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Essays on resale price maintenance and optimal retail contracts

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Essays on resale price maintenance and optimal retail contracts
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Blair, Benjamin Frederick, 1961-
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English
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vii, 96 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Cartels ( jstor )
Consumer prices ( jstor )
Manufacturing output ( jstor )
Marginal costs ( jstor )
Market prices ( jstor )
Prices ( jstor )
Resale price maintenance ( jstor )
Retail stores ( jstor )
Sales promotions ( jstor )
Wholesale prices ( jstor )
Price fixing -- United States ( lcsh )
Price maintenance -- United States ( lcsh )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1992.
Bibliography:
Includes bibliographical references (leaves 92-95).
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by Benjamin Frederick Blair.

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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ESSAYS ON RESALE PRICE MAINTENANCE AND OPTIMAL RETAIL
CONTRACTS












By

BENJAMIN FREDERICK BLAIR


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA














ACKNOWLEDGMENTS


It seems inappropriate to acknowledge those to whom you owe so much


with a brief statement of thanks.


I can only hope that those mentioned below


know how much their help and encouragement has meant.

I begin by thanking the faculty, staff, and students at the University of


Florida Department of Economics for their support, tutelage, and friendship.


my opinion no other department can compare with the atmosphere created here.

I thank Richard Romano for convincing me that I belonged at the

University of Florida, for guiding me in my studies, and for starting me on my

research.

When I began pursuing my doctorate I was unfunded and Sanford Berg

provided me with a research assistantship through the Public Utilities Research


Center.

research.


He continues to provide guidance and suggestions to strengthen my

To him I am indebted.


I thank Robert Lanzillotti and Michael Ryngaert for serving on my


committee and providing insightful comments.


Dr. Lanzillotti also provided me


with a fellowship through the Public Policy Research Center for which I am most

grateful.








The hope of all graduate students is to find a mentor that will treat them


as a friend and colleague.


For me this person is


Tracy Lewis.


Without him this


research would not have been completed.

To my mother, father, brother, and sisters who have provided financial

support, encouragement, and patience I am eternally grateful.

Finally, none of this would have been possible without the love and support


of my wife Aly

unattainable.


,son.


She gave me the courage to strive for goals that I believed


A lifetime of thanks cannot repay her for her unending support.















TABLE OF CONTENTS


ACKNOWLEDGMENTS


ABSTRACT


CHAPTERS


INTRODUCTION


AN OVERVIEW OF THE LEGALITY AND ECONOMIC
THEORY OF RESALE PRICE MAINTENANCE .


Introduction


An Overview of the U.S. Legal History of RPM...... 9
Economic Models of RPM .. ... .. .. .. .. 17


The Policy Debate ..
Concluding Comments......


INCENTIVES FOR RESALE PRICE MAINTENANCE UNDER


MORAL HAZARD AND RISK SHARING


Introduction .. .
M odel . .
Characterizations of Optimal Contracts
Concluding Comments .............


.. 40
. 44


OPTIMAL RETAIL CONTRACTS UNDER MORAL HAZARD


AND ASYMMETRIC INFORMATION


Introduction


Model ................. ......
Characterization of Optimal Contracts
Welfare Implications .. ..


vJ









APPENDICES


PROOFS FOR CHAPTER 3

PROOFS FOR CHAPTER 4


* S S .

. S 4 S S S S S S .


REFERENCES


BIOGRAPHICAL SKETCH













Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

ESSAYS ON RESALE PRICE MAINTENANCE AND OPTIMAL RETAIL
CONTRACTS

By

Benjamin Frederick Blair


December


1992


Chairperson:


Tracy R. Lewis


Major Department: Economics

Three essays regarding resale price maintenance (RPM) are presented.

The first provides an overview of the legal treatment and economic theory of


RPM.


The evolution of the current standard of per se illegality is described.


Economic theories of RPM are surveyed and a review of the debate over the

current per se standard is presented.

The remaining two essays provide alternative models explaining the use of


RPM.


In the successive monopoly manufacturer-retailer model with nonstochastic


demand and unobservable advertising, it is well known that the manufacturer can

attain the integrated profit level, without actually integrating into the retail market,


by using a two-Dart tariff. Under this scheme. the ner unit charge is enual to the








promotional incentives as in the vertically integrated structure.


then used to extract the retailer's profits.


The fixed fee is


In this setting there is no incentive for


the manufacturer to directly control retail price through RPM.


The second essay


shows that this result is no longer valid when demand is stochastic and the retailer


is risk averse.

impose RPM.


In this setting, the manufacturer will generally have an incentive to

The form of RPM, price ceilings or price floors, depends on the


balancing of pricing, promotional, and risk sharing incentives.


The last essay examines RPM in a more general framework.


Joint profit


maximizing contracts are derived when the retailer is privately informed about


demand conditions prior to contracting with the manufacturer.


The retailer can


increase customer demand by supplying promotion; however, these activities are


not observed by the manufacturer.


Consequently, when sales are low the


manufacturer does not know whether to attribute this to a decline in demand or


to a lack of marketing effort.


The manufacturer relies on contractual stipulations


to motivate the dealer to supply promotional service.

the optimal contract exhibits some form of RPM. Tt


It is shown that, in general,


ie type of RPM and quantity


fixing (quantity rationing or quantity forcing) depends on how price and quantity

affect the link between final sales and retailer service.













CHAPTER 1
INTRODUCTION



The use of vertical restraints by manufacturers has stirred much debate in


the areas of economic theory and antitrust policy.


Much of the attention focuses


on a single vertical restraint--vertical price fixing or resale price maintenance


(RPM).


In its simplest form RPM is the imposition of a particular price by the


manufacturer at which the retailers must sell the product.


In other instances RPM


may take the form of a price ceiling (maximum RPM) or a price floor (minimum

RPM).

Economic and legal scholars have tried to answer two fundamental

questions surrounding the use of RPM--what are the underlying market

characteristics that would drive a manufacturer to impose RPM and what effects


does the use of RPM have on consumer welfare?


As might be expected, there


are no clear cut answers to either of these questions and the issues continue to be


debated.


This dissertation adds to the discussion by providing alternative


explanations for the use and effect of RPM.

The impetus for the debate over vertical price fixing is its treatment by the


courts.


The first niece of legislation pertainine to RPM was the Sherman Act_










restrained trade or led to monopolization.


Under this Act and other legislation


that followed, the use of RPM has evolved from being considered per se legal to


being considered per se illegal.


It is this current standard of per se illegality that


fuels much of the debate.

In trying to explain the use of RPM, economists have provided many


models.


These models show that a manufacturer may impose RPM under a wide


range of circumstances and that the effect on consumers depends on the situation.

This has resulted in a range of prescriptions regarding the legal status of RPM.

The models presented in Chapters 3 and 4 of this monograph provide further

explanations for the use of RPM.

In a newly developing strain of the literature, researchers are providing

models in which both MRPM and XRPM arise from the same set of incentives.

In addition to providing new explanations for minimum RPM, this research may

aid in explaining why MRPM and XRPM are sometimes observed in the same

industry.1

In examining physician price fixing, Lynk (1988) explains why a cartel has


an incentive to invoke both minimum and maximum RPM.


explained by the traditional theory of collusion.


The use of MRPM is


A cartel wishes to keep members


from engaging in price cutting and the imposition of minimum RPM prevents the


practice.


But why would the cartel also wish to impose XRPM?


Lynk suggests








3
that the firms which compose the cartel compete along quality as well as price


dimensions.


An individual member of the cartel can increase profits by increasing


the quality of his product if the additional cost is outweighed by an increase in


sales volume.


In order to signal consumers of the increased quality and not be


noticed by other cartel members the cheating firm charges a higher price.


If the


cartel imposes XRPM, the cheating firm will have to resort to less efficient, more


costly forms of informing consumers of his high quality.


Thus, XRPM and MRPM


may be used in order for a cartel to better monitor its members.

When providing explanations for the use of MRPM by noncollusive

manufacturers, most authors rely on some sort of horizontal externality, e.g., free


riding on special services (Telser


1960, Mathewson and Winter 1984) or


quality/style certification (Marvel and McCafferty 1984) and the ability of discount


houses to use branded goods as loss-leaders (Marvel and McCafferty


1985).


models presented here abstract from these horizontal issues by examining the


manufacturer-retailer relationship in a successive monopoly setting.


This research


is significant in that it provides new explanations for MRPM that do not rely on

horizontal externalities and further, it demonstrates that the motivations for the

use of minimum and maximum RPM may arise from the same set of incentives.

Consider a retailer who provides some non-contractible2 promotion3


which enhances the demand for the manufacturer's product.


Fesmire and








4
Romano (1991) show that if the manufacturer is limited to uniform wholesale

pricing, RPM can be used to alleviate the vertical externalities associated with the


retailer's


choices of price and promotion which arise from the double


marginalization problem.


Imposing minimum RPM results in a decrease in


demand due to the increase in price, but the higher price induces additional


promotion by the retailer which increases demand.


the opposite effects.


Imposing maximum RPM has


Which type of RPM is chosen by the manufacturer depends


upon which of the two price effects dominates.

Chapter 3 extends this analysis by allowing the manufacturer to use a two-


part tariff when contracting with the retailer.


If the retailer is risk neutral, the


manufacturer maximizes profits by setting the wholesale price equal to the


marginal cost of production.


This aligns the retailer's pricing and promotional


incentives with that of the vertical structure.


profits through the fixed fee.


The manufacturer then extracts the


However, if the retailer is risk averse the


manufacturer provides risk sharing by increasing the wholesale price above the


marginal cost of production.


This perturbation leads to the type of RPM


incentives discussed in Fesmire and Romano.

Chapter 4 addresses the issue of RPM in the more general context of


optimal retail contracts.


It asks the question--why do manufacturers deal with


retailers and not directly with consumers through a single manufacturer outlet?










consumers.


Another explanation is that selling through an established retailer


allows the manufacturer to avoid the setup costs associated with retailing.

However, perhaps the most compelling reason for a manufacturer to

employ retailers is that they may have superior information about consumer


demand in the area they serve.


When promotional services (e.g. advertising,


product demonstration, outlet amenities, and point of sale service) are important

in stimulating final consumer demand, the manufacturer may choose to delegate

marketing decisions to a well informed retailer who is better able to tailor

promotion schemes to fit its customers.4

In this chapter joint profit maximizing retail contracts are characterized

assuming that the manufacturer delegates the sale of its product to a dealer who is


better informed about demand conditions at the time of contracting.


The dealer


is hired to market and stimulate final demand for the good by providing


promotional and quality enhancing services to consumers.


Neither the level of


service supplied by the dealer nor the state of demand can be observed by the


manufacturer.


Consequently, adverse selection and moral hazard problems may


arise in which the dealer can claim that high sales are due to his promotional


effort, while low sales result from sluggish demand.


The analysis shows how


vertical restraints are optimally employed to bring the interests of the

manufacturer and retailer into closer alignment.








6
Specifically, one can imagine that the manufacturer allows the privately

informed dealer to utilize his superior information by selecting from a menu of

contracts which stipulate both the resale price and quantity which the retailer must


The dealer retains all sales revenue, but he must pay the manufacturer a fee


for the goods that he markets.


While the level of promotion offered by the dealer


cannot be observed (and thus cannot be stipulated in the contract)5, the

provisions of the contract are used to influence the dealer's marketing effort.

The principle result is to show how the choice of price and quantity enables

the manufacturer to determine more accurately whether an increase in sales is


attributable to promotional effort or a high demand realization.


This allows the


manufacturer to supervise the dealer more closely and to extract greater returns

from the vertical relationship.

It is shown that the optimal choice of price and quantity typically involves


RPM and quantity fixing.


The form of RPM may either entail price ceilings or


price floors and the form of quantity fixing may either involve quantity rationing


or quantity forcing.


The author believes this is a new and possibly compelling


explanation for the use of price and quantity restraints.


Earlier studies (as


exemplified by


Telser and more recently by Mathewson and Winter


1984 and Rey


and Tirole


1986) argue that vertical restraints help to solve the free rider problem


associated with promotion.


In this chapter, a complementary explanation is








7
offered that vertical restraints also prevent dealers from fully exploiting their

private information about consumer demand.

Concluding comments are presented in chapter 5.













CHAPTER


AN OVERVIEW OF THE LEGALITY AND ECONOMIC THEORY OF
RESALE PRICE MAINTENANCE


Introduction


The use of vertical restraints by manufacturers has stirred much debate in


the areas of economic theory and antitrust policy.


Much of the attention focuses


on a single vertical restraint -- vertical price fixing or resale price maintenance


(RPM).


In its simplest form RPM is the imposition of a particular price by the


manufacturer at which the retailers must sell the product.


In other instances RPM


may take the form of a price ceiling (maximum RPM) or a price floor (minimum

RPM).

Economic and legal scholars have tried to answer two fundamental

questions surrounding the use of RPM -- what are the underlying market

characteristics that would drive a manufacturer to impose RPM and what effects


does the use of RPM have on consumer welfare?


As might be expected, there


are no clear cut answers to either of these questions.


The purpose of this chapter is threefold.


status of RPM is provided.


First, a background to the legal


Currently the use of RPM is judged as illegal per


however, through the years this status has changed.


Second, a survey of the more








9
the first of the fundamental questions mentioned above, i.e., what are the


underlying factors which might lead a manufacturer to impose RPM.


Third, the


chapter summarizes various viewpoints concerning the second fundamental


question--are consumers better off or worse off as a result of RPM.


This debate


draws upon the economic models and provides a range of prescriptions regarding

the legal status of RPM.


An Overview of the U.S. Legal History of RPM


This section is divided into two parts.


RPM will be examined.


First, the various laws regarding


These laws provide the foundation of any litigation


brought against a firm which uses RPM.


Second, an examination of specific cases


show how these laws have been interpreted through the years.


It will be shown


that the perceived status of RPM has varied from being legal to being per


illegal.


The Law


After the Civil War, mergers and trust arrangements resulted in an increase

in economic concentration and a decrease in competition in many industries (e.g.,


the railroad, fuel oil and sugar industries).


With the increase in market power,


firms could undertake abusive practices to drive remaining smaller firms out of


business.


Common law was unable to adequately deal with these issues and a








10
Antitrust Act was passed in 1890. The provisions of the Act which are most

important to the treatment of RPM are Section I:1

Every contract, combination in the form of trust or otherwise,
or conspiracy, in restraint of trade or commerce among the several
States, or with foreign nations, is declared to be illegal. Every
person who shall make any contract or engage in any combination
or conspiracy declared to be illegal shall be deemed guilty of a
felony, and, on conviction thereof, shall be punished by fine not
exceeding one million dollars if a corporation, or, if any other
person, one hundred thousand dollars, or by imprisonment not
exceeding three years, or by both said punishments, in the discretion
of the court.

and Section 2:

Every person who shall monopolize, or attempt to
monopolize, or combine or conspire with any other person or
persons, to monopolize any part of the trade or commerce among
the several States, or with foreign nations, shall be deemed guilty of
a felony, and, on conviction thereof, shall be punished by fine not
exceeding one million dollars if a corporation, or, if any other
person, one hundred thousand dollars, or by imprisonment not
exceeding three years, or by both said punishments, in the discretion
of the court.

Section 1 seeks to outlaw arrangements, explicit or implicit, between parties

which restrain trade. Section 2 seeks to outlaw individual acts which lead to

monopolization. The language of the Sherman Act is open to interpretation and

leaves one with many unanswered questions. What does it mean to restrain

trade? Is the issue the effect that the action in question has on the number of

competitors, the level of output, or some notion of economic efficiency? Exactly










what types of practices would violate Section 1?


Certainly Section 2 does not seek


to outlaw all types of monopoly, but which types would be in violation?


ambiguity inherent in the Sherman Act (or any piece major piece of legislation)


forced the task of interpretation upon the court system.


As is to be expected,


understandings and interpretations change over time, and thus the courts have not


handed down consistent decisions.


This has led to uncertainty over which vertical


restraints (including RPM) are legal and which ones are not.

In an attempt to clarify some of the ambiguity of the Sherman Act, the


Clayton Act of 1914 specified certain actions as illegal.


pertains to RPM.


Section 2 of this Act


This was amended by the Robinson-Patman Act in 1936.


wording of this Section is so convoluted that it is not reprinted here.2


In essence,


Section 2 declares the practice of price discrimination illegal where the effect

substantially reduces competition.

On the heels of the Clayton Act Congress also passed the Federal Trade

Commission Act under which "unfair methods of competition in or affecting


commerce are declared unlawful."3


Additionally, the Act created the FTC which


enforces this Act and which has come to enforce the Sherman Act and jointly

enforce the Clayton Act with the Department of Justice.








12
The legislation presented above, albeit somewhat ambiguous, provided the

basis for judging the legal status of RPM and many cases regarding its use were


litigated (Kleit 1992).

fair trade laws.4 Fair


Beginning with California in 1931, individual states enacted


trade laws allowed a manufacturer to enter into an


agreement with a retailer which stipulated the minimum resale price at which the


product could be sold.


These agreements got the attention of federal authorities


when fair traded goods were sold across state lines.


This conflict between federal


and state laws was resolved in 1937 with the passage of the Miller-Tydings Act

granting state fair trade laws exemption from the Sherman Antitrust Act.

Some manufacturers attempted to stipulate minimum resale prices not only

with retailers who signed fair trade contracts but also with those retailers who had


not signed.


This practice was ruled illegal by the Supreme Court in Schwegmann


Bros. v. Calvert Distillers Corp. (1951).


In response to this congress granted


more latitude to states regarding RPM by passing the McGuire Act in 1952.


allowed states to pass fair trade laws with nonsignor clauses.


This


In 1975, congress


repealed the Miller-Tydings Act and the McGuire Act thus removing RPM's

exemption from the legislation embodied in the Sherman, Clayton, and FTC Acts.








13

The Interpretation6

Kleit provides an excellent description of the early case law concerning


RPM.


The use of RPM in the U.S. was virtually unheard of prior to


1875


the first U.S. case involving RPM litigation was brought in 1885.8


the 49 federal RPM cases prior to


In examining


1918,9 Kleit concludes that RPM was


"virtually"10 per se legal prior to


1907


An appellate court decision in that year


marked a departure in how the courts would view RPM cases.


Minimum RPM


was deemed illegal on the view that it eliminated intrabrand competition.


Following this ruling "


. {from}


1915 to


1917 it was unclear exactly what the next


Supreme Court decision would generate"(Kleit, p.


Finally, the


1918 opinion


in Boston Store v. American Gramophone1 resulted in the standard of per se

illegality.

Perhaps the most famous case involving RPM is Dr. Miles Medical Co. v.


John D. Park & Sons Co.'2


Dr. Miles Medical Co., the producer of a


6This discussion draws from p. 32-33 and chapter
Gellhorn (1986) chapter 8.


15 in Bork (1978) and


Bowman (1955), p. 826, as cited in Kleit p. 8.


8Clark v. Frank, 17 Mo. Appeal 602 (1885).


9See Kleit,


Table One.


10l e Ottl.l t'A nL. 2I~n nC Ir~r nnn -C4f. n .nn ffN ln


~nnl ,,1,~ nnln


,C








14
proprietary medicine, sought to establish a uniform retail price for its product by


contracting with wholesalers and retailers.


John D. Park and Sons Co. was a


wholesaler that did not have a contract with Dr. Miles.

from other contracting wholesalers and then sold the

prices than those stipulated by Dr. Miles. Dr. Miles br


price cutting.


Park attained the product


good to consumers at lower


*ought suit against Park for


In ruling against the plaintiff the Supreme Court said that a


manufacturer who sells his product to a wholesaler cannot then interfere with that


wholesaler's pricing decisions.


The ruling in this case was based on property law


and the fact that the Court felt that ownership of the good had been transferred


from the manufacturer to the wholesaler.


From this viewpoint the Court ruled


that the price restraint was a restriction on the wholesaler's resale of the product.

This, in turn, was viewed as a restraint of competition and thus was not in the

public's best interest.

An additional factor which played a role in the per se ruling was that the

Court equated the incentives leading to horizontal price fixing with those leading


to vertical price fixing. In the Court's view, since the former was per se illegal

then the latter should be also. In sum, the Dr. Miles case established that when


the ownership of the product is passed along the distribution network then

minimum RPM is per se illegal.

In 1919, the Court seemingly retreated from the per se rule of Dr. Miles by









deal with any retailer who did not abide by the standard.13


By simply


announcing his wishes no agreement is made between manufacturer and retailer


and thus no violation of the Sherman Act occurs.


This exception was effectively


struck down in 1960 when, in United States v. Parke, Davis and Co.,


14 the Court


ruled any means of achieving compliance with announced resale prices that was as

effective as an explicit agreement illegal.

As noted above, one of the key ingredients in the Dr. Miles case which

resulted in the Court finding RPM per se illegal was that ownership of the product


was transferred in the chain of distribution from manufacturer to wholesaler.


United States v. General Electric Co.'5 this ingredient was not present.


distribution network, GE retained title to the product.

agent and received goods on consignment. The Court


In its


The retailer served as GE'


: ruled in this case that RPM


was not illegal.


The decision was not based on a consideration of RPM's


effect on


competition or consumer welfare but instead on the issue of ownership.16


In deciding the above cases and establishing the per


se rule for RPM, the


Court focused on peripheral issues and skirted what seems to be the more

important question -- how does RPM affect competition and consumer welfare?


13U.S. v. Colgate Co., 250 U.S. 300 (1919).


14362 U.S. 29.


15RO F Sunn QORO f' N V


1QAWf~








16
Economic theory has established that in some cases RPM may be welfare


enhancing.17


This has led some to call for the replacement of the per


se illegal


rule with either a rule of reason18 or even a per se legal rule.19


In a 1977 case


involving GTE Sylvania, the Court ruled that nonprice restraints such as exclusive


territories should be judged by a rule of reason.2"


This decision suggested that


the courts might be moving in the direction of relaxing the per se rule on RPM.


This possibility was dashed to some extent in 1984 when the Supreme Court'


ruling in Monsanto Co. v. Spray Rite Service Corp.21 upheld per se illegality.

Thus far, the cases discussed have been concerned only with the imposition


of minimum resale prices.


Although there is not much disagreement that


maximum RPM is beneficial to consumers,22 the Court, in Albrecht v. Herald


23 extended the per se illegal standard to include this type of RPM.


present, both forms of vertical price fixing--minimum RPM and maximum RPM--

are considered by the courts to be illegal per se.24


17For example see


Telser (1960).


Some authors suggest that the overriding


effect of RPM is to increase welfare.

8sFor example, Lamer (1989) and White (1985).

'For example, Bork (1978) and Posner (1981).


20Continental T.V


Inc. v. GTE Sylvania Inc.,


433 U.S. 36 (1977).


21465 U.S.


752 (1984).








17

Economic Models of RPM


This section briefly reviews the significant economic theories regarding


vertical price fixing.


These models present a wide variety of explanations


concerning the motives for RPM.


Instead of being able to apply a general rule,


the impetus for RPM must be considered on a case-by-case basis.

Perhaps the best known explanation of minimum RPM is that provided by


Lester


Telser.


Telser espoused the special services argument when explaining the


paradox that seemed to exist when manufacturers impose price floors.25

Suppose that consumer demand, in addition to being affected by retail price, is

affected by product specific services (e.g. product demonstrations or pre-sale


information about the product) provided by the retailer.


The manufacturer


desires retailers to provide these services and can increase the provision of


services by increasing the retailer's margin.


Telser describes how the incentive for


minimum RPM arises from the horizontal externality associated with free riding.


Suppose some retailer provides the desired services.


The retailer, in order to


cover the costs associated with the services, must charge a price above the


manufacturer's wholesale price.


Customers are not required to buy the product


from the retailer who provided the services and hence, upon receiving the services,

will purchase the product at a low-price store which provides no services.








18

Minimum RPM solves this externality by guaranteeing the retailers a minimum


margin.


Retailers then compete by providing the product specific services.


Just as


Telser's special services theory is the classic explanation for


minimum RPM, Spengler's (1950) analysis of vertical integration in response to

the double marginalization problem gives us the classic explanation of maximum


RPM.


Consider a manufacturer-retailer arrangement in which both firms have


some market power.


In order to earn positive profits, the manufacturer sells the


good to the retailer at a wholesale price above marginal production cost.


choosing the resale price the retailer considers his marginal cost, the wholesale


price, which is greater than the marginal cost of production.


Thus, we have a


double markup which results in the retailer choosing a price that is too high from


the manufacturer's point of view. In order

manufacturer may impose maximum RPM.


to solve this vertical externality, the

By stipulating the price at which the


retailer must sell the good and setting the wholesale price equal to the retail


price,


the manufacturer can achieve the maximum profits available to the


vertical structure.


Note that the manufacturer imposes maximum RPM since,


given this wholesale price, the retailer would want to increase price.

Yamey (1954) espoused the theory that in some industries the final demand

for a manufacturer's product is a function of both its price and the number of










retail outlets.


Examples are products which consumers buy on impulse such as


newspapers, candy, and cigarettes.


This theme is the basis for the "outlets


hypothesis" explanation for minimum RPM presented by Gould and Preston


(1965).


In their model, minimum RPM allows a manufacturer to increase the


margin of competing dealers above the minimum level.


In turn, this margin has


an effect on the size of an individual retail outlet and thus the number of retail


outlets in the market.


For these "impulse products" the greater the number of


outlets, the greater the final demand for the product.


Thus, in the outlets model,


the retail price has the usual direct effect on manufacturer profits as well as an

indirect effect due to the retail margins's influence on the number of outlets.

Mathewson and Winter (1984) describe externalities which lead to a failure


of simple uniform price contracts to maximize profits of the vertical structure.


a model consisting of a manufacturer and spatially differentiated retailers who


provide information about the product, three externalities arise.

vertical externality associated with double marginalization. Secc


First is the


)nd is the free-


rider problem described by


Telser.


Lastly is an externality of a pecuniary nature


in which changes in retail prices have effects on neighboring outlets.


When these


externalities are present, Mathewson and Winter describe sets of vertical restraints


that are minimally sufficient to achieve the joint profit maximum.


They find that








20

minimum RPM is an element of any minimally sufficient set of vertical

restraints.29

In another model, Mathewson and Winter (1983) examine an environment

in which consumers are informed about the product by competitive retailers and


have imperfect information about the location of the low-price outlets.


Once


consumers become informed about the product they may search for the lowest


price among the other outlets."


Search costs differ among consumers.


externalities present in this model are double marginalization and free riding by

low-price discount houses on the information provided by the high-price informing


retail outlets.


Mathewson and Winter show that the imposition of minimum RPM


by the manufacturer can be used to resolve these externalities.

Marvel and McCafferty (1984) argue that Telser's special services theory


does not explain a vast number of situations in which RPM is used.


They propose


a model in which retailers perform the task of quality or style certification for


consumers.


If consumers believe that certain stores are better able to certify the


quality/style of a product then the decisions of certain stores to stock a product


provides a signal to consumers about that product's quality/style.


However, since


consumers only care about where a product is sold and not where they buy the



"Mathewson and Winter (1984) restrict their attention to four vertical
TPPOrr oi-n+c t I nir'nn 0;rt-i lTl PAl Ullfl *nr-vn, ,+l c+r4 1,n nhmon+l+,r n4 r. r. .n










product, this certification or branding is open to free riding.


The authors show


that minimum RPM guarantees a margin to the certifying stores that cover the

costs of certification.

In Marvel and McCafferty (1985), a manufacturer of a well known product

may use RPM to prevent a new-entrant retailer from featuring his product as a

loss-leader in order to permit comparison of prices with those in established


stores.


Why would a manufacturer be averse to having his product featured as a


loss-leader? Competition drives down the price of his product and he earns

greater profits. However, having the product as a loss-leader in some stores


forces those outlets who have not imposed the below-cost prices to drop the


product.


This leads to an overall loss of availability of the product.


Declining


sales and diminished availability leads to a loss of status of the product and


eventually even the loss-leader stores drop it from the shelves.


Minimum RPM


does not allow a retailer to engage in loss-leading practices.

Klein and Murphy (1988) assert that in some instances the provision of

dealer services are solely enforced by the threat of termination and not by simply


(as proposed by


Telser) providing the dealer with a margin.


This will arise when


consumers cannot, prior to purchase, determine whether the dealer services have


been provided.31


When the manufacturer can observe the services provided but


cannot contract upon them, the manufacturer can induce the desired activity








22

through the use of vertical restraints, including RPM, but must provide the retailer

with a stream of quasi-rents which he forgoes if shirking is detected.

Springer and Frech (1986) consider a retailing model in which a


manufacturer produces multiple qualities (brands) of a good.


They demonstrate


that maximum RPM can prevent the retailer from using "misleading markups".

When price serves as a signal of quality, the retailer can earn a rent by pricing the

brands in such a way as to fool consumers about the quality of the different


brands.


RPM does not allow the retailer to use this strategy and, in addition,


provides the manufacturer with the means to properly signal consumers.

Most of the literature on RPM focuses on explaining the use of minimum


RPM.


This is probably due to two factors.


First, it is widely viewed that


minimum RPM and maximum RPM arise from different sets of incentives and


analysis requires wholly different models.


Second, there is general agreement


that the motivation for maximum RPM lies with the double marginalization

problem described by Spengler.

In a newly developing strain of the literature, researchers are providing

models in which both minimum RPM and maximum RPM arise from the same set


of incentives.


In addition to providing new explanations for minimum RPM, this








23

research may aid in explaining why minimum RPM and maximum RPM are

sometimes observed in the same industry.33

In examining physician price fixing, Lynk (1988) explains why a cartel has


an incentive to invoke both minimum and maximum RPM.

RPM is explained by the traditional theory of collusion. A


The use of minimum


cartel wishes to keep


members from engaging in price cutting and the imposition of minimum RPM


prevents the practice.


RPM?


But why would the cartel also wish to impose maximum


Lynk suggests that the firms which compose the cartel compete along


quality as well as price dimensions.


An individual member of the cartel can


increase profits by increasing the quality of his product if the additional cost is


outweighed by an increase in sales volume.


In order to signal consumers of the


increased quality and not be noticed by other cartel members the cheating firm


charges a higher price.


If the cartel imposes maximum RPM, the cheating firm


will have to resort to less efficient, more costly forms of informing consumers of


his high quality.


Thus, maximum RPM and minimum RPM may be used in order


for a cartel to better monitor its members.

When providing explanations for the use of minimum RPM by non-

collusive manufacturers, most authors rely on some sort of horizontal externality,


e.g., free riding on special services (Telser


1960, Mathewson and Winter


1984) or


quality/style certification (Marvel and McCafferty


1984) and the ability of discount










houses to use branded goods as loss-leaders (Marvel and McCafferty


1985).


Fesmire and Romano (1991) and chapters 2 and 3 of this dissertation abstract

from these horizontal issues by examining the manufacturer-retailer relationship in


a successive monopoly setting.


This research is unique in that it provides new


explanations for minimum RPM that do not rely on horizontal externalities and

further, it demonstrates that the motivations for the use of minimum and

maximum RPM may arise from the same set of incentives.

Consider a retailer who provides some non-contractible34 promotion35


which enhances the demand for the manufacturer's product.


Fesmire and


Romano show that if the manufacturer is limited to uniform wholesale pricing,

RPM can be used to alleviate the vertical externalities associated with the

retailer's choices of price and promotion which arise from the double


marginalization problem.


Imposing minimum RPM results in a decrease in


demand due to the increase in price but the higher price induces additional


promotion by the retailer which increases demand.


the opposite effects.


Imposing maximum RPM has


Which type of RPM is chosen by the manufacturer depends


upon which of the two price effects dominates.

Chapter 2 extends this analysis by allowing the manufacturer to use a two-


part tariff when contracting with the retailer.


If the retailer is risk neutral, the


manufacturer maximizes profits by setting the wholesale price equal to the










marginal cost of production.


This aligns the retailer's pricing and promotional


incentives with that of the vertical structure.


profits through the fixed fee.


The manufacturer then extracts the


However, if the retailer is risk averse, the


manufacturer provides risk sharing by increasing the wholesale price above the


marginal cost of production.


This perturbation leads to the type of RPM


incentives discussed in Fesmire and Romano.

This analysis is extended even further in chapter 3 where it is shown that

unobservability of the retailer's promotion and his superior knowledge of local

demand may lead the manufacturer to impose either type of RPM.

Unobservability and asymmetric information allow the dealer to misrepresent the


amount of promotion supplied.


The type of RPM chosen is the one which


provides the best monitoring of the retailer.


The Policy Debate


As was shown in section 1.2, the law concerning vertical price fixing has


evolved into a rule of per se illegality.


However, economists and lawyers are in


general agreement that, by keeping retail prices low, maximum RPM is beneficial


to consumers and thus should not be subject to the per se ban.

is general disagreement over the legal status of minimum RPM.


Conversely, there

This section


focuses on this debate.


I I ,, .. C -










impose {RPM}


his motive cannot be the restriction of output and, therefore,


can only be the creation of distributive efficiency.


That motive should be


respected by the law." (1978 p. 289)

Bork addresses various arguments that are frequently made to rationalize


the per se rule.


One argument suggests that RPM is not initiated by


manufacturers but is instead forced upon the manufacturer by resellers in order to


facilitate a dealer cartel. In this manner, dealers could enforce pricing rules

without horizontal agreements. Bork asserts that the antitrust authorities should


be able to distinguish this form of vertical price fixing as actually being horizontal

and can bring it to justice under laws governing horizontal price fixing.

A similar argument asserts that RPM may be used by manufacturers as a


way of policing their own cartel.


In this case, Bork suggests that RPM would not


be needed by the manufacturers since retailers would do the policing and report


any price cutting to the other cartel members.


Additionally, when product services


are offered, RPM would be ineffective at policing members.


Manufacturers would


still have an incentive to offer wholesale price cuts to dealers in order to stimulate


promotion which increases the manufacturer's sales.


Finally, if retail outlets were


differentiated, then the specific format of RPM would be hard to agree upon by

the cartel members.

In the main, Bork's argument for the legalization of vertical price fixing is








27

minimum RPM provides dealers with an incentive to provide product promotion


by eliminating the free-rider externality.


The RPM-induced promotion shifts the


manufacturer's demand and marginal revenue curves up and to the right.


This


yields an increase in output and, according to Bork, an increase in consumer


welfare.


This result is shown diagramatically in Figure


1, in which the 0 and 1


subscripts denote the state of nature before and after the imposition of RPM,

respectively.


Figure 1-1
Increase In Output Due


To RPM


In the figure, the MC represents the marginal cost of getting the product in

consumers' hands, i.e., the sum of the marginal production cost and the marginal


- 1 *1 .


"








28
assert that Bork's contention that output is necessarily increased with the


imposition of RPM is erroneous.


If the provision of product services causes the


retailer's marginal cost to increase enough then output will fall.


Bork counters by


suggesting that, while marginal cost may increase, it willil almost surely" not

increase to the extent suggested.6


Perhaps more damaging to Bork's

Scherer and similarly by Comanor (1985).


Spence's


analysis is the argument provided by

Comanor's perceptive analysis applies


(1975) theory of a monopolist's choice of quality to the subject of RPM.


He notes that "The conventional wisdom fails to acknowledge the importance of

differences among consumers regarding their preferences for dealer-provided


services." (1985 p. 990)


Spence observed the monopolist makes quality decisions


based upon the marginal consumer.


However, maximizing welfare requires


consideration of the marginal consumer as well as the inframarginal ones.


To the


extent that these two groups of consumers differ, the monopolist may under or


over supply quality from a social standpoint.


Applying this to RPM, Comanor


notes that if marginal and inframarginal consumers are different in their valuation

of RPM-induced services, then either an oversupply or undersupply of services

may be induced.


Comanor provides the following example.


Consider a case in which the


inframarginal consumers are completely knowledgeable and the marginal










consumers are ignorant of a product's characteristics and uses.


Whereas


additional dealer services are of no value to the knowledgeable consumers, they


may be of great value to the ignorant ones.


Basing his pricing decision upon the


marginal consumers, the manufacturer induces dealer services by imposing an


increase in retail price.


The marginal consumers experience an increase in welfare


due to the increased promotion but, due to the increase in price, the welfare of


the inframarginal consumers has decreased.


Depending on the size of the two


groups, the net effect may be a decrease in total consumer welfare.


This analysis


holds even when total output is increased.

The problem with the above argument, as noted by Bork (1978) and White


(1985),


is that it applies to all activities which increase the desireability of the


manufacturer's product.


As White notes,


few, if any, economists or lawyers


would seek to forbid producers from undertaking all of these activities because of


concerns about marginal and inframarginal customers." (1985 p. 18)


White goes


on to explain that RPM is only one instrument that the manufacturer can use to


induce dealer promotion.

efficient methods. This n


If RPM is illegal, manufacturers may turn to less


nay result in less promotion at a greater cost and thus


lead to even greater inefficiencies.

Based on his analysis Comanor does not concur with Bork's prescription of


a per se legal rule for RPM.


He suggests that for new products, i.e., products for










consumers, and thus RPM is likely to reduce consumer welfare.


For these


products Comanor suggests that the burden of proof be placed on the

manufacturer to show that RPM is in the best interest of consumers.37

Overstreet and Fisher (1985) view the debate over the legality of RPM as


divided into two camps.


In one are the "missionaries" who view


Telser's free-


riding theory as the explanation for the use of RPM.

anticompetitive arguments as insignificant. For exan


They consider any


iple, the missionaries assert


that RPM-induced collusion is easy to detect and can be prosecuted on horizontal


grounds.


In the other camp are the opponents of RPM who believe that its


overriding use is to facilitate collusion and this type of collusion is hard to detect.

Overstreet and Fisher view the first camp as ignoring historical fact and the


second camp as focussing on issues that may no longer be relevant.


In analyzing


historical data, the authors find that, prior to World War I, manufacturers of

trademarked goods used RPM to induce dealer promotion and to prevent free


riding.38


The use of RPM then shifted away from manufacturers toward


wholesalers and retailers who imposed price restraints to stave off more efficient


forms of distribution such as department stores and supermarkets.


These


practices were diminished by the rise in the effectiveness of television advertising








31
to create brand preference which gave manufacturers more power to encourage

price competition among retailers.

Based on their historical analysis, Overstreet and Fisher propose a relaxing

of the per se ban on vertical price fixing by allowing small firms in unconcentrated

industries to use RPM.9They argue that the use of RPM by wholesalers and


retailers should not be allowed.


This point is supported by Benjamin Sharp


(1985), drawing from his experience at the FTC in enforcement against RPM, he


asserts that 80% of RPM cases are dealer induced.40


Sharp views other


explanations of RPM as insignificant, and thus favors keeping the standard of per

se illegality except in the case of new products.

Leffler (1985) notes that antitrust laws address competition and not


efficiency.


He asserts that theoretical analysis of efficiency leads to ambiguous


results which is of no use to the courts.


effects that vertical restraints have on competition.


The courts should first examine the


For instance, if competitors


are not harmed by the imposition of vertical RPM then it should be legal. I

however, competitors show that harm has been done, the practice should be


deemed illegal.


If a practice is deemed illegal it should be the defendant's burden


39Scherer concurs with this prescription and suggests that in other cases the
burden of proof should be on the user of RPM to justify its use.










to show on efficiency grounds why the restraint should be allowed.


New product


RPM should be deemed legal since it cannot harm retailers.

Given the variety of RPM theories and the conflicting policy

recommendations, some authors have suggested that the courts extend the

Sylvania decision and move away from per se illegality toward a rule of reason.41


That is, assess the legal status of RPM on a case-by-case basis.


For example,


White suggests a policy in which the courts weigh the increased efficiency at the

retailer level against the likelihood of collusion at either the manufacturer or


retailer level.


According to Lamer "The range of effects that RPM can have is


too wide and the variety of market circumstances in which it may be used is too


diverse to justify its universal condemnation." (1989 p.


He also suggests that


RPM be made legal, except where the plaintiff can prove that its use facilitates

collusion at either the manufacturer or dealer level, facilitates market foreclosure,



41The rule of reason is described by Justice Brandeis in Chicago Board of
Trade v. United States:

The true test of legality is whether the restraint imposed is such as
merely regulates and perhaps thereby promotes competition or
whether it is such as may suppress or even destroy competition. To
determine that question the court must ordinarily consider the facts
peculiar to the business to which the restraint is applied; its
condition before and after the restraint was imposed; the nature of


the restraint and its effect, actual or probable.


The history of the


restraint, the evil believed to exist, the reason for adopting the
nartiruilar remardv the nurnnce nr and cnnwiht tn hb attained are all








33
or has led to anticompetitive effects that outweigh any gains in distributive

efficiency.

While the rule of reason may seem to be the logical course of action, its


critics abound.


According to Posner, the rule of reason standard is "...an


amorphous standard that requires or at least permits the antitrust adjudicator to

make a broad ranging assessment of all competitive, and perhaps all economic,


benefits and costs of the challenged practice.


(1981 p.


He goes on to say


that this


'"vagueness" would not be a problem if"


. antitrust cases were decided


by highly experienced and knowledgeable judges specializing in antitrust cases.


They are not, however.


(1981 p. 1


Posner supports a rule of per se legality


based on arguments similar to Bork's.

The rule of reason standard is described by Overstreet and Fisher as a

"litigation nightmare" (1985 p. 53) and that the outcome of a case would be


decided by who is assigned the burden of proof.

tempting to propose a rule of reason standard.


Comanor admits that it is

However, he argues that due to


scarce judicial resources, setting general rules, even though they may lead to

mistakes, is the proper policy.42








34

Concluding Comments

This chapter has provided an overview of the legal and economic issues


surrounding vertical price fixing.


It described the evolution of the present


standard of per se illegality and presented various opinions on the standard.

Many authors have expressed disdain for the current standard, but with the

multitude of theories and conflicting policy recommendations, how are the courts


to choose a replacement standard?


Is there any consensus to be found that might


guide the courts in assessing the legality of RPM?


The compromise standard that


seems to be evolving is to continue the per se ban on RPM except in the case of


new products and when it is used by small firms in unconcentrated industries.


other cases put the burden of proof on the user of RPM to show why its use is


beneficial.


However, whether the courts adopt this standard is a question that


only more litigation can answer.


In any case,


RPM promises to remain one of


the more lively topics in the economics and antitrust literature.













CHAPTER 3
INCENTIVES FOR RESALE PRICE MAINTENANCE UNDER MORAL
HAZARD AND RISK SHARING



Introduction


In many situations, the manufacturer of a product seeks to control the


prices at which a retailer resells the product to consumers.


This vertical control of


prices, formally known as resale price maintenance (RPM) can effectively take on

two forms--either maximum resale price maintenance (XRPM) or minimum resale


price maintenance (MRPM).


sets a price that the retailer cai


Under XRPM or price ceilings, the manufacturer

mot exceed. Under MRPM or price floors, the


manufacturer sets a price that the retailer cannot undercut.


What is the economic


rationale for these price restraints?


Many authors have provided explanations for the use of RPM.


best known explanation of MRPM is that provided by Lester


Perhaps the


Telser (1960).


Telser espoused the special services argument when explaining the paradox that


seemed to exist when manufacturers impose price floors.


Suppose that


'In this paper, the forms of resale price maintenance are defined by the
direction in which the retailer would like to change price.








36

consumer demand, in addition to being affected by retail price, is affected by

product specific services (e.g. product demonstrations or pre-sale information


about the product) provided by the retailer.


The manufacturer desires retailers to


provide these services and can increase the provision of services by increasing the


retailer's margin.


Telser describes how the incentive for MRPM arises from the


horizontal externality associated with free riding.


the desired services.


Suppose some retailer provides


The retailer, in order to cover the costs associated with the


services, must charge a price above the manufacturer's wholesale price.

Customers are not required to buy the product from the retailer who provided the

services and hence, upon receiving the services, will purchase the product at a low-


price store which provides no services.

guaranteeing the retailers a minimum m


Minimum RPM solves this externality by

margin. Retailers then compete by


providing the product specific services.


Just as


Telser's special services theory is the classic explanation for MRPM,


Spengler's (1950) analysis of vertical integration in response to the double


marginalization problem gives us the classic explanation of XRPM.


Consider a


manufacturer-retailer arrangement in which both firms have some market power.

In order to earn positive profits the manufacturer sells the good to the retailer at


a wholesale price above marginal production cost.3


In choosing the resale price


the retailer considers his marginal cost, the wholesale price, which is greater than








37

the retailer choosing a price that is too high from the manufacturer's point of


view.


In order to solve this vertical externality, the manufacturer may impose


maximum RPM.


By stipulating the price at which the retailer must sell the good


and setting the wholesale price equal to the retail price4 the manufacturer can


achieve the maximum profits available to the vertical structure.


Note that the


manufacturer imposes XRPM since, given this wholesale price, the retailer would

want to increase price.

Most of the literature on RPM focuses on explaining the use of minimum


RPM.


This is probably due to two factors.


First, it is widely viewed that


minimum RPM and maximum RPM arise from different sets of incentives and


analysis requires wholly different models.


Second, there is general agreement


that the motivation for maximum RPM lies with the double marginalization

problem described by Spengler.

In a newly developing strain of the literature, researchers are providing

models in which both MRPM and XRPM arise from the same set of incentives.

In addition to providing new explanations for minimum RPM, this research may


4Here it is assumed that the retailer's reservation wage is zero.


The wholesale


price could be lowered to accommodate a reservation wage greater than zero.








38

aid in explaining why MRPM and XRPM are sometimes observed in the same

industry.6

In examining physician price fixing, Lynk (1988) explains why a cartel has


an incentive to invoke both minimum and maximum RPM.


explained by the traditional theory of collusion.


The use of MRPM is


A cartel wishes to keep members


from engaging in price cutting and the imposition of minimum RPM prevents the


practice.


But why would the cartel also wish to impose XRPM?


Lynk suggests


that the firms which compose the cartel compete along quality as well as price


dimensions.


An individual member of the cartel can increase profits by increasing


the quality of his product if the additional cost is outweighed by an increase in


sales volume.


In order to signal consumers of the increased quality and not be


noticed by other cartel members the cheating firm charges a higher price.


If the


cartel imposes XRPM, the cheating firm will have to resort to less efficient, more


costly forms of informing consumers of his high quality.


Thus, XRPM and MRPM


may be used in order for a cartel to better monitor its members.

When providing explanations for the use of MRPM by non-collusive

manufacturers, most authors rely on some sort of horizontal externality, e.g., free


riding on special services (Telser (1960), Mathewson and Winter


quality/style certification (Marvel and McCafferty


1984) or


1984) and the ability of discount


houses to use branded goods as loss-leaders (Marvel and McCafferty 1985). The








39

model presented in this chapter abstracts from these horizontal issues by

examining the manufacturer-retailer relationship in a successive monopoly setting.

This research is significant in that it provides new explanations for MRPM that do

not rely on horizontal externalities and further, it demonstrates that the

motivations for the use of minimum and maximum RPM may arise from the same

set of incentives.

Consider a retailer who provides some non-contractible7 promotion8


which enhances the demand for the manufacturer's product.


Fesmire and


Romano (1991) show that if the manufacturer is limited to uniform wholesale

pricing, RPM can be used to alleviate the vertical externalities associated with the

retailer's choices of price and promotion which arise from the double


marginalization problem.


Imposing minimum RPM results in a decrease in


demand due to the increase in price but the higher price induces additional


promotion by the retailer which increases demand.


the opposite effects.


Imposing maximum RPM has


Which type of RPM is chosen by the manufacturer depends


upon which of the two price effects dominates.

This chapter extends this analysis by allowing the manufacturer to use a


two-part tariff when contracting with the retailer.


If the retailer is risk neutral, the


manufacturer maximizes profits by setting the wholesale price equal to the


marginal cost of production.


This aligns the retailer's pricing and promotional










incentives with that of the vertical structure.


profits through the fixed fee.


The manufacturer then extracts the


However, if the retailer is risk averse the


manufacturer provides risk sharing by increasing the wholesale price above the


marginal cost of production.


This perturbation leads to the type of RPM


incentives discussed in Fesmire and Romano.

In the next section, notation and assumptions of the basic model are


presented.


The main results are then presented.


The final section contains


concluding remarks.


All proofs are contained in Appendix A.


Model

Consider a model of successive monopoly in which the upstream firm

(manufacturer) is risk neutral and the downstream firm (retailer) is risk averse.

The setting considered is that of an upstream firm who has a diverse portfolio and


hence is able to spread risk out among various assets.


Conversely, the


downstream firm is assumed to derive a major portion of its income from the


retailing activity.


Restricting attention to a single retailer allows us to abstract


from horizontal externality issues (e.g., free riding) and to focus on the importance


of moral hazard and risk sharing in vertical relationships.


The upstream firm


produces a product at constant unit cost c and supplies the product to the


downstream firm at a constant per unit price w.


The retailer sells the product to


1 II 1 r' 11 r rr r 11








41

Consumer demand is denoted by Q=Q(p,x,0) where p is the retail price

per unit, x is the level of promotion, and 0 is an exogenous demand variable

unknown to both firms at the contract date.

The imperfect knowledge of consumer demand is represented by letting 0

be the realization of a random variable with density function f(0) and distribution


function F(0) for all 0 E [L,H].


Although both firms know f(0), neither is able to


observe the actual realization of 0 ex ante.

Consumer demand is related inversely to retail price (Qp<0) and related


directly to promotion (Qx>0).


returns (Q,< 0).


Further we assume promotion has diminishing


For any given price and promotion level a higher realization of


the demand parameter 0 increases the quantity demanded (Q6>O).


Supplying promotion is costly to the downstream firm.


For simplicity the


model is normalized so that x represents the total expenditure on promotion.

Only the retailer knows x, the amount of promotion which is supplied to market


the final good. The level of x is chosen prior to the realization of the random

demand component. This, in concert with the unobservability of 0, allows one to


consider contracts of the type {w,A,p} where A is a transfer from the retailer to

the manufacturer.


The timing in the model is as follows.


{w,A,p}.


The upstream firm offers a contract


Once agreed to, the downstream firm supplies promotional services x.










when the choice of promotion is made.


This timing describes perhaps the most


simple manufacturer-retailer arrangement with incomplete information.


example, consider the case of a retailer who advertises the price of the product in


a newspaper.


The advertising budget must be chosen before the final demand is


realized.


Formally, the upstream firm'


problem is


Max


(w-c)


Q(p,x,0)f(O)dO


w,A,p


subject to


OH


(p -w)Q(p,x,0)


x = argmax
x'


)f(O)dO


u(*)f(O)dO


where u' >, u"


The upstream firm seeks to maximize upstream profits by choosing the


contract {w,A,p}.


Equation (1) represents the individual rationality constraint


< 0.9









which insures that the downstream firm will accept the contract.


Equation (2)


defines the level of promotion chosen by the downstream firm.

From this point on, the limits of integration will be [0,0H] unless otherwise


stated.


Two simplifying assumptions will be employed.


First, assume that Qx<0.


This implies that the variance of the risky asset is decreased by increasing the level


of promotion supplied.10


Second, assume that u(-) is a member of the class of


utility functions that exhibit constant absolute risk aversion (CARA).11


Let r be


1oGiven p, w, A,


dVAR[(p-w)Q]


= (p-w)2 VAR[O]


= 2(p-w)2{f(Q(')


- E[Qx])Qf(0)d0)


Define


- E[Qx]


Then


h'(0)


fh(O)f(0)dO


- E[Qx])f(0)d0


Define


H(0)


fh(0)f(0)d0


Since QxO<0 we have H(0)>0 for all 0<0H.


This yields


dVAR[(p-w)Q]
dx


= 2(p-w)2fh(O)f(O)dO


Integrating by parts we have


d VAR[(p-w)Q]


= 2(p-w)2{H(0)Q(-)


- JH(0)Qd0)


Thus, since Qxe<0


= Qxe


Q,( ~


= I~a









the constant level of risk aversion.


Under CARA, risk preferences are constant


along the retailer's utility function.


Characterizations of Optimal Contracts


As a benchmark, consider the case in which the downstream retailing


activity is subsumed by the risk neutral upstream firm.


This integrated profit


maximization can be written as [I]:


Max


7r'(p,x)


= (p-c) Q(p,x,O)f(0)dO


Let the solution to [I] be denoted by (p*,x').


Lemma 1:


At the solution to [I],


- c)f Q(p*,x*,0)f(o)do


- c)f Op(p*,x,0)f()d


Proof:


+ Q(p*,x*,0)f(0)dO


In Appendix A.


In maximizing integrated profits, price and promotion are chosen so that

marginal revenue equals marginal cost as reflected in conditions (i) and (ii).


'-'(p ,x


*) represents the maximum level of profits attainable in the system prior to


any distortions due to agency issues.


Attention is now turned to the inclusion of two agency issues:


hazard and risk sharing.


moral


The interesting question is what contractual










retailing activity can be observed by the upstream firm is examined.


This non


integrated full information profit maximization can be written as [NIFI]:


Max
w,Ap,x


(w-c)f Q(p,x,O)f(O)dO


subject to


(p-w)Q(p,x,0)


)f(0)d0


> Uo


Let the solution to [NIFI] be denoted by (W,A,p


Lemma 2:
(i)
(ii)


,x).


At the solution to [NIFI],


< 0


Upstream firm imposes XRPM



Proof:


In Appendix A.


Property (i) implies that the optimal contract in the non integrated full

information environment yields full insurance--the downstream firm achieves u0 in


every state of nature.


This is achieved by a transfer from the manufacturer to the


retailer as stated in property (ii).


These results formalize the discussion of


Mathewson and Winter (1984).


The upstream firm chooses the optimal retail price


marginal cost of production c.


faces a marginal cost of W


based on the true


Given the contract in [NIFI] the downstream firm


Hence. the downstream firm has an


a>c







46
The environment presented in [NIFI] allows the levels of price and


promotion to be contracted on.


Since the optimal contract results in full insurance


via the choices of w and A, the choices of price and promotion can be made to


maximize total profits.


Thus the choices of p and x are identical to those in [I].


Now examine how the optimal contract changes when a component of


moral hazard is added to the model.


The statement of this non integrated


problem was presented in the previous section and is rewritten here.


[NI]:


Max
w,A,p


(w-c)


IQ(p,x,0)f(O)dO


subject to


(p -w)Q(p,x,0)


and


x = argmaxfu(-)f(0)d0
x/ J


Letting x (p,w,A)


= argmax


u(-)f(O)dO


, we can rewrite [NI] as [NI']:


Max
w,A,p


(w-c)


IQ(p,(*),0)f(O)dO


subject to


)f(0)d0








47

It will be useful to define the following three stochastic elasticities.


8=


pj QOf(0)d0
f Q(')f(0)d0


denote the price elasticity of expected demand; let


x QOf(O)dO
X = -J-----
0 )f (0 d


denote the promotional elasticity of expected demand; and let


denote the price elasticity of "induced promotion".


Let the solution to [NI'] be


denoted by (p,w,A).


Proposition 1:
(i)
(ii)


At the solution to [NI'],


:


p>w>c
The upstream firm imposes XRPM (MRPM) (no RPM) as


+718,


Proof:


In Appendix A.


At the solution to [NI'] the upstream firm sets the wholesale price such that


This is in contrast to that chosen in [NIFI] and in the well known risk


neutral case in which w=c (e.g., see


Tirole


1988).


In [NIFI], where promotion is


observable, the manufacturer sets the wholesale price equal to the retail price and


>>(=) 8










downstream firm's supply of promotion.


By introducing a (p-w) spread, a portion


of downstream profits is directly related to quantity sold, and hence a monetary


incentive to promote arises.


In the risk neutral case the upstream firm sets the


wholesale price equal to the marginal cost of production.


This gives the


downstream firm the correct promotional incentives to achieve the integrated


profit level given any price chosen by the upstream firm.12


However, when the


downstream firm is risk averse, as in [NI'], an insurance incentive to promote


arises and setting w=c no longer maximizes profits.


For any price the downstream


firm seeks to insure itself against the stochastic outcome through its choice of


promotion.


Since the variance of the risky asset is decreased by increasing the


level of promotion (since Qx


< 0), insurance is achieved by increasing promotion


above the level chosen by the risk neutral firm (see footnote


level is no longer optimal from the upstream firm's point of view.


firm desires to reduce the supply of promotion.


The promotion


The upstream


By increasing the wholesale price


above marginal cost (and thus reducing p-w), the upstream firm provides some

insurance to the downstream firm as well as reduces the gains to promotion to the


downstream firm.


These two effects, in concert, act to reduce the level of


promotion supplied by the downstream firm.13



'21n fact in the risk neutral case there is no incentive for the upstream firm to


nn n t rrtn tx,-r niu c II A n-Ic+ 'rion- f*r,, +1,0m nnrrnn+ n m1n n, r 4


rhnnfp n








49

Note also that, in contrast to the full information case, the manufacturer


does not find it optimal to provide full insurance.


As mentioned above, when


promotion is unobservable, the manufacturer induces the retailer to supply


promotion by introducing a (p-w) spread.


This provides the retailer with needed


promotional incentives but also increases the risk it faces.

The elasticity condition in property (ii) describes how the two vertical

externalities (downstream choice of price and promotion level) affect incentives


for resale price maintenance.


Due to double marginalization and risk aversion the


downstream firm does not, in general, choose the joint profit maximizing price and


level of advertising.


externalities.


By dictating the final price, the upstream firm can ease these


Imposing XRPM controls the double marginalization externality but


lowers the incentive to promote.


effect of RPM on upstream


measured by


MRPM increases promotional incentives.


profits through the promotional externality is


The upstream firm weighs this against the effect of RPM on


the pricing externality measured by -


. When these two effects exactly offset


each other, the retailer chooses the price which maximizes joint


profits.


When


= 0, i.e. downstream promotion has no effect on demand, property (ii)


indicates that the upstream firm imposes XRPM.

to the Spengler successive monopoly problem. W


This is the well known solution


ihen consumer demand is


affected by downstream promotion the effect of resale price maintenance on










promotional incentives must also be considered.


dominates, MRPM is imposed.


If the promotion effect


If the pricing effect dominates, XRPM is


prescribed.


Concluding Comments


This chapter has extended the literature on resale price maintenance by


considering a downstream firm that provides special services and is risk averse.


is a well known result in the literature that, if demand is nonstochastic (or the

firms are risk neutral), a two-part tariff is a sufficient instrument to alleviate the

pricing and promotion externalities when they are the only ones present in the


system.


The manufacturer can achieve the joint profit maximum by setting the


wholesale price equal to the marginal cost of production.


This gives the retailer


the correct promotional and pricing incentives to maximize joint profits.


profits can then be extracted through the fixed fee.


These


However, when the externality


associated with risk sharing arises, the two-part tariff is no longer strong enough to


achieve the joint profit maximum.


When the level of promotion provided by the


retailer is observable by the manufacturer, the use of XRPM in addition to the


two-part tariff are sufficient to maximize joint profits.


When the level of


promotion is unobservable to the manufacturer, incentives for either XRPM or


MRPM can arise.


It is shown that a manufacturer may impose either MRPM or


+- -










In addition, an explanation for MRPM that does not rely on horizontal


externality issuesis presented.


In a purely vertical model, the manufacturer may


impose MRPM to ease the externalities associated with pricing, promotion and risk

sharing.

The results presented in this chapter are derived from a special model and


should be interpreted with care.


An interesting extension of this model would be


to consider several downstream retailers serving different markets.


This would


combine the elements of this model with those of Mathewson and Winter (1984).

However, the results will probably be very hard to interpret because of all the

externalities present and since risk aversion may differ across retailers.

A more interesting extension of the model would be to introduce risk


aversion at the upstream level.


This would allow a further analysis of the role of


vertical restraints in risk sharing.

An important issue not covered in this analysis is the welfare effects of


imposing RPM.


It was shown, in general, that the manufacturer is better off and


the dealer worse off by allowing RPM.


The effect of RPM on consumers deserves


further attention and awaits further research.













CHAPTER 4
OPTIMAL RETAIL CONTRACTS UNDER MORAL HAZARD AND
ASYMMETRIC INFORMATION



Introduction


Why do manufacturers deal with retailers and not directly with consumers


through a single manufacturer outlet?


One explanation is that employing several


retailers reduces transportation costs to consumers.


Another explanation is that


selling through an established retailer allows the manufacturer to avoid the setup

costs associated with retailing.

However, perhaps the most compelling reason for a manufacturer to

employ retailers is that they may have superior information about consumer


demand in the area they serve.


When promotional services (e.g. advertising,


product demonstration, outlet amenities, and point of sale service) are important

in stimulating final consumer demand, the manufacturer may choose to delegate

marketing decisions to a well informed retailer who is better able to tailor

promotion schemes to fit its customers.1








53

In this chapter joint profit maximizing retail contracts are characterized

assuming that the manufacturer delegates the sale of its product to a dealer who is


better informed about demand conditions at the time of contracting.


The dealer


is hired to market and stimulate final demand for the good by providing


promotional and quality enhancing services to consumers.


Neither the level of


service supplied by the dealer nor the state of demand can be observed by the


manufacturer.


Consequently, adverse selection and moral hazard problems may


arise in which the dealer can claim that high sales are due to his promotional


effort, while low sales result from sluggish demand.


The following analysis shows


how vertical restraints commonly mentioned in the literature are optimally

employed to bring the interests of the manufacturer and retailer into closer

alignment.

Specifically, one can imagine that the manufacturer allows the privately

informed dealer to utilize his superior information by selecting from a menu of

contracts which stipulate both the resale price and quantity which the retailer must


The dealer retains all sales revenue but he must pay the manufacturer a fee


for the goods that he markets.


While the level of promotion offered by the dealer


cannot be observed (and thus cannot be stipulated in the contract)2, the

provisions of the contract are used to influence the dealer's marketing effort.








54

The principle result is to show how the choice of price and quantity enables

the manufacturer to determine more accurately whether an increase in sales is


attributable to promotional effort or a high demand realization.


This allows the


manufacturer to supervise the dealer more closely and to extract greater returns

from the vertical relationship.

It is shown that the optimal choice of price and quantity typically involves


resale price maintenance (RPM) and quantity fixing.


The form of RPM may


either entail maximum resale price maintenance (XRPM, price ceilings) or

minimum resale price maintenance (MRPM, price floors) and the form of quantity


fixing may either involve quantity rationing or quantity forcing.


The author


believes this is a new and possibly compelling explanation for the use of price and


quantity restraints.


Earlier studies (as exemplified by


recently by Mathewson and Winter


Telser 1960 and more


1984 and Rey and Tirole


1986) argue that


vertical restraints help to solve the free rider problem associated with promotion.

In this chapter, a complementary explanation is offered that vertical restraints also

prevent dealers from fully exploiting their private information about consumer

demand.


The body of the paper is as follows. The next section presents the model

and describes the manufacturer's contracting problem. The profit maximizing


contract assuming the dealer is privately informed about demand and the










implementing these contracts is described.


In the context of a specific example,


some insights into the welfare effects of vertical restraints are provided.

section summarizes the chapter and discusses extensions of this work. ]


The final


Proofs of


formal results are presented in the Appendix B.

Before preceding, it is useful to briefly relate this analysis to the literature


on vertical control.


This chapter attempts to model the important information


asymmetries which explain why manufacturers delegate marketing decisions to


retailers.


Most of the literature on vertical control abstracts from these


considerations.


Some notable exceptions include the papers by Crocker (1983),


Rey and Tirole (1986) and Katz (1989).

retailer is privately informed about its cos


Crocker considers the case where the

sts. He shows that the manufacturer may


vertically integrate to reduce the strategic use of information by the retailer.


model quite different from the one presented here, Rey and Tirole describe

contracts between a monopoly manufacturer and competitive retailers who are


symmetrically informed at the time of contracting.


The dealers acquire private


information about demand or costs after the contract is signed.


Rey and Tirole


analyze the private and social incentives for the use of various types of vertical


restraints.


Finally, the material in Katz (1989 p. 667-70) on a privately informed


dealer perhaps comes closest to this analysis.


Katz suggests how setting wholesale








56

price above costs can be used to sort among different privately informed dealers

according to their cost of operation.3


Model

The manufacturer produces a product at constant unit cost which is


assumed to be zero for simplicity.


The dealer sells the product to consumers and


provides additional demand enhancing service, called promotion.


Promotion


includes advertising, consumer education, product demonstration or some other

point of sale service.

To highlight the results, a successive monopoly model in which both firms


are risk neutral is employed.


Restricting attention to a single retailer allows one


to abstract from horizontal externality issues (e.g. free riding) and to focus on the


role of asymmetric information in vertical relationships.


The case where there are


multiple competing dealers is addressed briefly in section 5.

Market demand is denoted by Q(p,X,0) where p is retail price, X is the


level of promotion, and 0 is an exogenous demand variable.


Demand varies


inversely with price (Q,


decreasing rate (Qxx


< 0), and is increasing in promotion (Qx


< 0).


> 0) at a


Demand is increasing in 0, for a given p and X (Q9


Below an example is presented which generates market demand with these








57

characteristics from a more primative set of assumptions about consumer

preferences.

It is assumed that the dealer is privately informed about 0 at the time of


contracting because of his familiarity and direct contact with consumers.4


manufacturer's imperfect knowledge of consumer demand is represented by letting

0 be the realization of a random variable with density function f(0) and


distribution function F(0) for 0 e [0LH]

he does not know the realization of 0.


Although the manufacturer knows f(0),


To avoid technical complications, the


following regularity condition is imposed:5


d(1
dO


- F(0))


V E [0,0H]
LL' H


Supplying promotion is costly for the dealer.


For simplicity the model is


normalized so that X represents the total expenditure on promotion.


Throughout


most of the paper it is assumed that the manufacturer is unable to observe the


amount of promotion supplied by the dealer.


This seems reasonable when


promotion is determined by such intangibles as how diligent and hard working the

store employees are or how friendly and helpful the salesmen are to their


customers.


It is assumed, however, that the manufacturer is able to dictate the


4The assumption that 0 is known perfectly by the dealer could be relaxed


* nn rt-1 + lr r.nn.Cn r. n +1.. *^^-l4n Cna+-nn a. .r r All *trn. ;.-W ra n a h m c. + + +


All ~Lnl ;n +dnrr:+n~ natd :n in, c








58

retail price which the dealer must charge, and the level to sales which the dealer


must achi

appears.


eve.


Assuming that the manufacturer can set price is not as strong as it


Although the dealer must charge the manufacturer's suggested retail


price, he is able to control the effective price consumers pay by the promotional


services he offers.


These services may include free delivery, installation, and


repair service.

The timing in the model is that first the dealer learns the demand


parameter 0.6


Then the manufacturer offers a menu of contracts {p(0),


A(0)} which indicate the official retail price, the level of sales required, and A, the


dealer's


The dealer selects from the menu of contracts according to her


report of 0 to the manufacturer.


From the revelation principle (Myerson 1979)


one can restrict attention to contracts which induce the dealer to truthfully reveal

0. Finally, to complete the contract, the dealer supplies the amount of promotion

needed to achieve the required level of sales Q at price p.


There are certain features of the model which should be noted.


First, the


dealer,


who is a monopolist, offers a single price to its customers.


It is assumed


that it is illegal to price discriminate, or that customer resale eliminates


possibilities for discriminatory retail pricing.


Second, once 0 is known, sales are


ate),










deterministic. The analysis can be extended to allow for stochastic sales with

additive uncertainty.7


In what follows it is convenient to work with the promotion function

X(p,Q,0) which is obtained by inverting the demand function Q = D(p,X,0).


Given the assumptions on demand, Xp, Xo


> 0 and Xo


< 0 so that promotion is


increasing in price and sales, and decreasing in 0.

The profit of a dealer of "type" 0 (i.e. a dealer who has observed 0) who

reports 0' is given by


= p(0')Q(0')


- X(p(0'),Q(0'),0)


- A(0')


Since X is decreasing in 0, it is clear that higher 0 type dealers can earn greater

profits, this is because they only need to expend a smaller amount of promotional

effort to achieve the same level of sales at the same price as a lower type retailer.

This additional profit becomes an information rent for the dealer which cannot be

taxed away because the manufacturer is unable to observe 0.

Below it is shown that the information rents that the dealer commands

depends on the magnitude of -Xo = (D9/Dx) = MRSxG which is the marginal rate


of substitution of promotion for exogenous demand.


The optimal retail contract


will depend on how the manufacturer's choice of p and Q affects this marginal


rate of substitution.


In what follows three cases are studied:


,rrd(81











-
- XpO


= XQ, = 0
, -XQo < 0
, -XQo > 0


(P1)
(P2)
(P3)


In case P1, the ability of the retailer to substitute for low demand with greater


promotion expenditure is unaffected by either the price or quantity level.


arises when 0 and X are perfect substitutes.


This


In contrast, in cases P2 and P3 the


marginal rate of substitution depends on both price and quantity level.


following example illustrates the three cases.


Example

Assume that each consumer may purchase at most one unit of a commodity


(e.g. a car, stereo, or an appliance) from the dealer.


Consumer satisfaction with


the product depends on 0 which measures how familiar and knowledgeable

consumers are about the commodity, and on X which measures the amount of


point of sale service offered by the retailer.


The customer's type or taste is


represented by t e [tL,tH] and customers are distributed by F(t) which is assumed


to be uniform.


If the consumer doesn't purchase the good his utility is zero,


otherwise he receives utility, U(t,x,0,p) = t + u(x,0)


satisfaction is increasing with 0 and X, so that Ux, u0 > 0.


assumed that


Given X, 0, and p, the


demand for the product is


1-F(t) where


t satisfies U(t,X,0,p) = 0.


By inverting the demand function, one can obtain an expression for the
- f f.... l--- r A* / \ t i 1 1 ] J ] g Jl ,1









parameter.


For example, when 6 > 0, promotion is more valuable the higher the


demand.


One finds that case P1, P2, or P3 occur as Si = 0, 8


< 0, or s


respectively.8

Formally, the manufacturer's problem [M] is to design a menu of contracts

{p(0),Q(0),A(0)} to


Max


A(0)dF(0)


subject to (for all 0,0')


> 0


_> 'r~e'


(IR)


(IC)


where ird(O' I


0) is given by (1).9


In [M] the individual rationality condition (IR) stipulates that the dealer


must earn at least his reservation profit (which is zero) under the contract.


(IC) is


sit is easy to find other examples of demand specifications satisfying P1-P3.
As mentioned in the text P1 occurs whenever 0 and X are perfect substitutes in


demand.


P2 can be satisfied for separable demand specifications of the form Q =


H(0,X) G(p) where Hx>0, Hx9<0
demand is Cobb-Douglas with Q =


, Hxx<0, G'>0, G">0.
p X8" where a, 8, a >


Case P3 obtains when


,0 and S


< 1.


"(e


,rrd(8








62
an incentive compatiblility constraint, which implies that the dealer maximizes his

profits when he truthfully reports 0 in accord with the revelation principle.

The following lemma allows one to rewrite [M] as an unconstrained

maximization problem for the three cases P1-P3.


Lemma 1:


Necessary and sufficient conditions for implementing retail incentive


contracts are:


-f


Q'(0), p'(O)
O'(0), p'(o)


Proof:


< 0 for case P2
> 0 for case P3


In Appendix B.


According to part (i) of Lemma 1 dealer profits or information rents

increase at -X9, which is the rate which the dealer can reduce promotion with


higher realizations of 0 and still maintain the same level of sales.


are monotonicity conditions required to satisfy (IC).


Parts (ii) and


Part (i) allows one to


write the transfer fee as


A(0)


= p(O)Q(0)


- X(p (),Q(O),0)


-f


-XdO


Substituting this expression for A(0) in [M], integrating by parts and rearranging


terms allows one to rewrite the manufacturer's


problem as [M]'


rtV


-Xd0


rrd(8








63


Characterization of Ootimal Contracts


For purposes of comparison, it is useful to first examine the first best

contract {p*(0),Q*(0),A*(O)} which the manufacturer implements when he can


observe 0 and the level of promotion supplied by the retailer.


The first best


contract is described in the following Lemma.


Lemma 2:


In the first best contract:


p'(0)
Q*(0)


Proof:


= X
=xp
S0) = 0


In Appendix B.


According to conditions (i) and (ii), price and quantity are chosen so that


the marginal revenue equals the marginal cost.


Marginal cost is measured by the


increase in promotion required when either price or quantity are increased.

Condition (iii) implies that the manufacturer extracts all excess profits from the

dealer.


It is important to note that the franchise fee, A'(0) allows the manufacturer


to collect revenues from the retailer without distorting price or quantity.


In the


absence of a franchise fee or nonlinear prices, the manufacturer would need to

charge a wholesale price above marginal cost and invoke some form of resale


price maintenance and quantity fixing.


With full information, the manufacturer








64
could use these instruments to avoid the double marginalization problem


(Spengler


1950) without distorting price or quantity.10


Now suppose that the dealer has private information about demand.

profitable for the manufacturer to introduce price and quantity distortions?


Is it

As


before, the franchise fee allows the manufacturer to tax the dealer without


distorting price and quantity.


However, now the choice of price and quantity may


reduce the information rents which the dealer commands from his private


knowledge of demand.


Consider the characterization of the optimal contract for


cases P1-P3 as described in the following propositions.


Proposition 1:
(i)
(ii)


Given P1 (Xp = XQo = 0), the solution to [M]' involves
p(O) = p t0)
Q(o) = Q (0)


-X6dO


Proof:


In Appendix B.


Case P1 is interesting and special.


The optimal retail contract induces the


dealer to select the first best price and quantity even though he is privately


informed about demand.


To see why, consider a dealer who learns that demand


is high but reports that demand is lower.


By misreporting, the dealer earns a rent


since demand is higher than he reported, and he can reduce promotional

expenditures and still meet his sales requirement at the stipulated price.


,d(e







65
According to Lemma 1, rr'(0) = -X* = MRSOx, so that profits increase at the rate

which the retailer is able to reduce promotional expenditures with higher


realizations of demand. When X does not vary with p and Q (as in case P1) it is

not possible to affect the retailer's profits by varying price and quantity.


Consequently, it is unproductive to distort price and quantity from their first best


levels, as implied by parts (i) and (ii) of Proposition 1.11


Notice that although


the first best price and quantity are chosen, this contract is not first best since the

retailer earns strictly positive profits as indicated in part (iii).

In contrast to case P1, it is optimal to introduce price and quantity


distortions into the retail contract for cases P2 and P3.


describe the nature of these distorts

X(p(0),Q(0),0) be the joint profit.


The following Propositions


In what follows let &'(O) = p(O)Q(O) -


Denote pJ(Q(O),O) as the joint profit


maximizing price given Q(0) and 6, and QJ(p(0),0) as the joint profit maximizing

quantity given p(0) and 0.


Proposition 2:
(i)
(ii)


Given P2 (-X, -Xo, < 0), the solut
MRPM with p(O) > p'(Q(0),0)
Quantity forcing with Q(0) > (


ion to [M]'
(> for 0
)J(p(O),O) (


involves
< H)
> forO


< H)


-Xd0


Proof:


In Appendix B.


,rrd(8









Proposition 3:
(i)
(ii)


Given P3 (-Xp, -Xo0 > 0), the solution to [M]' involves
XRPM with p(0) pJ(Q(6),0) ( < for 0 < OH)


Quantity rationing with Q(0)


_ Q'(p(0),0)


< for 8


< H)


d d(e


-f


-Xd0


Proof:


In Appendix B.


The optimal pricing and output distortions are designed to decrease the


substitutability between X and 0.

decreasing in both p and Q. The


Consider case P2 where MRSOx = -X9 is


e optimal contract involves both MRPM and


quantity forcing as both the price and quantity are set above their joint profit


maximizing levels.12


The intuitive explanation is that starting with the joint profit


maximizing price, if one were to increase price slightly, to a first order this would


have no effect on joint profits.


However a price increase would reduce the


substitutability between X and 0 thus decreasing the information rents of the


retailer.


Consequently, manufacturer profits are higher with a price floor.


Similarly, because information rents are also declining with an increase in quantity,

it is optimal for the manufacturer to force the dealer to sell more than the joint

profit maximizing quantity.


In case P3 (-Xp ,


-Xoe


> 0) the substitutability between X and 0 is reduced


whenever price and quantity are reduced. Therefc


)re, to reduce the information









rents, price and quantity are set below their profit maximizing level.


These


distortions take the form of XRPM and quantity rationing as noted in Proposition
3.13


Propositions 1-3 characterize the optimal pricing and sales contracts when


the manufacturer is unable to directly specify the level of promotion to be


The question arises as to how the optimal policy described


and 3 changes
transferred to
Clearly, in cas
monitor sales
effective cap.


when the manufacturer is only able to dictate the n
the dealer but not the number of units actually sold
e P3, where the policy dictates quantity rationing, th
is of no consequence. The manufacturer is still able
However, in case P2, the policy of quantity forcing i


in propositions 2
umber of units
to consumers.
e inablility to
to impose an
is no longer


viable. The manufacturer tries to force the dealer to sell Q(0) units where, given
p(O), Q(0) solves
p(0) X,(p(0),Q(0),0) + h(0)X0o = 0
Call this equation Fl.
The dealer, on the other hand, chooses the number of units to sell, Q,
which maximizes 1d(Q,0) = p(0)Q X(p(0),Q,0) A(0) subject to Q S Q(0). Th
solution satisfies the following Kuhn-Tucker conditions.
p(0) Xo(p,Q,0) F 0 ; if > then Q = Q(0)


Q(0) Q > 0 ; if > then F = 0
where F is the lagrange multiplier on the constraint.
Now consider case P3 in which Xeo < 0. This implies, from equation Fl,
that p(0) Xo(p(0),Q(0),0) > 0. Suppose Q 4 Q(0), then F = 0. This implies


p(O) X,(p(0
P3, O = 0(0)
In case
Suppose 0 =
Xo(p(0),0,0)
In case


and
P2


) > 0, which implies
the results in Propo
(Xeo > 0), equation


0= Q(0); a contradiction.
sition 3 still hold.
F1 implies p(0)- X,(p(0),(


Thus, in case


(0),0) < 0.


Q(0), then since F > 0 by construction, equation 2 implies p(0) -
> 0; a contradiction. Thus O < Q(0).
P2, the manufacturer cannot force the dealer to sell more than 0


units. However, he still has full control over retail prices. Thus, the optimal retail
contract entails a p(0) and Q(0) which solve the following conditions.


0(0)


- X_(BO(0(.'0) + h(0)X._


It









supplied by the retailer.


An interesting question which is analyzed in the next


proposition is whether the level of promotion provided by the retailer is joint

profit maximizing, given price.


Proposition 4:
(i)
(ii)
(iii)


Proof:


Given p(0), promotion is
optimally provided in case PI,
overprovided in case P2, and
underprovided in case P3.


In Appendix B.


In case P1, MRSOx is unaffected by variations in p or Q so there is no


benefit in distorting price or quantity.


The same applies to promotion; given


price, it is optimal to induce the joint profit maximizing level of promotion.


contrast, in case P2, it is possible to reduce information rents by increasing Q.


Accordingly, Q is set above its profit maximizing level.


To induce such a level of


sales, promotion must be overprovided relative to the joint profit maximizing level.

In case P3, it is optimal to set sales below the joint profit maximizing level to


reduce information rents.


This requires that promotion be underprovided.


This section is concluded by explaining how these optimal retail contracts

can be implemented in practice by the menu of options which is offered.


Proposition 5:
(i)


In the solution to [M]' the menu of options satisfies14
in case PI: p(0)=p*, Q(0)=Q', A(0)=A(0L)


in case P2:
in case P3:


p'(0),
p'(0),


Q'(0)
Q'(0)


< 0, A'(0)
> 0, A'(0)


Proof:


In Appendix B.








69

In the case of P1, only the unique joint profit maximizing price and quantity

are offered, and the level of the franchise fee is set to insure that the retailer


breaks even under the least favorable demand conditions.


This implies that the


retailer almost always earns strictly positive profits.

In the case of P2, the manufacturer wants to induce the privately informed


retailer to select a price and quantity which is appropriate given demand.


X, and


Xo represent the marginal cost (in terms of required promotion expenditure) of


increasing price or quantity. Since these marginal costs are increasing with 0

under case P2 (since Xp, XoQ > 0) the dealer is induced to select a lower price

and quantity when demand is high. Accordingly, the retailer remits a greater


share of the revenues to the manufacturer with high demand since it is easier for

the dealer to achieve lower sales at a lower price.15


The situation is reversed for case P3.


When demand increases, the


marginal cost of increasing price and quantity are diminished since X., Xoe


< 0.


Joint profits are increased by inducing the dealer to increase price and quantity.

With higher price and quantity the dealer must expend more on promotion, so he

remits less back to the manufacturer when demand is high.


Welfare Implications


In this section, the welfare effects that the use of vertical restraints have on


i1 at -.. -l 1. I V


r


7








70

analysis comparing welfare before and after the imposition of vertical restraints is


quite difficult and leads to ambiguous conclusions.


However, using the framework


of the example presented earlier, one is able to draw some insights.

In the example, the demand function is given by


Q(x,6,p) =


-F(t) =


- p + u(x,0)


and the inverse demand function is given by


P(Q,x,O) =


- 0 + u(x,O).


Using the promotion function, expressions for consumer surplus and producer

surplus (joint profits) are given by

Q


CS(p,Q,0)


+ u(X(p,Q,O),O))]dQ'


- Q + u(x(p,Q,O),O))Q


= (1/2)Q2


PS(p,Q,0) = (1


- Q + u(X(p,Q,O),O))Q


- X(p,Q,O),


respectively.


Consider the state of nature before any vertical restraints are


imposed, i.e., the manufacturer only charges the dealer a fixed fee A(0).


In this


case the retailer's choices of price and quantity are exactly those that maximize


joint profits, namely p


* *


which satisfy the following,


-Xp(p,Q*,0) = 0

- X(p*,Q*,0) = 0








71

jointly concave in p and Q (this implies that the local deviations from the joint

profit maximizing price and quantity, as presented in Propositions 2 and 3, are


also the global ones).


One then has,


and Q = (


<) Q in case P1 (P2) (P3).


Thus,


Finding 1: The imposition of RPM and quantity fixing has no effect on
(increases) (decreases) consumer surplus in case P1 (P2) (P3).


This finding follows from the fact that, in this example, the value of consumer

surplus is directly related to the number of sales.

As mentioned above, the retailer's choices of price and quantity maximize


joint profits.


In case P1, the manufacturer can not affect the rents which the


dealer appropriates and does not deviate from this position.


In cases P2 and P3,


however, the manufacturer does move away from the joint profit maximum in


order to increase his profits by lowering the dealer's rents.


Finding 2:


Thus,


The imposition of RPM and quantity fixing has no effect on


manufacturers welfare, dealer welfare, or joint profits in case P1; increases
manufacturer welfare, decreases dealer welfare and decreases joint profits in case
P2 and P3.

Now, defining total welfare as the sum of consumer surplus and producer surplus

(joint profits) one has,


Finding 3:


The imposition of RPM and quantity fixing has no effect on total


welfare in case P1.


Total welfare is decreased in case P3.


In case P2, the effect


on total welfare is ambiguous (consumer surplus is increased but joint profits are
...-.- -----


p = (>)(


<)p








72

manufacturer trying to better monitor the dealer thereby limiting his rents.

particular, the manufacturer does not impose vertical restraints to extract


consumer surplus nor to maximize profits of the vertical structure.


In fact, in case


P2, consumers are better off and joint profits are decreased as a result of the

imposition of vertical restraints.

Also noteworthy is the fact that, in case P3, the package consisting of a

price ceiling and quantity rationing results in a decrease in consumer welfare.

This provides a counterexample to the conventional wisdom that price ceilings


cannot be harmful to consumers.


Although this example is highly stylized, it


makes clear the importance of examining the effects of vertical restraints on a

case-by-case basis.


Conclusion


Optimal retail contracts under conditions of asymmetric information and


moral hazard have been characterized.

some form of RPM and quantity fixing.


Generally, the optimal contract exhibits

The type of vertical restraint chosen


depends on how price and quantity choices affect the substitutability of the

random demand component for promotion supplied downstream.

Economists previously have argued that the incentive for a manufacturer to

impose price ceilings arises from the double marginalization problem when only


0J I0 4 *


-.-.- rtf *,1. -. t,, ----,, a n. uu ~ u r .r aa


I:.-


i








73

Using a specific example, insights were made as to the welfare effects of


vertical restraints.


It was found that consumer surplus may be increased or


decreased depending on local demand parameters. The case in which price

ceilings are detrimental to consumer welfare is surprising. This result arises from


the fact that quantity rationing is also imposed.


Thus, when considering the


effects of price restraints, it is important to consider them in conjuction with other

restraints that are used, as opposed to examining them in isolation.

This analysis may also help to explain the finding of Ippolito (1988) that

price ceilings and price floors are sometimes observed in the same industry across


different markets.


For example in 18 RPM cases involving gasoline retailing, price


ceilings were alleged in one half of the cases and price floors were alleged in the


remainder of the cases.


This could be explained by a variation in consumer


demand parameters across different markets in the industry.

The results presented in this chapter should be interpreted with care since


they are derived for a special model.


An important extension of this analysis


would be to consider a setting where there are several dealers serving different


markets.


In such a setting it is well known that price floors or quantity rationing


may be needed to solve promotional externality problems between different


dealers.


The choice of price and quantity would now be important in solving


externality problems as well as adverse selection and moral hazard problems.








74

may want to base compensation on relative performance among the different

dealers as suggested in Katz (1989) and Schleifer (1985).













CHAPTER


CONCLUSION


This dissertation has presented three essays.


The first provided an


overview of the legal and economic issues surrounding vertical price fixing.


described the evolution of the present standard of per se illegality and presented

various opinions on the standard.

Many authors have expressed disdain for the current standard, but with the

multitude of theories and conflicting policy recommendations, how are the courts


to choose a replacement standard?


Is there any consensus to be found that might


guide the courts in assessing the legality of RPM?


The compromise standard that


seems to be evolving is to continue the per se ban on RPM except in the case of


new products and when it is used by small firms in unconcentrated industries.


other cases put the burden of proof on the user of RPM to show why its use is


beneficial.


However, whether the courts adopt this standard is a question that


only more litigation can answer.


In any case,


RPM promises to remain one of


the more lively topics in the economics and antitrust literature.

The second essay extended the literature on resale price maintenance by

considering a downstream firm that provides special services and is risk averse.








76

firms are risk neutral), a two-part tariff is a sufficient instrument to alleviate the

pricing and promotional externalities when they are the only ones present in the


system.


The manufacturer can achieve the joint profit maximum by setting the


wholesale price equal to the marginal cost of production.


This gives the retailer


the correct promotional and pricing incentives to maximize joint profits.


profits can then be extracted through the fixed fee.


These


However, when the externality


associated with risk sharing arises, the two-part tariff is no longer strong enough to


achieve the joint profit maximum.


When the level of promotion provided by the


retailer is observable by the manufacturer, the use of XRPM in addition to the


two-part tariff are sufficient to maximize joint profits.


When the level of


promotion is unobservable to the manufacturer, incentives for either XRPM or


MRPM can arise.


We show that a manufacturer may impose either MRPM or


XRPM based on a simple elasticity condition which describes local demand


conditions.


This provides a competing explanation for the observation that


MRPM and XRPM are sometimes observed in the same industry.

In addition, the second essay provides an explanation for MRPM that does


not rely on horizontal externality issues.


In a purely vertical model, the


manufacturer may impose MRPM to ease the externalities associated with pricing,

promotion and risk sharing.

The results presented in this essay are derived from a special model and









to introduce risk aversion at the upstream level.


This would allow a further


analysis of the role of vertical restraints in risk sharing.

An important issue not covered in this analysis is the welfare effects of


imposing RPM.


It was shown, in general, that the manufacturer is better off and


the dealer worse off by allowing RPM.


The effect of RPM on consumers deserves


further attention and awaits further research.

Optimal retail contracts under conditions of asymmetric information and


moral hazard were characterized in chapter 4.

exhibits some form of RPM and quantity fixing.


Generally, the optimal contract

The type of vertical restraint


chosen depends on how price and quantity choices affect the substitutability of the

random demand component for promotion supplied downstream.

Economists previously have argued that the incentive for a manufacturer to

impose price ceilings arises from the double marginalization problem when only


linear pricing is possible.


This analysis shows, in an environment of asymmetric


information and moral hazard that price ceilings may be desirable even when

nonlinear pricing is possible.

Using a specific example, insights were made as to the welfare effects of


vertical restraints.


It was found that consumer surplus may be increased or


decreased depending on local demand parameters. The case in which price

ceilings are detrimental to consumer welfare is surprising. This result arises from








78

effects of price restraints, it is important to consider them in conjuction with other

restraints that are used, as opposed to examining them in isolation.

Again, the results presented in this chapter should be interpreted with care


since they are derived for a special model.


An important extension of this analysis


would be to consider a setting where there are several dealers serving different


markets.


In such a setting it is well known that price floors or quantity rationing


may be needed to solve promotional externality problems between different


dealers.


The choice of price and quantity would now be important in solving


externality problems as well as adverse selection and moral hazard problems.

Another interesting possibility is that demand conditions may be correlated


between different dealers serving separate markets.


In this case, the manufacturer


may want to base compensation on relative performance among the different

dealers as suggested in Katz (1989) and Schleifer (1985).












APPENDIX A
PROOFS FOR CHAPTER 3


Proof of Lemma 1.


The maximization in [I] yields the following first order conditions.


= (p-c)Q Op()f(0)dO


+ Q()f(0)dO


(Al)


(A2)


Assuming second order conditions hold (sufficient conditions are Q,


0, and 7r


- ( 2r


> 0), (Al) and (A2) define the optimal choices of p and x


-- (p


,x ).


Substituting (p',x') back into (Al) and (A2) yield the following


identities.


(p*-c)f Q(p,x*,0)f()de


+ Q(p*,x*,0)f(e)d0


-c) Qx(p*,x0)f(0)d0


Q.E.D.


(p


-OIQ,(~f(e)ds


< o, a,








Proof of Lemma


The program in [NIFI] implies the following Lagrangean,


= (w-c) Q(p,x,O)f(0)dO
.{fu((p-w)Q(p,x,0)


- x A)f(0)dO


Optimization yields the following first order conditions,


+ {f -u'()f(O)dO}


(A3)


= QO(-)f(0)d0 +


= (w-c) Oxf(O)dO


Mi-u'(-)Q(')f(O)dO}


(A4)


(A5)


+ f u'(.)[(p-w)OQ-l]f(O)dO}


= (w-c)fQpf(0)dO


+ X{fu'(.)[Q(.)


+ (p-w)Qp]f(0)d0}


(A6)


= fu(-)f(0)dO


(A7)


- U0o


Assuming second order conditions (A3)-(A7) yield (w,A,p,x).
Now, (A3) and (A4) imply


IO(-)f(0)d0


fu'/()f()d0


- Q(Qu'(.)f(0)de


which in turn implies that u'(-) does not vary with 0.

Now (A7) implies that it must be that A<0.


Hence it must be that p= w.

In order for the upstream


- uo


9(~wxpl)









(A6) can be rewritten as


(w-c)f Qf(O)dO


+ +d
dpJ


(A3) implies


>0 which yields


dp u()f(0)d0}
dp


Hence, the downstream


firm would prefer to increase price.

Equations (A5) and (A6) can now be written as


(p-c)f Opf(O)dO


+ JQ()f(O)dO


These are identical to the first order conditions on the choices of x and p in


program [I].


Thus, x=x


Q.E.D.


Proof of Proposition 1.


First note that if promotion is valuable the upstream firm must set p>w.

For if p
promotion is then


lu'[(P-m )Qx


- 1]f(0)d0


(P-Qlaf(B)de


P-P









Secondly note that under CARA,


Since


fu'((p-w)Q(p,2(.),O)


- A)[(p-w)Qx(p,2( ),0)


- 1]f(0)d0


= 1[u,,
D -


(*)[(p-w)Q,


- 1]f(0)d0]


where


du( )d


Under CARA,


[(p -w)Q,


- l]f(0)dO


= -ru' [(p-w)Q


- l1f(0)d0


Hence


The program in [NI'] implies the following Lagrangean,


-c)fQ(p,R(-),0)f(0)d0


A{ u()(p-w)(p,(),0)


- A)f(0)d0


-lii


Optimization yields the following first order conditions,


+x{f


-u' ()f(O)dO}


(A8)


= QO()f(0)do


-c) xf(O)dO


+ x{ -u'(*)Q(j)f(O)d0


(A9)


+ (W


+ A
R( ~


ft( ~


~e(~wpit)


~ (W









-c) [Qp


+ Qp]f(Oe)dO


+ x' u'()[Q(*)


+ (p -w)Qp]f(O)d})


(A10)


= u u()f(O)dO


- u


Assumming second order conditions (A8)-(A11) yield (w,p,A).


Now, (A8) and (A9) imply


(All)


J o(')f(O)dO


Su' ( *)f(O)dO


- Q(-)u' (*)f(O)dO


+ (w-c)fw Qxf(O)d0


Integration by parts yields


-c) QOxf(0)d0


and therefore sign(w-c)


= -sign(


Now,


Q[(p -w)Q,


+ u'Qx)f(O)dO}


sign(


= -sign{ (u" Q[(p-w)Q,


+ u'Ox)f(0)d0}


sign(Rt,)


= -sign{-r u'Q[(p-w) Qx


- l]f(O)dO


+ u'Qxf(O)dO}


~llc"


(W









Now, Qxo<0 implies that [(p-w)Qx


- 1] is decreasing in 6.


The downstream firm's


maximization implies


- l]f(0)dO


Since u'


> 0 for all 0 it must be true that for some 0 [(p-w)Qx


and [(p-w)Q,


< 0 for 0>0.


- 1] > 0for 0<@


Thus, we have


u [(p -w)Qx


for all 0< OH.


fu'Q[(p-w)Qx


thus,


- l]f(0)dO


Integration by parts yields


- 1]f(0)dO


< 0 and so w


Now note that (A10) can be rewritten as


(w-c) [Qp


+ Qoxp]f(0)d0


+ { fu(.)f(0)dO}


Employing the elasticity definitions this can be rewritten as


(w-c)


Q( )f(0)dO


d
+ {-fu(If(0)d0)
dpJ


Thus,


I'[(p-w)a,


+E nl
X 'r










So if


+ ex ]


<) 0, downstream expected utility is increased (decreased)


by decreasing (increasing) the retail price.


= 0 then downstream


expected utility is unaffected by a price change.

Q.E.D.


Erll












APPENDIX B
PROOFS FOR CHAPTER 4


Proof of Lemma 1.

Applying what are now standard arguments (see Baron and Myerson

(1982)) a necessary condition for local incentive compatibility is


ir~d(O)


- -X


(Bl)


Since rd(0) is increasing, individual rationality binds only at 0 = =L

implies


. Thus, (Bl)


17.d(o)


-Xd0


(B2)


The first order condition for local incentive compatibility implies that


(B3)


The second order conditions for local incentive compatibility require


(B4)


h


~TTdZ(


dl(B
'TT








87

Total differentiation of (B3) with respect to 0 and employing (B4) implies that the

following is required.


= X p'(0)


+ XeQ


Q'(o)


(B5)


which is satisfied trivially for P1.


In case P2 (P3) it follows that Q'


p' 0 (Q'


> 0) are sufficient to satisfy (B5).

The proof is completed by showing that local incentive compatibility implies


global incentive compatibility.


Given P1, P2, or P3 this is easily demonstrated


following the arguments of Matthews and Moore (1987)

Q.E.D.


Proof of Lemma


The first best problem is written


M~ax rr


= p(6)Q(0)


-X(.)


p,Q

Optimization yields


-0

- Xp(-)


In the first best case the upstream firm only needs to provide the downstream firm
a S no





= --_Td


= -d


cl (e>


p*(8)













Q.E.D.


Proof of Proposition 1.

Differentiation of [M]' with respect to Q and p yields:


= Q(0)


=p(0)


- X


- Xo


where ir9 is the profit of the manufacturer.


This implies that p(O) = p*(0) and


Q(0) = Q'(0).


Note that in this case (Xp =


XQo = 0), totally differentiating the


above first order conditions with respect to 0 and using Cramer's rule implies p'(0)


= Q'(0) = 0.


Thus, under P1, p6(0) and Q'(0) are constants.


From Lemma 1,


6


t~r(0)


-I,


-XdO


Q.E.D.


7T*


=7~~*







89

Proof of Propositions 2 and 3.

Under P2 or P3, differentiation of [M]' with respect to p and Q yields:


SQ(0)


= p(0)


- X


- Xo


+ h(O)


+ h(0)


implying that


J( p(0),Q(0),0)


p(0),Q(0),0)


= -h(O)Xop


= -h(0)Xo


where tJ is defined in the text.


Hence, under P2, rJ


< 0 and "n'o


< 0 for all 0


OH, i.e., price floors and quantity forcing are imposed.


> 0 for all 0


Under P3, rrJ


< OH, i.e., price ceilings and quantity rationing are imposed.


that h(0H) = 0, hence, when 6 = OH we have Wip


-IraQ


> 0 and To0


Note


= 0.


Part (iii) follows from Lemma


Q.E.D.


Proof of Proposition 4.

Given n. the ioint profit maximizing level of X is eiven bv:







90

Differentiating joint profits with respect to X reveals that XJ satisfies


(B6)


.Qx


For the solution to [M]'


, the profit maximizing level of X, denoted by


X(p,0) is characterized by


*Qx


+ h(0)X0oQx


(B7)


Comparing (B6) and (B7) it follows that X(p,0)


> (=) (<) XJ(p,0) for P3 (P1)


(P2).

Q.E.D.


Proof of Proposition 5


The proof of this proposition involves showing that the local incentive


compatibility conditions in Lemma 1 are satisfied.


To determine the sign of p'(0)


and Q'(0), totally differentiate the system of first order equations in [M]' with


respect to 0.


Employing Cramer's rule one finds that


sign[ p'(0) ] = sign[


oo'(Xpe
po' (Xoe


sign[ Q'(0) ] = sign[ trmpp,(Xo,
rp0 (Xpo


- h()Xp
- h(0)Xo


- h(0)XooQ
- h(0)XO


-
- h'(0)XO) -
- h'(0)X0o I


- h'(0)Xo,) -
- h'(0)Xp ]


In cases P2 and P3 it is readily verified that p'(0) and Q'(0) have the appropriate








91

Given the monotonicity conditions hold' it is straightforward to show that


A'(0)


> 0 in cases P2 and P3.


In Proposition 1 it was shown that, under P1


pC0B)


= O'(0)


= 0 and it is


easy to show that A'(0)


= 0.


Hence, under P1,


Q(0), and A(0) are single


valued.

Q.E.D.


p(8),














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]a


W. J.,




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