Chapter 18: Vertical Price Restraints1 Vertical Price Restraints.
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Transcript of Chapter 18: Vertical Price Restraints1 Vertical Price Restraints.
Chapter 18: Vertical Price Restraints 1
Vertical Price Restraints
Chapter 18: Vertical Price 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 18: Vertical Price Restraints 3
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 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
rAP D
Chapter 18: Vertical Price Restraints 5
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
2*
cArP
< Independent retailer’s price
Chapter 18: Vertical Price Restraints 6
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 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 18: Vertical Price 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 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 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 18: Vertical Price Restraints 10
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
Quantity
Demand with
retail servicess = 1
Demand with
retail servicess = 1
Demand 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 18: Vertical Price Restraints 11
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 12
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 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 18: Vertical Price Restraints 13
RPM and Retail Services (cont.) • 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 18: Vertical Price Restraints 14
RPM and Retail Services (cont.) • 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 18: Vertical Price Restraints 15
RPM and Retail Services (cont.) • 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 18: Vertical Price Restraints 16
RPM and Retail Services (cont.) • 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 18: Vertical Price Restraints 17
RPM and Retail Services (cont.) • 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 18: Vertical Price Restraints 18
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 profit-maximizing condition: 235 = 225s2 + r/2 leads to s = 1, the efficient level of services
Chapter 18: Vertical Price Restraints 19
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 20
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 21
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 22
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 23
RPM and Retail Services (cont.) • 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 18: Vertical Price Restraints 24
RPM and Retail Services (cont.) • We can determine the competitive service outcome
for any value of r by maximizingCS = 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 18: Vertical Price Restraints 25
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 26
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 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 18: Vertical Price Restraints 28
RPM and Variable Demand (cont.)• 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 18: Vertical Price Restraints 29
RPM and Variable Demand (cont.)
Price
Quantity
DH
DL
c MC
An integrated firm will not produce more than QUpper
MRH
QUpper
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 18: Vertical Price Restraints 30
RPM and Variable Demand (cont.)
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 18: Vertical Price Restraints 31
RPM and Variable Demand (cont.)
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 18: Vertical Price Restraints 32
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:
= (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 33
RPM and Variable Demand (cont.)
Price
Quantity
DH
c MC
Recall: The integrated firm never sells at a price below PMin
MRH
Q*
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 18: Vertical Price Restraints 34
RPM and Variable Demand (cont.)• 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.