1
Product Variety and Quality under Monopoly
2
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?
3
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?
4
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
5
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
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The spatial model
z = 0 z = 1
Shop 1
t
x1
Price Price
All consumers withindistance x1 to the leftand right of the shopwill by the product
All consumers withindistance x1 to the leftand right of the shopwill by the product
1/2
V V
p1
t
x1
p1 + tx p1 + t.x
p1 + tx1 = V, so x1 = (V – p1)/t
What determinesx1?
What determinesx1?
Suppose that the monopolist sets a price of p1
Suppose that the monopolist sets a price of p1
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The spatial model 2
z = 0 z = 1
Shop 1
x1
Price Price
1/2
V V
p1
x1
p1 + t.x p1 + t.x
Suppose the firmreduces the price
to p2?
Suppose the firmreduces the price
to p2?
p2
x2 x2
Then all consumerswithin distance x2
of the shop will buyfrom the firm
Then all consumerswithin distance x2
of the shop will buyfrom the firm
8
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 (N, 1) = N(V – t/2 – c) – F.
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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*?
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Location with two shops
Suppose that the entire market is to be servedSuppose that the entire market is to be servedPrice Price
z = 0 z = 1
If there are two shopsthey will be located
symmetrically a distance d from theend-points of the
market
If there are two shopsthey will be located
symmetrically a distance d from theend-points of the
market
Suppose thatd < 1/4
Suppose thatd < 1/4
d
V V
1 - dShop 1 Shop 2
1/2
The maximum pricethe firm can chargeis determined by the
consumers at thecenter of the market
The maximum pricethe firm can chargeis determined by the
consumers at thecenter of the market
Delivered price toconsumers at the
market center equalstheir reservation price
Delivered price toconsumers at the
market center equalstheir reservation price
p(d) p(d)
Start with a low priceat each shop
Start with a low priceat each shop
Now raise the priceat each shop
Now raise the priceat each shop
What determinesp(d)?
What determinesp(d)?
The shops should bemoved inwards
The shops should bemoved inwards
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Location with two shops 2
Price Price
z = 0 z = 1
Now suppose thatd > 1/4
Now suppose thatd > 1/4
d
V V
1 - dShop 1 Shop 2
1/2
p(d) p(d)
Start with a low priceat each shop
Start with a low priceat each shop
Now raise the priceat each shop
Now raise the priceat each shop
The maximum pricethe firm can charge is now determined by the consumers at the end-points
of the market
The maximum pricethe firm can charge is now determined by the consumers at the end-points
of the market
Delivered price toconsumers at theend-points equals
their reservation price
Delivered price toconsumers at theend-points equals
their reservation price
Now what determines p(d)?
Now what determines p(d)?
The shops should bemoved outwards
The shops should bemoved outwards
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Location with two shops 3
Price Price
z = 0 z = 11/4
V V
3/4Shop 1 Shop 2
1/2
It follows thatshop 1 shouldbe located at
1/4 and shop 2at 3/4
It follows thatshop 1 shouldbe located at
1/4 and shop 2at 3/4
Price at eachshop is thenp* = V - t/4
Price at eachshop is thenp* = V - t/4
V - t/4 V - t/4
Profit at each shopis given by the
shaded area
Profit at each shopis given by the
shaded area
Profit is now (N, 2) = N(V - t/4 - c) – 2FProfit is now (N, 2) = N(V - t/4 - c) – 2F
c c
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Three shops
Price Price
z = 0 z = 1
V V
1/2
What if there are three shops?
What if there are three shops?
By the same argumentthey should be located
at 1/6, 1/2 and 5/6
By the same argumentthey should be located
at 1/6, 1/2 and 5/6
1/6 5/6Shop 1 Shop 2 Shop 3
Price at eachshop is now
V - t/6
Price at eachshop is now
V - t/6
V - t/6 V - t/6
Profit is now (N, 3) = N(V - t/6 - c) – 3FProfit is now (N, 3) = N(V - t/6 - c) – 3F
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Optimal number of shops
• A consistent pattern is emerging.• Assume that there are n shops.
• We have already considered n = 2 and n = 3.
• When n = 2 we have p(N, 2) = V - t/4
• When n = 3 we have p(N, 3) = V - t/6
• They will be symmetrically located distance 1/n apart.
• It follows that p(N, n) = V - t/2n
• Aggregate profit is then (N, n) = N(V - t/2n - c) – nF
How manyshops should
there be?
How manyshops should
there be?
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Optimal number of shops 2
Profit from n shops is (N, n) = (V - t/2n - c)N - nFand the profit from having n + 1 shops is:
*(N, n+1) = (V - t/2(n + 1)-c)N - (n + 1)F
Adding the (n +1)th shop is profitable if (N,n+1) - (N,n) > 0
This requires tN/2n - tN/2(n + 1) > F
which requires that n(n + 1) < tN/2F.
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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.
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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
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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 = 2N(p – c)(V – p)/t – F• differentiate with respect to p and set to zero:• d/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.
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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
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Social optimumAre there too
many shops ortoo few?
Are there toomany shops or
too few?What number of shops maximizes total surplus?What number of shops maximizes total surplus?
Total surplus is therefore NV - Total CostTotal surplus is therefore NV - Total Cost
Total surplus is then total willingness to pay minus total costsTotal surplus is then total willingness to pay minus total costs
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 willingness to pay by consumers is N.V
So what is Total Cost?So what is Total Cost?
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Social optimum 2
Price Price
z = 0 z = 1
V V
Assume thatthere
are n shops
Assume thatthere
are n shops
Consider shopi
Consider shopi
1/2n 1/2n
Shop i
t/2nt/2nTotal cost istotal transport
cost plus set-upcosts
Total cost istotal transport
cost plus set-upcosts
Transport cost foreach shop is the areaof these two triangles
multiplied byconsumer density
Transport cost foreach shop is the areaof these two triangles
multiplied byconsumer density
This area is t/4n2 This area is t/4n2
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Social optimum 3Total cost with n shops is, therefore: C(N,n) = n(t/4n2)N + nF
= tN/4n + nF
Total cost with n + 1 shops is: C(N,n+1) = tN/4(n+1)+ (n+1)F
Adding another shop is socially efficient if C(N,n + 1) < C(N,n)
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
The monopolist operates too many shops and, more generally, provides too much product variety
If t = $1, F = $50,000,N = 5 million then this
condition tells usthat n(n+1) < 25
If t = $1, F = $50,000,N = 5 million then this
condition tells usthat n(n+1) < 25
There should be five shops: with n = 4 adding another shop is efficient
There should be five shops: with n = 4 adding another shop is efficient
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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
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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
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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.
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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 (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.
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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
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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
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Demand and quality 2Begin with a particular demand curve
for a good of quality Z1
Begin with a particular demand curvefor a good of quality Z1
Price
Quantity
P(Q, Z1)
P1
Q1
If the price is P1 and the product qualityis Z1 then all consumers with reservationprices greater than P1 will buy the good
If the price is P1 and the product qualityis Z1 then all consumers with reservationprices greater than P1 will buy the goodR1(Z1)
These are theinframarginal
consumers
These are theinframarginal
consumers
This is themarginalconsumer
This is themarginalconsumer
Suppose that an increase inquality increases thewillingness to pay of
inframarginal consumers morethan that of the marginal
consumer
Suppose that an increase inquality increases thewillingness to pay of
inframarginal consumers morethan that of the marginal
consumer
Then an increase in productquality from Z1 to Z2 rotates
the demand curve aroundthe quantity axis as follows
Then an increase in productquality from Z1 to Z2 rotates
the demand curve aroundthe quantity axis as follows
R1(Z2)
P2
Quantity Q1 can now besold for the higher
price P2
Quantity Q1 can now besold for the higher
price P2
P(Q, Z2)
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Demand and quality 3
Price
Quantity
P(Q, Z1)
P1
Q1
R1(Z1)
Suppose instead that an increase in
quality increases thewillingness to pay of marginal
consumers morethan that of the inframarginal
consumers
Suppose instead that an increase in
quality increases thewillingness to pay of marginal
consumers morethan that of the inframarginal
consumers
Then an increase in productquality from Z1 to Z2 rotates
the demand curve aroundthe price axis as follows
Then an increase in productquality from Z1 to Z2 rotates
the demand curve aroundthe price axis as follows
P(Q, Z2)
Once again quantity Q1 can now be sold for a
higher price P2
Once again quantity Q1 can now be sold for a
higher price P2
P2
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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
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Demand and quality 5P = Z( - Q)
Assume that marginal cost of output is zero: MC(Q) = 0
Cost of quality is C(Z) = Z2
This means that quality iscostly and becomesincreasingly costly
This means that quality iscostly and becomesincreasingly costly
Marginal cost of quality = dC(Z)/d(Z)
= 2Z
The firm’s profit is:
(Q, Z) =PQ - C(Z) = Z( - Q)Q - Z2
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Demand and quality 6
Again, profit is:
(Q, Z) =PQ - C(Z) = Z( - Q)Q - Z2
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
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Demand and quality 7Total revenue = P*Q* = (Z/2)x(/2) = Z2/4
So marginal revenue from increased quality isMR(Z) = 2/4
Marginal cost of quality isMC(Z) = 2Z
Equating MR(Z) = MC(Z) then gives
Z* = 2/8Does the monopolist produce too high or too low quality?
35
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
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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
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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
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Vertical differentiation 2• Firm cannot distinguish consumer types
• Must implement a strategy that causes consumers to self-select– 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
• MC = 0 for either quality type
z, z
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Vertical differentiation 3
For type 2 consumers charge maximum willingness to pay for the low quality product: p2 = 2z2
Suppose that the firm offers two products with qualities z1 > z2
Now consider type 1 consumers: firm faces an incentive compatibility constraint
1(z1 – z1) – p1 > 1(z2 – z1) – p2
Type 1 consumers prefer the high
quality to the low quality good
1(z1 – z1) – p1 >
Type 1 consumers have nonnegative consumer surplus from the high
quality good
These imply that p1 < 1z1 – (-2)z2 There is an upper limit on the price that can be charged for the high quality good
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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
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Vertical differentiation 5Profit is
N1p1 + N2p2 =
N11z1 – (N11 – (N1 + N2)2)z2
This is increasing in z1 so set z1 as high as possible: z1 =
For z2 the decision is more complex
(N11 – (N1 + N2)2) may be positive or negative
z
42
Vertical differentiation 6Case 1: Suppose that (N11 – (N1 + N2)2) is positive
Then z2 should be set “low” but this is subject to a constraint
Recall that p1 = 1z1 – (-2)z2 So reducing z2 increases p1
But we also require that 1(z1 – z1) – p1 >
Putting these together gives:21
112
zz
The equilibrium prices are then: 21
1122
zp
111 zzp
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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
44
Vertical differentiation 8Case 1: Now suppose that (N11 – (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: 11
2
21
1
NN
N
Offer only one product:
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!
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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.
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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.
If Store 1 cuts its price below V. It loses N/2 from all current customers
Setting it lower though gains nothing.What if stores operated by separate firms?
Imagine P1 = P2 = V. Store 1 serves N/4 price-sensitive customers and N/4 price-insensitive ones. The same is true for Store 2.
It gains N(V - )/4 by stealing all price-sensitive customers from Store 2
47
Price Discrimination and Imperfect Competition 3
MORAL 1: Both firms have a real incentive to cut price.
This ultimately proves self-defeating
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.
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 “brand-loyal” or price-insensitive customers
48
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.
49
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:
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.
a) passengers flying on a ticket with restrictions pay less;b) price reduction shrinks as concentration rises
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.
50
Price Discrimination and Imperfect Competition 5
Variable Coefficient t-Statistic Coefficient t-Statistic
SaturdayNight Stay – 0.408 – 4.05 ----- -----Required
Saturday Night Stay 0.792 3.39 ----- -----RequiredxHHI
Advance Purchase ----- ----- – 0.023 –5.53 RequiredAdvance Purchase ----- ----- 0.098 8.38RequiredxHHI
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.
51
Demand and quality A1Price
Quantity
Z1
P(Q,Z1)
How does increased quality affect demand?
How does increased quality affect demand?
Z2P(Q, Z2)
MR(Z1)
MR(Z2)
/2
Q*
P1 = Z1/2
P2 = Z2/2
When quality is Z1
price isZ1/2
When quality is Z1
price isZ1/2
When quality is Z2
price isZ2/2
When quality is Z2
price isZ2/2
52
Demand and quality A2Price
Quantity
Z1
Z2
/2
Q*
P1 = Z1/2
P2 = Z2/2
An increase in quality fromZ1 to Z2 increases
revenue by this area
An increase in quality fromZ1 to Z2 increases
revenue by this areaSocial surplus at quality Z1
is this area minus qualitycosts
Social surplus at quality Z1
is this area minus qualitycosts
Social surplus at quality Z2
is this area minus qualitycosts
Social surplus at quality Z2
is this area minus qualitycosts
So an increase is quality fromZ1 to Z2 increases surplus
by this area minus theincrease in quality costs
So an increase is quality fromZ1 to Z2 increases surplus
by this area minus theincrease in quality costs
The increase in total surplus is greater than the increase in profit.
The monopolist produces too little quality
53
Demand and qualityDerivation of aggregate demand
Order consumers by their reservation prices
Aggregate individual demand horizontally
Price
Quantity1 2 3 4 5 6 7 8
54
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: (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.
55
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: (d) = (p(d) - c)N
= (V - td - c)N
This is decreasing in d so if d > 1/4 then d should be decreased.
56
Commodity Bundling and Tie-In Sales
57
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!
58
Bundling: an example• Two television stations offered two old Hollywood films
– Casablanca and Son of Godzilla
• Arbitrage is possible between the stations
• Willingness to pay is:
Station A
Station B
Willingness to pay for
Casablanca
Willingness to pay for
Godzilla
$8,000
$7,000
$2,500
$3,000
How much canbe charged forCasablanca?
How much canbe charged forCasablanca?
$7,000
How much canbe charged for
Godzilla?
How much canbe charged for
Godzilla?
$2,500
If the films are soldseparately total
revenue is $19,000
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Bundling: an example 2
Station A
Station B
Willingness to pay for
Casablanca
Willingness to pay for
Godzilla
$8,000
$7,000
$2,500
$3,000
Total Willingness
to pay
$10,500
$10,000
Now supposethat the two films are
bundled and soldas a package
Now supposethat the two films are
bundled and soldas a package
How much canbe charged forthe package?
How much canbe charged forthe package?
$10,000
If the films are soldas a package total
revenue is $20,000
Bundling is profitable because it exploits
aggregate willingnesspay
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Bundling • Extend this example to allow for
– costs– mixed bundling: offering products in a bundle and separately
61
All consumers inregion A buyboth goods
All consumers inregion A buyboth goods
Bundling: another example
R2
R1
Consumer x hasreservation price px1
for good 1 and px2
for good 2
Consumer x hasreservation price px1
for good 1 and px2
for good 2
xpx2
px1
ypy2
py1
Consumer y hasreservation price py1
for good 1 and py2
for good 2
Consumer y hasreservation price py1
for good 1 and py2
for good 2
Suppose that the firmsets price p1 for
good 1 and price p2
for good 2
Suppose that the firmsets price p1 for
good 1 and price p2
for good 2
p1
p2
Suppose that there aretwo goods and thatconsumers differ in
their reservation pricesfor these goods
Suppose that there aretwo goods and thatconsumers differ in
their reservation pricesfor these goods
Each consumerbuys exactly one
unit of a goodprovided that price
is less than herreservation price
Each consumerbuys exactly one
unit of a goodprovided that price
is less than herreservation price
AB
DC
Consumerssplit into
four groups
Consumerssplit into
four groups
All consumers inregion B buyonly good 2
All consumers inregion B buyonly good 2
All consumers inregion C buyneither good
All consumers inregion C buyneither good
All consumers inregion D buyonly good 1
All consumers inregion D buyonly good 1
62
Bundling: another example 2
R2
R1c1
c2
Now consider purebundling at some
price pB
Now consider purebundling at some
price pB
pB
pB
Consumersnow split into
two groups
Consumersnow split into
two groups
E
All consumers inregion E buythe bundle
All consumers inregion E buythe bundle
F
All consumers inregion F do notbuy the bundle
All consumers inregion F do notbuy the bundle
Consumers in these two regions can buy each good even thoughtheir reservation price for one of
the goods is less than itsmarginal cost
Consumers in these two regions can buy each good even thoughtheir reservation price for one of
the goods is less than itsmarginal cost
63
Mixed bundling
R2
R1p1
p2
Now consider mixedbundling
Now consider mixedbundling
pB
pB
Good 1 is soldat price p1
Good 1 is soldat price p1
Good 2 is soldat price p2
Good 2 is soldat price p2
The bundle is soldat price pB < p1 + p2
The bundle is soldat price pB < p1 + p2
Consumers split into four groups:buy the bundle
buy only good 1buy only good 2
buy nothing
Consumers split into four groups:buy the bundle
buy only good 1buy only good 2
buy nothing
pB - p1
pB - p2
Consumers in thisregion are willing to
buy both goods. Theybuy the bundle
Consumers in thisregion are willing to
buy both goods. Theybuy the bundle
Consumers in thisregion also
buy the bundle
Consumers in thisregion also
buy the bundle
Consumers in thisregion buy nothing
Consumers in thisregion buy nothing
Consumers in thisregion buy only
good 1
Consumers in thisregion buy only
good 1
Consumers in thisregion buy only
good 2
Consumers in thisregion buy only
good 2
This leavestwo regions
This leavestwo regions
In this regionconsumers buy
either the bundleor product 1
In this regionconsumers buy
either the bundleor product 1
In this regionconsumers buy
either the bundleor product 2
In this regionconsumers buy
either the bundleor product 2
64
Mixed bundling 2
R2
R1p1
p2
pB
pB
pB - p1
pB - p2
x
p1x
p2x
p1x+p2x
Consider consumer x withreservation prices p1x for
product 1 and p2x forproduct 2
Consider consumer x withreservation prices p1x for
product 1 and p2x forproduct 2
Her aggregate willingness to pay for the bundle is
p1x + p2x
Her aggregate willingness to pay for the bundle is
p1x + p2x
Consumer surplus frombuying the bundle is
p1x + p2x - pB
Consumer surplus frombuying the bundle is
p1x + p2x - pB
Which is thismeasure
Which is thismeasureConsumer surplus from
buying product 1 isp1x - p1
Consumer surplus frombuying product 1 is
p1x - p1
The consumer x will buy only
product 1
The consumer x will buy only
product 1
All consumers inthis region buyonly product 1
All consumers inthis region buyonly product 1
Similarly, all consumers in
this region buyonly product 2
Similarly, all consumers in
this region buyonly product 2
65
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
66
An ExampleFour consumers; two products; MC1 = $100, MC2 = $150
ConsumerReservation
Price for Good 1
Reservation Price for Good 2
Sum of Reservation
Prices
A
B
C
D
$50 $450 $500
$250 $275 $525
$300 $220 $520
$450 $50 $500
67
The example 2
Consider simplemonopoly pricing
Consider simplemonopoly pricing
Good 1: Marginal Cost $100
Price Quantity Total revenue Profit
$450$300
$250
$50
12
3
4
$450$600
$750
$200
$350$400
$450
-$200
$250
Good 2: Marginal Cost $150
Price Quantity Total revenue Profit
$450$275
$220
$50
12
3
4
$450$550
$660
$200
$300$200
$210
-$400
$450
Good 1 should be soldat $250 and good 2 at
$450. Total profitis $450 + $300
= $750
Good 1 should be soldat $250 and good 2 at
$450. Total profitis $450 + $300
= $750
68
The example 3
ConsumerReservation
Price for Good 1
Reservation Price for Good 2
Sum of Reservation
Prices
A
B
C
D
$50 $450 $500
$250 $275 $525
$300 $220 $520
$450 $50 $500
Now consider purebundling
Now consider purebundling
The highest bundleprice that can be
considered is $500
The highest bundleprice that can be
considered is $500All four consumers will buy
the bundle and profit is4x$500 - 4x($150 + $100)
= $1,000
All four consumers will buythe bundle and profit is
4x$500 - 4x($150 + $100)= $1,000
69
The example 4
ConsumerReservation
Price for Good 1
Reservation Price for Good 2
Sum of Reservation
Prices
A
B
C
D
$50 $450 $500
$250 $275 $525
$300 $220 $520
$450 $50 $500
Take the monopoly prices p1 = $250; p2 = $450 and a bundle price pB = $500
$500
$500
$250
$250
All four consumers buysomething and profit is
$250x2 + $150x2= $800
All four consumers buysomething and profit is
$250x2 + $150x2= $800
Now consider mixedbundling
Now consider mixedbundling
Can the seller improveon this?
Can the seller improveon this?
70
The example 5
ConsumerReservation
Price for Good 1
Reservation Price for Good 2
Sum of Reservation
Prices
A
B
C
D
$50 $450 $500
$250 $275 $525
$300 $220 $520
$450 $50 $500
Try instead the prices p1 = $450; p2 = $450 and a bundle price pB = $520
$450
$520
$520
$450
All four consumers buyand profit is $300 +
$270x2 + $350= $1,190
All four consumers buyand profit is $300 +
$270x2 + $350= $1,190
This is actuallythe best that the
firm can do
71
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
72
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
73
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, high-
demand 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
74
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
75
Tie-in sales: an example 2
High-DemandConsumers
Low-DemandConsumers
Demand: P = 16 - QDemand: P = 16 - Q Demand: P = 12 - QDemand: P = 12 - Q
$
Quantity Quantity
$16
16
$12
$
12
Recall that the film sells at $2
per picture
Recall that the film sells at $2
per picture
$2 $2
14
Low-demand consumers take 10
pictures
Low-demand consumers take 10
pictures
10
Consumer surplus for low-demand
consumers is $50
Consumer surplus for low-demand
consumers is $50
$50
Consumer surplus for high-demand consumers is $98
Consumer surplus for high-demand consumers is $98
$98
High-demand consumers take 14
pictures
High-demand consumers take 14
pictures
So the firm can set a lease charge of $50
to each type of consumer: it cannot
discriminate
So the firm can set a lease charge of $50
to each type of consumer: it cannot
discriminate
Profit is $50 from each low-demand and high-
demand consumer. Total profit is $100,000
Profit is $50 from each low-demand and high-
demand consumer. Total profit is $100,000
76
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
77
Tie-in sales: an example 2
$16
16
$12
12
High-DemandConsumers
Low-DemandConsumers
Demand: P = 16 - QDemand: P = 16 - Q Demand: P = 12 - QDemand: P = 12 - Q
$
Quantity Quantity
$
$2 $2
12
Low-demand consumers take 8
pictures
Low-demand consumers take 8
pictures
8
Consumer surplus for low-demand
consumers is $32
Consumer surplus for low-demand
consumers is $32
Each high-demand consumer will lease the camera at $32
Each high-demand consumer will lease the camera at $32
Aggregate profit is now $48,000 + $56,000 =
$104,000
Aggregate profit is now $48,000 + $56,000 =
$104,000
$4 $4$32
Lease the camera at $32. Profit is $32 plus $16 in film
profits = $48
Lease the camera at $32. Profit is $32 plus $16 in film
profits = $48
$16
$32
Profit is $32 plus $24 in film profits =
$56
Profit is $32 plus $24 in film profits =
$56
$24
High-demand consumers take 12
pictures
High-demand consumers take 12
pictures
Tying increases thefirm’s profit
Tying increases thefirm’s profit
78
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
79
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
80
Tie-in sales: an example 2
$16
16
$12
12
High-DemandConsumers
Low-DemandConsumers
Demand: P = 16 - QDemand: P = 16 - Q Demand: P = 12 - QDemand: P = 12 - Q
$
Quantity Quantity
$
$2 $2
Low-demand consumers will pay up to $70 to lease
the 10-picure camera
Low-demand consumers will pay up to $70 to lease
the 10-picure camera
Aggregate profit is now $50,000 + $58,000 =
$108,000
Aggregate profit is now $50,000 + $58,000 =
$108,000
$70
101410
12
High-demand consumers get $40 consumer surplus by leasing the 10-
picure camera
High-demand consumers get $40 consumer surplus by leasing the 10-
picure camera
$40
$70
$16
So high-demand consumers can be
charged $86 to lease the 14-picture
camera
So high-demand consumers can be
charged $86 to lease the 14-picture
camera
81
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)
82
Complementary goods 2Demand 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 pricesAssume 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
83
Complementary goods 3Therefore 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
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
In equilibrium the price set by the two firms must be consistent
84
Complementary goods 4
PB
PN
Pricing rule for the Bolt
Producer:PB = (A - PN)/2
Pricing rule for the Bolt
Producer:PB = (A - PN)/2A/2
A
Pricing rule for the Nut
Producer:PN = (A - PB)/2
Pricing rule for the Nut
Producer:PN = (A - PB)/2
A/2
A Equilibrium iswhere these two
pricing rulesintersect
Equilibrium iswhere these two
pricing rulesintersect
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
A/3
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
85
Complementary goods 5What happens if the two goods are produced by the same firm?
The firm will set a price PNB for a nut/bolt pair.
Demand is now QNB = A - PNB so that PNB = A - QNB
$
Quantity
MRNB = A - 2QNB
A
A
DemandMR
MR = MC = 0 QNB = A /2
A/2
PNB = A /2A/2
Profit of the nut/bolt producer is PNBQNB = A2/4
Merger of the two firms results in consumers
being chargedlower prices and the firmmaking greater profits Why? Because the
merged firm is able to coordinate the prices of
the two goods
86
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
87
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
88
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
89
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
90
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
91
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
92
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
93
Competitive Bundling/Tying 3 Product
Pain Relief Decongestant Bundle
Demand 50 50 100Costs
Fixed Cost $300 $300 $300Marginal Cost $4 $4 $7
Feasible Prices
Separate Goods $6 $6 -----Pure Bundling ---- ---- $8.50
Mixed Bundling $10 $10 $10Bundle + Good 1 $10 ---- $9Bundle + Good 2 ---- $10 $9
$8.50 is lowest feasible price and is
achieve by only offering the bundled
product
Moral: competitive pressure may be the
underlying reason for much bundling
94
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-of-
reason standard with increasing recognition that whether price discrimination or competitive pressure is the reason, bundling/tying is often welfare-improving
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