Upload
dana-warren
View
226
Download
0
Embed Size (px)
Citation preview
Chapter 13: Vertical Restraints 1
Vertical Restraints
Chapter 13: Vertical Restraints 2
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 3
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 4
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, profit-maximizing output and upstream price are:
– Downstream price is:
B
cAQ
4
2
cAPU
and
4
3
2
cA
B
rAPD
Chapter 13: Vertical Restraints 5
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 2
*cA
rP
< Independent retailer’s price
Chapter 13: Vertical Restraints 6
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 7
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 8
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 9
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 10
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
$/unit
Quantity
Demand withretail services
s = 1
Demand withretail services
s = 1Demand withretail services
s = 2
Demand withretail services
s = 2
• But cost of providing retail services (s) rises as more services are provided$/unit
Service Level s
(s)
Chapter 13: Vertical Restraints 11
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 12
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 and with respect to s and set each equal to zero
Cancel the100s terms
Cancel the100s terms
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 13
RPM and Retail Services 5• Now take the derivative with respect to services s and set it
equal to
(P - cm - cr - (s)) = s’(s)
I/s = 100s(500 - P)(P - cm - cr - (s)) - 100s(500 - P)’(s) = 0
Cancel the100(500 - P)
terms
Cancel the100(500 - P)
terms
• Solving we obtain:
• 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 14
RPM and Retail Services 6 • We can use this equation to show how changes in the
production and retailing marginal cost (cm and cr) affect the optimal level of services
$/unit
Service Level s
(500 - cm - cr)/2 = (s)/2 + s’(s)
(s)/2 + s’(s)
(500-cm-cr)/2
s*
(500-c’m-c’r )/2
s**
The right hand side isincreasing in s
The right hand side isincreasing in s
The left hand side isdecreasing in cm and cr
The left hand side isdecreasing in cm and cr
Let cm and cr be initial marginal costs
Let cm and cr be initial marginal costs
Suppose now that there is an increase in marginal costs,
apart from services, at either the manufacturing or retail level
Let c’m and c’r be new marginal costs
Let c’m and c’r be new marginal costs
The rise in cost leads to a fall in the
optimal choice of s
from s* to s**
The rise in cost leads to a fall in the
optimal choice of s
from s* to s**
Chapter 13: Vertical Restraints 15
RPM and Retail Services 7• For example let cm = $20, cr = $30 and (s) = 90s2
(P - cm - cr - (s)) = 180s2 = 180 P= $320
225 = 45s2 + s180s ; OR 225 = 225s2 s = 1• Then, solving for P we obtain:
• Implying an output level of:Q = 100s(500 - P) = 18,000
• The integrated firm earns profit I = $3.24 million.
Then (500 - cm - cr)/2 = (s)/2 + s(s) implies
• It chooses the socially efficient level of retail services but sets price above marginal cost. This is our benchmark case.
Chapter 13: Vertical Restraints 16
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 cm
– The profit of the retailer is now:R = (P- r - cr - (s))100s(500 - P) = (P- r - 30- s2 )100s(500 - P)
– Retailer sets P and s to maximize retail profit
R/P = 100s(500 - P) - 100s(P - r - 30 – 90s2) = 0
Cancel the100s terms
Cancel the100s terms
R/s = 100(500 - P)(P - r - 30 – s2) - 100s(500 - P)180s = 0
Cancel the100(500 - P)
terms
Cancel the100(500 - P)
terms– P = (530 + r + 90s2)/2
– P – r – 30 = 270s2
Chapter 13: Vertical Restraints 17
RPM and Retail Services 9• Put the two profit-maximizing conditions together
– 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
(500 – r – cr)/2 = (s)/2 + s’(s) OR
225s2 = 235 – r/2
Chapter 13: Vertical Restraints 18
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 19
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 20
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 21
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 22
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 23
RPM and Retail Services 15 • By way of a diagram, we have:
$/unit
Quantity (000’s)
500
50s
P=r+cr+(s)
Q
Triangle = Consumer Surplus. Given r, cr, and (s), competitive retailers will compete by offering services that maximize this triangle
Chapter 13: Vertical Restraints 24
RPM and Retail Services 16• We can determine the competitive service outcome for any
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
Cancel the common term50(500 - r - cr - (s))
Cancel the common term50(500 - r - cr - (s))
• 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 25
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 26
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 27
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 28
RPM and Variable Demand 2• Suppose that demand is high, DH with probability 1/2
Price
Quantity
DH
• And that demand is low, DL with probability 1/2
DL
– Marginal costs are assumed constant at c
c MC
– Integrated firm has to choose in each period
stage 1: how much to produce
stage 2: demand known- how much to sellsince costs are sunk: maximize revenue
Chapter 13: Vertical Restraints 29
RPM and Variable Demand 3
Price
Quantity
DH
DL
c MC
An integrated firm will not produce more than QUpper
MRHQUpper
And will not produce less than QLower
QLower
MC = MR withhigh demand
MC = MR withhigh demand
MC = MR withlow demand
MC = MR withlow demand
the integrated firm will produce Q*
Q*
How is Q*determined
MRL
Chapter 13: Vertical Restraints 30
RPM and Variable Demand 4
Price
Quantity
DH
cMC
If demand is high the firm sells Q* at price PMax: MR = MR*H
MRH
If demand is low selling Q* is excessive the firm maximizes revenue by selling Q*L at price PMin: MR = 0
Q*
PMax
Q*L
PMin
MR*H
Expected marginal revenue is:
DL
MRL
MR*H/2 + 0 = MR*H/2 Q* is such that expected MR = MC . So, MR*H/2 = c
Revenue withlow demand
Revenue withlow demand
Revenue withhigh demand
Revenue withhigh demand
Expected profit is
I = PMaxQ*/2 + PMinQ*L/2 - cQ*
Chapter 13: Vertical Restraints 31
RPM and Variable Demand 5
Price
Quantity
DH
c MC
If demand is high the retail firms sell Q* at price PMax: MR = MR*H
MRH
Q*
PMax
DL
MRL
Suppose thatretailing iscompetitive
Revenue withhigh demand
Revenue withhigh demand
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
QL
Revenue is therefore zero in low demand periods if competitive firms stock Q*
Will competitive retailers stock the optimal amount Q*? What will happen if they do?
Chapter 13: Vertical Restraints 32
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:
= (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 33
RPM and Variable Demand 7
Price
Quantity
DH
c MC
Recall: The integrated firm never sells at a price below PMin
MRHQ*
PMax
Q*L
PMin
MR*H
DL
MRL
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
Chapter 13: Vertical Restraints 34
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
= 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 35
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 36
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 37
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
—
Retailer 1 Retailer 2
–
M
A B A B
Chapter 13: Vertical Restraints 38
Exclusive Dealing 3• With No Exclusive Dealing, A and B compete at each
location
Retailer 1 Retailer 2
A B A B
M
– 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 39
Exclusive Dealing 4• Exclusive Dealing, A and B at separate locations
Retailer 1 Retailer 2
A BM
– 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 40
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 41
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 42
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 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 43
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 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-competitive pricing
Chapter 13: Vertical Restraints 44
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 45
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 46
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 47
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 48
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 49
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:
– 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
cBqBQA *ijij 2
– Equating marginal revenue and marginal cost yields:
ijijijijijijij cqqqBQAQq ][,
Chapter 13: Vertical Restraints 50
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:
Bnn
cAqij 121
*
• Solving for industry output Q and price P, we have:
B
cA
nn
nnQ
121
21 and
121
21
nn
cnnAP
Chapter 13: Vertical Restraints 51
Franchising and Divisionalization 5• Given its optimal output, qij*, each division at each
firm will earn profit
• Firm 1’s total profit is: n1i,1 – Kn1 where K is the sunk cost of setting up each division. So
2
21
2
1
nnB
cAij
12
21
2
12111
, KnnB
cAnnn
Chapter 13: Vertical Restraints 52
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:
K
nn
n
nn
cA
1
21
1*2
*1
*1
2*2
*1
2
• Solving for the optimal number of divisions at any firm we have
1
2
1*
3
12
K
cAn
Chapter 13: Vertical Restraints 53
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 54
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 55
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 56
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 0.0001 (1.87)
MSD 0.0079 (2.79)
ADS -0.0017 (-2.10)
BAN -0.0002 (-0.38)
YRS -0.0095 (-2.12)
Chapter 13: Vertical Restraints 57
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 58
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.