit.
Take the choice of quantity first: this is easiest.
Marginal revenue = MR = Z - 2ZQ
MR = MC  Z - 2ZQ = 0  Q* = /2
 P* = Z/2
33
Demand and quality 7
Total revenue = P*Q* = (Z/2)x(/2) = Z2/4
So marginal revenue from increased quality is
MR(Z) = 2/4
Marginal cost of quality is
MC(Z) = 2aZ
Equating MR(Z) = MC(Z) then gives
Z* = 2/8a
Does the monopolist produce too high or too low quality?
34
Demand and quality: multiple products
• What if the firm chooses to offer more than one
product?
– what qualities should be offered?
– how should they be priced?
• Determined by costs and consumer demand
35
Demand and quality: multiple products 2
• An example:
– two types of consumer
– each buys exactly one unit provided that consumer surplus is
nonnegative
– if there is a choice, buy the product offering the larger
consumer surplus
– types of consumer distinguished by willingness to pay for
quality
• This is vertical product differentiation
36
Vertical differentiation
• Indirect utility to a consumer of type i from consuming a
product of quality z at price p is Vi = i(z – zi) – p
– where i measures willingness to pay for quality;
– zi is the lower bound on quality below which consumer type i will
not buy
– assume 1 > 2: type 1 consumers value quality more than type 2
– assume z1 > z2 = 0: type 1 consumers only buy if quality is greater
than z1:
• never fly in coach
• never shop in Wal-Mart
• only eat in “good” restaurants
– type 2 consumers will buy any quality so long as consumer
surplus is nonnegative
37
Vertical differentiation 2
• Firm cannot distinguish consumer types
• Must implement a strategy that causes consumers to selfselect
– persuade type 1 consumers to buy a high quality product z1 at a
high price
– and type 2 consumers to buy a low quality product z2 at a lower
price, which equals their maximum willingness to pay
• Firm can produce any product in the range
z, z
• MC = 0 for either quality type
38
Vertical differentiation 3
Suppose that the firm offers two products with qualities z1 > z2
For type 2 consumers charge maximum willingness to pay for the
low quality product: p2 = 2z2 Type 1 consumers
prefer the high quality
Now consider type 1Type
consumers:
firm have
faces an incentive
1 consumers
to the low
quality good
compatibility constraint
nonnegative consumer
high
1(z1 – z1) – p1 >surplus
1(z2 – from
z1) – pthe
2
quality good
1(z1 – z1) – p1 > 0
These imply that p1 < 1z1 – (1 2)z2
There is an upper limit on the price that can be charged for
the high quality good
39
Vertical differentiation 4
• Take the equation p1 = 1z1 – (1 – 2)z2
–
–
–
–
this is increasing in quality valuations
increasing in the difference between z1 and z2
quality can be prices highly when it is valued highly
firm has an incentive to differentiate the two products’
qualities to soften competition between them
• monopolist is competing with itself
• What about quality choice?
– prices p1 = 1z1 – (1 – 2)z2; p2 = 2z2
• check the incentive compatibility constraints
– suppose that there are N1 type 1 and N2 type 2 consumers
40
Vertical differentiation 5
Profit is
P = N1p1 + N2p2 = N11z1 – (N11 – (N1 + N2)2)z2
This is increasing in z1 so set z1 as high as possible: z1 = z
For z2 the decision is more complex
(N11 – (N1 + N2)2) may be positive or negative
41
Vertical differentiation 6
Case 1: Suppose that (N11 – (N1 + N2)2) is positive
Then z2 should be set “low” but this is subject to a constraint
Recall that p1 = 1z1 – (1 - 2)z2 So reducing z2 increases p1
But we also require that 1(z1 – z1) – p1 > 0
Putting these together gives:
The equilibrium prices are then:
z2 =
1 z 1
1   2
 2 1 z 1
p2 =
1   2
(
p1 = 1 z  z 1

42
Vertical differentiation 7
• Offer type 1 consumers the highest possible quality and
charge their full willingness to pay
• Offer type 2 consumers as low a quality as is consistent
with incentive compatibility constraints
• Charge type 2 consumers their maximum willingness to
pay for this quality
– maximum differentiation subject to incentive compatibility
constraints
43
Vertical differentiation 8
Case 1: Now suppose that (N11 – (N1 + N2)2) is negative
Then z2 should be set as high as possible
The firm should supply only one product, of the highest possible quality
What does this require?
From the inequality offer only one product if:
Offer only one product:
N1
2
 1
N1  N 2 1
if there are not “many” type 1 consumers
if the difference in willingness to pay for quality is “small”
Should the firm price to sell to both types in this case? YES!
44
Empirical Application: Price Discrimination
and Imperfect Competition
Although we have presented price discrimination and
product design (versioning) issues in the context of a
monopoly, these same tactics also play a role in more
competitive settings of imperfect competition
Imagine a two-store setting again
Assume N customers distributed evenly between the two
stores, each with maximum willingness to pay of V .
No transport cost—Half of the consumers always buys at
nearest store. Other half always buys at cheapest store.
45
Price Discrimination and Imperfect
Competition 2
If both stores operated by a monopolist, set price = V.
Cannot set it higher of there will be no customers.
Setting it lower though gains nothing.
What if stores operated by separate firms?
Imagine P1 = P2 = V. Store 1 serves N/4 pricesensitive customers and N/4 price-insensitive ones.
The same is true for Store 2.
If Store 1 cuts its price  below V.
It loses N/2 from all current customers
It gains N(V - )/4 by stealing all pricesensitive customers from Store 2
46
Price Discrimination and Imperfect
Competition 3
MORAL 1: Both firms have a real incentive to cut price.
This ultimately proves self-defeating
In equilibrium, both still serve N/2 customers but now
do so at a price closer to cost.
This is especially frustrating in light of the “brandloyal” or price-insensitive customers
Cutting their price does not increase their likelihood
of shopping at a particular place. It just loses revenue.
MORAL 2: Unlike the monopolist who sets the same
price to everyone, these firms have an incentive to
discriminate and so continue to charge a high price to
loyal consumers while pricing low to others.
47
Price Discrimination and Imperfect
Competition 4
The intuition then is that price discrimination may be
associated with imperfect competition and become more
prominent as markets get more competitive (but still less
than perfectly competitive).
This idea is tested by Stavins (2001) with airline prices.
Restrictions such as a required Saturday night stay-over
or an advanced purchase serve as screening mechanism
for price-sensitive customers. Hence, restrictions lead to
lower ticket price.
Stavins (2001) idea is that price reduction associated with
flight restrictions will be small in markets that are not
very competitive.
48
Price Discrimination and Imperfect
Competition 6
Stavins (2001) looks at nearly 6,000 tickets covering 12
different city-pair routes in September, 1995.
She finds strong support for the dual hypothesis that:
a) passengers flying on a ticket with restrictions pay less;
b) price reduction shrinks as concentration rises
In highly competitive (low HHI) markets, a Saturday
night restriction leads to a $253 price reduction but only
a $165 reduction in less competitive ones.
In highly competitive (low HHI) markets, an Advance
Purchase restriction leads to a $111 price reduction but
only a $41 reduction in less competitive ones.
49
Price Discrimination and Imperfect
Competition 5
Variable
Saturday
Night Stay
Required
Coefficient
– 0.408
t-Statistic
– 4.05
Coefficient
-----
t-Statistic
-----
Saturday
Night Stay
0.792
3.39
--------RequiredxHHI
Advance Purchase
--------– 0.023
–5.53
Required
Advance Purchase
--------0.098
8.38
RequiredxHHI
NOTE: HHI is the Herfindahl Index. A Saturday Night Stay or an
Advance Purchase lowers the price significantly. But the HHI terms
show that this effect weakens as market concentration increases.
50
Demand and quality A1
Price
Z2
P(Q, Z2)
When quality is Z2
price is
2/2
Howisdoes
WhenZquality
Z1 increased quality
price is affect demand?
Z1/2
MR(Z2)
Z1
P2 = Z2/2
P1 = Z1/2
MR(Z1)
P(Q,Z1)
/2
Q*

Quantity
51
Demand and quality A2
Price
Z2
Z1
P2 = Z2/2
P1 = Z1/2
So an increase is quality from
Z1 to Z
surplus
2 increases
Social
surplus
at quality
Z2
area
minus
the
is by
thisthis
area
minus
quality
increase in
quality costs
costs
An increase in quality from
The increase in total
Z1 to Z2 increases
surplus
revenue
by this
area Zis greater than
Social
surplus
at quality
1
the
increase
in profit.
is this area minus quality
The monopolist produces
costs
too little quality
/2
Q*

Quantity
52
Demand and quality
Derivation of aggregate demand
Order consumers by their reservation prices
Aggregate individual demand horizontally
Price
1 2 3 4 5 6 78
Quantity
53
Location choice 1
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 + td
 p(d) = V - t/2 + td
Aggregate profit is then: p(d) = (p(d) - c)N
= (V - t/2 + td - c)N
This is increasing in d so if d < 1/4 then d should be increased.
54
Location choice 2
d > 1/4
We now know that p(d) satisfies the following constraint:
p(d) + td = V
This gives: p(d) = V - td
Aggregate profit is then: p(d) = (p(d) - c)N
= (V - td - c)N
This is decreasing in d so if d > 1/4 then d should be decreased.
55
Commodity Bundling and Tie-In
Sales
56
Introduction
• Firms often bundle the goods that they offer
– Microsoft bundles Windows and Explorer
– Office bundles Word, Excel, PowerPoint, Access
• Bundled package is usually offered at a discount
• Bundling may increase market power
– GE merger with Honeywell
• Tie-in sales ties the sale of one product to the purchase of another
• Tying may be contractual or technological
– IBM computer card machines and computer cards
– Kodak tie service to sales of large-scale photocopiers
– Tie computer printers and printer cartridges
• Why? To make money!
57
Bundling: an example
How
much canfilms
• Two television stations offered two old
Hollywood
How much can
be charged for
– Casablanca and Son of Godzilla
be charged for
If the films are sold
Godzilla?
• Arbitrage is possible betweenCasablanca?
the stations
separately total
• Willingnessrevenue
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
$2,500
58
Bundling:
How much can
an
example
2
beBundling
charged
forprofitable
is
thebecause
package?
it exploits
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
59
Bundling
• Extend this example to allow for
– costs
– mixed bundling: offering products in a bundle and
separately
60
Suppose that there are
Consumer y Each
has consumer
reservation
price
two goods
and that
Bundling:
another
thatpy1
the
firm one
All
consumersexample
inSupposebuys
exactly
for goodsets
1 and
py2p for in
All
consumers
price
consumers differ inregion B buy
1
unit
of
ap good
for
good
2
region
A
buy
good
1
and
price
R
only Consumer
good 2
2
their
reservation prices
2
x hasprovided that
both 2goods price
for
good
for these
reservation price px1is less than her
B goods
A
for good 1 and px2
for good 2 reservation price
y
py2
p2
px2
x
All consumers in
region C buy
neither good
All consumers in
region D buy
Consumers
only good 1
split into
four groups
D
C
px1
p1 py1
R1
61
Bundling: another example 2
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
R1
62
R2
pB
p2
pB - p1
Mixed
bundling
In
this region
Now consider mixed
consumers
buy
Consumers
in Good
this
bundling
1 is sold
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
R1
buy only good 2
buy nothing
63
Mixed
bundling
2
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
64
Mixed bundling 3
• 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
65
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
66
The example 2
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
Profit
$300
$200
$210
-$400
67
The example
3 consider pure
Now
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
Sum of
Reservation
Prices
$500
$525
$520
$500
68
The example
Now4 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
Consumer
Price +
for$150x2 Price for
Can the$250x2
seller
improve
Good
1
Good 2
=
$800
on this?
Sum of
Reservation
Prices
A
$50
$450
$500
B
$250
$275
$525
$500
C
$300
$250
$220
$520
D
$450
$250
$50
$500
69
The example 5
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
70
Bundling again
• Bundling does not always work
• Mixed bundling is always more profitable than pure
bundling
• Mixed bundling is always better than no bundling
• But pure bundling is not necessarily better than no
bundling
– Requires that there are reasonably large differences in
consumer valuations of the goods
• Bundling is a form of price discrimination
• May limit competition
71
Tie-in sales
• 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
72
Tie-in sales 2
• 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 also that there are two types of consumer, highdemand and low-demand, with one-thousand of each type
– high demand P = 16 – Qh; low demand P = 12 - Ql
– the company does not know which type is which
73
Tie-in sales 3
• Film is produced competitively at $2 per picture
– so film is priced at $2 per picture
• Suppose that the company leases its cameras
– if priced so that all consumers lease then we can ignore
production costs of the camera
• these are fixed at 2000c
• Now consider the lease terms
74
Tie-in
sales:
an
example
2
So the firm can set a
$
$16
Recall
theof $50
lease that
charge
High-Demand
Low-Demand
film sells at $2
Consumers to each type of Profit
Consumers
is $50 from each
per
picture
consumer:
it cannotlow-demand and highHigh-demand
Demand: P = 16 - Q
Demand: P = 12 - Q
discriminate
consumers take 14
demand consumer. Total
pictures$
profit is $100,000
Consumer surplus
Consumer
surplus
for high-demand
$12
consumers is $98
$98
for low-demand
consumers
Low-demand
is $50
consumers take 10
pictures
$50
$2
$2
14 16
Quantity
10 12
Quantity
75
Tie-in sales example 3
• This is okay but there may be room for improvement
• Redesign the camera to tie the camera and the film
– technological change that makes the camera work only with
the firm’s film cartridge
• Suppose that the firm can produce film at a cost of $2
per picture
• Implement a tying strategy that makes it impossible to
use the camera without this film
76
Tie-in sales: an example 2
High-Demand Aggregate profit
Low-Demand
is
now the camera at
Lease
Profit
is $32 plus
Consumers
Consumers
$48,000 + $56,000
= Profit is $32
$32.
$24 in film profits =
Tying increases
theDemand:
$104,000
plusP =$16
Demand: P = 16 - Q
12 -in
Qfilm
Each
$56 high-demandfirm’s profit
profits
= $48
Consumer
surplus
consumer will lease
$
$
the camera at $32
High-demand
$12
consumers take 12
pictures
$16
$32
$4
$2
for low-demand
consumers
Low-demand
is $32
consumers take 8
pictures
$32
$4
$2
$24
12
Quantity
16
$16
8
12
Quantity
77
Tie-in sales example 3
• Why does tying increase profits?
– high-demand consumers are offered a quantity discount
under both the original and the tied lease arrangement
– but tying solves the identification and arbitrage problems
• film exploits its monopoly in film supply
• high-demand consumers are revealed by their film
purchases
• quantity discount is then used to increase profit
• arbitrage is not an issue: both types of consumers pay the
same lease and the same unit price for film
78
Tie-in sales example 4
• Can the firm do even better?
• Redesign the camera so that the film cartridge is integral
– offer two types of integrated camera/film package: high capacity
and low capacity
– what capacities?
• This is similar to second-degree price discrimination
– design two cameras with socially efficient capacities: 10 picture
and 14 picture
– lease these as integrated packages
79
Tie-in sales:
High-Demand
Consumers
$
$16
12
Aggregate profit is now
an $50,000
example
2
+ $58,000 =
$108,000
Low-Demand
Consumers
High-demand
Demand:consumers
P = 16 - Q get $40
Demand: P = 12 - Q
Low-demand
high-demand
consumerSo
surplus
consumers will pay
by leasingconsumers
the 10- can$ be
up to $70 to lease
picurecharged
camera $86 to lease
the 10-picure
$12
the 14-picture
camera
camera
$40
$70
$2
$70
$16
10 14 16
Quantity
$2
10 12
Quantity
80
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)
81
Complementary goods 2
Demand curve can be written individually for nuts and bolts
For bolts: QB = A - (PB + PN)
For nuts: QN = A - (PB + PN)
This gives the inverse demands: PB = (A - PN) - QB
PN = (A - PB) - QN
These allow us to calculate profit maximizing prices
Assume 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
82
Complementary goods 3
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
83
Complementary goods 4
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
84
Complementary goods 5
What happens if the two goods are produced by the same firm?
of the
The firm willMerger
set a price
PNBtwo
forfirms
a nut/bolt pair.
results in consumers
Demand is now QNB = A - PNB so that PNB = A - QNB
being charged
$
lower
prices
and
the
firm
 MRNB = A - 2QNB
Why? Because the
making greater profits
MR = MC = 0
A
merged firm is able to
 QNB = A /2
coordinate the prices of
 PNB = A /2
the two goods
Profit of the nut/bolt producer
is PNBQNB = A2/4
A/2
Demand
MR
A/2
A
Quantity
85
Complementary goods 6
• Don’t necessarily need a merger to get these benefits
– product network
• ATM networks
• airline booking systems
– one of the markets is competitive
• price equals marginal cost in this market
• leads to the “merger” outcome
• There may also be a countervailing force
– network externalities
• value of a good to consumers increases when more consumers use
the good
86
Network externalities
• Product complementarities can generate network effects
– Windows and software applications
• substantial economies of scale
• strong network effects
– leads to an applications barrier to entry
• new operating system will sell only if applications are written for it
• but…
• So product complementarities can lead to monopoly
power being extended
87
Anti-trust and bundling
• The Microsoft case is central
– accusation that used power in operating system (OS) to gain
control of browser market by bundling browser into the OS
– need\ to show
• monopoly power in OS
• OS and browser are separate products with no need to be bundled
• abuse of power to maintain or extend monopoly position
– Microsoft argued that technology required integration
– further argued that it was not “acting badly”
• consumers would benefit from lower price because of the
complementarity between OS and browser
88
Microsoft and Netscape
• Complementarity products
–
–
–
–
so merge?
what if Netscape refuses?
then Microsoft can develop its own browser
MC ≈ 0 so competition in the browser market drives price
close to zero
– but then get the outcome of merger firm through competition
• So Microsoft is not “acting badly”
• But
– JAVA allows applications to be run on Internet browsers
– Netscape then constitutes a threat
– need to reduce their market share
89
And now…
• This view gained more force & support in Europe
– bundling of Media Player into Windows
– Competition Directorate found against Microsoft
• Microsoft Appealed
• Microsoft finally lost its appeal in September, 2007
– Result: Microsoft ordered to stop bundling and
forced to pay fine of €497 (finally settled in October,
2007)
– Some economists upset by this decision arguing that
as price discrimination, bundling often expands the
market, AND also that bundling/tying can reflect
competition and not just market power
90
Competitive Bundling/Tying
• Bundling and tying are very commonly
observed phenomena
– Perhaps too commonly observed to be just the
outcome of monopoly power
– Is there a way to understand competitive bundling?
• Yes! Salinger and Evans (2005) and Evans (2006)
• It may well be the case that the structure of
demand and the nature of scope and scale
economies force competitive firms to bundle tie
their goods
91
Competitive Bundling/Tying 2
• Consider the table on the next slide and assume consumer
willingness to pay is $20 for most preferred option
– Competitive firm can’t offer pain reliever & decongestant
separately, To do so incurs
• total fixed cost of $600
• Marginal cost of $4
• Breakeven price = $6
– 50 by pain relief alone and pay $6 per unit
– 50 by decongestant alone and pay $6 per unit
– 100 buy both and pay $12 per combined unit
• Total Revenue = $1800; Total cost = $600 + $4x150 +
$4x150 = $1800
– Rival could sell bundled product for $10 and steal all 100
customers interested in joint goods who now pay $12
92
Competitive Bundling/Tying 3
Product
$8.50 is lowest
Pain Relieffeasible
Decongestant
price and isBundle
Demand
Costs
Fixed Cost
Marginal Cost
Moral:100
competitive
50 by only
achieve
pressure may be the
offering the bundled
underlying reason for
product
$300
$300
$300
much bundling
$4
$4
$7
50
Feasible Prices
Separate Goods
Pure Bundling
Mixed Bundling
Bundle + Good 1
Bundle + Good 2
$6
---$10
$10
----
$6
---$10
---$10
----$8.50
$10
$9
$9
93
Antitrust and tying arrangements
• Tying arrangements have been the subject of extensive
litigation
• Current policy
– tie-in violates antitrust laws if
• there exists distinct products: tying product & tied one
• firm tying the products has sufficient market power in
the tying market to force purchase of the tied good
• tying arrangement forecloses or has the potential to
foreclose a substantial volume of trade
• As time passes, approach is more and more of a rule-ofreason standard with increasing recognition that
whether price discrimination or competitive pressure is
the reason, bundling/tying is often welfare-improving
94