1 Product Variety and Quality under Monopoly. 2 Introduction Most firms sell more than one product...

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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

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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.

9

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


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)





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


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


the demand curve aroundthe price axis as follows


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

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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!

45

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

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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

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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.

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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.

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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.

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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






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


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


Casablanca


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

60

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


pB

pB

Good 1 is soldat price p1




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


good 1


good 2


good 2

This leavestwo regions

This leavestwo regions

In this regionconsumers buy

either the bundleor product 1







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


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


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



Can the seller improveon this?

Can the seller improveon this?

70

The example 5

ConsumerReservation

Price for Good 1


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


pictures

10

Consumer surplus for low-demand

consumers is $50


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


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


$16

16

$12

12


Low-DemandConsumers


$

Quantity Quantity

$

$2 $2

12


pictures


pictures

8


consumers is $32


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


$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


pictures


pictures

Tying increases thefirm’s profit

Tying increases thefirm’s profit

78


• 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


• 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


$16

16

$12

12


Low-DemandConsumers


$

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


$108,000


$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

1 Product Variety and Quality under Monopoly. 2 Introduction Most firms sell more than one product...

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Transcript of 1 Product Variety and Quality under Monopoly. 2 Introduction Most firms sell more than one product...