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 = MRD = A – 2BQ
• MRD =Upstream Demand
• Upstream Marginal Revenue = MRU = A – 4BQ
– With Manufacturer’s marginal cost c, profitmaximizing output and upstream price are:

A  c
Q
4B
– Downstream price is:
and
P
D
P
U

A  c


A  r  3 A  c 


2B
Chapter 13: Vertical Restraints
2
4
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 joint profit

A  c
P * r 
< Independent retailer’s price
2
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 PD = P* = (A + c)/2 and
earn profit = (A – c)2/4B
• 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
Demand with
$/unit
Demand with
retail services
retail services
s=1
s=2
Quantity
• But cost of providing retail services (s) rises as
more services are provided
$/unit
(s)
Service Level s
Chapter 13: Vertical Restraints
10
RPM and Retail Services 3
• As a benchmark, see what happens if manufacturing
and retailing are integrated in one firm
– suppose that consumer demand is Q = 100s(500 - P)
– Note how s shifts out demand
– assume that marginal costs are cm for manufacturing
and for the cr for retailing
– the cost of providing retail services is an increasing
function of the level of services, (s)
– the integrated firm’s profit I is:
– I = [P-cm-cr-(s)]100s(500 - P)
Chapter 13: Vertical Restraints
11
RPM and Retail Services 4
• The integrated firm has two choices to make:
– What price P to charge (what Q to produce); and
– The level of retail services s to provide
• To maximize profit, take derivatives of integrated
Cancel the
firm’s profit function both with respect to Q and100s
with
terms
respect to s and set each equal to zero
I/P = 100s(500 - P) - 100s(P - cm - cr - (s)) = 0
 500 - 2P + cm + cr + (s) = 0
 P* = (500 + cm + cr + (s))/2
Chapter 13: Vertical Restraints
12
Cancel the
RPM and Retail Services 5 100(500 - P)
terms
• Now take the derivative with respect to services s and set
it
equal to
I/s = 100s(500 - P)(P - cm - cr - (s)) - 100s(500 - P)’(s) = 0
• Solving we obtain:
 (P - cm - cr - (s)) = s’(s)
• Substituting the price equation into the service equation
then yields:
 (500 - cm - cr)/2 = (s)/2 + s’(s)
• The s that satisfies the above equation gives the efficient
(profit-maximizing) level of services
Chapter 13: Vertical Restraints
13
The left hand side is
RPM
decreasing in cm and
cr and Retail Services 6
right hand
• We can use this equation to show howThe
changes
in theside is
production and retailing
marginal
cost
(cincreasing
and cisr) an
affect
in s
Suppose
now
that
mthere
Let cm and cthe
initial level of services
r beoptimal
increase in marginal costs,
marginal costs
apart from services, at either
 (500 - cm - cr)/2 =the
(s)/2
+ s’(s)
manufacturing
or retail level
The rise$/unit
in cost leads
(s)/2 + s’(s)
to a fall in the
(500-cm-c
optimal
choice
of s
r)/2
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 cm = $20, cr = $30 and (s) = 90s2
Then (500 - cm - cr)/2 = (s)/2 + s(s) implies
225 = 45s2 + s180s ; OR 225 = 225s2  s = 1
• Then, solving for P we obtain:
(P - cm - cr - (s)) = 180s2 = 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
the
way that the manufacturer can earn profit Cancel
is by charging
a
100s terms
wholesale price r above cost cm
– The profit of the retailer is now:
R = (P- r - cr - (s))100s(500 - P) = (P- r - 30- 90s2 )100s(500 - P)
Cancel the
– Retailer sets P and s to maximize retail profit
100(500 - P)
R/P = 100s(500 - P) - 100s(P - r - 30 – 90s2) = 0
terms
– P = (530 + r + 90s2)/2
R/s = 100(500 - P)(P - r - 30 – 90s2) - 100s(500 - P)180s = 0
– P – r – 30 = 270s2
Chapter 13: Vertical Restraints
16
RPM and Retail Services 9
• Put the two profit-maximizing conditions together
(500 – r – cr)/2 = (s)/2 + s’(s) OR
225s2 = 235 – r/2
– It is clear that unless r = cm = 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 cm 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;
– A two-part tariff
• Under a profit-royalty contract, the manufacturer sells at cost
cm to the retailer but claims a percentage x of the retailer’s
profit
– 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 cm, the profit-maximizing
condition: 235 = 225s2 + 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 cm = $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, cr
– 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 > cm.
• 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 cr
– competition in retailing drives retail price to PC = r + cr +
(s)
– 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 + cr + (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 + cr + (s)
• Consumer Surplus is therefore:
CS = (500 – P)xQ/2 = 50s(500 – P)2
CS = 50s[500 – r – cr – (s)]2
Chapter 13: Vertical Restraints
22
RPM and Retail Services 15
• By way of a diagram, we have:
Triangle = Consumer
Surplus. Given r, cr,
and (s), competitive
retailers will compete
by offering services
that maximize this
triangle
$/unit
500
P=r+cr+(s)
Q
50s
Chapter 13: Vertical Restraints
Quantity (000’s)
23
RPM and Retail Services
16
Cancel the common term
• We can determine the competitive service50(500
outcome
- rfor
- crany
- (s))
value of r by maximizing
CS = 50s[500 – r – cr – (s)]2
with respect to s . This yields
CS/s = 50(500-r-cr-(s))2 -100s(500-r-cr-(s))(s) = 0
• So: 500 - r - cr - (s) = 2s(s)
 (500 - r - cr)/2 = (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* – cr – r = 90s2 = 320 – 30 – r
• By choosing, r = $200, the competitive service
level satisfies:
• 90s2 = 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, DH with probability 1/2
•
And that demand is low, DL 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
DL
c
DH
MC
Quantity
Chapter 13: Vertical Restraints
28
RPM and Variable Demand 3
 An
integrated firm will not
produce more than QUpper
Price
 And
will not produce less than
QLower
 the integrated firm will produce Q*
DH
How is Q*
MC = MR
with
determined
MC
= MR with
DL
low demand
high demand
c
MC
MRL
QLower
MRH
Q* QUpper
Quantity
Chapter 13: Vertical Restraints
29
RPM and Variable Demand 4
 If
demand is high the firm sells Q*
at price PMax: MR = MR*H

Price

Revenue with
low demand
Revenue with
DHhigh demand
PMax
PMin
DL

Expected marginal revenue is:
MR*H/2 + 0 = MR*H/2
 Q* is such that expected MR = MC .
So, MR*H/2 = c
 Expected
MR*H
c
MRL
Q*L
If demand is low selling Q* is excessive
the firm maximizes revenue by selling
Q*L at price PMin: MR = 0
Q*
MRH
MC
profit is
I = PMaxQ*/2 + PMinQ*L/2 - cQ*
Quantity
Chapter 13: Vertical Restraints
30
RPM and Variable Demand 5
 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 PMax: MR = MR*H
Suppose that
retailing is
competitive
Price
Revenue with
high demand
DH
PMax

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 QL at which price is zero
DL

MC
c
MRL
QL Q*
MRH
Revenue is therefore zero in low demand
periods if competitive firms stock Q*
Quantity
Chapter 13: Vertical Restraints
31
RPM and variable demand 6
• If competitive retailers stock Q*, their expected net revenue
is thus:
PMaxQ*/2 + 0 = PMaxQ*/2
• Competitive firms just break even. So, manufacturer can only
charge a wholesale price PW such that:
PWQ* = PMaxQ*/2 which gives PW = PMax/2
• The manufacturer’s profit is then:
M = (PMax/2 - c)Q*
• 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
Price

Recall: The integrated firm
never sells at a price below PMin

So, set a minimum RPM of PMin
In high demand periods Q* is
sold at price PMax
 In low demand periods the RPM
agreement ensures that only Q*L
is sold
 Expected revenue to the retailers
is PMaxQ*/2 + PMinQ*L/2

DH
PMax
PMin
DL
MR*H
c
MC
MRL
Q*L Q*
MRH
Quantity
Chapter 13: Vertical Restraints
33
RPM and Variable Demand 8
• With RPM, expected net revenues of retailers is
PMaxQ*/2 + PMinQ*L/2
• Manufacturer can now charge wholesale price PW such that:
PWQ* = PMaxQ*/2 + PMinQ*L/2
• which gives PW = PMax/2 + PMinQ*L/2Q*
• The manufacturer’s profit is
M = PMaxQ*/2 + PMinQ*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 r
– Manufacturer’s (A and B) products located on circle at
Given retail locations
—
A
B
Retailer 1
A
M
B
Retailer 2
–
Chapter 13: Vertical Restraints
37
Exclusive Dealing 3
• With No Exclusive Dealing, A and B compete at each
location
A
A
B
Retailer 1
M
B
Retailer 2
– Substitutes never more than 2r 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+ 4r 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?
– Intrabrand price competition can intensify interbrand
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
• The Kodak case
Aftermarkets
– 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 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
not leverage its power in the 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. Forwardlooking consumers will incorporate the cost of
expected repairs into their willingness to pay for a
new machine. But 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 supracompetitive pricing
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 1st period
• 50% breakdown chance in 2nd 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 ith division of jth firm given by:
 ij qij , Qij   [ A  BQij  qij ]qij  cqij
– qij is output of ith division of jth firm; Q-ij is output of all
other divisions of all industry firms; and c 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 n1 and n2 be the number of divisions at firms 1 and
2, respectively. Since all divisions are alike the , the
optimal output of any division is:
Ac
*
q ij 
n1  n 2  1B
• Solving for industry output Q and price P, we have:
A  n1  n 2 c
 n1  n2  A  c 

Q  
 and P 
n1  n 2  1
 n1  n2  1  B 
Chapter 13: Vertical Restraints
50
Franchising and Divisionalization 5
• Given its optimal output, qij*, each division at each
firm will earn profit
 ij 
 A  c 2
Bn1  n2  1
• Firm 1’s total profit is: n1i,1 – Kn1 where K is the
sunk cost of setting up each division. So
2

A  c
 1 n1 , n2   n1
 K1
2
Bn1  n2  1
2
Chapter 13: Vertical Restraints
51
Franchising and Divisionalization 6
• Maximizing firm 1’s profit with respect to n1 and
recognizing that by symmetry, each firm must have
the same optimal number of divisions then yields:
 A  c 2

2n1* 
1 
K
2
*
*
 n  n 1 
*
*
n1  n2  1 
1
2





• Solving for the optimal number of divisions at
1


any firm we have
2
1   A  c 
n*  
2 
K


Chapter 13: Vertical Restraints
3
  1





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
Variable
POP
Estimated
Coefficient
0.0001
t-statistic
(1.87)
MSD
ADS
BAN
0.0079
-0.0017
-0.0002
(2.79)
(-2.10)
(-0.38)
YRS
-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