Chapter 18: Vertical Price Restraints1 Vertical Price Restraints

Chapter 18: Vertical Price Restraints 1

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


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


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


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


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


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


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


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?


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)


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)


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


I/P = 100s(500 - P) - 100s(P - cm - cr - (s)) = 0

500 - 2P + cm + cr + (s) = 0

P* = (500 + cm + cr + (s))/2


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


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


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**


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.


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



R/s = 100(500 - P)(P - r - 30 – s2) - 100s(500 - P)180s = 0


terms


terms– P = (530 + r + 90s2)/2

– P – r – 30 = 270s2


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


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


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


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


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


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


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


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


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


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


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


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


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



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


Expected profit is

I = PMaxQ*/2 + PMinQ*L/2 - cQ*



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



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?


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?



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


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.

Documents

Chapter 18: Vertical Price Restraints1 Vertical Price Restraints