1. Vertical Price Restraints
Chapter 18: Vertical Price Restraints

2. Chapter 18: Vertical Price Restraints
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 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 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:
and
– Downstream price is:
Chapter 18: Vertical Price 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
< Independent retailer’s price
Chapter 18: Vertical Price 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 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 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 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 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 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

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, f(s)
the integrated firm’s profit I is:
I = [P-cm-cr-f(s)]100s(500 - P)
Chapter 18: Vertical Price 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 the
100s terms
pI/P = 100s(500 - P) - 100s(P - cm - cr - f(s)) = 0
 P + cm + cr + f(s) = 0
 P* = (500 + cm + cr + f(s))/2
Chapter 18: Vertical Price Restraints

13. RPM and Retail Services 5
Cancel the
100(500 - P)
terms
RPM and Retail Services 5
Now take the derivative with respect to services s and set it equal to
pI/s = 100s(500 - P)(P - cm - cr - f(s)) - 100s(500 - P)f’(s) = 0
Solving we obtain:
 (P - cm - cr - f(s)) = sf’(s)
Substituting the price equation into the service equation then yields:
 (500 - cm - cr)/2 = f(s)/2 + sf’(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 6
The left hand side is
decreasing in cm and cr
RPM and Retail Services 6
The right hand side is
increasing in s
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
Suppose now that there is an increase in marginal costs, apart from services, at either the manufacturing or retail level
Let cm and cr be initial marginal costs
 (500 - cm - cr)/2 = f(s)/2 + sf’(s)
$/unit
The rise in cost leads to a fall in the optimal choice of s from s* to s**
f(s)/2 + sf’(s)
(500-cm-cr)/2
Let c’m and c’r be new marginal costs
(500-c’m-c’r )/2
Service Level s
s** s*
Chapter 18: Vertical Price Restraints

15. RPM and Retail Services 7
For example let cm = $20, cr = $30 and f(s) = 90s2
Then (500 - cm - cr)/2 = f(s)/2 + sf(s) implies
225 = 45s2 + s180s ; OR 225 = 225s2  s = 1
Then, solving for P we obtain:
(P - cm - cr - f(s)) = 180s2 = 180 P= $320
Implying an output level of:
Q = 100s(500 - P) = 18,000
The integrated firm earns profit pI = $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

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
Cancel the
100s terms
– The profit of the retailer is now:
pR = (P- r - cr - f(s))100s(500 - P) = (P- r s2 )100s(500 - P)
Cancel the
100(500 - P)
terms
– Retailer sets P and s to maximize retail profit
pR/P = 100s(500 - P) - 100s(P - r - 30 – 90s2) = 0
– P = (530 + r + 90s2)/2
pR/s = 100(500 - P)(P - r - 30 – 90s2) - 100s(500 - P)180s = 0
– P – r – 30 = 270s2
Chapter 18: Vertical Price Restraints

17. 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 18: Vertical Price 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 18: Vertical Price 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 18: Vertical Price 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 18: Vertical Price 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 f(s) plus marginal costs cr
competition in retailing drives retail price to PC = r + cr + f(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 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 + f(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 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
Quantity (000’s)
Chapter 18: Vertical Price Restraints

24. RPM and Retail Services 16
Cancel the common term
50(500 - r - cr - f(s))
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-f(s))2 -100s(500-r-cr-f(s))f(s) = 0
So: r - cr - f(s) = 2sf(s)
 (500 - r - cr)/2 = f(s)/2 + sf(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 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:
f(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 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 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 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 DH DL c MC
Quantity
Chapter 18: Vertical Price Restraints

29. 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*
determined
MC = MR with
low demand
MC = MR with
high demand DL c MC
MRL
MRH
Quantity
QLower Q*
QUpper
Chapter 18: Vertical Price Restraints

30. RPM and Variable Demand 4
 If demand is high the firm sells Q* at price PMax: MR = MR*H
 If demand is low selling Q* is excessive
Price
 the firm maximizes revenue by selling Q*L at price PMin: MR = 0
Revenue with
low demand
 Expected marginal revenue is:
Revenue with
high demand
MR*H/2 + 0 = MR*H/2 DH
 Q* is such that expected MR = MC . So, MR*H/2 = c
PMax
PMin DL
 Expected profit is
MR*H
pI = PMaxQ*/2 + PMinQ*L/2 - cQ* MC c
MRL
MRH
Quantity
Q*L Q*
Chapter 18: Vertical Price Restraints

31. RPM and Variable Demand 5
Suppose that
retailing is
competitive
 Will competitive retailers stock the optimal amount Q*? What will happen if they do?
Price
 If demand is high the retail firms sell Q* at price PMax: MR = MR*H
Revenue with
high demand
 If demand is low each firm will sell more so long as price is positive DH
PMax
 So, if demand is low competitive retailers keep selling until they sell the total quantity QL at which price is zero DL
 Revenue is therefore zero in low demand periods if competitive firms stock Q* MC c
MRL
MRH
Quantity QL Q*
Chapter 18: Vertical Price 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:
pM = (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 7
 Recall: The integrated firm never sells at a price below PMin
Price
 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 DH
PMax
 Expected revenue to the retailers is PMaxQ*/2 + PMinQ*L/2
PMin DL
MR*H c MC
MRL
MRH
Quantity
Q*L Q*
Chapter 18: Vertical Price 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
pM = 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