Transcript Document

Vertical Price Restraints
Chapter 18: Vertical Price 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 18: Vertical Price Restraints
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Resale Price Maintenance
• Resale Price Maintenance is the most important type
of vertical price restriction
– Under RPM agreements retailer agrees to sell at manufactured
specified price
– RPM agreements have a long and checkered history
• In US, Miles Medical 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
Chapter 18: Vertical Price Restraints
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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
P
and
price is:
P
D
U

A  c

2

A  r  3 A  c


2B
Chapter 18: Vertical Price Restraints
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RPM & Double Marginalization (cont.)
• 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 
2
< Independent retailer’s price
Chapter 18: Vertical Price Restraints
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RPM & Double Marginalization (cont.)
• 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 6
• 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 18: Vertical Price Restraints
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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 18: Vertical Price Restraints
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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 leads to 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 18: Vertical Price Restraints
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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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• Think of retail services s and shifting out demand
curve similar to the way that quality increases
shifted out the demand curve in Chapter 7
$/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)
Service Level s
Chapter 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 QCancel
and the
with respect to s and set each equal to zero 100s 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 18: Vertical Price Restraints
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Cancel the
RPM and Retail Services (cont.) 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 18: Vertical Price Restraints
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The left hand side is
and
decreasing in cRPM
and
c
m
r
Retail Services (cont.)
Suppose now that there is an
The
right
hand side is
• We can use this equation
show
how
changes
increase intomarginal
costs,
increasing
in
s
in
the
production
and
retailing
marginal
cost
(c
apart
from
services,
at
either
m
Let cm and cr be initial
the manufacturing
or retail
level
and
cr) affect the
optimal level of
services
marginal
costs
 (500 - cm - cr)/2 = (s)/2 + s’(s)
$/unit
The rise
in cost leads
(s)/2 + s’(s)
to a fall in the
(500-c
)/2
m-crchoice
Let c’m and c’r be new
optimal
of s
marginal costs
from s* to s**
(500-c’m-c’r )/2
s** s*
Service Level s
Chapter 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• Now let manufacturer sell to monopoly dealer
• If we assume two-part pricing is notCancel
possible,
the then
the only way that the manufacturer can
100searn
termsprofit
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- 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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 profitmaximizing condition: 235 = 225s2 + r/2 leads to s = 1,
the efficient level of services
Chapter 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
Quantity (000’s)
23
RPM and Retail Services (cont.)
• We can determine the competitive service outcome
for any value of r by maximizingCancel the common term
CS = 50s[500 – r – cr – (s)]2
50(500 - r - cr - (s))
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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
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RPM and Retail Services (cont.)
• 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 18: Vertical Price Restraints
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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 18: Vertical Price Restraints
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RPM and Variable Demand (cont.)
•
•
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 18: Vertical Price Restraints
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RPM and Variable Demand (cont.)
 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*
determined
MC
MC
= MR with
DL = MR with
low demandhigh demand
c
MC
MRL
QLower
MRH
Q* QUpper
Quantity
Chapter 18: Vertical Price Restraints
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RPM and Variable Demand (cont.)
 If
demand is high the firm sells Q*
at price PMax: MR = MR*H

Price

Revenue with
high demand
DH
Revenue with
low 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
MC
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
MRH
Q*
profit is
I = PMaxQ*/2 + PMinQ*L/2 - cQ*
Quantity
Chapter 18: Vertical Price Restraints
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RPM and Variable Demand (cont.)
 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 18: Vertical Price Restraints
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RPM and variable demand (cont.)
•
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 18: Vertical Price Restraints
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RPM and Variable Demand (cont.)

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

Price
DH
PMax
PMin
Recall: The integrated firm
never sells at a price below PMin
DL
MR*H
c
MC
MRL
Q*L Q*
MRH
Quantity
Chapter 18: Vertical Price Restraints
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RPM and Variable Demand (cont.)
•
With RPM, expected net revenues of retailers is
PMaxQ*/2 + PMinQ*L/2
• Manufacturer
such that:
can now charge wholesale price PW
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 18: Vertical Price Restraints
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