Vertical Restraints

Chapter 13: Vertical Restraints 1

Introduction

• Many contractual arrangements between manufacturers – Some restrict rights of retailer • Can’t carry alternative brands • Expected to provide services or to deliver product in a specific amount of time – Some restrict rights of manufacturer • Can’t supply other dealers • Must buy back unsold goods – Some involve restrictions/guidelines on pricing Chapter 13: Vertical Restraints 2

Resale Price Maintenance

• Resale Price Maintenance is the most important type of vertical price restriction. Under RPM agreement – Retailer agrees to sell at manufactured specified price – RPM agreements have a long and checkered history •

In US, Dr. Miles case of 1911established per se illegality for any and all such agreements

• •

However, Colgate case of 1919 allowed some “wiggle room” Miller-Tydings (1937) and McGuire (1952) Acts even more supportive in allowing states to enforce RPM contracts

– Repeal of Miller-Tydings and McGuire Acts reverted legal status back to (mostly)

per se

illegal –

State Oil v. Khan

decision in 1997 allowed rule of reason in RPM agreements setting

maximum

price –

Leegin

case applies rule of reason to

minimum price

Chapter 13: Vertical Restraints 3

RPM Agreements & Double Marginalization

• Recall the Double Marginalization Problem – Downstream Demand is •

P

=

A – BQ

and Retailer has no cost other than wholesale purchase price

Downstream Marginal Revenue = MR

D

= A – 2BQ

•

MR D

=Upstream Demand

•

Upstream Marginal Revenue = MR

U

= A – 4BQ

– With Manufacturer’s marginal cost

c

, profit maximizing output and upstream price are:

Q

 

A

 4

B c

 and

P U

 

A

 2

c



–

Downstream price is:

P D

 2

B

4 Chapter 13: Vertical Restraints 4

RPM & Double Marginalization 2

• With a vertical chain of a monopoly manufacturer and a monopoly retailer, the downstream price is far too high – There is a pricing externality •

The manufacturer profit is the wholesale price r – cost c times the volume of output Q [= (r – c)Q]

• •

Once r is set, manufacturer’s profit rises with Q In setting a markup over the wholesale price, the retailer limits Q and cuts into manufacturer profit

•

But retailer ignores this external effect

– Retail (and wholesale) price maximizing

P

* 

r



 

2

<

joint

profit Independent retailer’s price Chapter 13: Vertical Restraints 5

RPM & Double Marginalization 3

• An RPM restriction that prohibits the retailer from selling at any price higher than

P*

would permit the manufacturer to achieve the maximum profit – There is though an alternative to the RPM, namely a Two-Part Tariff of the type discussed in Chapter 5 • •

Set wholesale price at marginal cost c Retailer will then choose P

D

earn profit = (A – c) 2 /4B = P* = (A + c)/2 and

•

Charge franchise fee of T = (A – c) 2 /4B

Chapter 13: Vertical Restraints 6

RPM & Price Discrimination

• An RPM to prevent double marginalization suggests problem is that the retail price is too high • Historical record suggests that perceived problem is often that retail price is too low –

Need to find reason(s) for RPM agreements aimed at keeping retail prices high

–

Retail Price Discrimination may present case where RPM specifying minimum price can help manufacturer

Chapter 13: Vertical Restraints 7

–

RPM & Price Discrimination (cont.)

• Suppose retailer operates in two markets

One has less elastic demand (monopolized)

–

One has elastic demand (due to potential entrant)—retail price P cannot rise above wholesale price r

• Manufacturer must use same contract for each –

Maximum profit in each market = (A – c) 2 /4B achieved at P* = (A + c)/2

–

No single price or single two-part tariff can maximize profit from both markets

– –

Unless r = (A + c)/2 in elastic demand market, P* cannot be achieved since in that market P = r But there is only one contract, so this implies r = (A + c)/2 in inelastic (monopolized) market and so to double marginalization

• Solution: write common contract that sets

r

=

c, and

imposes RPM minimum price of

P

=(

A

+

c

)/2 Chapter 13: Vertical Restraints 8

RPM and Retail Services

• So far the retailer has been a totally passive intermediary between manufacturer and consumer • Retailers actually provide additional services: marketing, customer assistance, information, repairs.

–

These services increase sales

–

This benefits manufacturers

• But offering these services is costly, and also –

both services and costs are hard for manufacturer to measure

–

Retailers interested in her profit not manufacturer’s

• How does the manufacturer provide incentives for retailer to offer services?

Chapter 13: Vertical Restraints 9

RPM and Retail Services 2

• Think of retail services

s

and shifting out demand curve similar to the way that quality increases shifted out the demand curve in Chapter 6

$/unit

Demand with retail services s = 1 Demand with retail services s = 2

•

Quantity

But cost of providing retail services  (

s

) rises as more services are provided

$/unit

 (

s

) Chapter 13: Vertical Restraints

Service Level s

10

RPM and Retail Services 3

• As a benchmark, see what happens if manufacturing and retailing are integrated in one firm – suppose that consumer demand is Q = 100

s

(500 - P) – Note how

s

shifts out demand – assume that marginal costs are

c m

and for the

c r

for retailing for manufacturing – the cost of providing retail services is an increasing function of the level of services,  (

s

) – the integrated firm’s profit 

I

– 

I

is:

= [P-c

m

-c

r

-



(s)]100s(500 - P)

Chapter 13: Vertical Restraints 11

RPM and Retail Services 4

• The integrated firm has two choices to make: – What price

P

to charge (what

Q

to produce); and – The level of retail services

s

to provide • To maximize profit, take derivatives of integrated firm’s profit function both with respect to

Q

Cancel the

and with respect to

s

and set each equal to zero  

I

/



P = 100s(500 - P) - 100s(P - c

m

- c

r

-



(s)) = 0

 

500 - 2P + c

m

P* = (500 + c + c

m r

+ + c

r



(s) = 0 +



(s))/2

Chapter 13: Vertical Restraints 12

•

Cancel the

RPM and Retail Services 5

100(500 - P)

• Now take the derivative with respect to services

s

and set it equal to 

I /



s = 100s(500 - P)(P - c

m

- c

r

-



(s)) - 100s(500 - P)



’(s) = 0

Solving we obtain: 

(P - c

m

- c

r

-



(s)) = s



’(s)

• Substituting the price equation into the service equation then yields: 

(500 - c

m

- c

r

)/2 =



(s)/2 + s



’(s)

• The

s

that satisfies the above equation gives the efficient (profit-maximizing) level of services Chapter 13: Vertical Restraints 13

The left hand side is

RPM and Retail Services 6

decreasing in c m and c r Let c m and c r

production and retailing marginal cost (

be initial marginal costs

c m

increase in marginal costs,



(500 - c

m

- c

r

)/2 =



apart from services, at either the manufacturing or retail level to a fall in the



(s)/2 + s



’(s)

from s * to s ** Let c’ m and c’ r be new marginal costs

(500-

c’ m

-c’

r

)/2

s** s*

Chapter 13: Vertical Restraints Service Level

s

14

• • • • •

RPM and Retail Services 7

For example let

c m

Then (500 - c m = $20,

c r

= $30 and  (

s

) = 90s - c r )/2 =  (s)/2 + s  (s) implies 2

225 = 45s 2 + s180s ; OR 225 = 225s 2



s = 1

Then, solving for

P

(P - c

m

- c

r

-

we obtain: 

(s)) = 180s 2 = 180



P= $320

Implying an output level of:

Q = 100s(500 - P) = 18,000

The integrated firm earns profit 

I

= $3.24 million.

It chooses the socially efficient level of retail services but sets price above marginal cost. This is our benchmark case.

Chapter 13: Vertical Restraints 15

RPM and Retail Services 8

• Now let manufacturer sell to monopoly dealer • If we assume two-part pricing is not possible, then the only way that the manufacturer can earn profit is by charging a wholesale price

r

above cost

c m

Cancel the 100s terms

– The profit of the retailer is now:



R

= (

P- r - c

r

 (

s

))100

s

(500 -

P

) = (

P- r

-

30

90

s 2

– Retailer sets P and s to maximize retail profit

)100

s

(500 -

P

)

Cancel the 100(500 - P)

 

R

/ 

P

= 100

s

(500 -

P

) - 100

s

(

P - r

- 30 – 90

s

2 ) = 0

terms

– P = (530 + r + 90s 2 )/2

 R / 

s

= 100(500 -

P

)(

P - r

- 30 – 90

s

2 ) - 100

s

(500 -

P

)180

s

= 0 –

P – r – 30 = 270s 2

Chapter 13: Vertical Restraints 16

RPM and Retail Services 9

• Put the two profit-maximizing conditions together (500 –

r

–

c r

)/2 =  (

s

)/2 +

s

 ’(

s

) OR 225

s

2 = 235 –

r

/2

– It is clear that unless r = c

m

= 20, s will be less than 1, i.e., less than the optimal level of services – – Yet absent an alternative pricing arrangement, the manufacturer only earns a positive profit if r > 20. From the retailer’s perspective, a value of r > 20 is equivalent to a rise in c

m

and as we saw previously, this reduces the retailer’s optimal service level

Chapter 13: Vertical Restraints 17

RPM and Retail Services 10

• Two contracts that might solve the problem are: –

A royalty contract written on the retailer’s profit;

– • Under a profit-royalty contract, the manufacturer sells at cost

c m

to the retailer but claims a percentage

x

of the retailer’s profit –

A two-part tariff This works because there is no difference between maximizing total retail profit or maximizing (1 – x) of total retail profit

–

Given that the wholesale cost is c

m

, the profit-maximizing condition: 235 = 225s

2

+ r/2 leads to s = 1, the efficient level of services

Chapter 13: Vertical Restraints 18

RPM and Retail Services 11

• Similarly, a two-part tariff could solve the problem: –

Again, sell at wholesale price c

m

= $20;

–

As before, this leads to the efficient level of services, namely, s = 1.

–

Now manufacturer can claim downstream profit (or some part of it) by use of an upfront franchise fee

• However, both royalty and two-part tariff requires that manufacturer know the retailer’s true profit level. This can be difficult if retailer has inside information on the nature of: – –

Retailing cost, c

r

Retail consumer demand

Chapter 13: Vertical Restraints 19

RPM and Retail Services 12

• Can an RPM solve the problem? – –

It has the advantage that it is easily monitored It also addresses the double-marginalization problem

–

However, it cannot solve the service problem in the present context

•

Without a royalty or up-front franchise fee, manufacturer

• •

can only earn profit if r > c

m

.

As we have seen, this in itself leads to a service reduction Imposing a maximum price via an RPM agreement intensifies this fall in service because it reduces the retailer’s margin, P – r, and it is that margin that funds the provision of services

Chapter 13: Vertical Restraints 20

RPM and Retail Services 13

• However, use of an RPM becomes considerably more attractive if retail sector is competitive –

large number of identical retailers

– –

each buys from the manufacturer at r and incurs service costs per unit of



(s) plus marginal costs c

r

competition in retailing drives retail price to P

C



(s)

= r + c r

+

–

competition also drives retailers to provide the level of services most desired by consumers subject to retailers breaking even

– –

so each retailer sets price at marginal cost chooses the service level to maximize consumer surplus

Chapter 13: Vertical Restraints 21

RPM and Retail Services 14

• With competition there is no retail markup and no retail profit –

P = r + c

r +



(s)

–

Profit royalty and two-part tariff will not work because there is no profit to share or take up front

–

Given wholesale price r, retailers compete by offering level of services s that maximizes consumer surplus

•

Recall: Demand is: Q = 100s(500 - P)

•

P = r

+

c r

+  (

s

) •

Consumer Surplus is therefore:

CS CS

= (500 – = 50

s P

)x

Q

/2 = 50

s

(500 – [500 –

r – c

r

–

 (

s

)] 2

P

) 2 Chapter 13: Vertical Restraints 22

RPM and Retail Services 15

• By way of a diagram, we have: $/unit 500

P=r+c

r

+

 (

s

) Triangle = Consumer Surplus. Given

r

,

c r

, and  (

s

), competitive retailers will compete by offering services that maximize this triangle

Q

50

s

Quantity (000’s) Chapter 13: Vertical Restraints 23

value of

r

RPM and Retail Services 16

Cancel the common term 50(500 - r - c r -



(s))

by maximizing

CS = 50s[500 – r – c

r –



(s)] 2

with respect to

s .

This yields 

CS/



s = 50(500-r-c

r

-



(s)) 2 -100s(500-r-c

r

-



(s))



(s) = 0

• So:

500 - r - c

r



(500 - r - c

r

-



(s) = 2s )/2 =

 

(s) (s)/2 + s



(s)

• This equation gives the competitive level of retail services when the manufacturer simply chooses

r

and lets retailers choose

P

and

s

Chapter 13: Vertical Restraints 24

• • • •

RPM and Retail Services 17

Recall: the integrated firm wants to set a price=

P

* = $320. RPM lets manufacturer impose this price on retailers. With retail price =

P

* = $320, competitive retailers offer services until they just break even, i.e., until: 

(s) = P* – c

r

– r = 90s 2 = 320 – 30 – r

By choosing,

r

= $200, the competitive service level satisfies: •

90s 2 = 90



s = 1 with P = $320

This is the optimal service level and price. The RPM has led to duplication of the integrated outcome Chapter 13: Vertical Restraints 25

RPM and Retail Services 18

• • Consideration of customer services with competitive retailing also gives another reason that RPM agreements may be useful—the free-riding problem.

• Many services are informational –

Features of high-tech equipment

–

Quality, e.g., wine

• Providing these services are costly – – – –

But no obligation of consumer to buy from retailer Discount stores can free-ride on retailer’s services Retailers cut back on services Manufacturers and consumers lose out

RPM agreements prevent free-riding discounters Chapter 13: Vertical Restraints 26

RPM and Variable Demand

• RPM agreements may also be helpful in dealing with variable retail demand • Retailer facing uncertain demand has to balance –

how to meet demand if demand is strong

–

how to avoid unwanted inventory if demand is weak

• monopoly retailer acts differently from competitive –

monopolist throws away inventory when demand is weak to avoid excessive price fall

–

competitive retailer will sell it because he believes that he is small enough not to affect the price

• Intense retail competition if demand is weak – –

reduces the profit of the manufacturer makes firms reluctant to hold inventory

Chapter 13: Vertical Restraints 27

• •

RPM and Variable Demand 2

Suppose that demand is high, D H And that demand is low, D L with probability 1/2 with probability 1/2 Price

– Marginal costs are assumed constant at c – Integrated firm has to choose in each period

stage 1: how much to produce stage 2: demand known- how much to sell since costs are sunk: maximize revenue

D L D H

c

MC

Quantity Chapter 13: Vertical Restraints 28

RPM and Variable Demand 3

Price D H

How is Q*

D L

determined low demand



An integrated firm will not produce more than Q

Upper



And will not produce less than

Q Lower



the integrated firm will produce Q*

c

MC MR L

Q Lower

Q*

Q Upper

MR H Quantity

Chapter 13: Vertical Restraints 29

Price

P Max P Min c

RPM and Variable Demand 4



If demand is high the firm sells Q* at price P

Max

: MR = MR*

H Revenue with



If demand is low selling Q* is excessive



the firm maximizes revenue by selling Q*

L

at price P

Min

: MR = 0



Expected marginal revenue is: D H MR*

H

/2 + 0 = MR*

H

/2



Q* is such that expected MR = MC .

So, MR*

H

/2 = c D L MR* H MC



Expected profit is



I = P Max

Q*/2 + P

Min

Q* L /2 - cQ* MR L Q*

L

Q* MR H Quantity

Chapter 13: Vertical Restraints 30

RPM and Variable Demand 5

Price

P Max c

D L

Suppose that retailing is competitive Revenue with high demand

D H 

Will competitive retailers stock the optimal amount Q*? What will happen if they do?



If demand is high the retail firms sell Q* at price P

Max

: MR = MR*

H



If demand is low each firm will sell more so long as price is positive



So, if demand is low competitive retailers keep selling until they sell the total quantity Q

L

at which price is zero MC



Revenue is therefore zero in low demand

periods if competitive firms stock Q *

MR L

Q L

Q*

MR H

Quantity Chapter 13: Vertical Restraints 31

•

RPM and variable demand 6

If competitive retailers stock Q*, their expected net revenue is thus :

P Max

Q*/2 + 0 = P

Max

Q*/2

• • Competitive firms just break even. So, manufacturer can only charge a wholesale price P W such that:

P W

Q* = P

Max

Q*/2 which gives P

The manufacturer’s profit is then:

W

 M

= (P Max

/2 - c)Q*

= P Max

/2

• This is well below the integrated profit. Competitive retailers sell too much in low demand periods • An RPM agreement can fix this. How?

Chapter 13: Vertical Restraints 32

RPM and Variable Demand 7

P P

Price

Max Min c

D MR L

Q*

L

L D H

Q*



Recall: The integrated firm never sells at a price below P

Min



So, set a minimum RPM of P

Min



In high demand periods Q* is sold at price P

Max



In low demand periods the RPM



agreement ensures that only Q*

L

is sold Expected revenue to the retailers is P

Max

Q*/2 + P

Min

Q*

L

/2

MR* H

MC

MR H Quantity Chapter 13: Vertical Restraints 33

•

RPM and Variable Demand 8

With RPM, expected net revenues of retailers is

P Max

Q*/2 + P

Min

Q*

L

/2

• • Manufacturer can now charge wholesale price

P W

P W

Q* = P

Max

Q*/2 + P

Min

Q*

L

/2

which gives

P W

=

P Max

/2 +

P Min Q

*

L

/2

Q

* such that: • The manufacturer’s profit is  M

= P

Max

Q*/2 + P

Min

Q*

L

/2 - cQ*

• This is the same as the integrated profit

– The RPM agreement has given the integrated outcome – Consumers can gain too because retailers now stock products with variable demand that would otherwise not be stocked.

Chapter 13: Vertical Restraints 34

Nonprice Vertical Restraints

• Vertical Price Restraints are not the only kinds of vertical restrictions • Other common vertical restrictions include – Exclusive Dealing: Manufacturer restricts retailer’s ability to buy and sell brands that compete with the manufacturer’s brand, e.g., Coca-Cola may restrain restaurants or other vendors from selling Pepsi products (

Interbrand competition

) – Exclusive Selling: Retailer restricts manufacturer from supplying other dealers, e.g., Lexus dealer obtains promise from Toyota not to authorize other Lexus dealers to sell in nearby locations

(Intrabrand competition)

Chapter 13: Vertical Restraints 35

Exclusive Dealing

• Exclusive Dealing as a way to deal with Free-Riding • Advertising and promotion by a manufacturer spills over to raise demand for similar products – Example: advertising Tylenol may raise demand not just for Tylenol but also for non-aspirin pain relievers in general – Pharmacist may respond to inquiries about pain relievers by substituting lower-cost non-aspirin pain reliever • •

Substitute costs less because it did not pay for advertising Substitute manufacturer free-rides on the advertising of Tylenol

•

No manufacturer advertising and so no information provision could be the result—This is inefficient.

• Exclusive dealing may solve this problem.

• No spillovers if dealer sells no substitute products Chapter 13: Vertical Restraints 36

Exclusive Dealing 2

• But exclusive dealing can compound monopoly problem • Assume two manufacturers and two retailers – Retailers (1 and 2) are spatially separated by distance

M

along a line – Consumers are spatially located around a circle at each retail location of radius

Given

r

– Manufacturer’s (A and B) products located on circle at retail locations —

A B A B Retailer 1

M

Retailer 2

– Chapter 13: Vertical Restraints 37

Exclusive Dealing 3

• With No Exclusive Dealing, A and B compete at each location

A B A

M

Retailer 1 Retailer 2

B

– Substitutes never more than 2

r

apart – Interbrand Price competition is tough – Retailer 1’s price for B also constrained by availability of A at Retailer 2

M

units away Chapter 13: Vertical Restraints 38

Exclusive Dealing 4

• Exclusive Dealing, A and B at separate locations

A B

M

Retailer 1 Retailer 2

– Interbrand competition greatly reduced – Retailer 1’s price for A less constrained by availability of B at Retailer 2 because this is now – just

M+

4

r

units away – Both manufacturers and retailers can gain at expense of consumers Chapter 13: Vertical Restraints 39

Exclusive Selling and Territories

• Again, there is a free-riding issue – Service and Promotion may benefit other Sellers, especially nearby ones – Each dealer may try to “free ride” on service and promotion of other retailers with result that no services are provided • There is also a price externality – Price cuts by one dealer cut into profits of other dealers – Each dealer considers only the effect on her own profit Chapter 13: Vertical Restraints 40

Exclusive Selling and Territories 2

• Exclusive Selling/Territories may solve these problems – With other dealers far away, each dealer can get the full – benefits of her selling and promotional services – No free riding • Intrabrand price competition lowers double marginalization problem. Why should manufacturer’s want to reduce such competition?

Intra

brand price competition can intensify

inter

brand competition – (Assume no two-part tariffs)Retailers can only pay high wholesale price if they can pass it on at retail level – This requires some monopoly power on part of retailers – Movements in wholesale price now only partly reflected in retail price  Wholesale price competition less intense Chapter 13: Vertical Restraints 41

Aftermarkets

• The Kodak case – Kodak makes micrographic equipment for creating and viewing microfilm as well as office copiers. This is the

Foremarket

.

– Kodak also has a network of technicians who maintain these machines pursuant to separate service and repair contracts – Other, independent service and repair companies compete with Kodak but both independent and Kodak service people rely on Kodak parts – The service and repair market is the not leverage its power in the

Aftermarket

.

– After losing a big service contract to an independent Kodak initiated a new policy of refusing to supply parts to any independent service company, i.e. foreclosing them – Independents sued, but Kodak’s defense was that it could

foremarket

into power in the

aftermarket

because rational consumes would look ahead and if they foresaw a higher price in the aftermarket would reduce their willingness to pay in the foremarket Chapter 13: Vertical Restraints 42

Aftermarkets 2

• The Kodak case (continued) – Kodak ultimately lost the case. – But the issue of using vertical restrictions and there ability of a firm to leverage

foremarket

power into the

aftermarket

remains • The logic of Kodak’s defense is clear. Forward looking consumers will incorporate the cost of expected repairs into their willingness to pay for a new machine.

But

competitive pricing this is not quite the same as saying price will equal marginal cost.

– As Borenstein, Mackie-Mason, and Netz (2000) showed, there can be a “lock-in” effect that shields the firm from aftermarket competition – This lock-in gives rise to a potential for supra Chapter 13: Vertical Restraints 43

Aftermarkets 3

• Lock-in and aftermarket power – Two producers of machines – Marginal Cost of making and repairing a machine = 0 – Machine runs at most two periods – Consumers value machine services at $50 per period – Machine is •

100% reliable in 1 st period

• •

50% breakdown chance in 2 nd period After 1 period of use, consumers are locked in to the technology of whatever brand they bought

•

If there is a breakdown in period 2, it is not worth buying a new machine

•

However, repair worthwhile if done at marginal cost

– Expected value of a new machine at start of period 1 (before purchase) is $50 + 0.5($50) = $75 Chapter 13: Vertical Restraints 44

Aftermarkets 4

• Repair would sell at marginal cost if repair was competitive • But aftermarket foreclosure prevents this – If a firm prevents any rival from repairing its machine, say by foreclosing parts supply then price of repairs can rise to (just under) $50, – For cohort of new customers who have not bought a machine, the machine is still valued at $75 – For those with a broken machine, paying the repair bill of $50 is now worthwhile even though it would not have been worth it ex ante – Of course, $50 is well above marginal cost • Such effects can also arise if some (not necessarily all) consumers are myopic Chapter 13: Vertical Restraints 45

Public Policy

• In the main, public policy toward nonprice vertical restrictions has been dominated by a rule of reason approach • In both Europe and North America, however, policy since the 1990’s has applied the rule of reason with a strong presumption that the restraint is justified • The basic argument is that since the restraint is a voluntary contract between an upstream and downstream firm, it must at least benefit these two parties and may benefit consumers, as well.

• However, policy-makers are not yet ready for a per se legal approach Chapter 13: Vertical Restraints 46

Franchising and Divisionalization

• Why Are There So Many Franchisees? Why do Firms Operate Many Different Divisions?

–Recall the Merger Paradox:  With Cournot or quantity , the merger of two firms makes those firms worse off and remaining firms better off  Why? Because the two merged firms act as one. If there were originally 6 firms and two merge, these two firms are now one of five whereas they were two of six. That is, the merged firms now constitute just one-fifth of the independent decision making units instead of one-third.

Chapter 13: Vertical Restraints 47

Franchising and Divisionalization 2

• This may be the logic behind franchising and divisionalization – By operating many independent divisions or franchises, firms may avoid the logic of the merger paradox •

But with each firm doing this, the industry becomes populated with many divisions and franchises

•

Perhaps more than is consistent with either joint profit maximization or efficiency

Chapter 13: Vertical Restraints 48

Franchising and Divisionalization 3

• Assume demand

P

=

A

–

BQ

and Cournot competition

– – –

Firm

j

has divisions denoted by

i

,

i

= 1,2 Profit of

i

th division of

j

th firm given by: 

ij



q ij

,

Q



ij

  [

A

 

BQ



ij



q ij

 ]

q ij



cq ij

q ij

is output of

i

th division of

j

th firm;

Q -ij

other divisions of all industry firms; and

c

is output of all is marginal cost – Equating marginal revenue and marginal cost yields:

A



BQ



ij

 2

Bq * ij



c

Chapter 13: Vertical Restraints 49

Franchising and Divisionalization 4

• Let

n

1 and

n

2 be the number of divisions at firms 1 and 2, respectively. Since all divisions are alike the , the optimal output of any division is:

q

*

ij

 

n

1 

A



n

2

c

 1 

B

• Solving for industry output

Q Q

   

n

1

n

1  

n

2

n

2  1     

A B c

   and and price

P,

we have:

P



A



n

1 

n

1 

n

 2

n

 2 1 

c

Chapter 13: Vertical Restraints 50

Franchising and Divisionalization 5

• • Given its optimal output,

q ij *,

each division at each firm will earn profit 

ij



B



n

1 

A

 

n c

2  2  Firm 1’s total profit is:

n

1 

i

,1 1  2 –

Kn

1 where

K

sunk cost of setting up each division. So  1 

n

1 ,

n

2  

n

1

B



n

1   

n

2 2  1 2  

K

1 is the Chapter 13: Vertical Restraints 51

Franchising and Divisionalization 6

• Maximizing firm 1’s profit with respect to

n

1 and recognizing that by symmetry, each firm must have the same optimal number of divisions then yields: 

n

1 *   2 

n

*  1 2 2     1

n

1 *  2

n

1 *

n

2 *   1     

K

• Solving for the optimal number of divisions at any firm we have

n

*  1 2       

A



K c

 2 1 3  1     Chapter 13: Vertical Restraints 52

Franchising and Divisionalization 7

• The implication is that the greater the potential for monopoly profit (

A

–

c

), the greater the incentive for firms to create more divisions.

But

– More independent divisions brings the industry profit down – Firms engaged in a prisoner’s dilemma gain in which each adds divisions to the detriment of joint industry profit – Depending on the nature of the sunk cost of creating a division, it is even possible that the total surplus may be reduced by excess divisionalization Chapter 13: Vertical Restraints 53

Empirical Application: Exclusive Dealing in the Beer Industry

• US beer market has three tiers – Brewers (Anheuser-Busch, Miller, Molson-Coors) sell to – Distributors who sell to – Retailers • It is common for brewers to adopt exclusive contracts and exclusive territories with distributors • Reasons for exclusive contracts – Foreclosure of rivals. If this is the motivation, exclusive contracts will become less likely as market grows because there will be room for lots of distributors and tying up one or a few will not keep out rivals – Protect advertising investment against free-riding. If this is the motivation, exclusive contract will become more likely as the national advertising level rises Chapter 13: Vertical Restraints 54

Empirical Application: Exclusive Dealing in the Beer Industry 2

• Sass (2005) analyzes 381 beer distribution contracts 69 of which have an exclusive dealing arrangement • Uses probit estimation to determine how probability of an exclusive contract rises as a function of: – Market size as measured by: • Regional population,

POP

• Market share of distributor’s largest supplying brewery,

MSD

– Advertising as measured by • National Advertising of distributor’s main supplier,

ADS

• Presence of a ban on billboard advertising in the state,

BAN

– Years distributor has been owned by one family, YRS, which may indicate how experienced distributor is. Highly experienced distributors may not want to be restricted by an exclusive contract Chapter 13: Vertical Restraints 55

Empirical Application: Exclusive Dealing in the Beer Industry 3

• Sass (2005) analyzes 381 beer distribution contracts 69 of which have an exclusive dealing arrangement. The results of his Probit estimation are shown below

Explanatory Estimated Variable Coefficient t-statistic

POP MSD ADS BAN YRS

0.0001

(1.87) 0.0079 (2.79) -0.0017 (-2.10) -0.0002 (-0.38) -0.0095 (-2.12)

Chapter 13: Vertical Restraints 56

Empirical Application: Exclusive Dealing in the Beer Industry 4

• Interpretation of Sass (2005) results – Foreclosure not a likely motivation for exclusive beer contracts because these become

more

likely as market size grow – Protection of advertising against free-riding seems to be a more compelling explanation for exclusive contracts.

•

Such contracts more likely as advertising expense rises; and

•

Such contracts less likely if billboard advertising is banned

– Experienced distributors with lots of specialized information about the local market like to be free to use that information as they see best and so such distributors are less likely to sign an exclusive contract Chapter 13: Vertical Restraints 57

Empirical Application: Exclusive Dealing in the Beer Industry 5

• Sass (2005) then examines the effect of the exclusive contracts. He finds that – Exclusive contracts raise the wholesale price by about six percent and the retail price by about three percent – Despite these price increases, exclusive contracts also raise total sales volume for both the brewer’s own brand and its rivals by about 30 percent.

• This again suggests that the exclusive contracts are being used to enhance the effectiveness of advertising. In so doing, they raise demand and thereby raise both price and output.

• Profit to brewers, wholesalers, and retailers rises. Given sales increase, consumer surplus likely rises, too. Chapter 13: Vertical Restraints 58