Common agency theory and the industrial organization of health care

MISSING IMAGE

Material Information

Title:
Common agency theory and the industrial organization of health care
Physical Description:
v, 83 leaves : ill. ; 29 cm.
Language:
English
Creator:
Encinosa, William Edward, 1966-
Publication Date:

Subjects

Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1995.
Bibliography:
Includes bibliographical references (leaves 79-82).
Statement of Responsibility:
by William Edward Encinosa, III.
General Note:
Typescript.
General Note:
Vita.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 002054368
notis - AKP2346
oclc - 33480393
System ID:
AA00003191:00001

Full Text









COMMON AGENCY THEORY AND THE
INDUSTRIAL ORGANIZATION OF HEALTH CARE











By

WILLIAM EDWARD ENCINOSA, III


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


1995









ACKNOWLEDGMENTS



This work was supported financially by a Jim Walter-Lanzillotti Dissertation Fel-


lowship.


I thank the Public Policy Research Center at the University of Florida for


their generous support.

I am indebted to David Sappington for his insightful comments, invaluable advice,

and constant support in the difficult task of translating economic theory into public


policy.


I am also grateful to


Tracy Lewis, Jon Hamilton,


Mike Ryngaert,


and Steve


Slutsky for many helpful discussions.


In particular,


thank David Martimort of


IDEI, France, for his help with common agency theory.


I also thank Professor Louis


Block of the Mathematics Department for providing me with very generous computer

facilities.
This work has benefited greatly from the comments of seminar participants at


Harvard


University's


John


Kennedy School of Government,


Carnegie Mellon's


Heinz School of Public Policy, and IUPUI. I am also grateful for the many helpful


discussions with


the faculty


and scholars participating in


1995


Robert


Wood


Johnson Health Policy Research Programs at the University of California-Berkeley,
the University of California-San Francisco, and the University of Michigan.
Finally, I am especially grateful to my parents for their continuous support and
encouragement during this work.











TABLE OF CONTENTS


ACKNOWLEDGEMENTS


. . . .* . a a S ii


ABSTRACT


CHAPTERS


GENERAL INTRODUCTION


COST SHIFTING AND GOLDPLATING IN HEALTH CARE


Introduction . . .
The Model. . .
The Overinvestment Problem
Mixed Payment Systems
Goldplating . .
Public Policy Implications
Conclusion . . .


* S S . S S S S S
. a a S S S S S S S .
* 0 0 5 5 S S S S S S S S S S S S S S S
* a . S S S S p a S . .
* S S S . 0 0 0 S 0 S S S
* p . 0 S S a S S


OPTIMAL HOSPITAL CAPITAL STRUCTURE


Introduction .
The Model .
Debt Strategies
Conclusion .


* S S p . . S S S 0 5 0 0
* . 5 S S 0 .*. S S S S S S
. S S S P 0 S S S S S S S 0 S S S S S
* a 5 S . . . P P 5 5 S S S


PRICING UNDER EXCLUSIVE DEALING


Introduction . . .
Common Agency .
The Monopoly Benchmark
Competition for an Exclusive
Hospital Exclusive Dealing
Conclusion . . .


* . S S 0 0 S S 5 S .
* S S 0 0 S S 0 5 5 S .


Dealer


. 5 5 0 5 0 5 5 S S S S S S P 5 5
a a S S S P 5 .


* 0 S S . S . 0 0 S S S 0
* S S P . S S S S S


CONCLUDING REMARKS


DTfl I D A DTXTrT A T cOTTTu


APPIENDIX

REFERENCES









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


COMMON


AGENCY THEORY


AND THE


INDUSTRIAL ORGANIZATION


OF HEALTH


CARE


William Edward Encinosa, III

May 1995


Chairman: Professor David E.


M. Sappington


Major Department: Economics

Common agency theory deals with a competitive version of principal-agent theory


in which multiple principals contract with the same agent.


This dissertation develops


common agency theory for applications to the industrial organization of the health
care industry.


In the first essay, the efficiency of three health care systems is examined.


In a


multi-payer system the public payer (Medicare) uses a mix of prospective payments
and pass-through payments, while the private payer (a managed care insurer) uses


a quality-based reimbursement rate through utilization review.


Cost-shifting in the


multi-payer system induces the hospital to overinvest in technology, even under pri-


vate insurer utilization reviews.


Furthermore, pass-through payments of capital are


scaled back in equilibrium since they create a moral hazard problem that allows the
hospital to goldplate, i.e, to invest in wasteful, non-technological capital. This may
explain Medicare's current policy to phase-out pass-through payments. In a single-


payer system investment in technology is curtailed,


and goldplating can arise.


When


+t*I I nt*" I niarfl nannn o k niaa +b0IQ n\t'no nn A +0 n I ni ,wa A ry 4 ^ n nyi lj-t fv^-









The second essay studies the interrelationship between a hospital's


capital struc-


ture and the payment plans designed by Medicare and the private insurance sector to


reimburse the hospital's


cost of capital and technology.


To counter the opportunism


of a managed care private insurance sector engaging in utilization review, the hospital
will use debt when bankruptcy is costly.
The final essay derives the equilibrium hospital contract with a physician group
that has private information on the risk rating of the health maintenance organization
it serves. Bundled physician charges are then derived when hospitals compete for an
exclusive contract.









CHAPTER 1
GENERAL INTRODUCTION


The United States is presently undergoing a national health care crisis. In 1994,
expenditures on health care exceeded $ 1 trillion, more than 14 percent of GDP. Med-
ical costs are projected to soar to 19 percent of GDP by the year 2000 (Clinton 1993).
Per capital, the United States spent 40 percent more on health care than Canada, the
second highest spender, and twice as much as the major European countries in 1991


(Starr


1994).


1990,


United States was spending more on health care than


on education and defense combined.


Yet, paradoxically, about 18 percent of Ameri-


cans do not have medical insurance. In fact, 26 percent of Americans had no health


insurance coverage at some time between 1987


1989 (Starr


1994).


Moreover,


86 percent of these uninsured were members of working households (Roberts 1993).
Among OECD countries, the United States ranks nineteenth in infant mortality and


twenty-first in life expectancy for men (Clinton 1993).


level of medical expenditures,


Thus, for its extremely high


United States does not seem to be delivering a


commensurate level of health care to its people.
This crisis has lead to an unprecedented public policy debate over federal reform


of the health care industry.


The last major federal health reform to occur was in 1965


with the establishing of Medicare to insure the elderly and the severely disabled. At


that time, health care was only 6 percent of GNP.


Yet, now Medicare spending is


running 23 percent higher than the rate of inflation (Clinton 1993).


Consequently,


the Medicare Trust


Fund will be empty by the year 2002.


The Reagan Adminis-


tration did make substantial changes in Medicare payments to hospitals with the


introduction of the Prospective Payment System (PPS) in 1984.


Under this system,


hospitals receive a fixed payment for each patient in a specific diagnostic group, in-






2


held Medicare reimbursement expenditures down initially. However, after 1989, hos-
pital expenditures began to soar again, accounting for about 40 percent of all medical
expenditures in the United States.
Parallel to this reform in the public sector, the private insurance sector and the


hospital industry


are undergoing major transformations.


Over the past


years,


more than 400 hospitals have sought mergers.


More importantly, there has been a


significant movement to merge insurance and health care provision.


These mergers


have taken the form of health care maintenance organizations (HMOs) and preferred


provider organizations (PPOs).


Over half of the urban population is projected to be


enrolled in HMOs by 1998. A key feature of these managed care facilities is that they
engage in utilization review. That is, they monitor the appropriateness of medical
treatment and review patient outcomes. This prevents doctors and hospitals from
performing unnecessary, expensive procedures. Arnold Relman, former editor of The
New England Journal of Medicine, estimates that roughly one third of health care


expenditures are medically unnecessary.
an initial one time savings of about 10


It appears that


percent.


HMOs have experienced


Beyond that, managed care cost


advantages seem to be waning.


Thus, we see a failure in both the private and public


sectors of the health care market to contain medical costs.
The following three essays in this dissertation will take an industrial organizational
approach to examining medical cost containment incentives under both regulation


and competition.


Industrial organization


provides a set of tools


to analyze these


changes in markets and the consequences of public policy initiatives.


we will focus on the the tool of common agency theory.


In particular,


This is the theory of multi-


principal agent


theory,


which investigates how two rival


principals should


design


incentive contracts for an agent that they happen to share.


frequently in the health care industry.


This scenario arises quite


For example, the first two essays consider






3


contrast, the third essay takes two rival hospitals to be the principals competing for


the exclusive patronage of an HMO (the agent).


Using this common agency approach,


I am able to gain new important insights into the industrial organization of the health
care industry.


The first


essay,


titled


Cost-Shifting


Goldplating in Health


Care, examines


the efficiency of three health care systems.


First, I show that a single-payer system


under PPS (similar to Canada's health system), in which the government is the sole
medical insurer, induces the hospital to underinvest in technology and to undersupply
treatment quality. However, I show that this single-payer system can be made efficient
by implementing a mixed payment in which a cost-based element is added to the PPS
rate.
Next, I examine a multi-payer system in which part of the market is insured by


Medicare (under PPS),


while the remainder of the market is insured by a Managed


Care private insurance sector (e.g.,


HMOs).


This system induces the hospital to


overinvest in


technology


to undersupply treatment quality.


This reflects the


current state of the United States'


multi-payer system. By using an inverse elasticity


rule in its reimbursing of technology and operating costs, Medicare is able to shift


operating costs to the private insurance sector.


Even though the private insurer is


allowed to engage in aggressive utilization reviews of the hospital, this is not enough


to counter the distortion caused by Medicare's cost-shifting.
in technology persists under utilization review. This result di
in health care that managed care will mitigate Medicare's cos


Thus, overinvestment
spels a common notion
t-shifting and bring the


multi-payer system back to efficiency.

Another commonly held belief is the idea that a mixed payment system (PPS
with a cost-based element) will correct the distortions in the multi-payer system as


it did in the single-payer system.


In fact, I show the exact opposite occurs.


Mixed


--- --





4


the multi-payer system. In essence, the mixed payment just gives Medicare another
instrument to shift costs to the private insurance sector.


Moreover


, I show that the multi-payer system induces the hospital to goldplate,


, to invest in wasteful capital such as fancy artwork and lobby waterfalls.


To deter


goldplating,


Medicare must scale back its pass-through


payment of capital.


This


may partially explain Medicare's


1991 decision to phase-out pass-through payments


of capital.
Finally, I introduce the all-payer system in which the private and public insurance
sectors trilaterally negotiate with the hospital over a uniform reimbursement rate.
By instituting a uniform rate structure, this all-payer system prevents Medicare from


cost-shifting.


Moreover,


by dismantling the pass-through


payment, this system is


immunized against goldplating.


The second


essay,


Optimal


version of the model in the first


Hospital


essay.


Capital Structure, introduces a stochastic
This enables me to examine how for-profit


hospitals should finance their investments under the risk arising from


volatile nature of hospital admissions.


highly


I show that the hospital will issue some debt


in order to counter the private insurer's opportunistic behavior in utilization reviews.
By using debt, the hospital purposely exposes itself to a positive risk of bankruptcy.
Since bankruptcy proceedings are costly, this forces the private insurer to increase its


reimbursement rate in order to reduce the risk of bankruptcy.


the hospital outweighs the risk of using debt.


This rate increase for


Thus, I predict that even as for-profit


hospitals lose their tax-shelter advantage with debt, hospitals will continue to issue
bonds in order to mitigate the ever-increasing practice of utilization review by the
managed care sector.
In the last essay, titled Pricing under Exclusive Dealing, I examine how hospital
competition for an exclusive contract with a physician group affects the physician


rourn's nririnu" of service to an lIMO.


This rnommnn a.pancv model is much more






5


information. Specifically, the physician group (the agent) has private information on


the HMO's


demand for health care.


The hospitals (the principals) do not know the


HMO's


demand, and so must design incentive contracts to induce the physicians to


reveal this information.


Each hospital offers a reimbursement rate to the physician


group for the use of the hospital's


technology.


The physician group than bundles this


hospital rate with a physician reimbursement rate and charges this price bundle to
the HMO.
I examine how hospital competition and integration affects the physician-insurer


bargaining over prices and utilization levels.


I derive the equilibrium hospital con-


tracts for two rival hospitals competing through the same shared physician group


which is privately informed about


the insurer's bargaining power.


For substitute


(complementary) medical procedures, competition through a common physician group
results in higher (lower) physician prices and less (more) severe under-utilization of
medical services when compared with a multi-specialty hospital merger. Under strong
substitutes, the hospitals instead compete head-to-head for the exclusive services of


the physician group.


For an insurer with a weak (strong) bargaining position, ex-


elusive dealing results in lower (higher) physician prices and under-utilization (over-
utilization) when compared with a hospital vertically integrated with the physician
group.









CHAPTER 2
COST SHIFTING AND GOLDPLATING IN HEALTH CARE


Introduction


Health care reform has been one of the most hotly debated public policy
issues during the Clinton Administration. It is widely agreed that any health care re-
form must first address cost containment. In 1994, expenditures on health care in the
U.S. are expected to exceed $1 trillion, more than 14 percent of GDP. Medical costs


are projected to soar to 32 percent of GDP by 2020.


Many health care economists


(Evans (1986), Newhouse (1988), and Weisbrod (1991), for example) argue that the
present system of financing high-tech medical technology is responsible for the rapid


explosion in medical costs.


According to the former long-time editor of the New


England Journal of Medicine, Arnold Relman, technology is the "engine behind the


rise in medical costs,"


driven by the


excessive


number of doctors "trained to provide


high-tech, expensive services" (Relman (1989)).


In the debate over how to deal with


this overinvestment in technology, controversy often erupts over the merits of three


different health care systems:


the all-payer system.


the single-payer system, the multi-payer system, and


In this paper we offer an economic analysis of these three


tems of health care and provide answers to the following key questions:


(1) Which


of the three systems best provides the hospital with the incentive to invest in the so-


cially efficient level of technology?


(2) What is the role of price negotiations in these


systems?


(3) How


do the incentives of cost-based reimbursement, prospective re-


imbursement, mixed reimbursement, and quality-based reimbursement differ among


the three systems?


(4) To what extent should the government make pass-through


payments of hospital capital in each system?


and (5) Which system is susceptible to






7


The United States' health care system is currently a multi-payer system, in which


the public and private insurers set reimbursement rates non-cooperatively.


A com-


mon criticism of multi-payer systems is that the public insurer (Medicare, Medicaid)


is able to shift costs to the private insurance sector.


While such cost shifting has long


been criticized for being unfair or inequitable for patients, it is only recently that
cost-shifting has been shown to lead to economic inefficiencies such as decreased pa-
tient hospital length of stay (Glazer and McGuire (1994)) and possible technological


underinvestment (Ma and McGuire (1993)).


However, it has yet to be demonstrated


how cost-shifting may induce


excessive


investment in high-tech medical equipment.


The goal of this paper is to link technological overinvestment to cost-shifting.


This


explanation of overinvestment is in contrast to the traditional "medical arms race"
(MAR) explanation in which it is argued that hospitals compete by providing too


many high-tech medical services.


The implication is that capital is wasted, leading to


higher costs without commensurate benefits (Robinson and Luft (1985), Kopit and


McCann (1988),


and McManis (1990)).


This seems to be the prevailing explanation


for hospital overinvestment. In fact, antitrust judges have even embraced this idea to
the extent of permitting hospital mergers on the grounds that it would bring the med-


ical arms race to an end 1


Over the last five years, more than 400 hospitals sought


mergers2. Nevertheless, hospital costs continue to escalate, suggesting that incentives


for overinvestment may not be due entirely to competition among hospitals3.


This


paper reveals and analyzes a more fundamental source of the overinvestment prob-


lem.


We show that excessive hospital investment can result from the cost-shifting


induced by competition among payers, even in the absence of any competition among
hospitals.
1For example, in a recent decision to permit a merger between the two largest hospitals in
Roanoke, Virginia, the district court judge wrote,"As a general rule, the hospital rates are lower,
the fewer the number of hospitals in an area"(United States v. Carilion Health System 892 F2d









Some argue that the government's


cost-shifting in a multi-payer system may be


counteracted by the rapid upsurge of "Managed


Care"


plans in the private sector


(such as


health maintenance organizations


preferred provider organizations).


However, a key finding here is that hospital overinvestment in technology persists
even in such a managed care environment, even if private insurers can set aggres-


sive quality-based reimbursement rates through utilization review.


That is, after a


utilization review of the hospital's quality and technology, the private insurer can


update its reimbursement rate.


This reflects the current


"Outcomes Movement,"


which Relman (1988) dubbed the "third revolution in medical care."


The basic goal


of the outcomes movement is to link reimbursement rates data on patient outcomes


and hospital quality.


An interesting result of our paper is that these quality-based,


or outcomes-based, hospital rates cannot resolve the overinvestment problem of the


multi-payer system.


That is, these aggressive payments do not provide strong enough


incentives to counter the cost-shifting problem.


The reason for this conclusion is that


with a first-mover advantage, the government can impose a cost-shifting externality
on the bargaining process between the hospital and the private payer by using a com-


bination of two payments:


(1) a prospective payment, which is a fixed payment per


patient, and (2) a pass-through payment which pays for a percentage of capital and


technology.


To compensate for this externality, the hospital must always overinvest


in technology in order to improve its bargaining position with the private insurance
sector.
Interestingly, Medicare used such a combination of pass-through payments and
prospective payments up until 1991, when it decided to phase-out pass-through pay-


ments over a ten year period.


Why would Medicare phase-out pass-through payments,


since doing so would seem to diminish its ability to shift costs to the other payer?


To answer this,


we show that the pass-through payment is susceptible to hospital









for doctors, etc.


While the investment in high-tech medical equipment is excessive,


it is still a productive asset in that it has value to patients. Goldplating, on the
other hand, is completely wasteful in that it has no value to patients. To deter gold-
plating, Medicare must scale back its pass-through payments, trading-off diminished


cost-shifting for less goldplating.


However, overinvestment in technology as well as


some goldplating may still persist in the multi-payer equilibrium.


How might these persistent


problems with


the multi-payer system


be solved?


A popular idea is to replace the multi-payer system with a single-payer system, in


which


the government is the only medical insurer4


While such


a change would


eliminate cost-shifting,


it would


also,


however,


severely


curtail socially


beneficial


investments in technology. A large strand of the literature has recently suggested that
the underivestment problem of prospective payments can be prevented by mixing the
prospective payment with a cost-based retrospective payment. In contrast, we show
that this restoration of efficiency will not occur in reality since the cost-based element


of the mixed payment is susceptible to goldplating.


As a result, goldplating as well


as underinvestment in technology persist in the single-payer equilibrium.
To solve the problems of the multi-payer and single-payer systems,we introduce


an all-payer system.


Here,


the public payer,


the hospital,


trilaterally negotiate a uniform reimbursement rate which can


quality.
However


d the private payer
vary with delivered


All-payer systems are used in Japan, Europe, and in four American states.


, these do not typically use quality-based reimbursement.


This is unique to


our all-payer model.


The key result of our paper is that this particularly aggressive


all-payer system is technologically efficient. Moreover, this all-payer system is immune
to cost-shifting and hospital goldplating.


This chapter is organized as follows.


In Section 2


, the three health care systems


are introduced.


In Section 3, the equilibrium reimbursement plans and investment





10


levels under the three health care systems are derived. Mixed payments are analyzed


in Section 4.


Goldplating is then introduced in Section 5.


Finally, in Section 6, the


public policy implications of the analysis for medical cost containment are discussed.
All proofs are relegated to the Appendix.


The Model


First,


we set up a model of a multi-payer health care system.


To begin,


we consider the demand side of the health care market. For simplicity, we assume
that consumers in the health care market are fully insured5. Thus, market demand is
assumed to be price inelastic with respect to the price of medical services. However,


following Rogerson


(1994) and Ma (1994),


we assume that


the hospital's


demand


for admissions X(I) is directly influenced by the quality of care or intensity of care


offered by the hospital.


ProPAC's


(1993) working definition of 'intensity' is the


number and complexity of patient care resources, or intermediate outputs,


used in


producing a patient care service. Intensity I may include length of stay, services per
admission, special amenities, etc.


Unlike Ma and McGuire (1993),


is a function of the hospital's


we do not assume that that hospital


level of technology


volume


T. Recent research (e.g., Dranove


and White (1992)) suggests that technology usually does not attract patients to the


hospital directly, but instead attracts physicians to the hospital.


This results in a


physician-driven 'medical arms race' (MAR) in which hospitals overinvest in high-


tech equipment just to attract the best doctors.


This phenomenon is the traditional


explanation for excessive investment in hospital technology. However, recent empiri-
cal evidence indicates that the MAR effect has diminished or disappeared altogether


(see Zwanziger and Melnick (1993)).


Thus, it remains to determine what else besides


5We assume that patients obtain insurance from only one insurer at a time.


For a discussion









a MAR may be driving the overinvestment in medical technology.


A central finding


of this paper is that payer competition can cause overinvestment in technology, even
in the absence of a MAR, and even under prospective payments.
In order to investigate payer competition in isolation, we first remove the incen-
tive for a MAR by assuming that the hospital's number of physicians with admitting


privileges is fixed exogenously.


Thus, the hospital will have no demand-side moti-


vation for over-capitalization through technology (however, demand will be induced


by hospital intensity


I). Instead,


the hospital's only incentive for overinvesting in


technology will be shown to arise from the supply-side effects of payer competition.


On the supply side, the hospital has an operating cost of c(I,T) per patient.


There


are no fixed costs associated with supplying I.


The hospital's


only fixed cost is T.


Following Ma and McGuire (1993), n will be the fraction of patients that are insured
by the public payer (Medicare, Medicaid); the other (1-n) of the market is insured


by the private payer6


. The public payer pays a reimbursement rate a per patient to


cover c(I,T) and to help pay for


T. In addition, the public payer can make a pass-


through payment pT that is independent of the number of discharges, where pE [0, 1].
This payment plan represents the Prospective Payment System (PPS) administered
currently by Medicare and by some state Medicaid programs (ProPAC 1993). The
private payer will pay a rate / per discharge. f is determined by negotiations between


the private payer and the hospital.


Historically, pass-through payments have never


been instituted by private payers, and so will not be considered here.


Our model of the health


care system focuses on


the interactions among three


actors: the public payer, the hospital, and the private payer7


The public payer and


the private payer will compete in setting their rates (a, p) and /, respectively, in order
to reimburse the hospital's operating cost c(I,T) and cost of technology T. However,
6We are essentially modeling the multi-payer system as a von Stackelberg common agency, where


the insurers are the principals and the hospital is the agent.


Our model departs from the usual





12


this payer competition will further entail opportunistic behavior on the part of each
payer.


First


, we describe how the public payer might be able to shift some of the costs of


treating Medicare patients on to the private payer. A well known problem in health
care is that public insurers, such as Medicare and Medicaid, often do not reimburse


the hospital for the fair share of their patient
unpaid costs to the private insurance sector8.


shift costs in this manner,


ts' costs, thereby shifting a burden of
To model the public payer's ability to


we give the public payer the first-mover advantage as a


price setter.


Thus, in stage 1


of the four-stage game, the public payer (Medicare)


sets the margin a and the pass-through payment parameter p. Medicare is presumed
unable to update its payment plan after the hospital selects I and T, perhaps due to
a lack of managerial resources9. Anticipating the results of the next two stages of the
game, the public payer will select a reimbursement plan (a, p) in order to maximize
the net social benefit to the segment of the market it serves:

M(a, p) = n[U(I, T) aX(I)] pT,

where U(I,T) is the gross social benefit when the hospital provides technology level
T and treatment intensity level I. Note that an incomplete contracts approach is
adopted. We assume that the insurers cannot write complete ez ante contracts con-


tingent on the hospital's


technology and treatment intensity.


State-of-the-art inno-


ovation in medical technology and medical procedures often advance so rapidly that it
is usually difficult, if not impossible, for the private insurance sector to characterize
precisely all relevant aspects of a hospital's technology in a contract.
In stage 2, anticipating the per patient fee that the private payer will negotiate

(f) in stage 3, the hospital chooses the level of investment T and intensity I in order
sThe American Hospital Association estimates that Medicaid payments covered only about 80%
of average costs in 1991. Hospital profit margins on Medicare's PPS patients averaged -4% in 1991
(AHA 1992).









to maximize profits:'0


Y(I,T) = [na + (1 n)/3]X(I) c(I,T) + pT


While public payer cost-shifting has been a major focus of recent research, oppor-


tunism on the part of private payers has been neglected in the literature.


The salient


feature of this paper is that it introduces two forms of private payer opportunism


that have recently emerged with the rapid upsurge of "Managed Care"


as preferred provider organizations


(HMOs))"


plans (such


(PPOs) and health maintenance organizations


A key feature of these managed care plans is that they often engage in


utilization review. That is, they monitor the hospital's choice of quality I and level
of technology T. This gives the private payer the ability and flexibility to quickly


update rates in response to the hospital's behavior.


Thus, the aggressive monitoring


of utilization review allows the private payer to behave opportunistically by basing


its rate p on the observed I and T. In ore
tween the hospital and the private payer,


der to avoid a complex dynamic game be-
we assume that the hospital's choice of I


and T in Stage 2 is immutable. One possible justification for the hospital to commit
to T and I is that it may be very costly for the hospital to constantly adjust T and


I in a dynamic pricing game.


For example,


to induce the full level of demand X(I)


may require a period of commitment to the level I. That is, the doctors must build a
relationship with their patients over a period of time in which they are credibly com-
mitted to a guaranteed level of care I. In addition, it may be costly for the hospital
to quickly purchase or resell high-tech equipment on the spot market.


Like the prospective payment a, the payment /f is a fixed rate per patient.


ever, unlike a, the payment B may depend explicitly on I and T


How-


Thus, to distinguish


p from a prospective payment, we will call f/ a quality-based reimbursement rate.
toWe assume that the hospital cannot discriminate by payer in their intensity provision.
o -. ,.. InA\A\ r ..... -. J. i :- C.^ ---..I .. ..









We assume the private payer has bargaining power vis a vis the hospital.


Such


power may arise in practice when, for example, the private insurer forms large net-


works of doctors and patient


s across


several markets.


To capture the private payer's


purchasing power, f/ is assumed to be determined in stage 3 as the solution to a


generalized Nash bargaining game12


. Presuming the private insurance sector to be


competitive, the private insurer's objective is to maximize the net expected social
benefit to the patients it represents:

V(3) = (1 n)[U(I, T)- X(I)].

Note that if the hospital leaves the bargaining table, it derives income only from


serving the patients insured by the government.


That is


, the hospital's


threat point


is endogenously determined by the public insurer's reimbursement plan. However, we

assume that the investment T is not hospital-specific and is completely reversible and


redeployable.


This is characteristic of hospital technology.


In such a case, Encinosa


(1994) shows that private owners of the hospital will always redeploy the hospital's


capital


to other markets if the hospital


makes the out-of-equilibrium decision


not negotiate with the private insurance sector.


Consequently, the hospital's


threat


point will always be zero.

any outside hospital. Sin


Next, the private insurer has no purchasing power with

ce the private payer cannot obtain a discount elsewhere,


we will normalize the private insurer's threat point to 0.


With a (0,0) threat point,


the generalized Nash bargaining solution f/* maximizes Y'V1i- while guaranteeing


0, where q


E [o,1


is the relative bargaining power of the hospital.


In the final stage 4, demand


(I) is realized (no rationing is allowed).


The public


insurer pays the hospital aX(I)+pT


, while the private insurer reimburses the hospital


px(i).


When n


E (0, 1), a multi-payer system emerges in which the public and private


r~~~CA ... I .La: a a: -D. 1. .. nL a a1 I. a~ 4A a~l nII ef a a ana4 1..n ta


IxTE -


1, ,.,, rL,


i






15


single-payer system, in which the government is the sole insurer and sets hospital


prices.


We shall refer to the n


= 0 case as the privatized system.


We will not


focus on the privatized system since it is a polar


all-payer system.


case of the much more general


The all-payer system embodies a multi-payer system in which the


government, the hospital, and the private insurer engage in trilateral negotiations to
set a uniform quality-based rate without a pass-through payment.
More specifically, instead of the government setting its rates before everyone else


in stage 1


the government, together with the hospital and private insurer, negotiates


a rate after the hospital selects T
trilateral Nash bargaining solution *


and I.


That is,


the all-payer system,


solves the program


max# YQ(I, T)WV"()MZ(#, 0)


such that Y, V, M


E [0, 1] such that q + x +


system is equivalent to the privatized system.


1. Note that when n=0 the all-payer
This all-payer model is very similar to


the all-payer systems found in Japan and in four American states in which a uniform
fee is negotiated by all payers. However, what is unique about our all-payer model is


that we consider a quality-based uniform rate.


That is, the fundamental differences


between the single-payer system and the all-payer system in our model are that the
all-payer system sets the uniform price after observing both T and I, and, moreover,


prohibits pass-through


payments.


We assume that it is beyond


the ability of the


government to monitor I and T in the the single-payer system.


We take this view of


the single-payer system since it is most reflective of the Canadian single-payer system
in which reimbursement rates are purely prospective and are rarely based on I and


T (Merrill (1994),


p. 251).


The Overinvestment Problem


where n, q, z, z








optimal investment level.


The socially efficient investment level TE


and intensity


level IE maximize the total expected social welfare U(I, T) c(I, T)X(I)


which


we assume to be concave in I and T. Before comparing the systems, we will define


A(I,T


= (1 n)U(I, T) c(I, T)X(I) + naX(I) + (p


to be the total surplus that is to be bargained over by the hospital and the private


insurer in the multi-payer system.


A is assumed to be concave in I and T.


Next,


it will be helpful to construct the following elasticities.


technology


The bargaining elasticity of


T is defined as


CTT = ETT(I,TIa,p) =


--TATT


(2.1)


Similarly, the bargaining cross-elasticity of intensity I is defined as


CIT = CIT(I


IATI
,TIc,p) =- --


(2.2)


see that cTT is an elasticity, observe that equation (1) can be rewritten as


CTT


-d(ATr)
Ar


dT


Thus, CTT gives the percent change in AT, the marginal bargaining value of tech-
nology T, over the percent change in T. Similarly, CIT is the percent change in the
marginal bargaining value of technology, when the treatment intensity I is changed,


over the percent change in I.
comparison of elasticities'3.


Throughout the paper we will maintain the following


Assumption 1


will hold


whenever treatment intensity


I and


technology T


sufficiently strong operating cost complements.


For most inpatient procedures it is


Assumption 1


1)T









operating cost of an additional unit of treatment intensity decreases as the medical


equipment accompanying the procedure becomes more advanced.


If I and


operating cost substitutes,
utility complements (UIT


then Assumption 1


Next


will hold if I and T


display sufficient


, we need the following additional assumption.


Assumption


-U'


This assumption is sufficient to ensure that the A


0 constraint is non-binding in


equilibrium.


This will simplify the equilibrium analysis


n the following comparison


of the three health care systems.


Proposition 1


When pass-through payments are allowed:


In the single-payer system equilibrium (Ts, Is,


in technology (Ts


the hospital will underinvest


of treatment intensity (Is


use pass-through paym




ents (ps


. Moreover, the government will choose not to
= 0). The hospital will earn nonnegative profits


(Is, Ts I).


Under bargaining, the all-paye


r system will provide the hospital with the incen-


tive to invest efficiently at T


less of its negotiating power q.


E and to supply the efficient intensity IE


hospital will earn nonnegative


, regard-


profits of


(IE, TEO).


In the multi-payer


em equilibrium,


(To, o,,po),


there


exists


a critical market


share no (

TE) if n <
regardless


0, 1) such that the hospital will overinvest in technology (To(n)
o. The hospital will undersupply treatment intensity (lo(n) < I


of its negotiating power q.


TV/en s-a


the government will use a


pass-through payment to pay for po percent of the hospital's


technology, where


=min t


- TnAr, 4- A ,r .4- n. 'l


(1'I.R


< TE) and will provide less than the socially efficient level


I


Irl





18


These results are illustrated in Figure 1. Since the MAR-effect has been removed
by decoupling demand from technology, the hospital has no incentive to invest in tech-
nology (beyond some mandatory minimum threshold) under a single-payer system.


The reason for this is that the payment system is "too prospective"


. To induce invest-


ment in technology, a complete pass-through (p=l) is not enough, the government
would also have to reimburse a portion of operating costs retrospectively (this will
be addressed in the next section). Similarly, the payment is also still too prospective


with respect to the demand-inducing treatment intensity.


in the literature (Glazer and McGuire (1994),


This is a common result


Ellis and McGuire (1986,1990)).


However, Proposition 1 reveals a more interesting consequence of prospective pay-


ments that warrants special attention.


Among the three systems, overinvestment in


technology is only induced by prospective payments under the multi-payer system.
The overinvestment results from externalities created by the uncoordinated dual reg-


ulation of the hospital.


see this, first note that the hospital now has an incentive


to invest in technology in order to increase its bargaining position with the private in-
surer. Next, since the investment is not hospital-specific, ex post negotiations do not
result in the hold-up problem of Klein, Crawford, and Alchian (1977) and Williamson


(1975,1977).


Thus, the private insurer cannot expropriate the investment. Therefore,


under the all-payer system, this investment is socially efficient since the public payer
cannot externally influence the bargaining process.
However, under the multi-payer system, the public payer imposes an externality on


the negotiation process.


More precisely, the public payer engages in cost-shifting by


employing an "inverse elasticity rule." That is, since technology is more inelastic than


intensity (CIT


> rTT),


the public payer increases the pass-through p (with respect to


the single-payer Ps) in order to increase reimbursement of T and lowers a to decrease
the reimbursement for I. As a result, the hospital now has the incentives to overinvest
S v r^/n nrnlvn r v rnla .,n A +n f,.C r vmA n.nlr 4+ r + wnn lifl+Of Oi+



















(p=l)







(p*)


m*m
---- -*


ALL-PAYER


MULTI-PAYER


SYSTEM


SYSTEM


SINGLE-PAYER


SYSTEM


FIGURE 2-1 : EQUILIBRIUM INVESTMENT









This result


may well


characterize the


present


health


care market


under


prospective rate setting. It is widely agreed that prospective payments from Medicare
as well as aggressive payments from HMOs induce too low of a treatment intensity,
while technology costs continue to soar (Newhouse (1992), Thorpe (1992)). As poten-
tial evidence of this overinvestment problem in multi-payer systems and the underin-
vestment problem in single-payer systems, it is interesting to note that Atlanta has
more Magnetic Resonance Imaging facilities (MRIs) than all of Cananda (Newsweek,


July 25, 1994).


At the beginning of Medicare's


Prospective Payment System (PPS)


in 1984, Atlanta had only one MRI facility. Now it has at least thirty (Eckholm and


Pear (1993)).


Overall, the U.S. has eight times more MRIs than does Canada on a


per capital basis (Starr (1994)).


Finally, if we interpret I


as patient length of stay,


it is interesting to note that the U


has the lowest average length of stay among


OECD nations,


with an average of 7.1


days, compared to


12 to 24 for most other


nations (Reinhardt (1992)).
Finally, we note how the results of Proposition 1 stand in contrast to the results of


Ma and McGuire (MM) (1993).
ating costs are constant, that de


MM assume that intensity is exogenous, that oper-
mand is induced by technology (an MAR-effect), and


that the private payer can set rates only before the hospital selects T.


Under these


assumptions, MM find that a multi-payer system results in technological underin-


vestment. Moreover, MM's single-payer system is efficient.


These two results do not


seem to support the general empirical evidence. In contrast, our characterizations of
the multi-payer and single-payer systems seem to be more realistic.
Moreover, in MM's model, the government will implement complete pass-through
payments (p=l) in both the multi-payer and single-payer system. In our single-payer


model the government completely dismantles pass-through


payments.


our multi-payer model supports the use of an interior pass-through


In addition,

p E (0,1) in


*1I 5 r 5.









payment will also diverge from Ma and McGuire's


policy recommendations.


This will


be explained more fully in Section 6.


Mixed Payment Systems


In the preceding section all government reimbursements of operating costs


were paid prospectively.


That is


, a fixed per patient rate was set in advance.


Proposition 1, we saw that this led to equilibrium rates that were "too prospective"


in the single-payer system,


leading to underinvestment, even when


the cost-based


pass-through payments could be made. In this section we show that the single-payer
system can be efficient when the government is allowed to use mixed payments in
which a portion of operating costs can be reimbursed retrospectively. In the spirit of
Ellis and McGuire (1986), mixed payment plans are defined by the expanded payment


plans (a,p,r) and (f, R),


in which the public insurer pays an additional rC(I,T) per


patient and


the private insurer pays an additional


RC(I,T) per patient.


As the


next Proposition demonstrates, these mixed reimbursement rates have very different
consequences under each health care system.


Proposition 2


Under mixed payments'4:


The single-payer system induces the


hospital to invest efficiently in technology


and to provide the socially efficient level of treatment intensity.


The govern-


ment's payment


is completely cost-based: a


1, and r


In the multi-payer system equilibrium under mixed payments, (Ti


II,pt),


there


exists nl


c (0,


1) such that the hospital will select TE


and IE


for n


> na, but


will overinvest at the level Ti(n) >


To(n)


> TE


and will under-supply intensity,


II(n)


= Io(T,)(n)


when n


Moreover, r


> 0 and R


=0.








22


9. The all-payer system admits an equilibrium that is efficient and uses no cost-
based payments (R = 0).

This Proposition reveals an important disparity between the single-payer system


and the multi-payer system when the government employs mixed payments.


Mixed


payments resolve the underinvestment problem that arises when prospective pay-
ments alone are employed in the single-payer system (recall Proposition 1). Not only


is it in the government's


best interest to use partially cost-based payments, but it


is socially optimal. In contrast, the government's actions are no longer aligned with


society's


best interest under a multi-payer system. Instead, the government will now


over-employ r, the cost-based element of the payment, in order to shift costs to the
private insurer. In fact, r gives the public payer even more cost-shifting leverage than
it had under the prospective payment plan. As a result, the overinvestment problem
of Proposition 1 is exacerbated under mixed payments.
The main result of this section is that mixed payments increase the degree of


cost-shifting in the multi-payer system.


Glazer and McGuire (GM)


(1994) find a


similar result in a related multi-payer model.


In the GM model, fixed costs (tech-


nology) are exogenous so that pass-through payments are unnecessary. Furthermore,
intensity does not induce demand. Moreover, actual costs are not contractible; only


allocated costs are contractible.


this setting,


GM show that both payers use a


mixed payment (in which the cost-based rate is approximated by a cost-allocation


formula), inducing the profit-maximizing hospital to under-supply intensity.


Here,


when technology is endogenous and actual costs are contractible, the hospital will


overinvest in technology and still under-provide treatment intensity.


This finding


reveals that cost-shifting does not necessarily result from an inability to contract on


actual costs.


Cost-shifting can arise when actual costs are contractible if the private


payer does not use a mixed payment in response to the government's


mixed payment.






23


Our result on the efficiency of mixed payments in the single-payer system is not


new.


Mixed payments have been advocated quite regularly for single-payer systems


(Ellis and McGuire (1986,1993),


Goodall (1990), Ma (1994), Pope (1989)).


However,


in the next section we show that
goldplating is possible.


this traditional result may be overturned when


Goldplating


In general,


may often include not just expenditures on technology, but


the entire capital costs of constructing a new facility to house the technology (e.g., a
new wing on the hospital for an open-heart surgery center). So far we have consid-
ered T to be a productive asset in that it had patient value U(I,T). In the preceding
analysis, it was implicitly assumed that the government monitors the hospital's in-
vestment T to insure that non-productive hospital assets with no value to patients
are not bought and reimbursed through the direct pass-through payment. However,


in reality


Medicare and state


Medicaid agencies often


do not


have the resources


to monitor the capital expenditures of hospitals.


Indeed, state certificate-of-need


laws, mandated by the National Health Planning and Resources Development Act of


1974, required


(1985)).


states to establish agencies to regulate hospital investments (Simpson


However, many states have since abandoned certificate-of-need laws since


they have failed to prevent excessive investment (Sloan (1988),


Salkever and Bice


(1976), Joskow (1981))'5


This problem is not restricted to the state level.


in no way rewards prudent behavior,' says
Care Financing Administration (HCFA),


" 'We've set up a system that


Gail Wilensky, former chief of the Health


which runs Medicare.


'In fact, the more


you spend, the more you get.'


And it doesn't much matter what the money buys.


re









(Medicare) pays as


willingly for


a lobby waterfall as for an inner-city emergency


room"(Business Week, April 22, 1991).
When a hospital's capital expenditures go unmonitored while being largely reim-
bursed with direct pass-through payments, the hospital may find it advantageous to
invest in capital that has value to management and doctors but not to patients. For
example, hospitals often build elaborate offices for doctors adjacent to the hospital.
Other examples of goldplating include elaborate architectural facades, overly plush
doctors' lounges, on-site athletic centers and child-care centers for the hospital staff,


elaborate artwork for private rooms, and general managerial slack.


Unfortunately,


the patients do not receive any direct benefits from these managerial resources, even
though they may be subsidized by Medicare.
One way to resolve this moral hazard problem is to set up proper managerial


incentives and


ex post utilization reviews (as analyzed in Encinosa and Sappington


(1995), for example).


However, the next Proposition shows that goldplating can be


deterred simply by restricting pass-through payments, without adversely distorting
the technological investment incentives. Let us assume that a non-productive hospital
capital expenditure of G has value b(G) to management and zero value to patients.


Moreover,


we will suppose that a hospital


which is vertically integrated


with


payers would never invest in G. That is, we assume G has negative net present value


in isolation, i.e., '(0)


1 and 4"


< 016


Note that if 4'


= 0, the hospital will choose


G=0.


That is, the hospital will never waste resources.


However


, when


> 0, then


the hospital will choose a positive G under a multi-payer system.


This is referred to


as abusing resources, following Blackmon (1992)17


Proposition 3


capital expenditures


are not monitored by the public


payer and if


mixed payments are prohibited, then:
16We are assuming that operating costs are independent of G. An interesting problem that we
- -. - ., a a i t









In the multi-payer system,


solves the equation


C"(G)[1


-Po


- GArr]


- "()'(G)


- ATTP'(G) + ATT


(2.4)


where


is the


pass-through payment in the monitored case of


equation


Moreover, the hospital will underinvest in technology if pass-through payments
are prohibited.


There


is no goldplating (G


n t/i


ngle-payer and the all-payer systems.


In general, it


quite difficult to verify whether equation (4) has a positive solution.


However


, if 4 is


quadratic,


then


we have the following existence result.


Corollary 1


If 4(G)


in the multi-payer system (without mixed


payments),


the hospital


abuse


resources


at the level G*


22
6-2ALIT


> 0.


Moreover, the government will scale


back its pass-through payment to p*


= bG*


forcing the hospital to scale back technology from the To level.


Goldplating


arises


only in the multi-payer system since pass-through


payments


are instituted only in the multi-payer system when mixed payments are prohibited


Proposition 1).


Note that in isolation


, the return on asset G is always negative


(since 4'


< 0).


However


, once a positive


pass-through payment is introduced,


there is always an


asset


level G that earns a positive return (4'(G)


-1+p


> 0).


If the public payer cannot monitor the hospital's


investment in order to weed out


unproductive


assets


, Corollary 1 indicates that it is then optimal for the government


to scale back its


pass-through


payment.


Note that


the pass-through


payment is


never fully dismantled.


in equilibrium.


Thus, goldplating,


or abuse, is never completely eradicated


The reason for this is that the government's


ability to shift costs is


eroded without the use of the pass-through payment.


In essence, the moral hazard


- '(G*) if there exists a positive G*


G








merit to scaling back pass-through


payments:


the hospital


will also scale back its


overinvesting in technology.
In Proposition 3, goldplating did not arise in the single-payer system since pass-
through payments are not used in that system when mixed payments are prohibited


(see Proposition 1).


However, recall from Proposition 2 that the government will im-


plement a complete pass-through (p = 1) of all capital in the single-payer system once


a mixed payment is allowed.


As a consequence,the single-payer system is susceptible


to goldplating under mixed payments.


Corollary


Under mixed payments,


we have G


> 0 and p, r


E (0,1)


in the single-


payer system, resulting in underinvestment in technology and under-provision of treat-
ment intensity.


The results of Corollary


2 stand in contrast


to the recent strand of literature


which suggests that single-payer systems are efficient under mixed payments (Ellis


and McGuire (1986, 1993), Goodall (1990),


Ma (1994), Pope (1989)).


These studies


do not address goldplating.


The salient finding of Corollary 2 is that if goldplating is


a problem as the empirical evidence indicates, then mixed payments cannot restore


efficiency in the single-payer system.


back both its cost-based rate and its pass-through payment.


The government must


trade-off less technology and less treatment intensity for less goldplating.


Together,


Proposition


Corollary


reveal


a single-payer system


will persistently


curtail socially efficient technological investment and treatment intensity.


Public Policy Imolications


When the Prospective Payment System was first introduced in 1983, it is
conceivable that Medicare failed to anticipate the incentive for hospital goldplating


To deter goldplating, the government must scale







27


Congress due to intense hospital lobbying. It was not until 1991 that HCFA succeeded
in persuading Congress to force Medicare to phase-out pass-through payments over


a ten year period.


Corollary


provides a possible theoretical justification for this


HCFA policy of prohibiting the cost-based pass-through payment.


Although many


have thought that the HCFA's primary motivation for a phase-out of pass-through


payments was to end a federally financed "medical arms race"


, we have shown that


the reform actually deters goldplating as well as eases the overinvestment externality


of dual regulation that persists in the absence of an "arms race"


Note that Corollary


1 reveals that it is not in HCFA's


best interest to lobby for


a full dismantlement of the pass-through payment.
HCFA to scale back the pass-through payment, it i
pass-through a small fraction of capital costs. Inde<
to maintain some degree of pass-through payments.


While it is indeed optimal for
is always optimal for HCFA to
ed, it is even socially beneficial
While a complete prohibition


on pass-through payments will completely deter all goldplating, it will nevertheless
induce the hospital to underinvest in technology and under-provide treatment inten-
sity.


Note that


(1993),


this policy recommendation does not go as far as Ma and McGuire


who advocate a complete restoration of the pass-through payment (p=l) in


order to ease the severity of the underinvestment.


MM's


Goldplating is not consider in


model. If it were, their model might also recommend an interior pass-through


p .
While the pass-through payment reduction of Corollary 1 does not necessarily lead
to efficiency in technology and intensity in the multi-payer and single-payer systems,
it is interesting to note that the hospital would perform at the efficient levels if the


public payer charged the hospital a fixed licensing fee (or entry fee).


Moreover, the


1 1 1 1 1 (i










Proposition A


If the public payer


is allowed to impose a fixed licensing fee L on the


hospital for any purchase of technology, then:


The single-payer system induces the hospital to invest at the socially efficient


technology level TE


and to provide the efficient level of intensity IE


under an


equilibrium fixed license fee L


= Y(I, TE)


The multi-payer system induces the hospital to invest at the socially efficient


technology level TE


and to provide the efficient level of intensity IE


under an


equilibrium fixed license fee L


= A(IE, TEn)


Moreover, the public payer will


still use a positive pass-through payment with L.


This Proposition is not surprising.


As expected


the public payer uses L to extract


all of the surplus from the hospital and the private insurance sector.


This full rent


extraction leads to efficiency since L allows (a, p) to be adjusted to essentially sell-out


Medicare to the hospital and the private insurance sector.


This sell-out equivalently


resets n to 0.


Thus


, as in the all-payer


case


(or privatized case),


it is in the interest


of the hospital to perform efficiently (Proposition


However, Medicare benefits


because it can then extract all of the surplus from the sell-out via the license L.


Note


that efficiency is obtained without the private payer charging a licensing or entry fee.
Interestingly, this licensing fee policy is in contrast to the two-part hospital tariff


policies of Gal-Or (1994) and Ma and Burgess (1993).


Gal-Or shows that overin-


vestment may be the result of hospital competition under stochastic demand in a


single-payer setting.


Ma and Burgess demonstrate that suboptimal intensity may


result from hospital competition.


However, both


papers reveal that efficiency can


be restored if the single payer provides the hospitals with lump sum subsidies.


contrast


, our model advocates the use of licensing fees when


there is no


hospital


-







29


purchases. However, Proposition 4 may reveal why these certificate-of-need laws have


failed to contain costs.


First,


the efficiency results of Proposition 4 work because


it is the public payer who collects the entry fee.


This allows the public payer to


adjust (a, p) in a way that does impose an externality on the hospital.


In contrast,


many states
to control tl


have set


up independent regulatory


he licensing of new


capital for hospital


health systems agencies (HSAs)
als. The HSA licensing fees are


set independently of Medicare and Medicaid's


reimbursement decisions.


According


to Reinhardt


(1992),


HSAs are completely divorced from


the reimbursement


decision. Proposition 4 indicates that efficiency obtains only if Medicare has complete
jurisdiction over setting entry fees and licensing fees.
A second problem with the HSAs is that they have tended to set fees that are


substantially below the optimal fee L recommended by Proposition 4.


For example,


in Florida the application fee to request permission to open an open-heart surgery


center is $ 22,000.


However, the hospital can make this back in the first 15 minutes of


the first operation they do (The Tampa Tribune, September 24, 1994).


The fixed fees


required by Proposition 4 are extremely large in that they must extract the entire
surplus from the hospital and the private insurance sector.
Such large licensing fees are obviously not feasible in reality. Instead, Proposition
1 offers a more viable alternative in order to obtain efficiency: the all-payer system. It
is interesting to note that in 1977 the Carter Administration proposed a series of all-
payer revenue controls on hospitals. However, after three years of legislative battles,


the initiative was defeated by intense hospital lobbying (Ginsburg (1988)).


About


the same time, all-payer systems were tried successfully in Maryland, Massachusetts,


New


Jersey, and New


York.


Medicare, Medicaid, and


private insurers cooperated


in setting a uniform rate (Thorpe (1993)).


int;l tbh 1QRn'A


Hospital costs were controlled somewhat


117b0~rrl~~ n ~ m t ~ NiA,-r ~xifAn axr a Vrrnrn #b00 tllnota cvl .a+ otonrn :a









since it can shift costs to the other payers.


As we have shown,


this cost-shifting


under the multi-payer system will encourage excessive technological investment.


Although the uniform rate structures in


the single-payer system and all-payer


system remove this cost-shifting externality of the multi-payer system, only the all-


payer system induces the hospital to perform efficiently.


The reason for this is that the


all-payer uniform rate is quality-based, linking the hospital's choice of I and T to its
reimbursement. In fact, quality-based reimbursement has recently become an issue in
the public sector. For example, Oregon recently passed legislation to link the approval


of capital projects to the hospital's


patient outcomes (Alter and Holtzman (1992)).


In addition, New York's


Commissioner of Health


, Mark Chassin, recently proposed


linking hospital reimbursement to quality-of-care measures in the 1993 renegotiations


of the state's prospective hospital reimbursement system (Darby (1993)).


The key


result of this paper is these new aggressive quality-based reimbursement mechanisms
will only work efficiently in the all-payer system in which cost-shifting and goldplating
are both eradicated.


Conclusion


The results of our theoretical paper suggests some important directions for


future empirical work.


First, how has Medicare's phase-out of the pass-through pay-


ment affected hospital investment? Second, what is the degree of cost complements


between I and T (clT


< 0) and what is the degree of EIT? Lastly, how hospital-specific


and redeployable is hospital technology?


If hospital capital is irreversible, then the


all-payer system will result in underinvestment due to


Williamson's (1985) hold-up


problem.


In such a case,


the multi-payer system may be more efficient,


with the


overinvesting problem mitigating the hold-up problem.










CHAPTER 3
OPTIMAL HOSPITAL CAPITAL STRUCTURE


Introduction


The most hotly debated public policy issue during the Clinton Administration is


the financing of health care.


It is widely agreed that any health care reform must


first address cost containment.


In 1990,


expenditures on health care in


the U.S.


exceeded 12 percent of GNP. Medical costs are projected to soar to 36 percent of
GNP by 2020. The key to successful reform is to understand the source of this rise
in health care cost. Unfortunately, in attempting to explain this explosion in medical
costs, many economists have failed to understand that the financing of health care


is subject to a fundamental paradox.


The health insurance market (composed of a


public sector: Medicare and Medicaid, and a private insurance sector) attempts to set


reimbursement rates to cover the hospital's


cost of capital and technology. However,


any reimbursement plan affects the hospital's expected future earnings,


turn, affects the hospital's cost of capital.


which, in


The circularity of this process suggests


that both


the hospital and the health insurance market should


take into account


the simultaneous determination of the cost of capital and the prices of health care


services.


This paper lays a foundation for the equilibrium determination of hospital


capital costs and medical insurance reimbursement.


This chapter is organized as follows.


In Section 2,


we explain how the capital


market prices the hospital's


financial securities. In Section 3, we examine the strategic


role of hospital debt. All proofs are relegated to the Appendix.









The Model


begin


we consider


a stochastic version of Ma and


McGuire's


(1993)


model of the demand side of the health care market.


For simplicity, we assume that


consumers in


the health care market are fully insured1


Thus


market demand is


assumed to be price


inelastic with respect to the price of medical services.


However,


market demand depends crucially on the level of advanced technology and state-of-


the-art care offered by the hospital.


Letting T be the hospital's


monetary level of


investment in technology, we define X(T


,z) to be the number of patients who demand


admission to the hospital in the realized state of nature
of acute medical services is highly stochastic. This vol


z. The demand for most types
latility will be modeled by the


demand shock


levels of


z E [0,1]


z correspond


generated


to greater demand


by the continuous distribution F(


so that X(T


,z) is increasing in


Higher
z for all


We assume that it is illegal for the hospital to ration services.


Thus


, capacity


(e.g.,


number of beds)


is fixed at a sufficiently large enough


level so


that health


care services are not rationed in equilibrium, even when demand is most pronounced


(i.e.,


when z=1)2


Since there is no rationing,


X(T,z) can also be considered as the


realized number of discharges from the hospital. Demand for hospital services X(T


is assumed to be increasing and concave in technology investment T


Finally, n will


be the fraction of patients that are insured by the public payer (Medicare, Medicaid);
the other (1-n) of the market is insured by the private payer3. For simplicity, we do


not allow patients to be covered by both insurers.


On the supply side,


the hospital has a constant operating cost of c per discharge.


The public payer pays c per discharge plus a margin a per discharge to help pay for
'We wish to show that overinvestment can occur under universal coverage. For a discussion of


the problems in supplying medical insurance,


see Diamond (1992) and Lewis and Sappington (1994).


2We are primarily concerned with the optimal T when there is a threat of bankruptcy when z is









T. In addition, the public payer can make a pass-through payment p(T


+ i) that is


independent of the number of discharges, where pE [0, 1] and where i is the risk-free


interest rate.


This payment plan represents the Prospective Payment System (PPS)


administered currently by Medicare and by some state Medicaid programs (ProPAC


1993)4


The private


payer will pay


c plus a margin (f per discharge.


6 will be


determined by negotiations between the private payer and the hospital. Historically,
pass-through payments have never been instituted by private payers, and so will not
be considered here.
Our model of the health care system focuses on the interactions among four ac-


tors:


the public payer, the hospital, the capital market, and the private payer.


timing of the game among these players is as follows.


In stage 1, the public payer


(Medicare) institutes the margin a and the pass-through payment parameter p.


stage 2, the hospital chooses the level of investment T,


and a mix of equity and debt


to externally finance the investment T by issuing new shares and bonds. At stage 3,
the capital market determines the market value of the hospital's securities. Finally,


in stage 4, the private payer's


margin p arises out of negotiations between the hospi-


tal and the private payer


as the Nash bargaining solution.


Then the demand shock


z is realized, medical services are delivered as demanded, and payments are made,


with bankruptcy being declared if necessary.


The exact details of each stage will be


discussed next.


Stage 1:


The Government's Payment Plan.


The public payer is the first institution that sets prices, establishing the margin a
and the pass-through payment parameter p. Medicare is presumed unable to update
its payment plan after the hospital makes its investment, perhaps due to a lack of









managerial resources.


Thus, while anticipating the results of the next three stages of


the game, the public payer selects a reimbursement plan (a, p) in order to maximize
the expected net social benefit to the segment of the market it serves:


M = M(a, p) = n[U(T) (c + a)X(T)]


-pT(1 + i),


where X(T) =


X(T


, z)dF(


where U(T) is the gross social benefit when the hospital provides technology


level T. Note that i is the risk-free interest rate.


Stage 2:


The Hospital's Financial Strategy


The hospital is assumed to maximize its profits.


can easily be constructed.


A nonprofit analog of our model


We choose to focus on the for-profit case since the number


of for-profit


hospital


beds increased by


percent between


1976


1986,


while


the total number of hospital beds declined by


10 percent during the same period


(American Hospital Association (1987)).
The hospital is assumed to have no retained earnings and no previous debt obli-
gations. It is owned by the shareholders of a previous issue of voting equity (common


stock).


These shareholders will be referred to as the


"old"


stockholders.


Next, the


hospital invests


dollars in


technology and finances its investment from external


sources.


When new shares are issued to new shareholders,


s'C1


will represent the


fraction of the hospital's


total number of shares that


these new shares comprise.


It is also possible for the hospital


s<0).


to repurchase some of its existing equity (i.e.,


The hospital can also issue debt with a face value of D. The hospital chooses


both the magnitude of the technology outlay T


(s,D)


= T(a, p) and the capital structure


= (s(a, p), D(a, p)) to finance T. In doing so, the hospital anticipates the out-


come of the next two stages of the game.


The presumed autonomy for the hospital







35


insurers typically do not have the expertise to specify technology and security design
for the hospital in detail.
The operating income of the hospital is

R(a, /, p, T, z) = [na + (1 n)] X(T, z) + pT(1 + i).

As the hospital takes on debt, there may be a critical value of the demand shock
z*, below which demand is too meager to enable the hospital to pay all of its debt.
This critical value is defined by


- min{z


R(a, 3, p, T


When the demand for hospital services is sufficiently low that


(3.1)


z < z*


limited


liability applies, the hospital declares bankruptcy, and the bondholders become the


residual claimant.


When demand is sufficiently high that


the hospital remains


solvent, and both the old and new shareholders remain the residual claimants. Note


that F(z*) is


the probability of bankruptcy.


Bankruptcy imposes costs on the bondholder due to legal fees, reorganization, and


disruption of services.


Moreover, a financially distressed hospital may cut back on


the quality of care, increasing the risk of malpractice. Following Brander and Lewis
(1988), we assume that bankruptcy costs are proportional to the size of the shortfall


in the hospital's


earnings from its debt obligation.


That is, realized bankruptcy costs


are b[D(a, p) R(a, /3, p, T, z)] for some positive exogenous cost b per unit of shortfall


when


z< z*


Since bondholders are also protected by limited liability, we assume


that the hospital is liquidated whenever b[D(a, p) R(a, /, p, T, z)] >
Let z** be the critical value below which the hospital is liquidated.


, the hospital is not liquidated, but is reorganized


R(a, /, p, T, z).


When


under the ownership of the


bondholders who receive R(a, /, p, T


, z) b[D(a, p)


R(a, p, T, z)].


Thus, expected









Given the hospital's
financial securities is


risky debt obligation D,


the total expected return on


Il(a, /, p,T) =


R(a, /, p, T, z)dF(z) L(a, /, p, T).


These expected profits are the combined expected returns to shareholders (old and
new) and bondholders, divided between them according to their respective claims.


However, hospital management will select
expected profit to the old shareholders s:


and D


in order to maximize the


=Y(T


,s,D,E,B) = (1 -s)


[R(a, /, p, T, z) D(a, p)]dF(z).


(3.2)


Stage 3:
Next,


The Capital Market.
the capital market establishes the market value E of the hospital's new


equity


and the market value B of its debt with face value D.


We assume that the


capital market is risk-neutral, competitive, and that investors correctly anticipate the
outcome of the private insurer's negotiations with the hospital over the reimbursement


margin p.


The hospital's securities are priced fairly so that both the new shareholders


and the bondholders earn an expected return equal to i, the risk-free interest rate.
That is, in equilibrium, the capital market sets the following valuations:


(1 + i)E


[R(a,, p, T


,z)- D(a,p)]dF(z),


(3.3)


(1+i)B


D(a,p)(1- F(z)) +


R(a, /3, p, T, z)dF(z)- L(a, f, p, T)(3.4)


with E + B

While the market only requires E + B


(3.5)


we assume the private insurer can


prohibit the hospital from accumulating discretionary cash flows.


Thus, equation (5)










is assumed to hold.


In equation (3),


the value of the equity is equal to the fraction


of the expected operating income of the hospital that goes to the new stockholders,


net of debt payments when the hospital is solvent.


The first term on the right side


of equation (4) is the expected return to bondholders when demand is high enough


to ensure that they are paid D


n full.


The last two terms represent the expected


operating income of the hospital when it becomes financially distressed due to low


demand, net of bankruptcy costs.


Combining equations (3),(4),


and (5),


we obtain


the capital market equilibrium condition:


(1 + i)T(a,p) = D(a,p)(1 F(


R(a,, p, T,z)dF(z) L(a,, p, T) +


+sJ


The hospital's
equation (6).


R(a, p,T,z) D(a,p)]dF(z)(3.6)


optimal capital structure (s, D) will always satisfy the capital market


Solving for


s in equation (6),


the hospital profits in equation (2) can


now be expressed as


1
-Jo


R(a, f, p,T


, z)dF(z)


- T(1 + i) L(a, p,T).


Stage 4:


Negotiations with the Private Insurance Sector.


Next, we model the private insurer as a managed care facility, such as an HMO,


engaging in utilization review.


That is, we allow the private insurer to negotiate the


margin p with the hospital after observing the hospital's


investment T, capital struc-


ture (s,D), and
we will derive /3


party


the market valuation (E, B).


To capture this aspect of negotiation,


as the generalized Nash bargaining solution.


's utility function.


First, we specify each


We assume that the private insurance sector is competitive


*>> -t









to the patients it represents:6

V(3) = (1 n)[U(T) (c + 3)X(T)].


When the hospital management goes to the bargaining table,


it will still represent


only the old stockholders,


seeking to maximize Y from equation (2)7


. If the hospital


backs away from the bargaining table, its only income will be from serving the patients


insured by the government.


That


, the hospital's


threat


point is endogenously


determined by the public insurer's


reimbursement plan.


Note


that if the hospital fails


to negotiate (i.e.,


= 0), it will prefer to serve the


publicly insured patients rather than to close the hospital.


serves only the public patients,


However, if the hospital


then the capital market will devalue the hospital's


securities from (E


B) to (Eo, Bo) (where the 0 subscript refers to the f/


= 0 case):


(1 + i)Eo


-4


(naX(T,z) + pT(1 + i)


D)dF(z


(1 + i)Bo


(naX(T


,z) + pT(1 + i))dF(


where


/0


(naX(T, z) + pT(l +i))dF(z)+ &J .[D
a"


- (naX(T, z) + pT(1 + i))]dF(z


= min{z


naX(T,z) + pT(1 + i)


= min{z


Although


the hospital


naX(T,z) +pT(1 +i)}.


will prefer to serve the public sector when P


bondholders and the new shareholders may instead want the hospital to liquidate T


and pay back as much of B and E


as possible.


We will assume that the discounted


resale value of T is 7T


, where 7


E {0,1}.


When 7


= 1 the technology is completely


6For simplicity, in V and M, we assume that patient welfare does not decline when bankruptcy


occurs. However


, welfare is affected indirectly by the risk of bankruptcy via 3.


In the stage 4 subgame, there is no conflict of interests between the old stockholders, the new


- (naX(T,z) + pT(1 + i))]


> +









redeployable.


In contrast,


when


0, the capital asset T is hospital-specific.


most cases medical technology is not hospital specific.


However, the accompanying


infrastructure (i.e., a new wing of the hospital) may be irreversibly sunk. Moreover,
7 may include the litigation cost of suing the hospital to liquidate T. In particular,


since Eo


< E and Bo


< B, the bondholders and new shareholders will always prefer


suing the hospital to liquidate T


when 7 = 1 (recall that T


= E + B from equation


(5)).


However, the investors cannot completely recover


resale value or when litigation is too costly (7 = 0).
keep their downgraded securities E0 and Bo.


when the asset


T has no


In this case the investors will


threat point for the bargaining game is


Consequently, the old shareholders'


r(7)= (1--7)(1 s)


Next, the private insurer has no purchasing power with outside hospitals.


Thus,


we will normalize the private insurer's threat point to 0. So, with a (r(7), 0) threat
point, the generalized Nash bargaining solution Jf* maximizes (Y r(7))Vl'-q while


guaranteeing V,
the hospital.


- r(7)


where q


E (0,1) is the relative bargaining power of


Debt Strategies


Suppose that there are no costs to bankruptcy (b


reversible (7 = 1).


= 0) and that technology is


In such a setting the hospital always chooses an all-equity capital


structure.


However,


once we introduce


bankruptcy


costs (b


> 0),


the hospital's


optimal capital structure will now involve debt.


When bankruptcy


costly (b


a positive level of


> 0)


debt D*


and technology is reversible (7 =
> 0, such that the probability of


(naX(T, z) + pT(1 + i) D)dF(z) for


Proposition 5


the hospital issues









further.


The Nash bargaining solution P*


satisfies


where X(T) =


X(T, z)dF(z).


increases in debt D*


This debt strategy warrants special emphasis in our tax-free setting.


Though


we have focused on for-profit hospitals, this debt strategy can be shown to hold for
nonprofit hospitals as well. In practice, since there is no applicable corporate income


tax for not-for-profit hospitals,


we would expect nonprofit hospitals to maintain an


all-equity structure in order to avoid the risk of bankruptcy8


. Yet both nonprofit and


for-profit hospitals are highly leveraged relative to most other industries. Proposition
6 offers an interesting explanation of this phenomenon. First, since the private insurer


enters price negotiations with the hospital after having observed the hospital's


capital


structure and investment level, the private insurer can behave opportunistically in


the negotiations, as we have seen previously.
pital precommits to a highly levered position.


To counter this opportunism, the hos-
This increases the risk of bankruptcy.


Since bankruptcy is now costly, the hospital now demands a higher margin Pf. since
both parties have equal bargaining power, the private insurer must concede to some


increase in /.


According to Proposition 6,


the hospital's


gain from this increase in


the price per patient discharge outweighs its inflated risk of bankruptcy9


Conclusion


Though


bankruptcy is rare in most regulated industries (e.g., public utilities),


bankruptcy is not


uncommon in the health care sector10


. The reason is that the


8See Kraus and Litzenberger (1973), Scott (1976), and Flath and Knoeber (1981) for a discussion
of the tax advantage of debt.
9Note that this result is very general in that we did not include a direct cost of bankruptcy in


Moreover, the rate *P


X(T)
~(lt- b-----)V,
X(T)










health


care market is much more stochastic than other regulated markets.


As a


result, future demand is difficult to forecast.


Our model indicates that hospitals are


willing to use debt in the shadow of this highly volatile demand in order to counter
the opportunism of the private insurance market.










CHAPTER 4
PRICING UNDER EXCLUSIVE DEALING


Introduction


Resale price maintenance (RPM) occurs when a manufacturer directly or in-
directly limits the price at which its product can be sold by an independent retailer.
Minimum RPM occurs when the manufacturer sets a price floor by enforcing only


a minimum resale price, allowing the retailer to charge a higher price.


RPM occurs when the manufacturer sets a price ceiling.


Maximum


Since the repeal of state


Fair
State


Trade laws in 1975, all forms of RPM have been


1S.


However, many economists question this current pe


se illegal in the United
r se illegality standard,


arguing that some forms of RPM may generate efficiencies that benefit consumers.
This debate has resulted in a large economic literature that analyzes the motives


underlying RPM.


Yet, this


body of theory has failed to explain two fundamental ob-


servations from the RPM litigation


Trade laws.


cases


that emerged with the repeal of state Fair


First, from the Federal Trade Commission Report by


Ippolito [1988]


which examined all RPM litigation from 1976 to 1982, it is evident that both mini-
mum RPM and maximum RPM are sometimes observed in the same industry across
different markets1. Second, only exclusive dealerships were observed in the industries
where both minimum RPM and maximum RPM were imposed. In contrast, common
retailers were employed in almost all of the industries in which only maximum RPM


appeared (i.e., rival manufacturers shared the same retailer2).


This paper presents a


model of manufacturer competition that explains these two findings concerning the
connections between RPM and industry structure.
1For example, in 18 cases involving gasoline retailing, half involved allegations of price floors
while the remainder involved rice ceilings.







43


In most manufacturing scenarios, retailers are often better informed about market
demand than manufacturers. Furthermore, a moral hazard problem is often present
because demand is influenced by the (unobservable) marketing intensity and pro-


motional efforts of the retailer.


We construct a model characterized by asymmetric


information and moral hazard and develop predictions consistent with the empiri-


cal findings of Ippolito.


More precisely, we find that if the manufacturers compete


through the same shared retailer, price ceilings emerge systematically for every real-


ization of demand.


In contrast


, if the manufacturers instead compete head-to-head


for the exclusive services of the retailer, price floors are optimal when demand is low
(i.e., in weak markets) while price ceilings emerge when demand is high (i.e., in strong


markets).


Thus, the manufacturer's use of RPM depends critically on the industrial


structure in a manner that is consistent with the empirical findings.
There are other interesting differences that emerge in the incentive contracts under


these two modes of manufacturer competition.


First,


when manufacturers compete


through


the same retailer,


the resale price and sales level that emerge in equilib-


rium will always differ as the level of the market demand differs.


In contrast,


when


manufacturers compete head-to-head for the exclusive services of the retailer, a fixed,
uniform retail price may emerge. In particular, the winning manufacturer institutes a
rigid resale price that does not vary with demand in a range of intermediate demand


levels.


Thus, in a dynamic setting, an intertemporal price "stickiness" may emerge


which is due entirely to healthy manufacturer competition.


This finding stands in


contrast to the traditional view that price rigidity is the result of tacit manufacturer
collusion (Maskin and Tirole (1988) and Eaton and Engers (1990)3).
Rigid prices emerge in our model because head-to-head competition for an exclu-


sive dealership creates countervailing marketing incentives for the retailer.


The usual


i,-n.-+, inC~oF*t~o*t9nr *bn r or ra t ssrlomanr r trrlt~ .irtnror)a+ vm Ac 2nA 2Aaa +~-r ffXtl'f b n2nlrtl









that high sales are due to the retailer's


diligent efforts, not exogenous demand.


This


incentive is countered by the following effect of competition. As market size increases,
the total value of the retail outlet increases, leading to higher manufacturer bids for


the retailer's services.


The prospect of higher bids can encourage the retailer to ex-


aggerate the size of the market.


These countervailing incentives give rise to partial


pooling in the equilibrium contracts. For weak markets, the incentive to exaggerate
the market size prevails, and, to mitigate this incentive, price floors are imposed. For


strong markets,


the incentive to understate demand dominates, and, to help control


this incentive, price ceilings are instituted.


In the intermediate market range, these


two incentives begin to conflict, as do the price ceilings and floors.


The result of this


conflict is to enforce the same uniform resale price regardless of demand, provided de-


mand is of intermediate size.


Consequently, in a dynamic setting, price adjustments


will be more sluggish in the interim period between booms and busts than during


booms or busts.


This prediction differs from Maskin and Tirole's


(1988) finding that


price adjustments should occur least often during booms.


The traditional explanation for


RPM


under manufacturer competition is that


manufacturers use RPM to sustain collusion (Telser (1960) and Posner (1977)).


contrast,


we find that RPM is the result of intense manufacturer competition for a


privately informed retailer. Although RPM under asymmetric information has been
investigated in a setting with downstream retailer competition (e.g., Katz [1989] and


Rey and Tirole [1986]4),


little attention has been afforded to RPM resulting from


upstream manufacturer competition. An exception is Perry and Besanko [1991] who


examine RPM under manufacturer competition for exclusive dealerships.


They ab-


stract from incentive conflicts and examine a restricted class of franchise contracts
with RPM. They find that if manufacturers are restricted to use only fixed fees and/or
linear wholesale prices with RPM, one equilibrium with maximum RPM arises, as











does a second Pareto-dominating equilibrium with minimum RPM.


Thus, their model


predicts that minimum RPM will appear systematically under competition for ex-


clusive dealers.


In contrast


, our exclusive dealing game exhibits an


undominated


equilibrium that supports both minimum and maximum RPM in different markets


at the same time


This is consistent with the RPM pattern that Ippolito finds under


exclusive dealing.


Moreover


, we do not restrict franchise contracts to any particular


form.


According to Ippolito's


second empirical finding, the systematic use of maximum


RPM is observed only in industries where retailers are shared by rival manufacturers.


We develop a common agency retailing model in the spirit of Stole (1992),


and Whinston (1992),


Bernheim


and Martimort (1992,1993) that supports this second finding


on RPM.


Although


these authors study the choice between exclusive dealing and


common retailing under manufacturer competition in detail6


, they do not examine


the important connection between RPM and the industry structure.


For example,


Bernheim and


Whinston


(1992)


allow resale price to


be an unobservable decision


of the retailer, and analyze a moral hazard common agency problem.


In contrast,


we assume resale prices are observable, and examine an adverse selection common


agency model in the spirit of Stole (1992) and Martimort (1992,1993).


Their models


of manufacturer competition consider retailers with private information about the


costs of supplying the final good.


contrast


The demand functions are common knowledge. In


, we allow the retailer to possess private information about market demand.


SThe single-manufacturer analog of our model is developed by Blair and Lewis (1994).


They find


that both forms of RPM may emerge in a monopolized industry across different markets, but only


when the standard Spence-Mirrlees sorting condition fails to hold.


This sorting condition ensures


that the retailer is compensated less when demand is high than when it is low for a given increase in
the sales level or resale price. In our model we show that both forms of RPM may emerge even when
this sorting condition is maintained. It is interesting to note that Romano [1994] has shown that
both forms of RPM may emerge under complete information, depending on an expanded elasticity


nn WOll 2ia tb. rohtilia r mieQt mrnuil nn uunnhloawl,,vshla.i eltiaiann thnt


mnrl;,;nn ;F thP m~nllflP)llrPP






46


As a result, our common agency model is multidimensional in the sense that both


price and


quantity must now


be controlled by the manufacturer's contract since


demand is not known ex ante by the manufacturers.


This chapter is organized


model.


as follows. In Section 2 we develop the common agency


We demonstrate that the equilibrium contracts result in maximum RPM in


every market when manufacturers compete through a common retailer.


rium contracts are nonlinear:


The equilib-


simple two-part wholesale price contracts with RPM


cannot be sustained in equilibrium. In Section 3, we contrast the distortions induced


in a common agency with those induced by a multiproduct monopolist.


Section 4


delineates conditions under which both forms of RPM may emerge when manufac-


turers compete head-to-head for the exclusive services of the retailer.


In addition,


rigid retail prices are shown


to emerge.


Finally, Section 5 offers some concluding


comments.


The proofs of all the key findings are provided in the Appendix.


4.2 Common Agency


In this section we will examine the case of manufacturers competing through


the same shared retailer


7. Consider two vertically differentiated duopolists, M1 and


M2, who wish to sell their products in the same market.
in this market can be parameterized by a scalar 0 E 0


The demand for both goods


to ~1


Higher realizations


of 9 correspond to higher market demand in the sense described below.


While 0 is


unknown to the manufacturers, it is common knowledge that 0 has distribution F(O).
In contrast, a potential retailer knows the demand realization 0 from the outset. The


7We are modelling a common agency with unknown demand. Recently, Stole [1992],
[1992,1994], Ivaldi and Martimort [1993], Mezzetti [1993], and Gal-Or [1991a] have exar


Martimort
mined com-


mon agencies with unknown costs. Our common agency model is multidimensional in the sense
that both price and quantity must now be controlled by the manufacturer's contract since demand


is not known ex ante by the manufacturers.


At the opposite extreme, Bernheim and Whinston


- ~ -a S era I 1 I iirl 11 U







47


manufacturers are assumed to offer take it or leave it contracts simultaneously to the
retailer.


On the demand side, we assume that the retailer cannot price discriminate.


retailer sets a single (observable)


linear price for


customers.


As a matter of


exposition,


we will first assume that the retailer's sales levels are observable.


show later that the manufacturers' optimal contracts would not change if sales could


not be monitored, provided resale prices are observable.


The demand for product


i is given by


retailer's


Ii p p e eL )


i -,2


Demand for product


i increases with


product-specific marketing intensity or promotional effort ei.


Moreover,


due to positive promotional spillover effects,


demand for product i may increase in


e-i. For a large class of demand functions and disutility functions e(ei, e2), there will
be a unique disutility minimizing effort pair (el, e2) which will ensure that (zl, zx),


and no more


, is sold at the price vector (pi, p2) in a market of size 08


. Thus, instead


of specifying the demand functions directly, it will be more convenient to work with
the well-defined composite disutility function e(xl, x2, pi,p2, ), which is the minimum
cost or disutility incurred by the agent in insuring that (xl, x2), and no more, is sold at
the price vector (pl, P2) in a market of size 0. As 0 increases, the level of effort needed


to sell (x, x2) at price (p1,P2) declines.


The retailer's


effort may include marketing


intensity, advertising, or such customer services as free delivery and installation, free


repair or consultation services, and product demonstration.


This type of effort is


not readily observed by the manufacturers, so a moral hazard problem arises.


That


is, the manufacturers cannot verify directly whether low demand occurs because the
retailer has supplied little effort or because demand is truly sluggish.
On the supply side, manufacturer Mr produces zi at constant marginal cost mi,
and imposes a tax Ai(xi, pi) on the retailer. Ax(z;, p9) is the amount the retailer must


pay to manufacturer Mi when he chooses to sell zi units


of Mi's


product at price pi.










Both pricing and sales decisions are delegated to the agent.


Although price is not


directly dictated by the manufacturer, she can indirectly control the price through the


tax since prices are observable.


Thus, manufacturer Mi seeks to solve the following


program in the common agency duopoly game:"


[CA]


maximizeA,(,.)


- miXi(0)} f(0)d0,


where the multi-outlay (zx, x2, p,p2) is chosen by the retailer to solve

max,, z2,P2 {xipi + xZ2p2 -e(x1,X2,pi,p2,) A1(ac,pi) A2-2p2) -


The timing in the game is as follows.


Next


First, the agent learns the realization of


, the manufacturers simultaneously offer the agent their tax schedules.


agent then accepts either both, one, or none of the tax schedules.


If the retailer


rejects both contracts, he earns his reservation wage, which is normalized to zero. In
this section, we will derive a perfect Bayesian equilibrium of this two stage game.
Given the complexity of the game, a characterization of the equilibrium is provided


for the


case


where the retailer's


disutility of effort is quadratic, and takes the general


form:


e(a1, z2,p2, 2,0)


2


+h2x2p2 CZl 2


x2 + -p + p+ hlxlxp +
- 2 2 2
- cplpz 0(zl + z2 + pl + p).-


(4.1)


Notice that the form in (1) admits an approximation of many disutility functions


up to a second-order Taylor expansion.
and large enough that the retailer's dis


We will assume that a; and bi are positive
utility of effort must increase as the price or


the required sales level increases, i.e., ex,, em,


> 0 fori=l


>0is


a necessary condition for the retailer's program in [CA] to be concave in equilibrium.
9WpJ n n t I nllnw mnif tnrr un A'd, t fln ntr nrn tQ ft that nra, rntinevont wiTnnn di nantaa r*k,,,


Also, aibi -(1- hi)2










In addition, we will require that hi


1 for i=1,2.


This natural assumption ensures


that as the resale price increases, each unit of sales becomes more profitable for the


manufacturer under complete information.


will be substitutes if c


Finally, note that the two product lines


< 0 and complements if c


When


the manufacturers


have complete information on


product demand,


equilibrium contract is extremely simple, consisting solely of a fixed franchise fee.


This fee extracts all the rents from the retailer.


But, more importantly, RPM does


not occur under complete information.


However


, if the retailer possesses private


information on product demand, the equilibrium franchise contracts become more


complex and involve RPM,


as the next Theorem illustrates10


. First


we will make


use of the following assumption throughout the paper.


Assumption 3 0 has an increasing affine hazard rate.


Due to the highly nonlinear nature of


e, it is extremely difficult to develop an


algorithm to compute the equilibria when the hazard rate of the distribution is also


nonlinear.


Under Assumption 1 we have the following existence and characterization


result.


Theorem 1


There


exists


a pure-strategy


equilibrium


for the


common


agency


game


[CA].


In th


equilibrium,


franchise taxes take the form


Ai(zi, pi)


= 7i + cii +


x] + SiPi + -pi + OTizipi
2 p


(4.2)


for every (zi, pi)


E31.


that it always induces


This


the retailer to


equilibrium schedule in (2) is fully separating in
select an outlay (x, pi) that differs strictly with


1oDue to the moral hazard problem, the first-best contract cannot be implemented as in the
asymmetric demand information models of Lewis and Sappington [1988], [1992].
1An increasing hazard rate ,' helps to ensure that the tax will be fully separating. The


hazard rate is affine if 0 is generated by a Beta(1,1) density on 6 with distribution 1


4-k4 for










the realized market


fee (7),


Furthermore, the equilibrium taxes entail a fixed franchise


a nonlinear wholesale price (a, /), a nonlinear tax on the retail price (6, 7),


and a royalty (a) on gross revenue.


Equilibrium royalty rates are ai


i=1.2.


There does not exist any simpler combination of a two-part wholesale price and/or

royalty on revenue in equilibrium.


The retailer's


equilibrium profits increase with demand,


When the products are


substitutes (c


the retailer earns rents even


in the weakest market 0.


Under


complements, the retailer earns only his reservation wage in the weakest market _.


Note


the resale price is


never


directly imposed on


the retailer,


but it


controlled indirectly. Resale price maintenance appears as a levy on resale price and


a royalty on revenue.


To understand the equilibrium pattern of rents,


first consider the case where the


two products are substitutes.


In this


case


, the retailer naturally has an incentive to


serve one manufacturer exclusively.


Thus


, the retailer has to be afforded extra partic-


ipation rents just to agree to serve both manufacturers.


So, to induce participation,


the retailer is allowed to retain a premium rent even in the weakest market 0.


complementary products,


Under


the agent does not have to be forced to serve as a common


agent,


and so the retailer can be


forced to zero rents in the weakest market13


To understand the nature of the royalties on revenue (ai),


recall that h, is the


degree of substitution between sales Xi and resale price pi in the promotional cost


function or marketing function


Since ai


the royalty on product i's


revenue


increases at the same rate that the degree of promotional substitution between the


resale price and the quantity of good i decreases.


In particular,


if resale price and


12Although taxes on the final resale price seem rare in practice, they have been advocated in the
regulation literature. Laffont and Tirole [1990] and Leung [1994] have proposed using a tax on price
to regulate a natural monopoly. Even though Ai is concave, it is still an open question of whether
thars ovicto an nhnivhl nt aniilhrinrm in whih hn th rptanilpr nffor a mnnn riif affine fn ntreta onf thetP


[










quantity are promotional


cost complements of degree hi


= 1,


then no royalty is


imposed on revenue. No

revenue from the agent's


,te that this equilibrium royalty on revenue extracts all the
sale of product i less the promotional cost term hixipi of e.


Consequently, the fixed franchise fee, the nonlinear wholesale price, and the nonlinear
surcharge on resale price must act as a combined subsidy to the retailer to recoup

the remainder of his promotional costs and to provide any necessary rents.
Next, we examine the more general case in which the manufacturers cannot ob-


serve the retailer's


final level of sales.


Below, Ai(xa,,pi), i=1,2, will refer to an equi-


librium of the common agency game [CA] in Theorem 1, where sales were monitored.


Corollary 3


Suppose the manufacturers cannot observe the retailer's level of sales, so


the retailer can sell any qi less than the ordered inventory xi, i=1,2.


Then Ai(xi, pi),


induce


retailer to


exact quantity that he orders,


= xi.


Moreover, the equilibrium franch


taxes Ai(xi, pi),


1,2, indirectly impose


price ceilings and quantity rationing on the retailer in every market 0.


That is, Ai(xi,pi), i=l


persists


as an equilibrium franchise tax for the more


general duopoly game where manufacturers do not monitor the retailer's sales lev-


In addition


, Ai(xi, pi) does not give the retailer the incentive to destroy or to


store


excess


goods.


In fact


the franchise taxes induce the retailer to choose resale


prices and sales levels that are lower than what he would choose if he were the full


residual claimant14


Thus, as a result of manufacturers competing through a shared


retailer, the franchise tax indirectly imposes maximum, not minimum, RPM for ev-


ery realization of demand.


This is in accord with Ippolito's


examination of RPM


litigation


cases.


In almost all the cases from 1976 to


1982 involving allegations of


only maximum RPM, the retailer was shared by rival manufacturers.
"The retailer would be the full residual claimant is if each manufacturer Mi offered a pooling









The MonoDolv Benchmark


As a benchmark, we now examine a monopolist who markets both xl and x2
through a single retailer when there is no threat of entry by a second manufacturer. To


facilitate comparison with the above duopoly


case,


we make the following definitions.


Let p?(0) and xD(0),


,2, be equilibrium resale prices and sales levels chosen by


the retailer in


the common agency


(duopoly)


game


pM(0) and


be the optimal resale prices and sales levels chosen by the retailer serving a


multiproduct monopolist.


Define pF(0) and zx(0),


i=1,2,


to be the corresponding


(first-best) levels for a monopolist who has perfect knowledge of demand. Similarly,


define the equilibrium disutility of effort levels eD


eF accordingly.


We can


now examine the efficiency of duopoly competition through a common retailer in the
game [CA].


Proposition 6


Total manufacturer profits are higher under monopoly than under the


duopoly of game [CA].


Furthermore:


For substitute products (c


pt'(0),


<0),


with equality


xF(e)


4D(0)


xy(0) and pf(0)


market 0.


pf (0)


The price ceiling


and quantity rationing are


severe under duopoly.


The retailer retains more


rents under duopoly than under monopoly and works more efficiently:


eF(0)


eD(0)


eM(0),


with equality only for the largest market 0.


For complementary products (c


>0),


4(0()


xM(e)


F((0)


and pD(0)


p(0)
ceiling


pm(0),


with equality only for the largest market 0.


quantity rationing


are more severe


under


duopoly.


The price


retailer


secures


less rents under duopoly than under monopoly and works less efficiently:


eF(0) > eM(0)


eD(0),


with equality only for the largest market 0.


Sy(0),


only for the largest






53


(see Figure 3). Although a duopoly provides higher-powered incentives to the retailer


than a monopoly would under substitutes,


the total manufacturer profits are still


higher for the multiproduct monopoly than for the duopoly.


recall that for substitutes,
only one manufacturer. TI


To understand why,


the retailer has a natural incentive to exclusively serve
ius, he must be provided with extra rents as an incentive


to serve as a common retailer for both manufacturers. In contrast, under a monopoly
the retailer does not have this outside opportunity, so the monopolist does not have
to afford the retailer these extra duopolistic participation rents.
Price ceilings persist in the duopoly common agency game [CA] when products


are complements.


Furthermore, competition induces lower price ceilings and more


severe rationing. Just as a monopolist will, the duopolists distort price and quantity
downward as the market gets weaker in order to limit the retailer's incentives to


understate demand.


, because the products are complements, if one duopolist


decreases her resale price and level of sales, it becomes advantageous for the rival to


also lower her price and sales level. As a result, the manufacturer's


trade-off between


efficiency and rent extraction becomes less severe as the rival reduces her price and


sales level in order to extract rents.


In essence, each manufacturer imposes a rent


extracting externality upon the other when they share the same retailer, resulting in


a double extraction of rents.


Consequently, the retailer prefers a monopoly when the


two product lines are complements.


When


the goods


are substitutes


, if one duopolist


reduces her price and sales


level,


the rival


will find it beneficial to increase both sales and


price.


Thus


duopolist's trade-off between efficiency and rent reduction becomes more severe as
the rival reduces her price and level of sales in order to extract rents. Because of this
externality under substitutes, the duopolist extracts less rents than the monopolist.


As a result, incentives under a duopoly are higher-powered than


the monopolist's






54


Finally, the underprovision of effort is worse under duopoly when the products


are complements.


Since a duopoly results in a lower level of sales at a lower resale


price when compared with a multiproduct monopoly under complements,


the level


of effort required in a duopoly will be lower, and,


level.


hence


The exact opposite occurs for substitute product 1


further from the first best

ines; duopoly competition


will induce the retailer to provide a higher, more efficient level of marketing intensity.


Competition for an Exclusive Dealer


In the last section we saw that when products are substitutes the retailer

had to be afforded extra rents just to agree to serve both manufacturers. Eventually,

these participation rents can become so costly for a manufacturer that her expected


profits are higher if she


instead hires the retailer as an exclusive dealer.


To consider


this possibility,


we now analyze the


case


where, instead of sharing the same agent


non-cooperatively, the manufacturers compete head-to-head for the exclusive services

of the agent.


The salient feature of this model


that head-to-head competition for exclusive


services creates countervailing marketing incentives for the


retailer15


The usual


incentive for the retailer to understate demand arises to convince the manufacturer


that high sales are due to the retailer's


diligent efforts,


not exogenous demand.


This


incentive is countered by the following effect of competition.


As market size increases,


the total value of the retail outlet increases.


Hence


the manufacturers' bids for the


15For a general discussion of countervailing incentives in principal-agent problems,


Sappington [1989a,b].


see Lewis and


Our model of exclusive agency differs significantly from the model of Biglaiser


and Mezzetti [1993]. They examine the optimal labor contract that emerges when two firms compete


for a manager whose ability is hidden.


do not arise.


(1993).


Their model is structured so that countervailing incentives


Our model of exclusive dealing also differs from Gal-Or (1991b) and Martimort


They consider two manufacturers, each of whom operates through an exclusive dealer.


The manufacturers compete through wholesale price
rtlwnt.rpam etnrnnstitinn (lal-Ofr alsn ennsirlrs the


es, leaving the resale price to be determined by
case of RPML. Instead. we follow Bernheim and









retailer's services increase with the perceived market size. The prospect of higher bids
can encourage the retailer to exaggerate the size of the market. These countervailing
incentives will give rise to partial pooling in the equilibrium contracts.
In this competitive scenario, each manufacturer offers the retailer a menu of con-


tracts (xi(0),pi(), Ti(0)) in exchange for his exclusive services.
No wholesale price is necessary since now xi is dictated directly.


cepts Mi's


Ti(0) is a fixed fee.
Once the agent ac-


contract, he is prohibited from dealing with manufacturer MA-, who then


has no access to this particular market.


Since this is a static model, we assume that


a manufacturer can never credibly bid more than the maximum total surplus value


of her product.


That is, the most that Mi can bid to attract the retailer is


1n,(0)


where (xf


S(p;(0) mi)xy(O)


- e


, p) is the outlay that the retailer would choose if the manufacturer's ex-


clusive contract consisted solely of a wholesale price equal to marginal cost mi.


Thus,


II,(0) is the profit that the retailer would obtain if he were the full residual claimant of
product line i. Equivalently, II(0) is the vertically integrated profit for Mi. Note that


the total surplus IIi(O) increases


as the market demand 0 increases. For simplicity, we


will assume that manufacturer M1 dominates M2 in the sense that II1(0)


every 0.


II2(0) for


This will be the case, for example, if the two product lines are homogeneous


and M1 has a lower marginal cost than M2. Alternatively, M1 could dominate M2 if


product 1 possesses a stronger brand loyalty than M2's


product.


Since M1 dominates, we will observe that the retailer always chooses to exclusively


serve M1 in equilibrium.


Thus, an equilibrium strategy for MA is simply to offer the


pooling contract consisting of a wholesale price equal to marginal cost m2, while M1's


I~tl rQ inr ro\
V, Pi \VI, 0, 8)~









equilibrium strategy (zl, pl,


Ti) solves the following restricted program:


[ED]


- mxxl(


maxp,t, lTl {Tl(


u'(e)

U(0)


)dz such that


= x() + p(0o),


112(0),


Pi and x1 are nondecreasing in 0,


where


U(0)


= U(0, ) and U(, 0)


- i(0)pi(0)


- e(x1(0),, p (), 0, )


- T1 (O).


To facilitate a comparison with the duopoly model, we will continue to assume
that e has the general quadratic form given in equation (1). In addition to Assumption
1, we will restrict attention to those Beta distributions with fO nondecreasing in 0.


An example is the uniform distribution (A = 1
following characterization of the optimal verti


). With these assumptions we have the
cal restraints under competition for an


exclusive dealer.

Proposition 7 The participation constraint (2} in program [ED] is binding at a unique


Moreover, at the solution (xl,pi) to [ED] we have the following 17


the optimal vertical restraint involves resale price


Also, p(0))


p;(O) and Xi(0)


a;(0) for 0


'6We


assume that M/1 wins any ties, that H11 is concave in zi and pi,


and that, in equilibrium, the


agent will be employed for any realization of demand.


how program [ED] is restricted.


constraint U(0, 0)
However, in most


In addition, it is important to understand


Note that the optima under the more general program with the


> U(0, 0) (instead of constraints (1) and (3)) are not always nondecreasing.


cases,


these optima are nondecreasing


so that program [ED] is indeed the correct


program.
1'Since II2(0) is increasing in O, it is not immediately clear for which O's the participation con-


strain (2) will be binding. However, due to the strict convexity of U(0)


that constraint (2) binds only at one point, 9.


We assume that H'2(0)


(


- H2(0), we can conclude
E(x(f() + p (), x( ) +


pfi ()) for .
(1) modified


all 0


so that 0 E (6,0), where (zf (), pf ()) solves program [ED] with constraint


;d as U'(6) = z2i() + pl(0) A, where A is sufficiently lai


rge so that constraint (2) binds


z)}f(z


point B


. For sluggish markets (0 < 0
floors and quantity forcing.


E (8, s>


E [8, 8],












with equality only at and 0.


zero


The retailer's


informational rents decrease in 0


Moreover, there is an overprovision


of promotional effort,


For strong markets (0


with efficient effort supplied only at and 9.


the optimal vertical restraint entails resale price


ceilings


and quantity rationing.


Also,


p1(O)


*;e


and xi(9)


*la
x1(O)


0, with equality only at 0 and 6.


The retailer's


informational rents increase


in 0 with zero rents at 0.


Moreover, there is an underprovision of marketing


effort, with efficient effort supplied only at 0 and 0.

Quantity forcing requires that the manufacturer be able to monitor the retailer's


level of sales.


If such monitoring


not possible,


the following adjustments in the


optimal vertical restraints arise.


Corollaru S


If the manufacturer cannot monitor the


retailer's


level of sales,


the man-


ufacturer elevates the price floor


The retailer


then induced to provide the


efficient


level of sales for the accompanying inflated price floor.


Proposition


Corollary


clusions reported in Proposition


4 are illustrated in Figures
7 warrant special emphasis.


Three con-


First, price


floors can


be optimal vertical restraints in sluggish to intermediate-sized markets, regardless of
whether sales are monitored. Due to the head-to-head competition between the man-


ufacturers, the retailer's


reservation utility increases with the market size, giving rise


to incentives for the retailer to exaggerate the strength of the market.


this incentive


To mitigate


, the manufacturer calls upon the retailer to generate performance that


is particularly difficult to achieve if demand is below its reported level.


The elevated


price floor forces the retailer to put forth an above-normal level of marketing inten-
sity to promote demand at this artificially high price, particularly if demand is low.


rents at 0 (wages at 0 are II2(0))




















Resale
Price


Q


Monitored
Sales


FIGURE 4-1


MONITORED SALES.






59


Second, for an industry in which only exclusive dealers are employed, both price


ceilings and price floors should emerge across different markets.


price floors should appear in weak markets.


We saw above that


In contrast, price ceilings arise to limit


the retailer's incentive to understate the size of strong markets. Recall that this was


the prevailing incentive in the common agency model of Section 2.


Thus


as in a


common agency, this incentive is mitigated by the use of price ceilings and quantity


rationing.


In summary, we should thus observe both price ceilings and price floors


across different markets.


This prediction is consistent with the empirical findings of


Ippolito


1988].


For example, in 18 resale price maintenance cases involving gasoline


retailing, half involved allegations of price floors while the remainder involved price
ceilings.


Third


, rigid retail prices may emerge.


For intermediate-sized markets, it is op-


timal for the manufacturer to institute a single, fixed resale price.


Recall that the


head-to-head competition between the manufacturers creates countervailing incen-


tives for the retailer.


The intermediate-ranged markets in which pooling occurs are


essentially those markets in which the retailer has a


"conflict"


between the incen-


tive to overstate and understate the size of the market 0.


For sluggish markets and


booming markets, the price mechanism is sensitive to market demand, continuously


increasing in 0.


However, the optimal retail price does not vary with the size of the


market for intermediate-sized markets.


This price rigidity can be interpreted as an intertemporal price stickiness. In a
dynamic setting, each manufacturer would prefer to commit to the static contract


(derived above) in each period (see Laffont and Tirole (1990)).


That is, they would


prefer to offer the same static contract each period if they could credibly commit


to this without renegotiating1s


In such a case we would observe intertemporal price


rigidities in intermediate markets even when demand is non-stationary.


Consequently,





















Resale
Price


0N6 B


Unmonitored
Sales


FIGURE 4-2


: UNMONITORED SALES
















Resale Prices When Sales Are Monitored


(Complements)











(Independent)






(Substitutes)


Prices:
D
P -duopoly


P -multiproduct monopoly
ED
P -exclusive dealing
L H
P, P -single good monopoly


0 P


Demand


FIGURE 4-3


-multiproduct first-best
-single good first-best


: COMMON AGENCY VS. EXCLUSIVE AGENCY










across time and across markets of considerably different


sizes,


we may observe the


dominant manufacturer instituting the same exact retail price!


There is no price


discrimination.


Note that


price stickiness does not arise out of


risk-sharing


concerns.


The price rigidity is solely the consequence of incentive contracting under


manufacturer competition. Fina
perfectly competitive price of mi
products are homogeneous.


lly, note that
as Hii() -+


this constant


price approaches the


H2(0) for all pooling 0's,


if the two


These results are due to intense manufacturer competition.


In conclusion,


present Figure 3 to compare the vertical restraints that emerge under exclusive dealing
with those that occur under duopoly. Figure 3 illustrates the predominant case where
exclusive dealing results in a lower (higher) resale price when compared with the
common agency retailing of complementary (substitute) goods.


4.5 Hospital Exclusive Dealing

The above common agency and exclusive dealing models can be reinterpreted to


explain hospital competition rather than retailing in general.


Consider the manu-


facturers to be hospitals offering a facility (such as an open heart surgery facility)


to a physician group (the agent or retailer).


The hospital Mi charges the physician


group Ai(xi, pi) for the use of the hospital facility. Here zi is the number of patients


that the physicians treat at hospital Mi.


The price pi is the fee the physicians charge


each of those patients. Moreover, following Chapter 2, physicians can induce patient


demand with their unobservable effort, intensity, or quality ei.
the healthiness of the patient pool (HMO) that they serve. T


High 0 is an unhealthy pool of older patients,


The physicians know
'his risk is indexed by


while lower 0 is a pool of young,


healthy patients.


In contrast, the hospitals do not know the HMO's


risk factor 0,


and so must design incentive contracts to induce the physicians to reveal this infor-






63


The physician group than bundles this hospital rate with a physician reimbursement
rate and charges this price bundle to the HMO.
In particular, when the two hospitals have complementary technologies, they will


share the same physician group.


The resulting price bundle will offer a discount to


the HMO.


When hospital


technologies are substitutes,


the dominant hospital


win an exclusive contract with the physician group.


The resulting HMO price bundle


will now involve


"balanced


billing"


low risk HMOs (e.g.,


HMOs with


young,


healthy enrollees).


That is


, the low risk HMO will be over-billed beyond what a


vertically integrated hospital would charge. However, high risk HMOs will be offered
a discounted price. Intermediate risk HMOs will be offered a uniform, risk-invariant


price bundle.


This competitive model may help explain many pricing structures


observed in the health care industry.


Conclusion


In this paper we have derived equilibrium retail contracts for two rival manu-
facturers competing through a shared retailer who is privately informed about market


demand.


This scenario is very common in many industries.


The equilibrium fran-


chise taxes we identified are nonlinear,


they


can be implemented by


a menu


of linear franchise contracts.


characteristics.


The duopoly equilibrium has the following additional


For substitute (complementary) products, duopolistic manufacturer


competition through a common retailer results in higher (lower) price ceilings, more
(less) efficient underprovision of retailer promotional effort, and less (more) severe


quantity rationing when


compared


with a multiproduct monopolist.


contrast,


competition for the exclusive services of the agent results in price floors and an over-


provision of effort in weak markets.


This upward distortion was shown to be due to


a nr no\ nmynror rrnTn~n'non ;nrnnfhiloar Par csrnnn ni 2Yn a TnMlt iD RPM a at1 fl






64


Our model predicts that in industries where the rival manufacturers share a com-
mon retailer (e.g., newspaper distributors, food and beverage distributors, clothing
distributors, etc.), only maximum RPM should arise. In contrast, in industries where


retailers are exclusive dealers
neously in different markets.


, both maximum and minimum RPM may arise simulta-
These are precisely the patterns observed in Ippolito's


(1988) study of RPM litigation cases.
An additional consequence of manufacturer competition for an exclusive dealer
is that the same uniform resale price may be instituted in markets that may differ


significantly in size.


This, in turn, may lead to an intertemporal price stickiness.


The price rigidity emerges in our model because of intense head-to-head competition
between manufacturers, not because of tacit collusion among manufacturers, as other
authors have suggested.
A direction for future research would be to investigate the effect that a ban on


RPM


would have on equilibrium contracts.


In particular,


it would be interesting


to determine whether the final market structure (exclusive vs.


common retailer) is


affected systematically by a ban on RPM. Moreover, if sticky resale prices do not
emerge systematically with a ban on RPM, then our model suggests that resale price
rigidity (across markets and across time) may indicate that resale price maintenance
is being practiced.









CHAPTER 5
CONCLUDING REMARKS


Common agency theory deals with a competitive version of principal-agent theory


in which multiple principals contract with the same agent.


This dissertation develops


common agency theory for applications to the industrial organization of the health
care industry.


In the first essay, the efficiency of three health care systems is examined.


In a


multi-payer system the public payer (Medicare) uses a mix of prospective payments
and pass-through payments, while the private payer (a managed care insurer) uses
a quality-based reimbursement rate through utilization review. Cost-shifting in the
multi-payer system induces the hospital to overinvest in technology. Furthermore,
pass-through payments of capital are scaled back in equilibrium since they create a
moral hazard problem that allows the hospital to goldplate, i.e, to invest in wasteful,


non-technological capital.


pass-through


payments.


This may explain Medicare's current policy to phase-out
In a single-payer system investment in technology is cur-


tailed, and goldplating can arise. Whei
and the hospital is admitted, technology
based reimbursement rate is negotiated.


n trilateral negotiations between the payers
:al efficiency results when a uniform quality-
Moreover, this all-payer system is immune


to goldplating.


The second essay studies the interrelationship between a hospital's


capital struc-


ture and the payment plans designed by Medicare and the private insurance sector to


reimburse the hospital's cost of capital and technology.


To counter the opportunism


of a managed care private insurance sector engaging in utilization review, the hospital
will use debt when bankruptcy is costly.
The final essay derives the equilibrium hospital contract with a physician group






66


it serves. Bundled physician charges are then derived when hospitals compete for an
exclusive contract.


Finally,


we suggest some theoretical extensions to our model.


First,


we have


considered only deterministic patient demand in the first essay. In reality, the demand
for medical services is highly stochastic. In such a case, some range of pass-through


payments may be optimal if the hospital is risk averse.


Moreover, as shown in the


second essay's


stochastic model,


ex post negotiations may no longer be optimal since


they may induce a for-profit hospital to increase its debt-to-equity ratio,


turn increases the hospital's risk of bankruptcy.


static model.


which in


Second, we have only considered a


In a dynamic model, insurers may try to behave opportunistically by


renegotiating reimbursement rates. Martimort's


(1994) model of a dynamic common


agency suggests that a multi-payer system may be optimal if the hospital has private
information concerning its costs.









APPENDIX

Proof of Proposition 1:


The Single-Payer System. First note that the equi
tion Ts = 0. So the Lagrangian of the public payer's


Ibrium Ts is the boundary
program is


- aX


- pT


+ pY + AY.


The Y>
equilibrium


0 constraint will be nonbinding.


Thus


the first order condition


We will later verify that indeed A


= 0 provides p


= _x
~ XI


=Oin


Next


=UI


X XXII
- aX + Y + (1- X--)
Aj Ar


=UI


-cXr


X
- cX + Y.
xryI


(Al)


Thus


. Next we verify that A


Therefore


crX2
XI


= 0.


From YI


= 0 we have a


_ cXl+clX
- XI


Hence


(2) The Multi-Payer System.
such that for all n < n1, the I


First


, note that there exists a maximum nl


program maxyA has an interior solution solving


= (1 n)Ur


- crTX +p


E (0,1)


(A2)


For n > ni, the equilibrium To i
Lagrangian for the public payer's


s the boundary solution To
program is


= 0.


For n


=n(U


-aX)


-pT


+ pAt + 7AT + AA.


We will for now assume that A


= 0 provides p


= x
XI


Thus


= 0 and later verify this.
S= 0 reveals that


The first order condition


ATTrr


Next


-nUT


from the first order condition


X
XI


= 0 we obtain 7


(A3)


when po


case,


equation (A3) reveals that


= TATT + UT -


AIT.


(A4)


Define K(I, T)


= TATT +


Using equation (A4),


equation (A2) becomes


AT(I


= UT(I, T) cTX(I) nUT(I, T) + nUT(Iro, To) + K(lo, To).


(A5)


nr..4n 4k.a. ... (F PErF \\l ..-j /A\--. .-


(1)
solU


I/


,Y


E (O,


T


m,


4V


hf,,,e


IAE\,,I..,,, L,









when po
K(Io, To)


E (0,1).
> 0. First


Next


we claim


since eTT


Assumption


we have 1


1 (cTTT
= -IA T
- ArT


< err)
Thus.


implies that


TATT + IAIT


(A7)


However,


that K(I,T)


concavity of X(I),


=- TATT +


we have


> 0.


Next


Thus,


equation


(A7)


, we claim that Ar(Io, TE(o))


implies
> 0 (in


equation (A6)) when K(lo, To)


K( o, To)


Then


, by concavity, A


Suppose instead that AT(Io, TE(Io))
T(lo, TE(Io)) < 0 implies that TE(0o)


< 0 when
> To(Io).


then nUT(Io, To)


- nUT(lo, TE(Io))


, implying that


K(lo, To)


< 0 from


equation (A6).
when K(lo,To)
when K > 0 a


This is a contradiction.


I,


> 0 and po E
d Po E (0,1).


(0, 1).
If po


Therefore, we must have AT(lo, TE(Io)) > 0
tat is, the hospital overinvests in technology
1 for all n, then by the intermediate value


theorem, there exists an ft


E (0,1) such that nUT(Io, TE( o))


< 1 for all n


< n. Thus,


ArT(o, TE(o))


- nUT(Io, TE( o))


for all n
when Po


< n when po
= 1 for all n.


a m


Now we define no


That is


as the largest n


, the hospital overinvests in technology for n


E (0,1) such that


(lo(n), To(n))


= (o(n),


TE(Io(n)))


(A8)


From the above analysis,


we know that no exists by continuity.


To show that over-


investment in technology occurs for all n
only when po = 1. For, using equation


note that equation (A8) can hold


(A8),


equation


(A5)


can be reduced


AT(lo(no),TE(Io(no))) = K
since AT = 0 at TE. Thus.


that A


a


= no.


P


I.


Therefore, for n


> 0 when po
'o = 1 at no.


no, either po


S(0,1).


-land?'o


However, this is a contradiction


= 1, implying
E (0,1) with


> TE or Po


To_
Next
(Al).


since 7
Next, r


Tb.
, we claim that Io
When n < nl ai


U(


a


< IE when K(lIo, To)
d po (0,1),


- aoXI) + PIlAI + PAII + 7AIT


= (Ur


= T from the first order condition for p.
ate that K(I, T) > 0 implies that


For n


- crX


, Io


< IE from equation


- cX) + xA + TAIr = 0
(A9)


Define L(I, T)


= J
X
-XI


Air + TArT


TXIA


-ATr


(A10)


and that L(I, T)


> 0 implies that


Moreover, noUT(Io, TE(lo))


= n(U


Th


n






69


Thus, multiplying equations (A10) and (All) together provides ATrA1 < AyT.
However, this violates the hospital's second order condition ATTAII Ay > 0.
Therefore, to satisfy this second order condition, we must have L(I, T) < 0 when
K(I, T) > 0 and po E (0, 1). As a result, equation (A9) reveals that BC = L(IE(To), To)
0 when po E (0,1). Thus, the hospital undersupplies intensity. A similar proof holds


when po = 1.
Finally, we verify that A


-i)


= 0 under Assumption 2 ( t


xi.


We must show that


A(lo, To) > 0 for all n. Define & to be the maximum out-of-equilibrium a that forces
A = 0 for a fixed (I, T) when p = 1. Then n& = c (1 n) while the equilibrium


x
noo = Cy+c-
holds if < A.
U-x.


(3) The All-Payer System.
max4YqVXMz is


Thus, ao


& at (lo, To) if c,-


0 and A


>(1-n)[


-K],


which


= 0 under Assumption 2.


The first order condition for the Nash bargaining program


qMV


= nzVY


+(1 n)MY.


(A12)


Fron equation (A12) we can derive etX


= qU + (x +


z)(cX + T).


Therefore,


-cX


= qU+(x+z


- 1)(cX + T) = q(U -cX


-T)


since q + x +


Therefore,


= 0 and BY


= 0 at (IE, TE).


Proof of Proposition 2:


(1) Single-Payer System. Note that the public reimbursement plan (a = 0, r = 1,p =
1) would ensure that Y = 0 for any I and T. Since the hospital is indifferent, (IE, TE)
is an equilibrium.
(2) Multi-Payer System. First note that if r > 0, then


AT = UT


-CT


X-1+p


- nUT + nrcTX.


(A13)


From equation (A2), we see that equation (A13) reduces to AT = nrcTX > 0 at To(I).
Thus, T7 > To. To verify that r > 0, we examine the public payer's Lagrangian:


n(U aX) nrcX


-pT


+ pAI + 7AT + AA.


Assume for now that A


= 0.


The first order condition for a implies that p =


Thus, the first order condition for p then provides 7


=Tifp


e (0,1).


Next


= -ncX


implies that r =
(A9) above. Thus


nX
+ --[ciX + cXi] + ncTXT
Xr


1 in equilibrium. Next, the first order condition on I is equation
, (T) = Io(T) for all T when po,pi E (0,1).


Proof of Proposition 3:


Thus, A(Io, To)










The government's program is now


maxa,p,G,T n(U aX) p(T


Differentiating with respect to a provides p


+ G) + PAI + 7ArT + AAc.


Sx
qX'


Differentiation with respect to G


reveals that A


-
- l~c


The first order condition for


T is still equation (A3).


Next,


solving for 7 in equation (A3) and substituting into the first order condition for p


when p


E (0, 1) provides the equilibrium pass-through payment


ATTI/$'


ATT + -"


(nUT +


ATI)


(A14)


Using the the definition of po in equation (A4), equation (A14) reduces to


.t, [Po + GATT].
ATT + 4"'


(A15)


However, since AG = 0 in equilibrium, we must also have p =
equilibrium, equation (A15) implies that


1 '(G).


Thus, in


4"(G)
S+ Po + GArr]TT
ATT + "(G)


(A16)


Letting 4(G)


=aG


A-G2
2


, it is straightforward to show that G*


= po
b-2AsTT


> 0 solves


equation (A16) and reduces equation (A15) to p


=bG*


Proof of Proposition 5:


Suppose that
H = Y= V1-'


D* = 0. Then z, z = 0. First, we claim that > 0. Let
. The private insurer will choose Pf to maximize H by solving the first


order condition qV(1 + b4)


- q)Y. Next note that


98* -HpD
OD H0p


By concavity of H, H0p < 0.


(A17)


Moreover,


HRY 9Y OV
HOD = qV + (1 Vq)-
800D aD ap


ATT


p
-t G) ~r+
~I~N(G)


- (T


+ G $-


---










Thus


> 0. Hence,


Now now that


dY
I-=- (


)apO
- n)x-


- bF(


z*) + b(1 n) f


X~dF.


(A18)


Since we assume D*


ever


since


, the hospital's


we must also have


first order condition must be d
dD


How-


dY
- = (


9/"
-n dx


from equation (Al
D* > 0.O


However, this is a contradiction.


Therefore,


we must have


Proof of Theorem 1:


We will der
ture that A


ive the equilibrium form (4-2) in the following manner. First,
2 takes this form in equilibrium. Then we show that M 's be


also takes the quadratic form in (4-2).


To do


we conjec-
st response


so, the following Lemma is useful.


Lemma A
in a market


Given the conjecture A2 as defined in (4-2), thi
t of size 6 is U(O) = w2(O) + maxe1,1 (tK(xl,pi


e agen
,0)-


t's equilibrium utility
Ai(xi,pi)), where


wt(0)


= maxxa2,p


- 02)


x2p2 -


- 2)p2- 72


K(zx,pi,0)


-= "2x yp + (k3 + (Oki)x1 + (k4 + (02)p1 + ksxip1 for
2 21


= 1 + cti + csiti


-Ct1(62 +


a2sli)


-ct2(62 + a2S2


=(1


--z2)


(a2 + 12)(b2 + q?2) (1 h2 a2s)2

(a2 + P2)


- O2)22


'a


r I r


Hpo


at + Pt


bz + ~2


2 1 rn
p, t ([7


1- (8


--al +


--bl $-


- hl)S


fc









The proof is tedious, and so is omitted.
From the Revelation Principle, for any


The details are available upon request.
r tax A1 : 3I -- R+ that is a best response to


the conjecture Az, there exists a direct revelation vertical restraint (pi(0), x1(O), T (0))
such that Ti(0) = A(0a O),pi(0)) when restricted to the domain D = {(xi(0),pi(G)) l
o} and (zi(p(0),pi (0), T()) solves the program


max, ,x ,TJ / {Ti(

u(0, 0) > U(, ),

U(, 8) > max{0,i


pl, Xl


z) mlx (z)}f(z)dz such that


w2(0)}, and


for all 0,0


u(,0e)


- w(O) +


+ P


+ (3 + 1)x1i()+


+(k4 + 0),pi() + kx(0)pi(0)


- TI(0).


It is important to note that the Revelation Principle does not in general hold simul-
taneously for both manufacturers unless we restrict reports of 0 to 0 (see Martimort
and Stole [1993]). Next, let u(0) U(O, )- w2(8) be the rent function corresponding
to A1 and suppose that that (xil, p) is a solution to the program


[Mi]


maxpi,." e {Ti(z) mlxi(z)}f(z)dz such that


u'(0) = q1xi(0) + #2p1(0),


max{0, w2(0)}, and


SP, Xi


0 for all 0,0


Then (xl,pi) will also be an optimum of the program [Mi] iff #1ii(0) + 2zp1(0)
is strictly increasing in 0. This conclusion follows from Theorems 7.1 and 7.3 of
Fudenberg and Tirole [1991]. Since -w2(0) is decreasing and u(0) is increasing, the
participation constraint of program [Mi] holds under assumptions (A22) and (A23)
below. In fact, if fi 0, i=1,2, then program [Mi] is equivalent to program [M1] if zx
and pi are strictly increasing. We will assume a priori that 61 and #2 are nonnegative
and then check ez post to see when this is indeed the case at the identified solution.
Also, we will assume the following:


(A19)
(A20)
I A


a2 + /32


S S-


> 0, b2 + r2


-1)


> 0, and (a2 + z)(b2 + ) r( (1 h 2)"


= 1,2;


- a


U -,


a 1


where


EO,


-- -









(A23) x1(0)p1(8) e(x1(0),x2(8),p1(0),p2(0),8) -mi1 > -w2(0 at 0 = where
ai(0) and p1(0) are given below and x2(0) and p2(0) optimize wa2 0).
Conditions (A19) and (A20) insure that w2(0) is the optimum of a concave pro-
gram, attained at a positive level of sales. Similarly, [Mi] is a concave program if
the inequalities in (A21) hold. Under (A22) and (A23), the agent will be employed
by manufacturer M1 for any realization of the demand. Clearly, all five assumptions
must be checked ex post since they involve the equilibrium parameters of A2. The
Hamiltonian for program [M1] is


H(u,p,x,0) = f(O)[IC(x1,pi,0)


- u(O) mpx3] + p(0)[iaxx + #2P1],


(A24)


where u is the state variable.


The Pontryagin principle yields /(0)


f(0).


Further-


more, O is a free boundary so that p(0) = 0. Integrating provides p(O)
Substituting this back into the Hamiltonian, we have


= F(9)


f()O- = ka + x + k3 + 0 + kspl


1- F(O)
f()= 0


(A25)


f(6) -p1


=kzp1 +k4~+6~2 +ksxi.


1- F(0)
-- / 771- 2


(A26)


Solving (A25) and (A26) provides


xi(6) -

p (0) =
piW=)


z'


k" -"k2 l

-ks


)


- k2kl)


- F()\ k52 k k4 m
f(O) +k- km
f (0) k2 k hj


1-


F(0) ti + k -k4
,k1t- ~+k3 k~-Tmln
:0) kCg s ks


(A27)


(A28)


and TI(0) = AC(0) fS {t1x1(


z) + 2p1(


z)}dz


- max{0


-w2(0)}, where


W2(0)


_2-


- ~2)po + (1


- h2 a2)xoPo


It is immediate from (A27) and (A28) that xz and pi will be increasing in 6
if the inverse hazard rate of f(0) is weakly decreasing when k2qA ks52 < 0 and
k51 kq12 > 0. Note that these last two inequalities hold when ks > 0. Finally,
from Lemma A, it is evident that k5 > 0 if 1 > h2 +oa, since assumed that 1 > hi
(we verify below that 1 = hz + a2 in equilibrium).
Next we show that the best response to A2 is of form (4-2) for all (x,,pi) E V.


For the Beta(l, j) density,


1- F()
fWe


- 0).


Thus,


-"lz:


-- 9n 1--


at $- P2


bz $- )72


+ (8 CY2)50 + (B


8(~2


--l)t-rE4


-1)+ IC3


x(e









Solving (A29) for 8 provides


k2 )


A -
+ --
1+X


(A 30)


1+A


In terms of pi,


- k2kI
-ks )


-4%)l


A -
+ 1-
1+ A


(1 + t)(1
1
1 #


(A 31)


1+)A


(A30) and (A31) can be rewritten


-AC]


(A32)


1
=+[zBp+ A O0
1+ A


- BD3.


Then


T1(O)


I1
2


(lyA
2(1 + A))


2 k2
2 2
^(^


2zB
2(1 + A)


qS (AO


1+)


AC) xl+
-hja.+k+


1-


- BD)
-BD- pi +ksxipi+
i-A


AC)


- BD)2


,1(xe


-AC)


- BD)


2yA(1 + A)


2zB(1+ A)


2zB


- max{0,-w2(0)}


(A33)


(A32) provides \A AC = (1 + A)_2 yAx_1.
that we the tax parameters can be rewritten


This allows a simplification of (A33) so
as


-~1P1,


=Ic4+ 2


-El',


= kl + r,


= k2 +r


= ks


where


1-4-\


(A
t\ k ,


- kik2
- le.,,I


1-i-I


fkAs,


- kIlk2
-- eA


= 1-- [yAxz + \


+ k3+


1x 6


h


~
kz


(1 + ~)((61


SICQ
k:2


~,(xe


~z(Xe


~,e(xe


(61(1+~)82


dz(l+ ~)82


~ Ic~ + (618


7.










S- e+
2 1 +A


- k4k1x


The conclusion that al = -ks warrants
ks = 1 hi + c2tl. Now note that from
then t = 0, resulting in al = ks = 1 -
that can indeed be sustained in equilibr
i=l,2,ifc 2 -max{(bi+'1i) (ai+/9i) I


by assum
Next,
the fixed


ption (A19). Thus qi
we solve for the fixed
franchise fees are


> 0 at l
franchise


special
Lemma
hi. Thu
,ium. FiI
i = 1,2
east for
e fees. F


attention. Recall that by defti
A, if we conjecture that Oa = 1


nation
--- 2,


s, ao = 1 hi, i=1,2, is a royalty rate
nally, note that qi > 0 in equilibrium,
} Note that this maximum is negative
complements and weak substitutes.
rom T1 (0) above, it can be show that


71= +
2 2


~2P
---2 -2
7 2 2


if w2(_) > 0. We will show that w2 () > 0 iff c < 0.
First, note that 72 is chosen as large as possible by Ms so that as much rent is
extracted while still ensuring that the agent's rent in common agency is not below the
level of rent the agent would obtain for exclusively serving M1. At 0 this constraint
is binding, i.e.,


max ,2p, {zipi + X2p2 e( 1i,pi,2,2,1P,#)- A A} =


= max,,,, {zlp e(l, pi, 0,0,0) A1}.


(A34)


(A34) isolates

72 = maxzzr2p1 {xipi + x2p2 e(Zx,p1,x2,pp2p,) -a1 1 6 1l-


P1 2 71 P2
--ai -p: oalzpi iax2 62P2
2 2 2


'_22 _
-nP-aM


- max,,, {zpI e(xl,pl,0,0,9) -"a li -- 61P


- 2 1- 2 OlZiPI}.
-YiPiip}


(A35)


Refering to Lemma A, we can define Kt1 and KA2 so that t
so that KCi is the value of the second maximization in the (
iff Ki + K2 > max x2p{,p^L}, where L is the first maxin
Next, we have L < L- cxx2 cplp2 iff c < 0. However
max1a:21p2m {L 1C2l2 cp1P2}. Therefore, we indeed have KC1
Hence, w2(0) > 0 iff c < 0.
Next. for c > 0. suDDose that both narticioation constrain


S7


w2(_) = -72 + K2 and
A35). Then w2(0) > 0
land in equation (4-3).
, note that XKC + AC2 =
+AC2 maxazlp,2 p{L}.


nts are binding:


7i = max,2P1p2{L} AK2


(A36)


72 =


Then -71 -


maxxa22pvp{L} KC1.


72 +maxa p2m,1p {L} 'i+ 1K2-max,,aap, {L


(A37)


}. However, the right-hand


- k5mi1


- kik2


..


J


C ~ "" ~"r ~"~ """









Finally,


we must show that A1


can be extended from VD to 32.


with the same


quadratic specification (4-2). For any xz pi E 3R+, let I(x, pi 0) be the tax level
for which the retailer's utility from (I(xz, pi| ), zi,pi) is u(0). That is, the retailer
is indifferent between choosing either (Ai, x (0),pi(0)) and (I(xl,pl|O),xa,p1), for


any xz


and pi


To show that AR


is implementable on S.


it suffices to show that


I(%a,pi08)<
and p1 = pi(
can write I(a


Al(xl,pi) for all xa, p E + and all 80, with equal
9), where x1(0) and pi(0) are equilibrium choices.
"i,Pi 0) = IK () u(O). Then


ity only at xl = x
From Lemma A


(0)
. we


Ai(zi,pi)


-I(x,piJl0)


-zx(0)) + xr1(x(0)


- p(0))+p1 Fr(pl(O)


2


-pl)+


-pi(0)).


2
2 (Pl


Note that indeed Al(z1(0),p1(0))


- I(ai,piO)


= 0. Next,


O(A1(xl,Pi)


- I(x ,pr|0))


- 0) + ri(z1


However


, we claim that 4x*


= xl(0).


Note that


-x,1(0)


- ) + ;1


_ 1 +
r-l 1-+
P1 l A


- 1 k12


= ( +
P1


- k4ks5


- k2mi


. )
1+)A


+x1


= -~1+ :


Similarly,


O(A1i(x,pi)


at pi(O)
I(xal,pI 6)


Note also that A
> 0, for all (x1,Pi)


1(x,>Pi) I(xl,pilO)
# (x(0),pi(0)). 0


is convex.


Thus


, Al(zl,Pi) -


Proof of Proposition 6 and Corollary 3:


Let HD


and HM be the Hamiltonians for the duopoly and monopoly cases.


Then


OHD
Oxl


OHM


a2 + #2


-(a+ f)z2 +c a+ (0


1- F(8)
f(0)


OHM


OUcD


- F(0)


f(0)


from Lemma A.


1f en


However


(1 .;nr, .4. IR


oW'


= OH
ari


= 0 in equilibrium.


SnA irr coamimnnn (A 1


Thus


Thb orfnra D


aOHM(xl p


p


- zi)+


for xa*


=


- k2m1


-


~l(s


--e:(s))+ 92 (88>(pl


~1C8


-- :1>


8)+:,


s41
(e
rr


- jb~41Cg


- El IC2


at + 82


>) o


,\ rFM f ~P \









Next, let HF be the Hamiltonian for the completely informed monopolist.
?= H- n) Thus, Oz(pj) > fM, with equality at 8. Also,


Then


9HD


a9HF


1-F(O) +
1fifi


Hence, xz < zxF(p ). Similarly, p4'
tioning and price ceilings. O


Ca
a2 + /A


< pf (af).


8HiF


1 F() .
f(O)


Thus, duopoly involves quantity ra-


Proof of Proposition 7


and Corollary 4:


First


, note that program [ED] is equivalent to the following program:


maxp-i, (Pl ml)zl e(xl
It


z)(xl + pi H'


z)dz


-e(x1


,O,pi


,O,z)


z))(1 i+pi


-n'2(


z)dz


such that


(1)

(2)


xl(0))

xl(0)


xi(0)
z,( )


pdGe)


p1(O)


for all 8

for all 0


S[, l],

E [0,0].


Necessary first order conditions are


Gl(xl, pi)


= pi


- hip +0 +


F(9)
f(9)


= 0 and


G2(zx,pi)


=a z


- 6ibP


F(0)
f(0)


E [2,03i


(A38)


-Tn1


- alx,


- hip + 0


-F(0)


hllx + 0


-F(0)


=0 for


E ,[3],


where i, and r7 are the Lagrangian multipliers for constraint (i) above, i=1,2.


> 0 and ri


Clearly,


on some common nondegenerate interval containing 0 (when


E (, l)) or else one of the optimal controls will not be nondecreasing.
Finally, to prove Corollary 4, we show that the price floor increases if sales cannot


be monitored.


Thus


Without monitoring the agent will choose x;(pi)


a-i


= tp, + e-


So with the no-monitoring constraint binding,


equation


I A soc t


-0


- ml )ix


dP1


-F(


,0, z)+ Fl


)))f(


O, pi


z)))f(


-- mi al~cl


-- hlsl~8~


-- blpl --










(A39)


Ship +- 1+ al
axI f ati


on the non-pooling region.


(A39) reduces to


1- h\ N\
G2( (pi),p ) + 1-h Gl(x(p ),p )
al


where p1 is optimal for this no-]
4z(pV) < z1(pl). Consequently,
due to pi(xi) decreasing in zl. 0


monitoring


> pi(_(p ))


case.


Hence, G((p), p


since


where the last inequality is









REFERENCES


Aghion, P. and P. Bolton
Economic Review 77, 388-401.


(1987),


Contracts as a Barrier to


Entry,


American


Banerji, S. and C. Simon (1992), Franchising
Explanation, mimeo, University of Chicago.


Ownership:


Contracting


Bernheim, D.
for Facilitating
--(1986), Com
--(1992), Excl
nomic Research


and Whinston, M.(1985), Common Marketing Agency as a Device
Collusion, RAND J. Econ. 16, 269-281.
lmon Agency, Econometrica 54, 923-942.
usive Dealing, discussion paper no. 1622, Harvard Institute of Eco-
.


Besanko, D. and M. Perry (1993), Equilibrium Incentives for Exclusive Deal-
ing in a Differentiated Products Oligopoly, RAND Journal of Economics 24, 646-667.

Biglaiser, G. and Mezzetti, C. (1993), Principals Competing for an Agent in
the Presense of Adverse Selection and Moral Hazard, J. Econ. Theory 61, 302-330.

Blair, B. and Lewis,T. (1994), Optimal Retail Contracts with Asymmetric Infor-
mation and Moral Hazard, mimeo, University of Florida, RAND J. of Econ.,forthcoming.


Clinton,


William (1993),


The President's Health Security Plan, Times Books.


Comanor, W. and H. Frech (1985), The Competitive Effects of Vertical Agree-
ments?, American Economic Review 75, 539-546.


Diamond, Peter (1992),
60, 1233-1254.


Organizing the Health Insurance Market, Econometrica


Dranove, David, Shanley, Mark, and
petition Wasteful? RAND J. Econ. 23, 247


Carol Simon (1992), Is Hospital Com-


Dranove, David and William White (1994), Recent Theory and Evidence on
Competition in Hospital Markets, Journal of Economics and Management Strategy
3, 169-210.


Eaton, J. and
rica 58, 637-60.


Engers (1990),


Intertemporal Price Competition, Economet-


Encinosa, William (1994), Optimal Hospital Capital Structure under Negotiated
Prices, mimeo, University of Florida.


Encinosa, William and
Optimal Prudency Review,


David Sappington (1993), Towards a Benchmark for
Journal of Regulatory Economics, forthcoming.










Fraysse, J. (1993), Common Agency: Existence of
of Two Outcomes, Econometrica 61, 1225-29.


an Equilibrium in


the Case


Fudenberg, D. and Tirole, J. (1991), Game Theory, MIT


press.


Gal-Or, E. (1991a), A Commom Agency with Incomplete Int
Econ. 22, 274-86.
--(1991b), Optimal Franchising in Oligopolistic Markets with
International Journal of Industrial Organization 9,365-388.


formation,


RAND J.


Uncertain Demand,


--(1994), Excessive Investment in Hospital Capacities, Journal of Economics and
Management Strategy 3, 53-70.


Ginsburg, Paul (1988), Public Insurance Programs:
Health Care in America, ed. Frech, H., 179-220.


Medicare and Medicaid, in


Glazer, Jacob, and Thomas McGuire (1994), Payer Competition and Cost Shift-
ing in Health Care, Journal of Economics and Management Strategy 3, 71-92.

Hackey, Robert (1993), New Wine in Old Bottles: Certificate-of-Need Enters the
1990s, Journal of Health Politics, Policy and Law 18, 927-35.


Hall,R. and
nomic Papers


SHitch (1939), Price Theory and Business Behavior,
12-45.


Ippolito,


tion.


(1988),


Washington, DC,


Resale Price Maintenance:


Federal Trade Commission.


Ivaldi
mimeo


,M.
.. IDEI


and Martimort,
. Toulouse.


(1993),


Competition


under


Nonlinear


Pricing,


Katz, M.
Willig, eds.


(1989), Vertical Contractual Relations, in R.
The Handbook of Industrial Organization, New


Schmalensee and R.
York: North Holland.


Kopit, W., and McCann, R. (1988), Towards a Definitive Anti-trust Standard for
Non-profit Hospital Mergers, Journal of Health Politics, Policy and Law 13, 635-62.


Laffont, J. and Tirole, J. (1986), Using Cost (
Journal of Political Economy 94, 614-41.
--(1990), The Regulation of Multiproduct Firms,
37-66.


observation


Part


J. c


to Regulate Firms,

,f Public Econ. 43,


--(1990a), Adverse Selection and Renegotiation in Procurement, Review of Eco-
nomic Studies 57, 597-626.

Lafontaine, F. (1993), Contractual Arrangements as Signalling Devices: Evidence
from Franchising, Journal of Law, Economics, and Organization 9(2), 256-89.


Oxford Eco-


Economic Evidence


from Litiga-










Lewis, T. and Sappington, D.(1988), Regulating a Monopolist with
Demand, American Economic Review 78, 986-98.
--(1989a), Countervailing Incentives in Agency Problems, J. Econ. Theo


-(1989b),
69-84.
-(1991),


Unknown


ry 49, 294-


Inflexible Rules in Agency Problems, American Economic Review


Technological Change and the Boundaries of the Firm, American Eco-


nomic Review, 81, 887-900.
--(1992), Incentives for Conservation and Quality-Improvement by Public Utilities,
American Economic Review 82, 1321-40.
--(1994), Insurance, Adverse selection, and Creamskimming, Journal of Economic
Theory, forthcoming.


Ma, Ching-to Albert (1994), Health Care Payment Systems: Cost and
ity Incentives, Journal of Economics and Management Strategy 3, 93-112.


Qual-


Ma, Ching-to Albert, and Thomas McGuire (1993), Paying for Joint Cost
in Health Care, Journal of Economics and Management Strategy 2, 71-95.


Martimort, D. (1992),
et de Statistique 28, 1-37.
--(1993), Exclusive Dea
ory, mimeo, IDEI, Toulou
--(1994),Multiprincipal
zations, mimeo, IDEI anc


Multi-Principaux avec Anti-Selection, Annales d'Economie

ding, Common Agency, and Multiprincipal Incentive The-
ise.
Charters as a Safeguard Against Opportunism in Organi-
1 INRA-ESR.


Martimort, D. and L. Stole (1993),
mon Agency Games, mimeo.

Maskin, E. and J. Tirole (1988), A
petition, Econometrica 56, 571-600.

Mathewson, F. and R. Winter (198
ments: Comment, American Economic


A Note on the Revelation Principle in Com-


Theory of Dynamic Oligopoly, II: Price Com-


7), The Competitive Effects of Vertical Agree-
Review 77, 1057-62.


McManis, G. (1990), Competition's
Modern Health Care 20, 57-58.


Failure Means It's


Time for Collaboration,


Merrill, Jeffrey (1994),


The Road to Health Care Reform, Plenum Press.


Mezzetti, C. (1993), Common Agency with Horizontally Differentiated Principals:
Regulating a Multinational Firm, mimeo, University of North Carolina.

Newhouse, Joseph (1988), Has Erosion of the Medical Marketplace Ended?, Jour-
nal of Health Politics, Policy and Law 3,, 263-78.
--(1994), Symposium on Health Care Reform, Journal of Economic Perspectives 8:3.


I









Posner, R. (1977), The Rule of Reason and the Economic Approach:
on the Sylvania Decision, University of Chicago Law Review 45, 1-20.


Reflections


Prospective Payment Assessment Commission (1993), Medicare and the Amer-
ican Health Care System: Report to Congress, Washington, D.C.


Relman, Arnold (1989),
view 92, 30-40.


Confronting the Crisis in Health Care,


Technology


Rey, P. and J.
nomic Review 76


Tirole.
921-939.


(1986),


The Logic of Vertical Restraints, American Eco-


Roberts, Marc (1993),
plained, Doubleday.


Your


Money


or Your


Life:


Health


Care


Crisi


Robinson, J. and Luft, H. (1985), The Impact of Hospital Market Structure
on Patient Volume, Average Length of Stay, and the Cost of Care, Journal of Health
Economics 4, 333-56.

Rogerson, William (1994), Choice of Treatment Intensity by a Nonprofit Hos-
pital Under Prospective Pricing, Journal of Economics and Management Strategy 3,
7-51.

Romano, R. (1994), Double Moral Hazard and Resale Price Maintenance, RAND
Journal of Economics, forthcoming.

Schwartz, M. (1987), The Competitive Effects of Vertical Agreements: Comment,
American Economic Review 77, 1063-68.


Simpson, J. (1985), State Certificate-of-Need Programs: The Current Status, Amer-
ican Journal of Public Health 75, 1225-29.


Starr, Paul (1994), The Logic of Health Care Reform,


Stigler, G. (1947), The Kinky Oligopoly
nal of Political Economy 55, 442-444.


Whittle Books.


Demand Curve and Rigid Prices, Jour-


Stole, L.
of Chicago.


(1992),


Mechanism Design


under Common Agency,


mimeo,


University


Sweezy, P.
Economy 47,


(1939),
568-73.


Demand


under Conditions of Oligopoly,


Journal of Political


Telser, L. (1960), Why Should Manufacturers
and Economics 3, 86-105.


Want Fair Trade?,


Journal of Law


Thorpe, Kenneth (1993), The American States and Canada: A Comparative Anal-









BIOGRAPHICAL SKETCH


William Encinosa, III,


was born in


Tampa, Florida, in


1966.


He received his


B.A. in Mathematics at the University of South Florida in 1988, and his M.A.


Mathematics at the University of Florida in 1990.


He entered the doctoral program


in the Economics Department at the University of Florida in 1991, and expects to


receive a Doctor of Philosophy


degree in May


1995.


Encinosa has accepted


the position of Robert


Wood Johnson Scholar in Health Policy at the University of


Michigan-Ann Arbor.









I certify that I have read this study and that in my opinion it conforms to accept-
able standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.


David E. M. Sappington, Chairman
Lanzillotti-McKethan Eminent Scholar
and Professor of Economics
I certify that I have read this study and that in my opinion it conforms to accept-
able standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

Tracy Lewis
James Walters Eminent Scholar of
Entrepreneurship and Professor
of Economics
I certify that I have read this study and that in my opinion it conforms to accept-
able standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.

Jonathan Hamilton
Associate Professor of Economics
I certify that I have read this study and that in my opinion it conforms to accept-
able standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.


David Brown
Nationsbank Associate Professor
of Finance, Insurance, and
Real Estate
This dissertation was submitted to the Graduate Faculty of the Department of
Economics in the College of Business Administration and to the Graduate School
and was accepted as partial fulfillment of the requirements for the degree of Doctor
of Philosophy.
May 1995














L D3
1780
1993










U II I Iiiii iiiii I IIII II lIII i
3 1262 08553 8832