Industrial Organization: Chapter 41 Chapter 4 Product and Pricing Strategies for the Multiproduct...

Industrial Organization: Chapter 4 1

Chapter 4

Product and Pricing Strategies

for the

Multiproduct Monopolist


Introduction

• A monopolist can offer goods of different varieties– multiproduct firms

• The “big” issues:– pricing

– product variety: how many?

– product bundling:• how to bundle

• how to price

• whether to tie the sales of one product to sales of another

• Price discrimination

4-1


Price Discrimination

• This is a natural phenomenon with multiproduct firms– restaurant meals: table d’hôte or à la carte

– different varieties of the same car

– airline travel• “goods” of different quality are offered at very different prices

• Note the constraints– arbitrage

• ensuring that consumers buy the “appropriate” good

– identification

• How to price goods of different quality?


Price discrimination and quality

• Extract all consumer surplus from the low quality good

• Use screening devices– Set the prices of higher quality goods

• to meet incentive compatibility constraint

• to meet the constraint that higher price is justified by higher quality

• One interesting type of screening: crimping the product– offer a product of reasonably high quality

– produce lower quality by damaging the higher quality good• student version of Mathematica

• different versions of Matlab

• the “slow” 486SX produced by damaging the higher speed 486DX

– why?• for cost reasons


A Spatial Approach to Product Variety• Approach to product quality in Chapter 3 is an example of

vertical product differentiation– products differ in quality

– consumers have similar attitudes to quality: value high quality

• An alternative approach– consumers differ in their tastes

– firm has to decide how best to serve different types of consumer

– offer products with different characteristics but similar qualities

• This is horizontal product differentiation


A Spatial Approach to Product Variety (cont.)

• The spatial model (Hotelling) is useful to consider– pricing

– design

– variety

• Has a much richer application as a model of product differentiation– “location” can be thought of in

• space (geography)

• time (departure times of planes, buses, trains)

• product characteristics (design and variety)


A Spatial Approach to Product Variety (cont.)

• Assume N consumers living equally spaced along Main Street – 1 mile long.

• Monopolist must decide how best to supply these consumers

• Consumers buy exactly one unit provided that price plus transport costs is less than V.

• Consumers incur there-and-back transport costs of t per unit

• The monopolist operates one shop– reasonable to expect that this is located at the center of Main Street


The spatial model

x = 0 x = 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 + t.x p1 + t.x

p1 + t.x1 = 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


The spatial model

x = 0 x = 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


The spatial model

• Suppose that all consumers are to be served at price p.– The highest price is that charged to the consumers at the ends of

the market

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

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

– So p = V – t/2.

• Suppose that marginal costs are c per unit.

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

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


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*?


Location with Two Shops

Suppose that the entire market is to be servedSuppose that the entire market is to be served

Price Price

x = 0 x = 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



Price Price

x = 0 x = 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



Price Price

x = 0 x = 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


Three Shops

Price Price

x = 0 x = 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


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) – n.F

How manyshops should

there be?

How manyshops should

there be?


Optimal number of shops (cont.)

Profit from n shops is (N, n) = (V - t/2n - c)N - n.F

and 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.


An example

Suppose that F = $50,000 , N = 5 million and t = $1

Then t.N/2F = 50

So we need n(n + 1) < 50. This gives n = 6

There should be no more than seven shops in this case: if n = 6 then adding one more shop is profitable.

But if n = 7 then adding another shop is unprofitable.


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.


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 to be served then price is p(N,n) = V – t/2n

• Only part of the market should be served if p(N,n) > p*

• This implies that V > c + t/n.


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


Social Optimum Are there toomany shops or

too 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 N.V - Total CostTotal surplus is therefore N.V - 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?


Social optimum (cont.)

Price Price

x = 0 x = 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


Social optimum (cont.)

Total cost with n shops is, therefore: C(N,n) = n(t/4n2)N + n.F

= tN/4n + n.F

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


Monopoly, Product Variety and Price Discrimination

• Suppose that the monopolist delivers the product.– then it is possible to price discriminate

• What pricing policy to adopt?– charge every consumer his reservation price V– the firm pays the transport costs– this is uniform delivered pricing– it is discriminatory because price does not reflect costs

• Should every consumer be supplied?– suppose that there are n shops evenly spaced on Main Street– cost to the most distant consumer is c + t/2n– supply this consumer so long as V (revenue) > c + t/2n– This is a weaker condition than without price discrimination.– Price discrimination allows more consumers to be served.


Price Discrimination and Product Variety

• How many shops should the monopolist operate now?

Suppose that the monopolist has n shops and is supplying the entire market.

Total revenue minus production costs is N.V – N.c

Total transport costs plus set-up costs is C(N, n)=tN/4n + n.F

So profit is (N,n) = N.V – N.c – C(N,n)

But then maximizing profit means minimizing C(N, n)

The discriminating monopolist operates the socially optimal number of shops.


Bundling• Firms sell goods as bundles

– selling two or more goods in a single package

– complete stereo systems

– fixed-price meals in restaurants

• Firms also use tie-in sales: less restrictive than bundling– tie the sale of one good to the purchase of another

– computer printers and printer cartridges

– constraining the use of spare parts

• Why?

• Because it is profitable to do so!


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


Bundling: an example

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


Bundling (cont.)

• Extend this example to allow for– costs

– mixed bundling: offering products in a bundle and separately


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


Bundling: the example (cont.)

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


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








Mixed Bundling (cont.)

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


Mixed Bundling (cont.)

• What should a firm actually do?

• There is no simple answer– mixed bundling is generally better than pure bundling

– but bundling is not always the best strategy

• Each case needs to be worked out on its merits


An Example

Four 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


The example (cont.)

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


The example (cont.)

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


The example (cont.)

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?


The example (cont.)

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


Bundling (cont.)

• Bundling does not always work

• Requires that there are reasonably large differences in consumer valuations of the goods

• What about tie-in sales?– “like” bundling but proportions vary

– allows the monopolist to make supernormal profits on the tied good

– different users charged different effective prices depending upon usage

– facilitates price discrimination by making buyers reveal their demands


Tie-in Sales

• Suppose that a firm offers a specialized product – a camera? – that uses highly specialized film cartridges

• Then it has effectively tied the sales of film cartridges to the purchase of the camera– this is actually what has happened with computer printers and ink

cartridges

• How should it price the camera and film?– suppose that marginal costs of the film and of making the camera

are zero (to keep things simple)

– suppose also that there are two types of consumer: high-demand and low-demand


Tie-In Sales: an Example

High-DemandConsumers

Low-DemandConsumers

Demand: P = 16 - QDemand: P = 16 - Q Demand: P = 12 - QDemand: P = 12 - Q

$

Quantity Quantity

$16

16

$12

$

12

Low-demand consumers are

willing to buy 12 units

Low-demand consumers are

willing to buy 12 units

Suppose that the firm leases the

product for $72 per period

Suppose that the firm leases the

product for $72 per period

$72

High-demand consumers buy 16

units


units$128

Profit is $72 from each type of consumer

So this gives profit of $144 per pair of high-

and low-demand consumers

Profit is $72 from each type of consumer

So this gives profit of $144 per pair of high-

and low-demand consumers

Is this the best that

the firm can do?




Low-DemandConsumers


$

Quantity Quantity

$16

16

$12

$

12

Suppose that the firm sets a price of $2 per

unit

Suppose that the firm sets a price of $2 per

unit

$2 $2

14

Low-demand consumers buy 10

units

Low-demand consumers buy 10

units

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


units


units

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 $70 from each low-demand consumer:

$50 + $20and $78 from each

high-demand consumer: $50 + $28

giving $148 per pair of high-demand and low-

demand

Profit is $70 from each low-demand consumer:

$50 + $20and $78 from each

high-demand consumer: $50 + $28

giving $148 per pair of high-demand and low-

demand




Low-DemandConsumers


$

Quantity Quantity

$16

16

$12

$

12

Suppose that the firm can

bundle the two goods instead

of tie them

Suppose that the firm can

bundle the two goods instead

of tie them

Low-demand consumers can be sold this bundled product for $72

Low-demand consumers can be sold this bundled product for $72

$72

Profit is $72 from each low-demand consumer

and $80 from each high-demand consumer giving $150 per pair of high-demand and low-

demand

Profit is $72 from each low-demand consumer

and $80 from each high-demand consumer giving $150 per pair of high-demand and low-

demand

Produce a bundled product of camera

plus 12-shot cartridge

Produce a bundled product of camera

plus 12-shot cartridge

12

$72

$48

High-demand consumers get $48 consumer surplus

from buying it

High-demand consumers get $48 consumer surplus

from buying it

So produce a second bundle of camera plus

16-shot cartridge

So produce a second bundle of camera plus

16-shot cartridgeHigh-demand

consumers will pay $80 for this bundled camera ($128 - $48)

High-demand consumers will pay $80 for this bundled camera ($128 - $48)

$8


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)


Complementary goods (cont.)

This demand curve can be written individually for nuts and bolts

For bolts: QB = A - (PB + PN)

For nuts: QN = A - (PB + PN)

These give the inverse demands: PB = (A - PN) - QB

PN = (A - PB) - QN

These allow us to calculate profit maximizing prices

Assume that nuts and bolts are produced by independent firms

Each sets MR = MC to maximize profits

MRB = (A - PN) - 2QB

MRN = (A - PB) - 2QN

Assume MCB = MCN = 0



Therefore QB = (A - PN)/2

and PB = (A - PN) - QB = (A - PN)/2

by a symmetric argument PN = (A - PB)/2

The price set by each firm is affected by the price set by the other firm

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



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



What 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


Product variety (cont.)

d < 1/4

We know that p(d) satisfies the following constraint:

p(d) + t(1/2 - d) = V

This gives: p(d) = V - t/2 + t.d

p(d) = V - t/2 + t.d

Aggregate profit is then: (d) = (p(d) - c)N

= (V - t/2 + t.d - c)N

This is increasing in d so if d < 1/4 then d should be increased.


Product variety (cont.)

d > 1/4

We now know that p(d) satisfies the following constraint:

p(d) + t.d = V

This gives: p(d) = V - t.d

Aggregate profit is then: (d) = (p(d) - c)N

= (V - t.d - c)N

This is decreasing in d so if d > 1/4 then d should be decreased.

Industrial Organization: Chapter 41 Chapter 4 Product and Pricing Strategies for the Multiproduct...

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