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Essays on the economics of vicarious liability

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Essays on the economics of vicarious liability
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Garmon, Christopher, 1969-
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English
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vii, 104 leaves : ill. ; 29 cm.

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Subjects / Keywords:
Accidents ( jstor )
Civil negligence ( jstor )
Federal preemption ( jstor )
Financial investments ( jstor )
Health maintenance organizations ( jstor )
Independent contractors ( jstor )
Malpractice ( jstor )
Physicians ( jstor )
Vicarious liability ( jstor )
Wage contracts ( jstor )
Dissertations, Academic -- Economics -- UF ( lcsh )
Economics thesis, Ph. D ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1997.
Bibliography:
Includes bibliographical references (leaves 101-103).
Additional Physical Form:
Also available online.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Christopher J. Garmon.

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University of Florida
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ESSAYS ON THE ECONOMICS OF VICARIOUS LIABILITY



















BY

CHRISTOPHER J. GARMON












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 1997














ACKNOWLEDGMENTS

I have benefitted immeasurably from the help and support of many people while completing this dissertation. It goes without saying that I could not have completed this dissertation without the help of my advisory committee. Dr. David Sappington made numerous, valuable suggestions on various drafts, always prodding me to give more intuitive explanations of my results. Dr. Steven Slutsky was always unselfish with his time, helping me understand the intuition of complex maximization problems. Most of all, I would like to thank, my advisor, Dr. Tracy Lewis, for his many illuminating insights, his constant encouragement throughout (but particularly in the less productive phases of my research), and his never ending patience with my often stubborn mind. I learned a great deal under his tutelage. A.Iso, much of my interest in the economic effects of laws and institutions was gained in the courses I have taken with Drs. Lewis, Sappington, and Slutsky.

I would like to thank my officemate and friend, Michael Blake, for his support and encouragement and for lending an ear when the sense of my results was eluding me. I would also like to thank Dr. Sanford Berg, Dr. Margaret Byrne, Dr. Glenna Carr, Dr. Jonathan Hamilton, and Dr. Jeffery Harrison for their helpful suggestions.

Finally, I would like to thank my parents and Andie for their love and support which Sustained me these past four years.














TABLE OF CONTENTS


ACKNO W LED GM EN TS .............................. ................ 11

L IST O F F IG U R E S ................... .............................. ., v

A B S T R A C T . . . . . . . . . . . . . . v i

CHAPTERS

I IN T R O D U C T IO N ... ............................................... 1

2 VICARIOUS LIABILITY AND BARGAINING POWER .................... 6
2 .1 In tro d u ctio n . . . . . . . . . . . . 6
2.2 Vicarious Liability Benchmark M odel .............................. 9
23 Vicarious Liability with Variable Bargaining Power .................. 17
2.4 C om parison of M odels ........................................ 23)
2 .5 C o n clu sio n . . . . . . . . . . . . 2 7
A 2. 1: Proof of Theorem 2.1 ....................................... 28
A2.2- Proof of Theorem 2.2 ....................................... 32
A23 : Proof of Theorem 2.3 ......... ....................... ..... 3 3
A 2,4- Proof of Theorem 2.4 ........................ .............. 34
A 2,5 Proof of Theorem 2.5 ...................................... 33 5

VICARIOUS LIABILITY, NEGLIGENCE, AND MONITORING ............ 3 6
3 .1 Intro du ctio n . . . . . . . . . .. 3 6
3.2 Collusion-Proof Negligence and Vicarious Liability ...................
3.3 M onitoring and Vicarious Liability ............................... 45
I Benchmark Vicarious Liability M odel ..................... 45
).3.2 Vicarious Liability and Endogenous Monitoring .............. 49
.3.4 C o n clu sio n . . . . . . . . . . 57
A 3. I -. Proof of T heorem 3.1 ....................................... 57
A 3.2: Proof of Theorem 3.2 ........................ .............. 58
A ')'.' Proof of Theorem 3.3 ....................................... 61




iii







4 AVOIDING VICAR10US LIABILITY: THE INDEPENDENT CONTRACTING
RULE AND THE ERISA PREEMPTION CLAUSE .................... 67
4 .1 Intro du ctio n . . . . . . . . . . . 67
4.2 Vicarious Liability and the Independent Contracting Rule ........... 68
4.3 The Efficiency of the IC Rule and Its Exceptions .................... 71
4 .' ).1 T he M o del . .. . . . . . . . . .. 7 1
4.3,2 O bservable C are ......................... ........... 73
4.3.3 U nobservable Care .................................. 74
4. 3 ). 4 Effi ciency of the I C Rule ............................... 78
4.3.5 The Efficiency of the Exceptions to the IC Rule .............. 79
4.4 Vicarious Liability, Medical Malpractice, and the ERISA Preemption Clause
. I . . . I . I . . . 8 1
4.5 Efficiency of the ERISA Preemption Clause ........................ 86
4 .6 C o n clu sio n . . . . . . . . . . . . 9 2
A4,0- Legal Definition of a Servant ... ............. ............... 9 -)
A 4.1 Proof of Theorem 4.1 ....................................... 94
A4.2: Proof of Theorem 4.2 ....................................... 95
A4.3: Proof of Theorem 4.3 ....... ............................... 95
A 4.4 Proof of Theorem 4.4 ....................................... 96
A 4.5: Proof of C orollary 4.5 ...................................... 97

5 CONCLUDING REMARKS AND EXTENSIONS ......................... 99

R E FE R E N C E S ................. ................................... 10 1

BIOGRAPH ICAL SKETCH ........................................... 104





















iv











LIST OF FIGURES

F ig u r e I . . . . . . . . . . . . . 1 6

F ig u r e 2 . . . . . . . . . . . . . . 2 5

F ig u r e 3 . . . . . . . . . . . . . . 5 1









































v










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

ESSAYS ON T14E ECONOMICS OF VICARIOUS LIABILITY By

Christopher J. Garmon

August, 1997

Chairman- Professor Tracy Lewis
Major Departmenv Economics

This dissertation, a compilation of three essays, investigates the economic

efficiency of vicarious liability relative to direct liability when the former is used to solve the judgement-proof problem, The first essay analyzes how the relative bargaining power of the principal and agent affects vicarious liability's efficiency in preventing accidents when the agent is judgement-proof When the agent has no bargaining power, vicarious liability induces a more efficient level of care than direct liability when the agent is judgement-proof In addition, it is shown that the preventive care induced by vicarious liability 'increases as the agent's bargaining power increases.

The second essay investigates the accident-preventing efficiency of various liability rules when the principal can monitor the agent's care. It is shown that strict vicarious liability induces the same level of preventive care as strict joint liability and coltusion-proof negligence. The paper also investigates the efficiency of vicarious liability when the principal's level of monitoring is endogenous. It is shown that vicarious liability induces vi







monitoring if the agent is sufficiently judgement-proof and if monitoring is not too expensive. In addition, preventive care when monitoring is possible is at least as great (and often greater) than that induced without monitoring. Finally, it is shown that the principal does not gain by using ex post investigation instead of ex ante monitoring.

The third essay explores two tactics firms use to avoid vicarious liability: the

Independent Contracting (IC) Rule and the ERISA Preemption Clause. This paper shows that the use of a judgement-proof independent contractor to avoid liability leads to insufficient accident-preventing care. It is shown that the exceptions to the IC rule are justifiable, both ex ante and ex post, on efficiency grounds. This paper also shows that, under the protection of ERISA, a health maintenance organization will not only authorize too few medical tests and procedures, but will require an insufficient level of care from the physician. This result is generalized to dispel the belief that direct liability induces excessive care in avoiding an accident while producing too little output.





















vii













CHAPTER 1: INTRODUCTION



Vicarious liability occurs when one party causes an accident and another party is held liable for at least a portion of the damages. As a rule for assigning liability and recovering damages, vicarious liability is used by the courts in many different contexts. For example, fleet companies may be held liable for accidents caused by their truck drivers 16] and oil companies may be held liable for accidents occurring at their franchised gas stations [4],[5]. Recently, vicarious liability has been applied in some areas that were previously exempt. For example, hospitals and health maintenance organizations have been found liable for the malpractice of independent physicians working, on their premises [11], [21 ]. In addition, banks now face an increased threat of liability for environmental damages caused by their debtors [ 17],[27]. There is also a trend within state legislatures to make parents liable for damages caused by their children [6].

When applying vicarious liability, courts usually justify their action using one of three arguments [10]. First, under the "deep pockets theory," vicarious liability is seen as beneficial because it allows the victim to be fully compensated for the inflicted damages. Second, vicarious liability is used to induce the principal (e.g,, employer) to be more careful in selecting and monitoring her agents (e.g., employees). Third, the "modern justification" sees vicarious liability "as a means of allocating, to business enterprises the


I







2

costs of accidents caused by those enterprises"' to induce the efficient amount of accidentpreventing care.

The first justification highlights a common factor in virtually all vicarious liability cases: the "judgement-proof problem." Vicarious liability is almost always applied in cases in which the party responsible for the accident has insufficient assets to fully compensate the victim for his or her damages. Indeed, if the accident- causing agent has sufficient assets for compensation, there is no reason for the victim to seek compensation from a third party. Thus, a feature prevalent in most vicarious liability cases is a judgement-proof agent.

The second justification highlights the fact that, in many vicarious liability cases, the behavior of the accident-causing agent is difficult for any party to observe. Vicarious liability is applied by the courts with the belief that, of all parties, the principal is best able to monitor the agent. Thus, vicarious liability is seen as a way to induce the principal to monitor the agent, even when monitoring is difficult and costly.

The third Justification highlights the commonly held legal belief that accidents are an "externality" associated with many business activities. If a principal hires an agent to complete a productive activity which is potentially damaging to a third party, and only the agent can be held liable in the event of an accident, then the principal-agent business enterprise may avoid some of the potential accident costs which are bom by society. For this reason, the principal-agent enterprise may take too little care in preventing an




[10], p. 183.









accident. From this point of view, vicarious liability is seen as a way of assuring that the total accident costs are born by the principal-agent enterprise in the event of an accident, so the proper amount of care will be taken to avoid an accident.

This dissertation investigates the accident-preventing efficiency of vicarious liability relative to direct liability (where the agent alone is liable) when the agent is Judgernent-proof and his actions may be difficult to observe. The dissertation proves that vicarious liability is more efficient in preventing accidents than direct liability in most contexts in which it is applied. In addition, vicarious liability can sometimes induce the principal to expend resources to monitor the agent. Finally, common methods of avoiding vicarious liability are shown to produce various inefficiencies in accident prevention.

In particular, Chapter 2 analyzes how the relative bargaining power of the principal and agent affects vicarious liability's efficiency in preventing accidents when the agent is judgement-proof When the agent has no bargaining power, vicarious liability induces a more efficient level of care than direct liability when the agent is judgement-proof In addition, it is shown that the preventive care induced by vicarious liability increases as the agent's bargaining power increases. Thus, vicarious liability is more efficient than direct liability regardless of the principal and agent's relative bargaining power.

Chapter 3 investigates the accident-preventing efficiency of various liability rules when the principal can (imperfectly) monitor the agent's care. It is shown that strict vicarious liability induces the same level of preventive care from the agent as strict joint liability and collusion-proof negligence. The chapter also investigates the efficiency of strict vicarious liability when the principal's level of monitoring is endogenous. It is shown







4

that vicarious liability induces monitoring of the agent if the agent is sufficiently judgement-proof and if monitoring is not too expensive. In addition, preventive care when monitoring is possible is at least as great (and often greater) than that induced when monitoring is not possible. Finally, it is shown that the principal does not gain by using ex post investigation instead of ex ante monitoring.

Chapter 4 explores two tactics firms use to avoid vicarious liability- The

Independent Conti-acting Rule and the ERISA Preemption Clause. The "Independent Contracting Rule," the general legal rule courts use to impose vicarious liability, states that principals are vicariously liable for the torts of their "servants," but not those of independent contractors. This gives principals an incentive to avoid vicarious liability with the use of an independent contractor. The chapter shows that the use of a judgementproof independent contractor to avoid liability leads to insufficient accident-preventing care. Two categories of exceptions to the Independent Contracting Rule have emerged in recent court rulings. The chapter shows that these exceptions are justifiable on efficiency grounds, Ex ante, these exceptions discourage the use of an independent contractor to avoid liability. Ex post, these exceptions induce the efficient care level in some principalindependent contractor relationships.

Recently, health maintenance organizations (MMOs) have begun to use a

preemption clause in the Employee Retirement Income Savings Act of 1974 (ERISA) to avoid vicarious liability for physician malpractice. Chapter 4 shows that, under the protection of ERISA, the HA40 will not only authorize too few medical tests and procedures, but will require an insufficient level of care from the physician. This result is







5

generalized to dispel the commonly held belief that direct liability induces the agent to take excessive care in avoiding an accident while producing too little output. Direct liability induces too little care and too much production relative to the social optimum when the agent is judgement-proof



A preliminary comment about the content of subsequent chapters is warranted at this time. Each substantive chapter is written to be a self-contained analysis of an issue related to the efficiency of vicarious liability. For this reason, the reader may notice some interchapter redundancy. In particular, a benchmark model of vicarious liability is contained in all three chapters as a basic framework for each chapters analysis of vicarious liability. This is done because this benchmark model gives the best understanding of the basic workings of a principal-agent relationship under vicarious and direct liability. Thus, it serves as the best foundation for the models contained in each chapter.














CHAPTER 2: VICARIOUS LIABILITY AND BARGAINING POWER



2.1 Introduction

Vicarious liability is applied by the courts in many different business contexts, from HM0 liability for physician malpractice to bank liability for environmental damages. Given the scope of vicarious liability, it is natural to question its efficiency in preventing accidents. In many circumstances, vicarious liability and direct liability (in which the agent alone is liable) are identical in their ability to deter accidents. For instance, if both the principal (e. a_ employer, hospital, lender, etc,) and the agent (e.g., employee, physician, firm, etc.) have adequate wealth to cover the damages from an accident, if there are no information asymmetries, and if contracting costs are negligible, then vicarious liability and direct liability will induce the same level of preventive care from the agent. Under vicarious liability, the principal can simply pass along the liability to the agent through the wage contract and make the agent's incentives identical to those under direct liability. This equivalence can also be thought of as an application of the famous Coase Theorem [9].

However, vicarious liability is applied most often in cases where the agent does not have sufficient wealth to satisfy a liability claim (often referred to as the "judgement-proof problem") and where the agent's preventive care is difficult to monitor. In these cases, the efficiency of vicarious liability is not as clear. In the last fifteen years, a few articles have


6







7

analyzed the efficiency of vicarious liability in this context. The conclusions of these studies are mixed. Shavell (1987) [26] shows that under vicarious liability, if the agent is judgement-proof and the principal cannot observe the agent's care, the agent "may take suboptimal care, but at least as much as he does when he alone is liable."' Kornhauser (1982) [ 13] reaches a similar conclusion, but with more qualifications: "The agent will clearly take less care [under direct liability] when the agent is close to risk-neutral, has limited assets, a small reservation wage, and the damages are greatly in excess of his assets. ,2 On the other hand, Sykes (1984) [29] argues that vicarious liability will most likely induce le.5,5 preventive care than direct liability in this context. Pitchford (1995) [20] proves this assertion in the context of a lender liability model.' Considering the similarities in these authors' models and assumptions, the conflicting results are particularly puzzling,

One possible explanation for these opposing results is that the authors adopt

different assumptions about the relative bargaining power of the principal and the agent. Both Shavell and Kornhauser assume implicitly that the principal can make a take-it-orleave-it ofFer to the agent (i.e., the agent has no bargaining power). However, Syke's argument that vicarious liability may be less efficient than direct liability is predicated on the assumption that the agent may have some bargaining power:

In labor markets that are not perfectly competitive, some agents possess
bargaining power or special skills that enable them to obtain a fee in excess
of their reservation wage--an economic rent. Because vicarious liability


[26] p. 18 5
2 [13] p.1363

' Other papers which relate to this topic include [8], [15], [18], [25], and [28].







8

reduces the profitability of the enterprise relative to its profitability under
personal liability, principals may succeed in bargaining away some of these rents ... Then, because vicarious liability reduces the demand for agents' services, the market will tend to equilibrate at a lower wage rate and thus
provide smaller incentives to avoid losses. Thus, although potentially
insolvent agents invest inefficiently little in loss avoidance under personal liability, vicarious liability conceivably aggravates the inadequacy of their
loss-avoidance incentives.'

5
In a subsequent footnote Sykes claims that Kornhauser's opposing result emanates from the "highly restrictive" assumption that the agent has no bargaining power. In addition, Pitchford shows that vicarious liability can be less efficient than direct liability in preventing, accidents when the principal has no bargaining power. In his model of lender liability, Pitchford assumes that the lending industry is perfectly competitive and, therefore, each lending institution earns zero economic profit. Thus, if vicarious liability is imposed on a lending institution in the event of an accident, the lending institution will require an increased premium from the agent in the no-accident state in order to break even. This increased premium in the no-accident state will reduce the agent's incentives to avoid an accident by making the no-accident state relatively less attractive to the agent. Therefore, vicarious liability may be less efficient than direct liability when the principal has little bargaining power relative to the agent.

While a close reading of the previous literature suggests that bargaining power

plays a role in the efficiency of vicarious liability, no analysis has characterized the nature of this relationship. This paper will analyze how the relative bargaining power of the



[29] pp. 1248-9.

ibid, Footnote 450, p. 1249,







9

principal and agent affects vicarious liability's efficiency in preventing accidents. Specifically, this paper will first present a benchmark principal-agent model describing the efficiency of vicarious liability when the agent has no bargaining power. In this case, it will be shown that vicarious liability induces a more efficient level of care than direct liability when the agent is judgement-proof A closely related model is then presented in which the agent's bargaining power is allowed to vary. Contrary to Sykes and Pitchford, it will be shown that the preventive care induced by vicarious liability increase.5 as the agent's bargaining power increases. This is because the agent's share of the enterprise's joint profit increases with his bargaining power. An agent with bargaining power therefore has more to lose in the event of a liability claim on the principal and her business. For this reason, an agent with bargaining, power is apt to be more careful in preventing accidents than an agent with little bargaining power, Furthermore, this implies that vicarious liability is more efficient than direct liability regardless of the principal and agent's relative bargaining power.

The chapter is organized as follows. Section 2.2 presents the benchmark model of vicarious liability in which the agent has no bargaining power. Section 2.3 contains the closely related model in which the bargaining power of the agent is allowed to vary parametrically, Section 2.4 compares the results of these models and discusses the effects of bargaining power on preventive care when the principal is vicariously liable.

2.2 Vicarious Liability Benebmark Model In order to understand how bargaining, power affects the efficiency of vicarious liability, it is useful to look first at an extreme case in which the agent has no bargaining







10

power. In this case, it will be assumed that the principal can make a take-it-or-leave-it offer to the agent (i.e., the agent has no power to negotiate the terms of the contract).

Consider a principal who hires an agent to complete a productive activity. This

activity will produce a revenue of R for the principal. However, there is also a probability p that the agent, while completing this activity, will cause an accident. The probability of an accident is a function of the precaution or care x the agent takes when completing the activity. It is assumed that increasing care decreases the probability of an accident at a decreasing rate (p'(x)O). The agent's personal marginal cost (or disutility) of taking care is assumed to be constant and is normalized to unity. In addition, assume the agent's initial wealth is limited to A.

The timing of the principal-agent relationship is as follows. First, both the principal and the agent learn the principal's vicarious liability L in the event of an accident. Second, the principal offers a contract to the agent that specifies a non-accident wage of w" and an accident wage of w, Third, the agent chooses to accept or reject the principal's contract offer. If the aaent accepts the contract, the agent then chooses his level of care, x, in the activity. This care cannot be observed by the principal or the courts. Fourth, the state of the world is realized (either accident or no-accident), the liability payment is collected from the principal in the event of an accident, and the appropriate wage is paid to the agent.

In choosing a contract to offer the agent, the principal solves the following problem:










(ii) T004,_11),-I1=

s (f. () pixvw ( -A->







Constraint (i) is the agent's participation constraint. The agent will only accept the principal's offer if the expected wage net of effort costs is at least as great as the agent's reservation wage (here normalized to zero). Constraint (ii) is the incentive compatibility constraint which reflects the principal's inability to observe the agent's care. Since the principal cannot make the wage contract contingent on the agent's care level, the agent will choose a care level that is personally optimal given the wage contract.' Constraint (iii) reflects the agent's limited wealth and the principal's "right to indemnification." When a principal is found vicariously liable, she has the right to be compensated by the accidentcausing agent [7]. However, this compensation cannot exceed the agent's wealth. Therefore, the agent's accident wage must be at least -A.

In [P], it is implicitly assumed that both the principal and the agent are risk neutral. Kornhauser (1982) [1 31 demonstrated that, if the agent is not judgement-proof, vicarious



6 Actually, an additional condition is needed to insure that the stationary point specified by
(11) is indeed optimal for the agent. This condition is:.
p ()w0-w1) 0

for all x. Since p "(x) > 0, this condition is equivalent to (w, wJ) 0. Yet, since p'(x) < 0, condition (ii) implies (w, w,,) < 0. Therefore, condition (ii) specifies an optimal care level for the agent. See [22] for a thorough discussion of the first-order approach in moral hazard problems.







12

and direct liability have identical efficiency effects regardless of the risk aversion of the agent, Therefore, to isolate the effects of judgement -prooffiess on efficiency, this analysis makes the assumption (common in this literature) that both the principal and agent are risk neutral,

Before characterizing the solution to [P], it will be useful to characterize the

socially optimal care level. Suppose a revenue-producing activity has a potential accident damage of D associated with it. The social welfare of this activity is: S W = R -1) (,Y)D -x



Therefore, the socially optimal care level is given implicitly by:

-p'(x)D -I 0



At the socially optimal care level, the marginal cost of increasing care equals the marginal decrease in expected damage associated with increasing care. Let this care level be denoted by x*(D).

For the vicariously liable principal in [P], the profit-maximizing level of care is x*(L) (i.e., that which is socially optimal if the liability, L, equals the damages, D). The principal can induce this level of care by setting Wn w, = L. As mentioned before, the principal simply passes along the liability to the agent through the wage contract by penalizing the agent L in the event of an accident. However, as the principal's liability increases, there comes a point (denoted by L = K) at which passing the liability to the agent becomes costly to the principal. This occurs because of the agent's limited wealth.









Recall that the principal can take no more than the agent's wealth through indemnification (w, -A). Therefore, in order to induce x*(L) from the agent, the agent's no-accident wage (wJ, must be at least L A. However, if L A > x -(L) + p(x*(L))L, then the principal can only induce x*(L) from the agent by giving the agent an expected wage above his reservation wage (see constraint (i) in [P]). Therefore, if L K, the principal can costlessly pass on the liability, L, to the agent. If L > K, then the principal faces a tradeoff: she can maximize the joint surplus only by sacrificing some of her share of the surplus. Faced with this tradeoff, the principal will sacrifice less profit by inducing a suboptimal care level from the agent.

To be specific, the principal is faced with the following trade-off for liability levels greater than K. At one extreme, the principal could continue to pass the full liability onto the agent through the contract inducing the profit-maximizing care (x*(L)). However, the principal incurs a cost of L A [x*(L) + p(x'(L))L] when pursuing this approach, since the principal must give the agent a share of the Joint profits in order to fully pass the liability onto him. At the other extreme, the principal could simply offer the contract which is profit -maximizing for L =K (I.e., freeze the accident penalty at K). This approach allows the principal to avoid giving the agent an economic rent. However, this will induce a level of care from the agent that is too low given the principal's vicarious liability of L. The principal will, therefore, incur an expected Cost Of [p(x*(K)) p(x*(L))]L since the probability of an accident will be too high given this approach.

At first (i.e., for L e (K,p]), the latter approach is least costly for the principal, so the principal sets w,, w, = K, even though L > K. Eventually (i.e., for L > p), this







14

approach leads to a probability of an accident that is too great relative to the principal's liability, L. In this case, the principal uses a combination of the two strategies. The principal gives the agent a share of the joint profits to induce a higher level of care, but not enough to induce x*(L). (In other words, the accident penalty will fall between K and L.) Therefore, even though the induced care is inefficient for L > K, it is never less than x*(K). In particular, it is non-decreasing in L, reflecting the principal's desire to pass on as much of the liability as possible while protecting her profits. This is summarized in the following theorems.

Theorem 2.1: Let K be defined implicitly by x*(K) + p(x*(K))K =K A, p be defined implicitly by R(p) + (P3+l)'p(R(p))p = ([3+)9'p A, and let c be implicitly defined by V([) = 0 where V is the maximized value function of [P]. (In other words, K is the liability level at which the agent's wealth constraint begins to bind, p is the liability level at which the agent's participation constraint no longer binds, and is the liability level at which the expected gains from trade are no longer positive.) The care x which solves [P] is given by:7


x(L) =,y*(L) .for Le[O,K]
=x*(K) forL G(K,p)
= (L) for Le[p,"7]
= 0 for L>,:


where R(L) is implicitly defined by:


7 (ii) IfK > then the care x which solves [P] is given by: x(L) = x *(L) for Le[0,= 0 for L>r
This occurs when A is large (i.e. the agent has substantial wealth).







15





and:

Q3x-( -P(-X))p "(,Y) >o







Proof: See Appendix A2. 1 Theorem 2.2: (i) For all L 0, x *()>: (L)



(ii) For all L _> 0, dx* >0 dY>0
dl, dL



In other words, x* and R are both strictly increasing in L. Therefore, the care which solves [P] is non-decreasing in L. Proof: See Appendix A2.2.

Theorems 2.1 and 2.2 characterize the care induced by vicarious liability in this benchmark case in which the agent has no bargaining power. How do these care levels compare with those induced by direct liability? If the agent is directly liable, he will exert the socially optimal amount of care (x*(L)) as long as the liability is no greater than his







16
X Care w/ Vicarious Liability
Care w/ Direct Liability


x*(L)
x(L)











A T L
Figure 1


wealth (L A). However, if the agent is potentially judgement proof (L > A), he will exert just x*(A) since the penalty he receives in the event of an accident is only the loss of his wealth, A.

In Figure 1, the care levels induced by vicarious and direct liability are juxtaposed for all liability levels. As mentioned previously, when the agent is not judgement-proof (D = L : A), vicarious and direct liability lead to the same levels of care. The difference between these two liability schemes occurs when the agent is judgement-proof (D = L > A). From Figure 1, it is clear that vicarious liability is more efficient than direct liability in this case. When the accident damages exceed the agent's wealth by a relatively small amount (D c- [AK]), vicarious liability equal to the damages will induce efficient care whereas direct liability will not. In this region, the principal can still costlessly pass on the total liability to the agent through the wage contract, because the agent's wealth shortfall







17

(L A) is less than the no-accident wage required by the agent for participation (x*(L) + p(x*(L))L). However, direct liability applied in this region results in a penalty (A) that is less than the damages and, thus, direct liability induces insufficient care.

For D = L > K, vicarious liability will no longer result in efficient care. However, vicarious liability will still induce a larger, more efficient level of care than that induced by direct liability. This is because care under vicarious liability is non-decreasing in this region while care under direct liability is constant at x*(A). Essentially this is due to the principal's increased incentive to reduce the probability of an accident as her vicarious liability increases. Thus, she will increase the agent's incentive to take care, although not perfectly. Under direct liability an increase in liability will not result in an increased penalty for the agent and, therefore, it will not result in increased care. Therefore, vicarious liability is more efficient than direct liability in preventing accidents when the agent has no bargaining power and is j udgement-proof

2.3 Vicarious Liability with Variable Bargaining Power

The previous section illustrates the effects of vicarious liability on preventive care when the agent has no bargaining power. In this case, vicarious liability is more efficient than direct liability in preventing accidents. Is this still true when the agent has bargaining power? How does preventive care under vicarious liability change as the agent's bargaining power increases In this section, a model with variable relative bargaining power is presented to answer these questions.

The model in this section is identical to the model in section 2.2 with the following exceptions. First, there are many agents, instead ofjust one. Second, before learning the







18

potential liability she faces, the principal makes a sunk "safety" investment, 1. This could be thought of as training in safety procedures for the agent or the purchase of equipment which assists the agent in taking preventive care. Along with care, the safety investment reduces the probability of an accident at a decreasing rate (p,,, p, < 0, p,,,, pjj > 0). However, the safety investment is specific to one agent (denote him as the primary agent

(PA)). If it is used with any other agent, its effectiveness is equivalent to an investment of al (a e [0, 1]), Since the safety investment is sunk, a can be considered an exogenous parameter and I can be normalized to one. In addition, assume p(lx) = p(x) from Section

2.2.

The third difference between this model and the previous model concerns the

principal's choice of a contracting agent. After the principal and agents learn the principal's liability, L, the principal chooses whether to contract with PA or with one of the many other agents. If the principal contracts with PA, it is assumed that the contract is the result of a bargaining process consistent with Nash's Axioms of Bargaining.' In other words, it Is assumed that the resulting contract maximizes the product of the principal and agent's net returns from trade with each other. If the principal contracts with one of the other agents, it is assumed that the principal can make a take-it-or-leave-it offer. Since there are many identical alternative agents, each individual agent has no bargaining power with the principal, As in the previous model, the principal cannot observe the care of any agent, nor can agents observe each other's care.




See [23].







19

Before describing the problem the principal faces in this model, an additional

comment is needed about the sunk safety investment assumption. The safety investment is assumed to be exogenous to abstract from questions about the principal's optimal safety investment under vicarious liability and the disincentives for specific investment due to the agent's possible opportunism. These are important and interesting issues, but they are left out of this analysis in order to isolate the effects of bargaining power on preventive care under vicarious liability. In this model, the principal's investment and, particularly, its specificity a are used simply to reflect the agent's bargaining power. A specific safety investment is but one of many means by which an agent can become more productive in preventing accidents, In general, a can be thought of as a parameter which reflects any distinctive characteristic of PA relevant to the principal's expected profits. For instance, PA could have an acquired or inherent skill that makes it easier for PA to prevent an accident (e.g., a firm with previous experience disposing hazardous waste or a surgeon with steady hands). Therefore, the probability of an accident for PA is less than that for his colleague agents for a given level of care (p(x) < p(ax) for (X < 1). If a = 1, all agents, including PA, are identical and, thus, PA has no bargaining power. If a = 0, then the specific investment is completely ineffective with agents other than PA, so PA's bargaining power is maximized. Therefore, PA's bargaining power is inversely related to a.

If the principal decides to contract with one of the many alternative agents, she can make a take- it-or-leave-it offer as mentioned before. Therefore, the principal's problem in this case is identical to that presented in section 2.2, except that p(x) is replaced with P(ax):







20

[aP] V(a,L) = Max ,,. [R-p(a,x)wa -(1 -p(a,x))w, -p(a,x)L] s.t. (i) p(a,x)w.+(1 -p(a,x))w, -x> 0
(ii) px(a,x)(wc,-w )-1 = 0 (iii) 14)C > -A



The care level which solves [aP] (denote as x,(L)) is also analogous to that which solves [P]:


xJ(L)= x *(L) fjbr Le[0,K ] = x *(K,) for Lc(K,p) = (L) for LE[p ,t ] = 0 for L>



where xc*(L), 2 ((L), K,, Pa, and c, have definitions analogous to those in section 2.2. As in section 2,2, x(L) reflects the tradeoff the principal faces when the agent is judgementproof When L > K,, the principal induces suboptimal care from the agent because of the principal's tradeoff between maximizing the joint surplus and maximizing the principal's personal share of the surplus.

If the principal decides to contract with PA, then the principal and PA will

negotiate a contract consistent with the Nash bargaining process. Therefore, the problem facing the principal and PA is: BP] V ",(1,L) =Max.,,, [R-(1 -p(x))w -p(x)wo-p(x)L V(a,L)] [(1 -p(x))w +p(x)w -x s.t. (i) p'(x)(w1-w,)-1 = 0
(ii) w, > -A







21

The principal and PA negotiate a contract which maximizes the product of their individual gains from trade net of the opportunity costs of trading with each other. If the principal chose not to contract with PA, she could receive V(c',L) by contracting with another agent. As before, PA's opportunity cost/reservation wage is normalized to zero. As in [P], constraint (i) is the agent's incentive compatibility constraint, which reflects the principal's inability to observe the agent's choice of care. Constraint (ii) reflects the limited wealth of the agent, as before.

A comparison of [caP] and [BP] reveals that the principal will always choose to

contract with PA. Since p(x) p(a,x) for all a c [0, 1], PA holds a cost advantage over all of the other agents. Therefore, for a given level of care, the joint surplus with PA is at least as much as that with any other agent. If the principal chooses to contract with PA, she can capture some of this extra surplus in the bargaining process. Therefore, she receives at least as much profit by contracting with PA as she does with any other agent.

The care level induced when the principal contracts with PA is characterized by the following theorem:

Theorem 2.3: Let Kb be implicitly defined by R+x *(K b) tp(x *(Kb))Kb -V(UKb) = K b-i(1
2

and let 7, be implicitly defined by Vbja,Tb) = 0. (As in Theorem 1, Kb is the liability level at which the agent's wealth constraint begins to bind and trb is the liability level at which the expected gains from trade are no longer positive). For a e [0, 1), the care which solves [BP] is given by:







22

x1,(L) =x*(L) fbr Lc[O,K,,]
=-F,(L) for Lc(K brb]
= 0 for L>u1


where R (L) is implicitly defined by:


-pO( )L I b) b
( O ( .i ) + 1 1p ( F b) )


(0 is the lagrange multiplier for the agent's wealth constraint (ii) and 1iP is the principal's net surplus from trade.)

Proof See Appendix A2.3.

The solution to [BP] is, in many ways, similar to that of [P]. As in section 2.2, care level x*(L) maximizes the joint profits of the principal and agent. Therefore, passing the principal's liability, L, to the agent through the wage contract is optimal for both the principal and the agent if this can be done at no cost to either party. Recall, in section 2.2, the principal faced a tradeoff, in some cases, when deciding how much of the liability to pass on to the agent. IfL > -K, the principal could only maximize the joint profit by sacrificing some of her share of the profit. Therefore, the principal maximized her profits by penalizing the agent less in the event of an accident, thereby inducing suboptimal care. A similar tradeoff faces the principal and agent in [BP] when L > Kb. To see this, it is useful to rewrite condition (1), which implicitly defines Kb, as follows:


R -x *(Kb) -p(x *(Kb))Kb T(a, Kb)
2 +JY (K b) +p(x *(K b ))Kb -- K -







23

In [BP], the principal and agent negotiate a wage contract which maximizes the product of their net profits. This simply means the principal and agent will write a contract which splits the expected joint profits in half, if this is feasible. Therefore, if the wage contract induces the optimal care, x*(L), from the agent, then the agent's no-accident wage will be: vi R-xy *(Z)I-)(x *(L))L -V(a,L) +iX *(L) -ip(x *(L))L (2) ~1 2


Recall that, because the agent's wealth is constrained to A, the no-accident wage must be at least L A in order to induce x*(L) from the agent. Therefore, if




-A> R -x *(L) -p(x *(L))L V(a,L) +X *(L) -ip(x *(L))L

the only wage contracts that induces x*(L) from the agent will also give the agent more than half of the expected Joint surplus. So, again the principal faces a tradeoff when L > Kb. She can negotiate a wage contract with the agent which induces the optimal care only by accepting a share of net profits which is less than the agent's. Instead, the principal and agent will negotiate a contract which gives more equitable profit shares to each, while inducing a suboptimal care level.

2.4 Comparison of Models

Even though they are similar, the solutions to [BP] and [P] differ in two important ways. First, when the agent has bargaining power, the liability level at which the previously described tradeoff first occurs is different from the analogous liability level when the agent has no bargaining power (K # Kb when a 1). Second, when the agent has bargaining power, the care induced when this tradeoff is present is different from that







24

induced when the agent -has no bargaining power (R(L) Rb(A) when u # 1). These observations are described in the following two theorems: Theorem 2.4:

(i) Kt, > K for all a e [0, 1),

(11) K,, increases as the agent's bargaining power increases:.


-~b<0
da




Proof See Appendix A2.4.

The agent's share of the expected joint profit increases with his bargaining power (iLe., it decreases with a). This is because the net surplus (that in excess of what the principal could earn elsewhere) decreases with a. Thus, the agent's no-accident wage, given by (2), increases with the agent's bargaining power (decreases with a). Recall, the no-accident wage must be at least L A to costlessly induce efficient care from the agent. Therefore, as the agent's bargaining power increases, this inducement can be made for larger liability levels. Hence, Kb, in creases as the agent's bargaining power increases. Theorem 2.5:

(i) R 1,(L) >R(L) for all a e [0, 1),

(ii) For L > Kb, the care induced by vicarious liability increases as the agent's bargaining power increases:



da







25



Proof See Appendix A2.5. Again, as the agent's bargaining power increases, so does the agent's share of the expected joint surplus. However, for L > Kb, the costless transfer of the liability from the principal to the agent is not possible. This is because the agent's accident wage can fall no lower than A due to the agent's limited wealth. Since w, = -A in this case, the only way for the agent's profit share to increase with his bargaining power is for the agent's no-accident wage to


X Care w/ VL & Barg. Power
Care w/ VL & no Barg.
Power
Care w/ Direct Liability
x*(L)













A T L
Figure 2


increase. However, this will also make the agent's penalty in the event of an accident (w,, w,,) greater. Therefore, the agent will take more care as his bargaining power increases. Essentially, the agent has more at stake with respect to the success or failure of the







26

enterprise as his bargaining power increases. Hence, the agent has a greater incentive to prevent an accident as his bargaining power increases.

This increased incentive to prevent an accident and the resulting increased care are illustrated in Figure 2. Here the care induced when the agent has no bargaining power (x(L)) is compared with the care induced when the agent has some bargaining power (Xb(L), a < 1). Notice that, with bargaining power, there is a larger range of liability levels for which the efficient level of care is induced (from Theorem 2.4). In addition, for those liability levels in which efficient care is not induced, the care associated with bargaining power is greater than that without bargaining power (from Theorem 2.5). For these reasons, vicarious liability is more efficient when the agent has bargaining power. In addition, the presence of bargaining power increases vicarious liability's superiority over direct liability. This, of course, is due to the agent's increased incentive to take care when his bargaining power is non-negligible. With direct liability, his incentive to take care is capped at a maximum loss of his wealth, A.

Clearly this result contradicts Syke's reasoning that vicarious liability will reduce the agent's loss-avoidance incentives when the agent has some bargaining power, With bargaining power, the agent has a larger stake in the profits of the principal-agent enterprise. If the agent is potentially judgement-proof, vicarious liability exposes more of this profit to liability claims than does direct liability, Therefore, as shown above, vicarious liability will induce greater care from the agent, particularly when the agent has some bargaining power. The result above also suggests that Pitchford's conclusion about the effectiveness of vicarious liability is not robust to contexts other than lender liability.







27

Pitchford illustrates how vicarious liability can reduce incentives for care when the principal belongs to a perfectly competitive industry. The analysis above suggests that Pitchford's result does not hold for other market structures. In particular, if the agent belongs to a perfectly competitive labor market, or if bilateral monopoly prevails, then vicarious liability will increase the agent's incentive to take care.

2.5 Conclusion

When the agent is potentially judgement-proof and his actions are difficult to

monitor, vicarious liability and direct liability produce different incentives for the agent to exert preventive care. In this case, vicarious liability will induce more care from the agent than direct liability. Although not completely efficient, vicarious liability is more efficient than direct liability. This relative advantage of vicarious liability is heightened when the agent has some bargaining power. As the agent's bargaining power increases, so does his share of the joint profit of the enterprise. Therefore, the agent has more to lose in the event of an accident under vicarious liability, so the agent will take more care as his bargaining power increases.

This result implies that vicarious liability can be used by the courts in a variety of different contexts to reduce the likelihood of accidents while fillly compensating the victims of accidents. Since the effectiveness of vicarious liability increases with the agent's bargaining power, vicarious liability is particularly appropriate when applied in situations where the agent is highly skilled (e.g,, physicians) or where agents have collective bargaining power (e.g., unions). In addition, the previous analysis suggests one benefit of employee-owned firms. Employment contracts that incorporate profit-sharing or employee







28

ownership of some kind may induce more preventive care from employees since they have more to lose if the firm is subject to a liability claim.



A2.1: Proof of Theorem 2.1

Using constraint (ii), [P] can be rewritten as follows:


[P)] Max R p(x) p(X)

p' (x)(iii) +)n > -A (0) p'(x)

The first order necessary conditions for a solution to [P'] and [P] are therefore:9


(a) -p'L-1 +(I-X)-P -0 p, =0
(p')2 (p')2
(b) X+0=1
(C) w4 +-L) o (=oif) >o)
1
(di) -+w +A 0 (=0if0>0)

(e) ,0 0



From conditions (b) and (e), it is clear there are three possibilities:

1. 0 = 0 (which implies X = 1),

2. A = 0 (which implies 0 = 1), or

3. 0, X c (0,1).



10 These Kuhn-Tucker conditions are indeed necessary since the Jacobian of the effective constraints has full rank in all of the cases which follow.







29

Case 1. Binding Participation Cons'traint (0 = 0 and = 1)

In this case, condition (a) becomes :

-p'L-I=0



so the care which solves [P] is given by x*(L). From conditions (a) and (c): S= p(x *(L))L +,x *(L)



Therefore, from condition (d): p(x *(L))L +x *(L) L -A (A1)



(Al) reflects the fact that x*(L) solves [P] as long as the agent's wealth constraint does not bind. If, as a result of a binding wealth constraint, the principal cannot set w. w, = L without giving the agent an economic rent (w, > p(x*(L))L + x*(L)), then x*(L) does not solve [P]. Let K equal the liability level L for which (Al) holds with equality. Then x*(L) solves [P] for all L K. Case 2.'Binding Wealth Constraint (X = 0 and 0 =1)

In this case, condition (a) becomes:


Dp'L a(-p)P" F c i ( d
-p (p,)2




Denote the care which this implicitly defines as R(L). From conditions (a) and (d):







30

L
n = _+-A (A2)




Therefore, from conditions (c) and (a): L-A> p(i(L))t +(L) (A3)



(A3) characterizes the liability levels in which only the agent's wealth constraint binds. Let p equal the liability level for which (A3) holds with equality. Then R(L) solves [P] for all L > p.

Case 3: Both Constraints Bind (0, ; e (0, ]))

In this case, conditions (c) and (d) imply:

-I-A -P-+x

p p

Therefore, when both constraints bind, the care which solves [P] is constant at x*(K). From Lemma A2. 1.1 (see below), x('(K) solves [P] for L c (K,p).

Since dC/dL > 0 (see Lemma A2.1.1), there exists a liability level such that R C = 0. Therefore there exists a liability level such that V(L) = 0. Denote this level as 'r. For L >

-, the principal is better off not contracting with the agent. Therefore, for L > U, the principal and agent will not contract and the induced care equals zero. U Lemma A2.1.1 K and p exist and p > K. Proof of Lemma A2. 1.1: Let C = p(x*(L))L + x*(L). To show that i< exists, it is sufficient to show that:







31

dC
-<1
dl

Recall that x'(L) minimizes C, so: dC
-p(x*(L)) < 1 dL


by the envelope theorem.

p is implicitly defined by:

1 -p((p)) +(p) p' (,(p))

To show that p exists, it is sufficient to show that: d -p(k(L)) I d[A +(L)] dL p'((L)) AL



since x(L) is increasing in L.

d 1-p(f(L)) +)di> di d [A+()]
= (1+@3)->- -[A (L)] dL p'(i(L)) dL dL dL



Consider the problem:


Max,, [R-w -p(x)L p(x) xw ),p'(x) s.t. (i) w + p(x) -x 0 p' (x)







32

Constraint (i) will always bind. Hence, in [P'], constraint (i) will not bind only when constraint (iii) binds. Constraint (iii) binds when L > Constraint (i) binds only when L < p. Therefore, p K



A2.2: Proof of Theorem 2.2 i) Since P > 0,


-p'(x *(L))L- 1< -p'(.f(L))L- 1


or


p '(x '(L))>p '((L))


Since p" > 0, this implies x*(L) >x(L) for all L. ii)

dx* p/
-__- >0
dL p"L






dx p' >
>0
dL dp
dx


since second-order sufficient conditions dictate that the denominator is positive. M







33

A2.3: Proof of Theorem 2.3

Using constraint (i), [BP] can be rewritten as follows:


[BP'] Max ,W,, [R-i, +-p(x)(L + I) V(aL)] [w + p(x) -x] 1p'(x)
p' (x) np' (x)
1
s.t. (ii) +w, > -A (6)
p' (x)



Therefore, the first-order necessary conditions for a solution to [BP] and [BP'] are:

() [-p'L-1][w +- -x]+PP [(w, +P--x)-(R-w,-p(L+ )-V(a,L))]- 2 =0
n(p)2 )I,2
(b) -(i,,+--x)+(R-wp )p(L+ )-V(L,L))+0 = 0 p'p

P P
(c) +w+A > 0 (=0 if 6>0)
P
(d) 6 > 0


Case 1: Wealth Constraint does not Bind (0 O)

From (b), this implies that the agent's share of the net surplus from specific trade (wn+p/p'-x) equals the principal's net surplus from specific trade (R-wn-p(L+1/p')V(a,L)). This implies that (wn+p/p'-x) > 0 for a < 1 (i.e. the agent's share of the net surplus can only equal zero if there is no net surplus, which only occurs when the agent is identical to all other agents (a = 1)). Therefore, from (a), the care which solves [BP] in this case is x*(L). From conditions (b) and (c): R +x-pL V(a,L) p > 1 -A
2 p' p'

Therefore, the wealth constraint is not binding when:







34


R x *(L) +p(x *(L))L V(a,L) L-A (A4)
2



Denote Kb as the liability level for which (A4) holds with equality. Then x*(L) solves [BP] for L < Kb.

Case 2: Binding Wealth Constraint (0 0)

Denote IIHp R-wn-p(L+l/p')-V(ca,L). Therefore, from conditions (a) and (b), the care which solves [BP] for L > Kb is given implicitly by:


-p'L-1 3o
6 +I
P
p




Notice that 0/(0+II,)) approaches zero as 0 approaches zero, so Xb(L) is continuous (although not differentiable) at Kh,

As before, since dC/dL > 0, there exists a liability level such that Vb(a,L) = 0. Denote this level as tb. For L > Tb, the principal and agent are better off not contracting and, therefore, the induced care is zero. (If Kb does not exist, the solution to [BP] is given by footnote 8.) U



A2.4: Proof of Theorem 2.4 i) K, is implicitly defined by:

R-x *(K,)-p(x *(K ))Kb (,K)
x *(K) +p(x *(K)) = K-A
2







35

which implies


X *(K/,) +p(X *(K ))K, < K1, -A since R-*K,-(*K)K-(,b > 0 for cY < 1. Therefore, Kb > K.




dK~b V T~aUK b) < 0
du~ dC Tf(a~ K1) -2 since V,,>O0, dC/dL < 1 (see Lemma A2. 1. 1), and VL.(a,K1,) = -P(a,XJKb)) > -.



A2.5: Proof of Theorem 2.5 i) For a~ e [0, 1), H11)> 0. Therefore,






implying R A() >R(L) for all L and ac~ [0, 1). ii)




a p "L(O +Hfl )+0 dP 2p2_ 2___dx 0 +~lip


since V,,(c,L) > 0 and the denominator is positive by second-order sufficient conditions. U













CHAPTER 3: VICARIOUS LIABILITY, NEGLIGENCE, AND MONITORING



3.1 Introduction

Vicarious liability is applied by the courts in many different business contexts. In contexts where the principal can easily observe and control her agent's actions, the principal is almost always found vicariously liable in the event of an accident. Increasingly, vicarious liability is being applied in contexts where the principal cannot easily observe the agent's behavior. (See Chapter 4.) In these cases, the courts often justify the use of vicarious liability as a way to make principals monitor and control their agents. In light of this, it is surprising how few articles address this justification in the vicarious liability literature, To my knowledge, no paper has systematically analyzed the principal's incentive, under vicarious liability, to monitor her agent. Only one paper (Chu and Qian (1995) [8]) has investigated the efficiency of vicarious liability when the principal is able to (imperfectly) monitor her agent."

Chu and Qlan (1995) analyze the efficiency of vicarious liability under a negligence rule. They find that vicarious liability induces the principal to underreport any evidence of



10
Lewis and Sappington (1996) [15] show how vicarious liability can beneficially supplement an industry-wide liability rule termed the "access principle" if the vicariously liable party can monitor the agent,

36







37

necFligence gathered while monitoring the agent. If the principal is best able to monitor the agent and the courts only apply liability when the agent is found negligent (i.e., when the agent has used insufficient care), then both the principal and the agent will benefit if the principal falls to report any evidence of negligence. However, Chu and Qian assume the principal's monitoring capability is exogenous. Thus, they do not investigate the principal's incentive to monitor the agent under vicarious liability. In addition, although Chu and Qian successfully demonstrate that negligence liability, as currently applied by the courts, induces the principal to underreport evidence of negligence, they fail to investigate other it collusion- proof' forms of negligence liability which do not give principals this incentive.
I

The objective of this chapter is twofold. First, this chapter investigates the ability of collusion-proof negligence liability to prevent accidents, In a collusion-proof liability scheme, the total amount paid by the principal-agent enterprise does not vary with the agent's negligence, while the agent's share of this liability is greater if he is found negligent. Under collusion-proof schemes the principal will report all evidence of the agent's negligence. Failure to do so would only increase the principal's share of the liability payment, In this chapter, it is shown that the preventive care induced by collusion-proof negligence liability is the same as that induced by strict vicarious liability. Furthermore, it is shown that any liability scheme which fully compensates the victim in the event of an accident will induce the same level of preventive care as strict vicarious liability.

Second, this chapter investigates whether vicarious liability gives the principal an incentive to monitor the agent when monitoring is costly and whether preventive care is more efficient under vicarious liability when monitoring is possible. This chapter will show









that vicarious liability induces monitoring of the agent if the agent is sufficiently judgement-proof When the principal monitors the agent, the level of monitoring increases as the principal's liability increases and decreases as the cost of monitoring increases. In addition, this chapter will show that preventive care when monitoring is possible is at least as great (and often greater) than that induced when monitoring is not possible.

The chapter is organized as follows. Section 3.2 presents a model of collusionproof liability when the principal can monitor the agent for negligence. Section 3 ), 3 investigates the principal's incentive to monitor under vicarious liability. Section 3.3.1 presents a benchmark vicarious liability model in which the principal cannot monitor the agent, Section 3.3.2 contains a closely related model in which the principal can monitor and choose the monitoring intensity.

3.2 Collusion-Proof Negligence and Vicarious Liability

Consider a principal who hires an agent to complete a productive activity, This

activity will produce a revenue of R for the principal. However, there is also a probability p (e (0, 1 ]) that the agent, while completing this activity, will cause an accident. The probability of an accident is a function of the precaution or care x the ai=t takes when completing the activity. It is assumed that increasing care decreases the probability of an accident at a decreasing rate (p'(x)O). The agent's personal marginal cost (or disutility) of taking care is assumed to be constant and is normalized to unity. In addition, the agent's initial wealth is A.

The principal cannot directly observe the agent's care. However, with probability q (c [0, fl), the principal can observe verifiable evidence that the agent was negligent in







9

completing the productive activity. As with p, it is assumed that increasing care decreases the probability of observing negligence at a decreasing rate (q'(x)O). The principal's ability to possibly observe negligence is assumed to be exogenously given. This assumption will be relaxed in subsequent sections of this chapter.

The timing of the principal-agent relationship is as follows. First, both the principal and the agent learn the relevant liability rule. Second, the principal offers a contract to the agent that specifies accident and non-accident wages of v, and Vn, respectively, when evidence of negligence is found and accident and non-accident wages of w, and w" when no evidence of negligence is found. 12 Third, the agent chooses to accept or reject the principal's contract offer. If the agent accepts the contract, he then chooses his level of care, x, for the activity. The courts cannot observe this choice of care. Fourth, the state of the world is realized (either accident or no-accident, evidence of negligence or no evidence), the liability payments are collected from the principal and the agent in the event of an accident, and the appropriate wage is paid to the agent.

If the liability rule applied by the courts is based on a report of negligence, there is an incentive for the principal and agent to collude to avoid liability, For instance, if the agent is found liable when an accident occurs only when evidence of negligence is


11
Notice, this allows for the possibility of "framing" (i.e., the principal could present evidence of negligence even when the agent has taken due care: q(x) > 0 for x x', where x' is the established due care level set by the courts). In addition, it is assumed that p and q are independent.
12
Notice this allows for the possibility that w,:, v, (Le., the verifiable evidence of negligence could be used in contracting even if it is not used in a tort proceeding).







40

reported, both the principal and agent can gain if the agent bribes the principal to withhold evidence of negligence. If the courts stipulate vicarious liability in the event of negligence, the principal's incentive to withhold evidence of negligence is magnified.

For this reason, the liability scheme applied by the courts is assumed to be a it collusion- proof' scheme." In other words, the scheme provides the agent with no incentive to bribe the principal with an amount sufficient for the principal to withhold evidence of negligence." Specifically, the total liability assigned to the principal and the agent in the event of an accident does not vary with the agent's negligence, although the agent's share of this liability may vary with negligence." In this way, the agent's gain from avoiding negligent liability is exactly the principal's loss. Therefore, on net, the principal cannot gain through any bribe the agent would be willing to offer to avoid negligent liability. Hence, a collusion-proof liability scheme can be summarized by the total liability of the principal and agent (L), the agent's share of this liability when there is no evidence of negligence and the agent's share when there is evidence of negligence A). Besides negligence (P, this specification allows for other types of liability schemes including strict vicarious liability 0) and strict Joint liability (P,, = P > 0).



13
Tirole (1992) [3 1 ] has shown that there is no loss of welfare associated with the use of collusion- proof contracts.
14
For this reason, in the event of an accident, the principal will present the court with evidence of negligence if she observes such evidence. 15
In addition, the total liability could also vary with the damages inflicted upon the victim as we would expect.







41

In choosing a contract to offer the agent, the principal solves the following problem:

[NP] Max., EU

s.t.(a) EU./I > 0
dELI
(b)
dy
(c) v >_ -A
(d) w,-PL -A
(e) vi,-P,3L -A




where the principal's objective (EU,) is:

AV5 P) = R -q[p(i,,+( 1 -[ P,)L) +( 1 p).,,] -(I1 -q)[p(ii, +(I -P)L) + pw



and the agent's objective (EUa) is:

Ll,, q[p(v,3- P,L)+(1 -p)v] +(1 -q)[p(wa- PL) +(I -p)w,] -x



Constraint (a) is the agent's participation constraint. The agent will only accept the principal's offer if the expected wage, net of effort costs, is at least as great as the agent's reservation wage (here normalized to zero). Constraint (b) is the incentive compatibility constraint which reflects the principal's inability to observe the agent's care. Since the principal cannot make the wage contract contingent on the agent's care level, the agent



16
The principal and the agent are both assumed to be risk neutral. This is a standard assumption found in most of the previous vicarious liability literature. See [ 13] for implications of general risk aversion.







42

will choose a care level that is personally optimal given the wage contract. 17 Constraints

(c), (d) and (e) reflect the agent's limited wealth and the principal's "right to indemnification." When a principal is found partially or completely liable, she has the right to be compensated by the accident- cau sing agent [7]. However, this compensation plus the agent's assigned liability cannot exceed the agent's wealth. Therefore, the agent's accident wage (with or without negligence) plus the agent's assigned liability must be at least -A."

The main result of this section is the following:

Theorem 3.1: The care (x) which solves [NP] is independent of P and Proof See Appendix A3. 1.

In other words, collusion-proof negligence, strict vicarious liability, and strict joint liability all induce the same level of accident-preventing care. In fact, theorem 3. 1 implies that all liability schemes in which the principal and agent fully compensate the victim (i.e. L = the total accident damages) will induce the same level of preventive care,



17
Constraint (b) assumes the use of the "first-order approach" is valid in this case. Normally, the use of the "first-order approach" requires that the cumulative distribution function be convex and exhibit the monotone likelihood ratio property (NERP). However, NdELRP is meaningless in this context since the potential states of the world (no accident w/o negligence, accident w/o negligence, no accident w/ negligence, and accident w/ negligence) cannot be ordered, a priori, from best to worst from the point of view of the principal. See [22] for a thorough discussion of the validity of the first-order approach in moral-hazard problems and its relation to N/ILRP and convexity of the distribution function (CDFQ.
18
Constraint (a) implies that Wn is non-negative, so a separate wealth constraint for wn is not needed.







4 3

To understand how this result comes about, it is useful to rewrite the agent's objective as follows:

E(U0 v +p[w0, -u, P3L] +q[i.0,-w,4 -qp[(v, i)-(w, -iv,)-(P, )L] -x (3)



Expression (3 ) highlights an alternative interpretation of the contract between the principal and the agent. In addition to the penalties the government specifies in its liability rule, the principal offers the agent a contract characterized by a base wage (wn) and three penalties: a penalty if an accident occurs without negligence (w, wn), a penalty if no accident occurs but the agent is found negligent (v, wn), and an additional penalty when an accident occurs and the agent is found negligent ((v,, v,1) (w, w,)). These penalties are the principal's tools for inducing the profit -maximizing level of care from the agent, given the total liability, L. However, the government also penalizes the agent and these penalties also affect the agent's choice of care. Therefore, if the government changes its distribution of liability between the principal and agent (i.e., changes P3 or flu), the principal will compensate for this change by altering the penalties in the wage contract. In this way, the principal ensures that the agent will continue to exert the profit-maximizing level of care given the total liability. For instance, if the agent's share of liability (f3) is increased, then the agent's accident wage (w, ) will increase to compensate for this change. If the agent's additional liability for being negligent in causing an accident On3 f3) is increased, then the agent's negligent accident wage (v,,) will increase to compensate for this change. In both







44

cases, the total penalties the agent is subject to will not change with P or P, Therefore, the agent's choice of care will not vary with P or P, "

The intuition of this result resembles the well-known theoretical macroeconomic result of "Ricardian equivalence," Ricardian equivalence states that a change in the mix of public debt and taxes will not result in any change in most real macroeconomic variables, including consumption and interest rates. The logic behind this is the following, If government expenditures remain the same while taxes fall, disposable income will increase. However, individuals recognize that the increase in debt implied by lower taxes in the present implies higher taxes in the future. Therefore, individuals will increase their current savings to compensate for the increased debt and future tax obligations, Hence, consumption will not change. Likewise, in the present liability model, preventive care does not change with changes in the principal and agent's liability mix because the contract between the principal and agent will exactly compensate for any changes in the liability

mix. 20

The accident-preventing care induced by any collusion-proof liability scheme is the same as that induced by strict vicarious liability, even when the principal can monitor the agent for negligence. Therefore, negligence liability rules offer no improvement in


19
Another way to explain Theorem I is by using constraints (a), (c), (d), and (e) in [NP]. If P or (P, P) is increased and the participation constraint (a) binds, then the agent's wages must increase in order for the agent to still receive his expected reservation wage. If P or (Pn P) is increased and the wealth constraints bind, then the agent's wages must increase so that the total penalty is not greater than the agent's wealth (i.e., there is less left over for the principal to collect in indemnification). 2' For a thorough review of the literature on Ricardian equivalence, see [24].







45

accident-prevention over strict vicarious liability. As Chu and Qian detail, when negligence rules are not collusion-proof, they can often lead to inefficiencies.

Still, these results assume the principal's monitoring ability is given exogenously. If the principal can choose her level of monitoring, will strict vicarious liability induce more monitoring than direct liability (in which the agent alone is liable)? If so, does this increased monitoring lead to improvements in accident prevention? These questions will be addressed in the following section.

3.3 Monitoring and Vicarious Liability

3.3.1 Benchmark Vicarious Liability Model

In order to understand how vicarious liability affects the principal's monitoring

choice, it is useful to look first at a benchmark case in which the principal cannot monitor

21
the agent's care.

The model in this section is the same as that in section 3.2 except that the principal is unable to observe the agent's care or any evidence of negligence, Therefore, the contract between the principal and agent is made contingent only on the observation of an accident or no accident. In addition, since preventive care does not change with the liability mix, it is assumed that strict vicarious liability holds (i.e., P = 0).

In choosing a contract to offer the agent, the principal solves the following problem in this case.21
A complete description of this subsection's model and results can be found in Chapter 2, section 2.2.







46

[P] Ma~ [ p)W -1-x)w-p)]
st. (a) p(xvCI +(0 -p~x))wn -x 0
(b) p'(x) (w.,- w)-I = 0
(c) w ), -A





As before, constraint (a) is the agent's participation constraint. Constraint (b) is the incentive compatibility constraint which reflects the principal's inability to observe the agent's care. Constraint (c) reflects the agent's limited wealth and the principal's right to indemnification.

Before characterizing the solution to [P], it is useful to characterize the socially optimal care level. Suppose a revenue-producing activity has a potential accident damage of D associated with it. The social welfare of this activity is: SW = R -p3(x)D)-x



Therefore, the socially optimal care level is given implicitly by:


-p'(x)D-lI = 0



At the socially optimal care level, the marginal cost of increasing care equals the marginal decrease in expected damage associated with increasing care. Let x*(D) denote this care level.

For the vicariously liable principal in [P], the profit-maximizing level of care is x*(L) (i.e., that which is socially optimal if the liability, L, equals the damages, D). The







47

principal can induce this level of care by setting wn w, = L. The principal simply passes along the liability to the agent through the wage contract by penalizing the agent L in the event of an accident. However, as the principal's liability increases, there comes a point (denoted by L = K) at which passing the liability to the agent becomes costly to the principal.2 This occurs because of the agent's limited wealth. Recall that the principal can take no more than the agent's wealth through indemnification (w, -A). Therefore, in order to induce x*(L) from the agent, the agent's no-accident wage (wn) must be at least L

- A. However, if L A > x*(L) + p(x*(L))L, then the principal can only induce x*(L) from the agent by giving the agent an expected wage above his reservation wage (see constraint

(a) in [P]). Therefore, if L < K, the principal can costlessly pass on the liability, L, to the agent. If L > K, then the principal faces a tradeoff: she can maximize the joint surplus only by sacrificing some of her share of the surplus. Faced with this tradeoff, the principal will sacrifice less profit by inducing a suboptimal care level from the agent.

To be specific, the principal is faced with the following trade-off for liability levels ,greater than K. At one extreme, the principal could continue to pass the full liability onto the agent through the contract inducing the profit -maximizing care (x*(L)). However, the principal incurs a cost of L A [x*(L) + p(x*(L))L] when pursuing this approach, since the principal must give the agent a share of the Joint profits in order to fully pass the liability onto him. At the other extreme, the principal could simply offer the contract which is profit-maximizing for L = K (i.e., freeze the accident penalty at K). This approach allows



K (the point at which the wealth constraint first binds) is implicitly defined by x*(K) + P(X*(K))K =K A.







48

the principal to avoid giving the agent an economic rent. However, this will induce a level of care from the agent that is too low given the principal's vicarious liability of L. The principal will, therefore, incur an expected cost Of [p(x*(K)) p(x*(L))]L since the probability of an accident will be too high given this approach.

At first (i.e., for L e (K, p]1), the latter approach is least costly for the principal, so the principal Sets wn Wa =K, even though L > K. Eventually (i.e., for L > p), this approach leads to a probability of an accident that is too great relative to the principal's liability, L. In this case, the principal uses a combination of the two strategies. The principal gives the agent a share of the joint profits to induce a higher level of care, but not enough to induce x*(L). (In other words, the accident penalty will fall between K and L.) Therefore, even though the induced care Is inefficient for L > K, it is never less than x*(K).

For this reason, vicarious liability is at least as efficient as direct liability in

preventing accidents and more efficient when the agent is judgement-proof (L > A). If the agent is directly liable, he will exert the socially optimal care (x*(L)) as long as the liability is no greater than his wealth (L A). However, if the agent is potentially judgement-proof (L > A), he will exert just x*(A) since the penalty he receives in the event of an accident is only the loss of his wealth, A. As shown above, when the principal is vicariously liable, she induces the efficient level of care from the agent not only when L 5 A, but also when L C [A,K]. In addition, when L > K, the inefficiently low level of care induced under vicarious liability is never less than X*(K)(> x"(A)). Hence, when the agent is judgement-proof, vicarious liability is more efficient than direct liability. 23 p is the liability level at which the participation constraint no longer binds.







49

3.2 Vicarious Liability and Endogenous Monitoring

Now, suppose the principal has access to a (costly) means of monitoring the

agent's care. Specifically, the principal can invest in a monitoring technology which gives the principal the ability to observe the agent's care perfectly with probability q (e [0, The cost of this technology is assumed to be c(q) where c is an increasing, convex fiinction of q, c(O) = 0, and lim,, lc'(q) = -. For the purpose of calculating comparative static derivatives, c(q) = aq/(l -q) where u. is a cost parameter.

The timing of the principal/agent relationship is now the following. First, the

principal and agent both learn of the principal's strict vicarious liability, L, in the event of an accident. The principal then invests in the monitoring technology by choosing q and the agent observes this choice, Next, the principal offers the agent a contract contingent on both the possible observation of the agent's care and the observation of an accident or no accident. In particular, the contract specifies a wage schedule of [v,(x),v,,(x)] if the principal can observe the agent's care and a wage schedule of [w,,w,] if the principal can only observe the occurrence of an accident, where the subscripts a and n denote the "accident" and "no-accident" states of the world, respectively. The agent then chooses to accept or reject the contract. If the agent accepts the contract, the agent chooses his care in completing the activity knowing q, but not knowing whether the principal can observe his care or not. Finally, the state of the world is realized (care can or cannot be observed, accident or no accident) and the appropriate payments are made.

In choosing a contract to offer the agent, the principal solves the following problem:







50

IMP] Max.q,,,, ,1(4 (x) EUp

s.t.(a) EUa > 0
(b) x = argmax[EUJ]
(c) w -A
(d) v,(x) -A Vx i=a,n
(e) qc[0,1]



where the principal's objective (EU,) is:

E(U =R-pL-q[pv,(x)+(1-p)v,(x)]-(1-q)[pwa+(1-p)w,,]-c(q)



and the agent's objective (EUa) is:

EUC, = q[pv',(x)+(1 -p)v (x)] +(1 -q)[pw +(1 -p)w, -x



As in sections 3.2 and 3.3.1, constraint (a) is the participation constraint which assures that the agent's expected wage, net of effort costs, is at least as great as his reservation wage and constraint (b) is the incentive compatibility constraint reflecting that the agent's choice of care will be that which maximizes the agent's expected wage, net of effort costs.24 Likewise, constraints (c) and (d) reflect the agent's limited wealth.

Let the care level which solves [MP] (i.e. the care level which the principal wishes to induce from the agent) be denoted as X. Notice that, given the wage schedule {v,(x),v,,(x) }, only the payments v(XZ) and vn(X) enter the principal's objective. v, and v, for values of x other than X only enter the incentive compatibility constraint (b).


24
The first-order approach is not used in this case since the agent's objective may not be differentiable.







51

Therefore, it is in the principal's interest to set v, and vn as low as possible for any values of x # Hence, vi(x) = -A for all x X and i = a,n.















EU(x)







EU(x)






Figure 3


The following change of variables simplifies the analysis significantly. Let K = wa wn (the penalty inflicted upon the agent in the event of an accident if the principal cannot observe the agent). Let v(x) p(x)v,(x) + (1 -p(x))vn(x) (the agent's expected wage if the principal can observe the agent and his care is x). Since only v(x) is present in [MP] (and not v,(x) or v,(x) separately), the principal does not gain by paying different accident and







52

no-accident wages when she can observe the agent's care. Therefore, when the principal can observe the agent's care, the wage contract can be characterized completely by v(x). With these variable changes, the agent's objective can be expressed as: EU = qv(x) +(I -q)(w, +pK) -x (4)



One example of EUa is graphed in Figure 3. Let: x- argmax[( 1 -q)(w ,+pK)-x] (= x(q,K))



In other words, x (a local maximizer of EUa) is the agent's best alternative level of care apart from X, the care the principal would like to induce. Therefore, in order to induce X from the agent, the principal must set v(X), q, wn, and K so that:


qv'(X) +( -q)(w,,+p(X)K)-7 2- q(-A) +(1 -q)(w,,+p(x)K)-x or:

qv(X) _> -qA +(1 -q)(p-p(X))K-(x-7) (5)



where, for simplicity, p p(x). Expression (5) replaces constraint (b) in [MP]. Likewise, constraint (a) can be expressed as: qv(x)> -(1 -q)(w, +pK) +x (6)



Therefore, using (5) and (6), constraints (a) and (b) in [MP] can be expressed as:







53

qv(x) >_ Max[ -qA +(1 -q)(p-p)K-(x-x), -(1 -q)(w, +pK) +x]





or:

qv(x)> -(1 -q)(,1 +pK) +x +Max[-qA +(1 -q)(w0 +pK) -x, 0] (7)



Without an additional constraint on the principal's wealth, [MP] has only a trivial limiting solution in which the principal sets v(x) = oo and sets q arbitrarily close to zero in the limit. (See [2] p. 183) Let v(x) B, where B is a parameter reflecting the principal's wealth. In this problem, the principal is considered a "deep pocket." Her wealth, while finite, is an order of magnitude greater than the vicarious liability. To be specific, suppose all plausible liability levels fall in the interval [L1, Lj]. Let B = 2L2.

Now the principal's problem can be expressed as follows25:


[iP /] Max ,,,. [R -pL -qv(x) (1 -q)(w, +pK) -c(q)]
s.t. (i) qv(x) > -(1 -q)(w, +pK) +x+Max[-qA +(1 -q)(w ipK) -x, 0]
(ii) w,, +K > -A
(iii) q > 0
(iv) v(x) B


Although written differently, this problem is equivalent to [MP] (with the exception of the added constraint (iv)). First, v(x) replaces va and v, and K replaces w,. Second, constraints

(a) and (b) in [MP] are expressed in constraint (i) and constraint (ii) replaces (c) in [NIMP]. Finally, the q 1 portion of constraint (e) in [NIP] is not needed since limq..c'(q) = 0 25 I am thankful to Tracy Lewis and Steve Slutsky for suggesting this approach.







54

Since qv(x) enters the principal's objective negatively in [MP'], constraint (i) will bind in equilibrium. Therefore, if both sides of (iv) are multiplied by q (>0) and qv(x) from

(i) is substituted into (iv) and the principal's objective, then the principal's problem can be expressed as:

[MP] ]Max.q.,,., [R-pL-x-Max[ -qA +(1 -q)(w,+ K) -F, 0]-c(q)]
s.t. (iv) qB -(1 -q)(w,, +pK) +x +Max[ -qA +(1 -q)(w +pK) -x, 0]
(ii) w, +K > -A
(iii) q > 0



If, at the solution to [MP"], -qA+(1-q)(wn+pK)-x < 0, then an equivalent solution exists in which -qA+(1-q)(wn+pK)-x = 0. If-qA+(1-q)(wn+pK)-x < 0, then wn can be increased without affecting the principal's objective while still satisfying all of the constraints. Therefore, [MP"] is equivalent to:

[MP ///'] Max ,K ,,[R-pL-x-c(q)-(-qA +(1-q)(w iK)-i)]
X'q,K ,11,'.
s.t. (a)qB > -qA +(1 -q)(p-p)K-(x-x)
(b) -qA +(I -q)(w,,o+pK)-x 0
(c)w, +K> -A
(d) q 0


Unlike [MP], traditional methods of non-linear programming can be used to solve [MIP'"] for induced levels of monitoring and care. Solving [MP'"] produces the following results: Theorem 3.2: (i) For L K (the liability level at which the wealth constraint (c) begins to bind), the solution of [MP" '] is q = 0, x = x*(L), K = -L, and w, = x*(L) + p(x*(L))L.

(ii) For L > K, the solution of [MP"'] is q > 0, x < x*(L), w,, = -A-K, and v(x) = B. Proof: See Appendix A3.2.







55

Theorem 3.2(i) states that the principal will never monitor when L K. To

maximize her expected profits given a potential vicarious liability of L, the principal would like the agent to exert x*(L). When L K, the principal can induce this level of care costlessly. She can set w, w, = L without sharing any of the joint profits with the agent. Therefore, investing in monitoring will not produce any benefits for the principal. It will only serve to decrease profits by c(q), Therefore, when L :! K, the principal will choose q

0.

Theorem 3 ). 2(ii) shows that, when it is costly for the principal to pass the vicarious liability onto the agent (i.e., when it is costly to set K = -L), the principal will employ monitoring as an additional means to induce care from the agent. As mentioned in section

1, when L > K, the principal can no longer pass the full liability to the agent costlessly. To make the agent's penalty in the event of an accident equal to the principal's vicarious liability, the principal must give the agent a share of the expected profits from the activity. Therefore, the principal only passes a portion of the liability to the agent, resulting in suboptimal care. However, with monitoring, the principal has another option. When L > K, the principal can induce a level of care x > X*(K) from the agent, without giving the agent an expected economic rent, by investing in the monitoring technology, Essentially, this is because monitoring gives the principal another means by which to punish the agent for suboptimal care. With monitoring, if the agent chooses a suboptimal level of care, the principal can penalize the agent after observing the suboptimal care. Therefore, the principal can use monitoring (q) as a substitute for the accident penalty (K) to induce care. This is particularly useful when L > K and any increase in the accident penalty is costly to







56

the principal. Notice this implies that vicarious liability with monitoring induces at least as much preventive care as vicarious liability without, because the principal has one more tool with which to control the agent's behavior. Theorem 3.3: For L > K, the principal's monitoring (q) will decrease as the cost of monitoring increases (i.e., dq/da < 0) and the principal's monitoring will increase with the principal's vicarious liability (L) (i.e., dq/dL > 0). Proof See Appendix A33.

When the principal employs monitoring, the level of monitoring used is inversely proportional to the cost of monitoring, as one would expect. A less obvious implication is that monitoring will increase as the principal's vicarious liability increases. When L > K, it becomes increasingly costly for the principal to fully penalize the agent as the principal's vicarious liability increases. Therefore, the benefits of monitoring (q) to induce care, relative to the use of the accident penalty (K), increase as the principal's vicarious liability increases. Hence, when accident damages are large and the agent is severely judgementproof, a principal faced with potential vicarious liability will employ a higher level of monitoring than that used when damages are relatively small.

In summary, a principal facing vicarious liability for a judgement-proof agent will not monitor the agent when the liability is relatively small (Le (AK]). In these cases, the accident penalty (K) in the wage contract is sufficient to induce the profit-maximizing care, and can be employed by the principal without sacrificing any of her profits. When the principal's liability is relatively large (L > K), the accident penalty in the wage contract can







57

no longer be used without cost. Therefore, the principal will use monitoring to supplement this accident penalty.

3.4 Conclusion

Although vicarious negligence liability, as it is currently applied by the courts, can lead to inefficiencies in monitoring, collusion-proof negligence liability avoids this weakness. In addition, collusion-proof liability (and any other liability scheme in which the principal and agent fully compensate the victim) induces the same amount of preventive care as strict vicarious liability. This result resembles the famous theoretical macroeconomic result of "Ricardian Equivalence" in which changes in the debt-tax mix do not change real macroeconomic variables such as consumption and the real interest rate.

When the government does employ strict vicarious liability, this gives the principal an incentive to monitor the agent when the agent is sufficiently judgement-proof (L > K). This incentive is heightened when monitoring is inexpensive and when the principal's liability is large. In all cases, the efficiency of vicarious liability in preventing accidents is
pI

not diminished, and sometimes enhanced, by the ability of the principal to monitor,



A3.1: Proof of Theorem 3.1

Using expression (3), constraint (b) in [NPI becomes:

dT
= +q/P)Pa n a
dx







58

Solving (A5) for v, and plugging it into EUP, EU,, and constraint (e) of [NP] produces the following equivalent problem:

[NP R-pL-4,,-b[cy+qlp'(w,,- v,-PL)+plq'(v,,-w,)]
S.I.(a) i4)ri+8[clp+qlp'(ilcl-w,,-PL)+plq'(vn-w,)]-X !0
(C) 1 > 0
(C IV, PL -A
(e) 6 [ I -p /(it) 67- J",-PL)-q /(V n -WO] +"n +(-"', -Wn PL) > -A




where 6 1 /(qp+qp). Let y Wa Wn PL. [NP'] can now be rewritten as follows:


[NP Va R -pL -5 [cy +qp'y +p /q'(i) n- A),)]
s.t.(a) i4,,,,+6[qp+q 'y+p1q '("n -"VA -X 0
(C) 17
(d) v, + y -A
(e) 8[l-py-q1(v n-TQ] +v, +y -A




Therefore, the x which solves [NP] is independent of P and P,. 0



A3.2: Proof of Theorem 3.2 The lagrangian for [NIP"'] IS"

= R -pL -x-c(q) -(-cA +(I -q)(w, +pK) -i) + JqB+cjA -(I -q)(fi7-p)K+()-C-'C)] + 21-qA +0
+0["' n +K+A] +Tc[q]







59

Using the fact that (1-q)p'(x)K-1=0, the first-order necessary conditions for the solution to [MP"'] can be written as:

(1) .,= -p L-1 +,[p'(1-q)K-1]= 0
(2) 9 = -c (q)-(1 -X2)[-A -(w +pK)] +X [B+A +(p-p)K] +7r = 0
(3) 2K.= -(2 -q)[(1- (p2)fi..) ,-p)]+6=0
(4) = -(1 -q)(1 -12)-+0 = 0
(5) 2, = q(B+A)-(1-q)(p-p)K+(x-x)>0 (=0 if X1>0) (A6)
(6) 92, = -qA +(1 -q)(w,,+pK)-x> 0 (= 0 if 12>0)
(7) 90=w +K+A>O (=0 f 0>0)
(8) 9=q> 0 (=0 f xr>o0)
(9) X1,2,0,rC > 0



Conditions (3) and (4) in (A6) can be combined to produce: (1 -q)[(1 -)(1 -X2)-X1(p-p)] = 0 (A7)



Case 1: 1 = 0.

From (1) in (A6), this implies x = x*(L). In addition, from (A7), this implies = 1 since q < 1. Therefore, (2) in (A6) becomes -c'(q) + r = 0 which, from (8), implies q = 0.

(5) in (A6) now becomes -(p-p)K+(x-x)_0 or -pK+x_-pK+x or:

pK-x pK-x (A8)


From the definitions of x and x*, if q = 0, then x = x*(-K), which implies pK-xpK-x for all x. Therefore, pK-x-=pK-x which implies x = x and K = -L.

Hence, from (6) in (A6), wn = p(x*(L))L + x*(L) and (7) becomes p(x*(L))L +

x'(L) > L A. Recall, p(x*(K))K + x*(K) = K A. Therefore, (7) cannot hold when L > K.







60

Case 2: X1 > 0 and X, = 0. First, notice 1, > 0 implies 0 > 0 from (A7) and (4) of(A6). Therefore, wn = -A-K from

(7).

Case 2.1: q = 0. From (5) and (6) of(A6), this leads to the solution found in case 1. Case 2.2: q > 0. Since A1 = (1-p)/(p-p) from (A7), x, q, and K are given implicitly by: F, = q(B +A)-(1 -q)(p-p)K +(x-x) = 0 F2 = -p'L-1+ -P) [p/(1-q)K-1 0 (pV-p) (A9)
S= -c (q)+ (1P)[B+A] =0 (p -p)


where F1 is from (5) of (A6), F2 is from (1), and F3 is from (2) and (8). Notice, F2 implies x < x(L).

Case 3: X, > 0 and 12 > 0. Again, this implies w, = -A-K as in case 2. Case 3. 1: q = 0.

Again, this leads to the solution in case 1, except that it only holds for L = K. Case 3.2: q > 0. Since 1 = c'(q)/(B+A) from (A7) and (2) of(A6), x, q, and K are given implicitly by:


G = q(B+A)-(1 -q)(p-p)K+(x-x) = 0 G2 _p (c I(q) [p /(1 -q)K- 1] = 0 (A10)
(B+A)
G = -A -(1-q)(1-o)K-x= 0







61

where G1 is from (5) of(A6), G2 is from (1), and F3 is from (6). Notice, G, implies x < x*(L).

Therefore, when LK, there are two candidate solutions, from case

2.2 and case 3.2. It cannot be determined which is optimal for the principal in this case. However, in both cases, q > 0, wn = -A-K, and x < x*(L). In addition, since X1 > 0 in both cases, v(x) = B. (See problems [MNP'] and [MP"].) E



A3.3: Proof of Theorem 3.3 If the solution to [MP"'] when L > K is given by (A9), the principal solves the following problem:


aq
MaxeqX [R-pL-x- q +A+(1-q)(1-p)K+x] l-q
s.t. q(B+A)-(1-q)(ji-p)K+(x-x)= 0


where c(q) = aq/(1-q) has been employed. The lagrangian for this problem is:


=R-pL -x- aq +A +( 1 -q)(1 -p)K+x+X[q(B+A)-(1 -q)(l-p)K+(x-x)] 1-q

and the necessary first order conditions are:







62

S ; =q(B +A) -(I -q)(fi7-p)K+(X_-X) = 0 9,,= -1)'L- I + [p'(l -q)K-1] =0 sp =_ a + [B+A]-K[(I-, )- (F-p)]=O (I -q)'
-q)[(] -p-) V-p)] = 0




Let i denote the bordered Hessian matrix of this problem. Using the implicit function theorem and Cramer's Rule:

0 ukv 0 9 2LK

91;L 9. 0 SkxK
gg 91,, (1 -q) -2 qgK dq gK gKx 0 qKA
da IHI


whereq, =p'(1 -q)K- I q L(I=gc =B+A+KV-p)

SiV Si"I p IK S2, :X 9,,,;: p'(l -q) 9qK S Kq (I + )
V(I -q), 9,,,, -p [L -X(I -q)K] S (lei I (+ ) -2a (I -q)' K "
_(I
K'(1







63

Therefore:


S V g ,,XK dq 1 2, ,, :K 0
-<0
du (1-q)2 The sign of dq/da follows from second order sufficient conditions which imply that IHI <

0 and the numerator matrix is positive. Likewise:

0 k2 0 9 K s u P Sk xK qX q. 0 9qK dq 2K2 Kx 0 9 dL


or:


dq -p(B +A) (1 -q)2(-p)p '-(p /(1-q)K-1)K -)
dq _K(1 -q)p"l
dL


Hence, dq/dL > 0 since x > X, K < 0 (since w, > 0 from the agent's participation constraint), and p'(1-q)K-1 < 0.

If the solution to [MP"'] when L > K is given by (A10), the principal solves the following problem:







64


Max ,,,I [R -p)L --aq +A +-(1 -q)( 1 -fi3)K+-x] I1-q
st. q(B--A)-(1 -q)(p-p)K+(x-x)= 0
-A -(1 -q)(1 -j5)K-x-i= 0 The lagrangian for this problem is:



1-q





~ =(B--A)( +)(Iq)-p)K) =0





q2= -A -(1 -q)(1 -j3)K-x-= 0 = -p'L- IX1[p'1 -q)K- 1] 0 [ XBA]-K[(1-X2)(l-p)-X0(--P)]=0
(-q)'




where 9i = 69/KX1 for 1=1,2. Let H! denote the bordered Hessian matrix of this problem. Using the implicit function theorem and Cramer's Rule:


0 0 91X 0 ~1K

0 0 9 2 0 q2K

Xl 9x2 si% Xk
9q q2 9qx (-q) -2 g dq KI SK2 gK, 0 9AIK
du.







65

where.




igi =BA--K(p-p)

S 2 = 9 = 0 92q =9c2 = K(1 p 92K = 9K = -(I -q)(1-p


~qk K I-(1X-) qK K K2(1 -q)T7" = -p A'L-X(I --q)K] 9qq = I- I_2 c
(I -q)' K
(I X11 2) K K(1-qp




Therefore:


0 0~ Ix 91K 0 0 S92x 92K xI 9x2 9XI SXK dq 'I ~K K K <0
dca (Il-q)' IH



The sign of dq/da follows from second order sufficient conditions which imply that HR <

0 and the numerator matrix is positive. Likewise:







66


0 0 l x 0 1 K o 0 S 2,v 0 2K SIX qx2 gx, P ~XK 9qI qq2 q qx 0 9 q dq KI gK2 gKx 0 9K
Adl.





or:


dq --p'(B +A)(1 -q)2(l -j5)2(p '(1-q)K- 1)





Hence, dq/dL > 0 since p'(1 -q)K-I < 0.

Therefore, dq/dL > 0 and dq/dca < 0, regardless of which solution is optimal for the agent when L > K. U














CHAPTER 4: AVOIDING VICARIOUS LIABILITY: THE INDEPENDENT
CONTRACTING RULE AND THE ERISA PREEMPTION CLAUSE


4.1 Introduction

The recent trend of the courts to expand the scope of vicarious liability has left

newly afflicted third parties searching for ways to avoid this liability. Some, such as banks threatened with liability for environmental damages, appeal to established principles of tort law in their attempt to avoid liability. Others, such as HMOs threatened with liability for physician malpractice, use new and creative methods to avoid liability. The goal of this chapter is to survey vicarious liability avoidance strategies, both old and new, and investigate the effect their success has on accident prevention. In particular, two avoidance tactics will be explored- one based on the "Independent Contracting Rule" and the other based on the "ERISA Preemption Clause."

The "Independent Contracting Rule," the general legal rule courts use to impose vicarious liability, states that principals are vicariously liable for the torts of their servants," but not those of independent contractors. This gives principals an incentive to avoid vicarious liability with the use of an independent contractor. The chapter shows that the use of a j udgement-proof independent contractor to avoid liability leads to insufficient accident -preventing care. Two categories of exceptions to the Independent Contracting Rule have emerged in recent court rulings. This chapter shows that these exceptions are 67







68

justifiable on efficiency grounds. Ex ante, these exceptions discourage the use of an independent contractor to avoid liability. Ex post, these exceptions induce the efficient care level in some principal-independent contractor relationships.

Recently, health maintenance organizations have begun to use a preemption clause in the Employee Retirement Income Savings Act of 1974 (ERISA) to avoid vicarious liability for physician malpractice. This chapter shows that, under the protection of ERISA, the FfMO will not only authorize too few medical tests and procedures, but will require an insufficient level of care from the physician. This result is generalized to dispel the commonly held belief that direct liability induces the agent to take excessive care in avoiding an accident while producing too little output. Direct liability induces too little care and too much production relative to the social optimum when the agent is judgementproof

The chapter is organized as follows. Section 4.2 describes the Independent

Contracting (IC) Rule and its use by the courts. Section 4.3 investigates the efficiency, in accident prevention, of the IC rule and its exceptions. Section 4.4 surveys the history of third party liability for physician malpractice and describes the evolution of the ERISA preemption clause as a tool used by HMOs to avoid liability. Section 4.5 explores the efficiency implications of the ERISA preemption clause.

4.2 Vicarious Liability and the Independent Contracting Rule

The general legal rule for the application of vicarious liability is the following: "A master is vicariously liable for the torts of his servants committed while the latter are







69

acting within the scope of their employment. '2' There are two key parts to this general rule. First, in order for the principal to be held liable for an agent's damaging conduct, the conduct must fall within the scope of employment. For example, if an agent commits a crime unrelated to his work for the principal, the principal usually escapes any criminal or civil liability. Unfortunately, determining whether an agent's conduct falls within the scope of his employment is often difficult and many controversial court rulings are based on this determination. For example, there are some cases in which the courts have held firms vicariously liable for damages resulting from assaults between employees, even when the motive for the assault is personal and unrelated to the firm's business." Following much of the previous literature, the models described subsequently assume that all of the agent's torts are directly related to the principal-agent enterprise to avoid the "scope of

21
employment" complication,

The second key part of the general vicarious liability rule is the requirement that the principal-agent relationship be one of master and servant. The level of control the principal exercises over the agent is the primary factor courts use to determine whether a business relationship is a master-servant relationship p 21. If the principal can easily observe



21 [10] p.176.
27
Carr v. Wm. C. Crowell Co., 28 Cal 2d 652, 171 P.2d 5 (1946); Lebrane v. Lewis, 292 So.2d 216 (La. 1974).
28
[30] analyzes the economic effects of the scope of employment rule in vicarious liability law.
2' The exact legal definition of servant can be found in Appendix A4.0.







70

and control the agent's level of care, then the courts usually find the principal to be vicariously liable for any accidents caused by the agent. For example, the courts usually determine that the principal has adequate control if the principal has a good understanding of the technology used by the agent, if the principal and agent work in the same location, if the principal supplies the necessary equipment to the agent, if the principal and agent are engaged in a long-term business relationship, etc. If the principal cannot readily observe or control the agent's level of care, then the courts usually will assign the liability for an accident to the agent who caused it whether or not the agent has enough wealth to cover the damages. For example, the courts will usually find the agent solely liable if the principal has little knowledge of the agent's technology, or if the agent is an independent contractor with which the principal has no long-term business relationship. Therefore, in general, a principal is held vicariously liable for the torts of his employees, but not for the torts of independent contractors which she has hired. This is commonly referred to as the "Independent Contracting Rule." Thus, if the principal wishes to avoid vicarious liability, she can do so by hiring an independent contractor, although this may result in lack of complete control over the work to be accomplished.

There are, however, many exceptions to the general independent contracting rule, In fact, the exceptions are so numerous that, as one judge put it, "it would be proper to say that the rule is now primarily important as a preamble to the catalog of its exceptions,"" Yet, as stated in the Restatement (Second) of Torts (Sect. 409),




" Pacific Fire Ins. Co. v. Kenny Boiler & Mfg. Co., 2 10 Minn. 500, 277 N.W. 226 (193 7).







71

In general, the exceptions may be said to fall into three very broad
categories
1. Negligence of the employer in selecting, instructing, or
supervising the contractor,
2. Non-delegable duties of the employer, arising out of some
relation toward the public or the particular plaintiff.
3. Work which is specially, peculiarly, or inherently dangerous.


Included in (1) are some cases in which the contractor chosen by the principal was underinsured or undercapitalized.

4.3 The Efficiency of the IC Rule and Its Exceptions

One commonly used justification of vicarious liability is the argument that it helps to deter the carelessness which leads to damaging accidents. Is this justification correct? Does the use of vicarious liability (as opposed to direct liability) increase the accidentpreventing care of the agent" How does the Independent Contracting (IC) Rule affect the relative efficiency of vicarious liability in preventing accidents? This section will examine the efficiency of vicarious liability in preventing accidents, particularly when it is applied by the courts using the IC rule and its exceptions.

4.3.1 The Model

Consider a principal who hires an agent to complete a productive activity. This

activity will produce a revenue of R for the principal, However, there is also a probability p (c (0, 1]) that the agent, while completing this activity, will cause an accident. The probability of an accident is a function of the precaution or care x the agent takes when completing the activity. It is assumed that increasing care decreases the probability of an accident at a decreasing rate (p'(x)O), The agent's personal marginal cost







72

(or disutility) of taking care is assumed to be constant and is normalized to unity, In addition, assume the agent's initial wealth is A, while the principal's wealth is unlimited."

Suppose a revenue-producing activity has a potential accident damage of D associated with it. The social welfare of this activity is: ,5W=R-p(x)D-x



Therefore, the socially optimal care level is given implicitly by.-p'(x)D I = 0



At the socially optimal care level, the marginal cost of increasing care equals the marginal decrease in expected damage associated with increasing care. Let x*(D) denote this care level.

The IC rule essentially applies Vicarious liability when the principal can observe the agent's care and applies direct liability when the principal cannot observe the agent's care, Therefore, to investigate the efficiency of the IC rule, the relative efficiency of vicarious and direct liability must be determined when the principal can and cannot observe the agent's preventive care.







31
In addition, the principal and the agent are both assumed to be risk neutral. This is a standard assumption found in most of the previous vicarious liability literature. See [13] for implications of general risk aversion,







7 3

4.3.2 Observable Care

When the principal can observe the agent's care, the principal can dictate what care the agent will exert. Therefore, concerning preventive care, the principal and agent will behave as if they are a united enterprise. The principal will dictate that the agent exert a level of care appropriate considering the potential losses the enterprise may face in the event of an accident.

For instance, when the principal faces a vicarious liability of L, the principal would like to maximize her expected profits of'.

Ell R -p(x)L -x



where the last term in this expression reflects the fact that the principal must compensate the agent for his exertion of care and its associated cost. (Otherwise, the agent will not participate in the productive activity.) Notice, ER is simply the expected profits of the principal-agent enterprise. Therefore, to maximize her profits, the principal will dictate that the agent exert x*(L). Hence, vicarious liability will lead to the socially efficient level of care if the assigned liability equals the damages (L = D).

When the agent faces a direct liability of L, the principal not only has to

compensate the agent for the cost of care, but also has to compensate the agent for his potential liability. Therefore, the principal must pay the agent an expected wage of p(x)L-x



32
This assumes the principal can make a take-it-or-leave-it offer to the agent (i.e., the agent has no bargaining power). See Chapter 2 for the implications of an alternative assumption.







74

if the principal dictates a level of care equal to x. Again the principal would like to maximize expected profits of R-p(x)L-x and will dictate a care of x*(L) for the agent to exert, However, if the liability is greater than the agent's wealth (L > A), the agent will only lose his wealth (A) in the event of an accident. In this case, the principal would only need to compensate the agent with an expected wage of p(x)A-x and, thus, would dictate a care of x*(A) for the agent to exert. This is the crux of the judgement-proof problem. When an agent is judgement-proof and the accident damages exceed his wealth (D > A), direct liability (with L = D) will lead to an inefficiently low level of care (x*(A) < x*(D)).

When the principal can observe the agent's care, both vicarious and direct liability lead to efficient care if the agent is not judgement-proof However, if the agent is judgement-proof, only vicarious liability insures that the agent will exert the socially efficient level of care. Thus, the IC rule, which requires vicarious liability when the principal can observe the agent, will lead to efficient care in this case.

4.3.3 Unobservable Care

When the principal cannot observe the agent's care, the principal cannot effectively dictate to the agent the care he will exert. In this case, the principal can only induce preventive care from the agent through provisions in the contract signed between the principal and the agent.

To be specific, if the principal is vicariously liable, the nature and timing of the principal-agent relationship is as follows. First, both the principal and the agent learn the principal's vicarious liability L in the event of an accident. Second, the principal offers a contract to the agent that specifies a non-accident wage of w,, and an accident wage of w,







75

Third, the agent chooses to accept or reject the principal's contract offer. If the agent accepts the contract, he then chooses his level of care, x, in the activity. This care cannot be observed by the principal or the courts. Fourth, the state of the world is realized (either accident or no-accident), the liability payment is collected from the principal in the event of an accident, and the appropriate wage is paid to the agent.

In choosing a contract to offer the agent, the principal solves the following problem:

[P] V(L) = Allax,.,,, ", LR-p(x)w4,,-(1 -p(x))w,-p(x)L] s1. W(I) px O+(1 -p(x))Wn-x 0
Wi) p, (X)(Wa I = 0
(Wi) w v, -A



Constraint (i) is the agent's participation constraint. The agent will only accept the principal's offer if the expected wage net of effort costs is at least as great as the agent's reservation wage (here normalized to zero). Constraint (ii) is the incentive compatibility constraint which reflects the principal's inability to observe the agent's care. Since the principal cannot make the wage contract contingent on the agent's care level, the agent will choose a care level that is personally optimal given the wage contract.3 Constraint



Actually, an additional condition is needed to insure that the stationary point specified by (11) is indeed optimal for the agent. This condition is: p "(x)(w7 -,)0

for all x. Since p"(x) > 0, this condition is equivalent to (w, wn) 0. Yet, since p'(x) < 0, condition (ii) implies (w, w,,) < 0. Therefore, condition (ii) specifies an optimal care level for the agent. See [22] for a thorough discussion of the first-order approach in moral hazard problems.







76

(iii) reflects the agent's linuited wealth and the principal's "right to indemnification." When a principal is found vicariously liable, she has the right to be compensated by the accidentcausing agent [7]. However, this compensation cannot exceed the agent's wealth. Therefore, the agent's accident wage must be at least -A.

For the vicariously liable principal in [P], the profit-maximizing level of care is x*(L) (Le., that which is socially optimal if the liability, L, equals the damages, D). The principal can induce this level of care by setting Wn Wa = L. The principal simply passes along the liability to the agent through the wage contract by penalizing the agent L in the event of an accident. However, as the principal's liability increases, there comes a point (denoted by L = K) at which passing the liability to the agent becomes costly to the principal. This occurs because of the agent's limited wealth. Recall that the principal can take no more than the agent's wealth through indemnification (w,, -A). Therefore, in order to induce x*(L) from the agent, the agent's no-accident wage (Wn) must be at least L

- A. However, if L A > x*(L) + p(x*(L))L, then the principal can only induce x*(L) from the agent by giving the agent an expected wage above his reservation wage (see constraint

(i) in [P]). Therefore, if L K, the principal can costlessly pass on the liability, L, to the agent. If L > K, then the principal faces a tradeoff, she can maximize the joint surplus only by sacrificing some of her share of the surplus, Faced with this tradeoff, the principal will sacrifice less profit by inducing a suboptimal care level from the agent. Even though this care level is suboptimal, it is non-decreasing in L, reflecting the principal's desire to pass on as much of the liability as possible while protecting her profits.







77

To be specific, the principal is faced with the following trade-off for liability levels greater than K. At one extreme, the principal could continue to pass the full liability onto the agent through the contract inducing the profit-maximizing care (x*(L)). However, the principal incurs a cost of L A [x*(L) + p(x'(L))L] when pursuing this approach, since the principal must give the agent a share of the joint profits in order to fully pass the liability onto him. At the other extreme, the principal could simply offer the contract which is profit-maximizing for L = K (i.e., freeze the accident penalty at K). This approach allows the principal to avoid giving the agent an economic rent. However, this will induce a level of care from the agent that is too low given the principal's vicarious liability of L. The principal will, therefore, incur an expected cost Of [P(X*(K)) p(x*(L))]L since the probability of an accident will be too high given this approach.

At first (i.e., for L e (KP]"), the latter approach is least costly for the principal, so the principal sets w, W, = K, even though L > K. Eventually (i.e., for L > p), this approach leads to a probability of an accident that is too great relative to the principal's liability, L. In this case, the principal uses a combination of the two strategies. The principal gives the agent a share of the joint profits to induce a higher level of care, but not enough to induce x*(L), (In other words, the accident penalty will fall between K and L.) Therefore, even though the induced care is inefficient for L > K, it is never less than X*(K).

For this reason, vicarious liability is at least as efficient as direct liability in

preventing accidents and more efficient when the agent is judgement-proof (L > A). If the



34
where p is the liability level at which the participation constraint no longer binds.







78

agent is directly liable, he will exert the socially optimal care (x*(L)) as long as the liability is no greater than his wealth (L : A). However, if the agent is potentially judgement proof (L > A), he will exert just x*(A) since the penalty he receives in the event of an accident is only the loss of his wealth, A. As shown above, when the principal is vicariously liable, she induces the efficient level of care from the agent not only when L :5 A, but also when L G [AK]. In addition, when L > K, the inefficiently low level of care induced under vicarious liability is never less than x*(i<)(> x*(A)). Hence, when the agent is Judgement-proof and the principal cannot observe the agent's care, vicarious liability is more efficient than direct liability.'5

4.3.4 Efficiency of the IC Rule

The previous analysis illustrates one shortfall of the IC rule. In general, the IC rule dictates direct liability when the principal cannot observe the agent. However, if the agent is judgement-proof, vicarious liability is more efficient than direct liability regardless of whether the principal can or cannot observe the agent's care. Therefore, if the prevention of accidents is the courts' primary goal, the application of vicarious liability should not be made contingent on the agent's status as a servant or independent contractor as in the IC rule.

The IC rule has an additional drawback. It gives the principal an incentive to avoid vicarious liability with the use of an independent contractor. If the agent is Judgementproof (L > A), the principal earns greater Profits by using an independent contractor which she cannot observe than by using an employee which she can observe. Under the IC rule, 15 The preceding model is discussed in more detail in Chapter 2.







79

independent contractors are directly liable, so the principal need only compensate the independent contractor for his potential loss of wealth in the event of an accident (p(x)A). If an employee is used, the principal is vicariously liable and faces a greater expected loss (p(x)L). Therefore, under the IC rule, the principal prefers to use an independent contractor to avoid vicarious liability, even though this involves a loss of direct control over operations. This result is summarized in the following theorem. Theorem 4. 1: If the agent is judgement-proof, the principal earns greater profits when she cannot observe the agent and the agent is directly liable than when she can observe the agent and the principal is vicariously liable. Proof See Appendix A4. 1.

The IC rule, thus, creates both ex ante and ex post inefficiencies. Ex ante, the IC rule gives the principal an incentive to give up control by using an independent contractor to avoid liability, Ex post, after the principal has chosen to use an independent contractor, the IC rule imposes direct liability when vicarious liability would be more efficient in preventing accidents.

4-3.5 The Efficiency of the Exceptions to the IC Rule

In light of this, it is useful to note again the presence of many exceptions to the IC rule. As shown above, any exception to the IC rule could be justified on efficiency grounds, since vicarious liability is at least as efficient as direct liability and more so when the agent is judgement-proof Still, some exceptions, such as those for severely undercapitalized contractors and inherently hazardous activities, may be particularly justifiable on efficiency grounds,







80

To investigate the efficiency of these exceptions, consider a specific form of the previous model. Suppose p(x) = e-". This functional form allows the introduction of a parameter (a) which reflects the inherent danger of an activity. For example, for a given level of preventive care, activity I (e.g., driving) is more dangerous (i.e., the probability of an accident is higher) than activity 2 (e.g., flying) when a, < a2. This leads to the following result-.

Theorem 4.2: If the principal cannot observe the agent and the liability level is relatively large (L > p), then the difference between the care induced under vicarious liability and that induced under direct liability increases as the activity becomes more dangerous. Proof See Appendix A4.2.

As we have seen, when the agent is judgement-proof, vicarious liability is more efficient in preventing accidents than direct liability, Theorem 4.2 illustrates that the difference in the preventive care induced by the two schemes grows as the productive activity becomes more hazardous. Therefore, the use of the IC rule when an activity'is inherently dangerous is particularly detrimental to accident prevention. While any exception to the IC rule is justified, this shows that an exception based on an inherently hazardous activity is particularly justifiable on efficiency grounds.

The exception for severely undercapitalized contractors can also be justified on efficiency grounds:

Theorem 4.3: If the principal cannot observe the agent and the agent is judgement-proof, then the difference between the care induced under vicarious liability and that induced under direct liability is non-decreasing in the agent's wealth shortfall (L A),







81

Proof See Appendix A4.3.

Theorem 4.3 simply states that the relative efficiency of vicarious liability grows as the agent becomes more judgement-proof Therefore, an exception to the IC rule when contractors are severely judgement-proof is warranted in promoting accident prevention.

In summary, the IC rule is inefficient on two grounds. Ex ante, the IC rule gives the principal an incentive to give up control by using an independent contractor to avoid liability. Ex post, after the principal has chosen to use an independent contractor, the IC rule imposes direct liability when vicarious liability would be more efficient in preventing accidents. However, the dangerous activity exception and the undercapitalization exception eliminate these inefficiencies in those instances in which they are particularly damaging to accident prevention,

4.4 Vicarious Liability, Medical Malpractice, and the ERISA Preemption Clause

Traditionally, third parties have not been held vicariously liable for medical

malpractice. For instance, hospitals were often immune from vicarious liability for the malpractice of their physicians because hospital physicians and other professional hospital personnel were considered independent contractors. In the first half of this century, this legal tendency sometimes lead to bizarre and self-contradictory rulings. For example, "in Bernstein v. Beth Israel Hospital, a nurse was considered an independent contractor when she scalded a patient, yet an employee for the purpose of receiving compensation when she scalded herself in the process,""




16 [12], p.28- Bernstein v. Beth Israel Hospital, 140 N.E. 694 (N.Y. 1923).







82

Courts soon began to realize that the use of the independent contracting rule for hospitals and physicians was often inappropriate. It became clear that hospitals have significant control over the quality of the medical care provided by their physicians and nurses. In addition, many competing hospitals made claims concerning the quality of their care which suggested that their physicians were employees, not independent contractors. So, in the late 50's and early 60's, courts began to hold hospitals liable for the malpractice of their physicians."

In recent years, a new type institution--the health maintenance organization

(HMO)--has emerged as a dominant form of health care provision. In 1996, 77 percent of U.S. workers belonged to an HMO (up from 49 percent in 1992)." The term "health maintenance organization" has actually come to describe many different types of health care institutions, some which resemble hospitals and others which more closely resemble insurance companies. However, all HMO's have one thing in common. Participants of HMOs, instead of paying a fee for each medical service they require, pay an up-front lump sum fee for their complete medical coverage.

The vicarious liability of HMOs for medical malpractice is far more complex than that of hospitals. One reason for this is the heterogeneity of organizational structures which fall under the title of HMO, The "staff model" HMOs, which directly employ their physicians and staff and own the hospitals, clinics, and laboratories in which their staff




" One landmark case in this area is Bing v. Thunig, 143 N.E. 2d 3 (N.Y. 1957), 38 [14].







83

work, are generally held vicariously liable for malpractice."9 The vicarious liability of "group" and "IA model" HlMOs is not as clear cut. Group and IPA model H-MOs contract with independent physicians groups to provide medical care for the 1-liM's members. These physicians take fee-for-service customers in addition to their HMVO customers, so they are sometimes seen as independent contractors in the eyes of the law. For this reason, group and IPA model H-lMOs are sometimes found immune from vicarious liability for physician malpractice."0 But, more often than not, group and IPA model HMVOs cannot escape vicarious liability on these grounds."

Recently, HMOs have begun to use a creative approach to avoid much of the vicarious liability they face. This strategy involves the use of a clause in the federal "Employee Retirement Income Savings Act" (ERJSA) of 1974. Prior to 1974, pensions and other employee benefit plans were regulated by a patchwork of state laws. This often created problems for firms wishing to design benefit plans for employees in different states. In addition, some state regulations were inadequate and allowed abuses in pension administration and disclosure of pension funding and vesting. Congress responded to these inadequacies by passing ERISA to make the regulation of employee benefit plans a federal



39
One example is Sloan v. Metropolitan Health Council, 516 N.E.2d 1104 (Ind. Ct. App. 1987).
40
Two examples are Raglin v. HIMO Illinois, 595 N.E.2d 153 (Ill. App. Ct. 1992) and Chase v. Independent Practice Association, 5 83 N.E.2d 251 (Mass. App. Ct. 199 1).
41
Two examples are Schleier v. Kaiser Foundation Health Plan, 876 F.2d 174 (D.C. Cir 1989) and Boyd v. Albert Einstein Medical Center, 547 A.2d 1229 (Pa. Super. Ct. 1988).







84

responsibility. To supersede the patchwork of state laws regulating benefit plans, section 514 of ERISA contains a preemption clause which states that ERISA "shall supersede any and all State laws insofar as they may now or hereafter relate to any employee benefit plan. ,12 It is this preemption clause that HJAOs have used, somewhat successfully, to avoid much of the vicarious liability they would normally face.

HMOs can use the ERISA preemption clause because most of their members join through employee health insurance. In particular, many large companies fully fund their employee health benefits and contract with an HMO to administer these health plans. Approximately half of all American workers receive their health benefits through employer-funded health plans." In addition, medical malpractice traditionally falls under the jurisdiction of the state courts. HMOs argue that they simply administer these employer-funded health benefit plans and, therefore, medical malpractice claims made in connection with these plans in state courts are superseded by ERISA. As a lawyer for U.S. Healthcare recently stated, "ER-ISA pre-empts state law medical malpractice claims against entities involved in the administration or delivery of health care benefits under an ERISA plan. ,44

One may wonder, why is this significant? If ERISA preempts state medical

malpractice claims against FMOs, why can't a victim bring his or her claim against an FMO in federal court? The problem with this approach is that ERISA has no provisions


-) p. 1023, 29 U.S. C. I 144(a).
41 [12], p.9.

44 [ 19], p.1 6.







85

relating to medical malpractice. If a victim's medical malpractice suit is moved from state to federal court, this leaves the victim with no means of recovering damages from the HMO." Therefore, if an HMO is successful in moving a medical malpractice suit from state to federal court, it effectively avoids all vicarious liability.

HMOs generally have been successful in their use of the ERISA preemption clause. In the majority of cases in which HMrvOs have claimed immunity from liability through ERISA, the federal appeals courts have invoked the preemption."6 The courts have done so despite the knowledge that victims have no recourse under ERISA. As one judge stated, "the lack of an ERISA remedy does not affect a preemption analysis."147 In this reasoning, the courts have followed the example of the Supreme Court, which has broadly interpreted the "relate to" verb in the preemption clause. The Supreme Court has asserted that "a law relates to an employee welfare plan if it has a 'connection with or reference to such a plan. "'4' This leaves federal appeals courts little room to uphold a malpractice claim against an HMO administering an employer-funded health plan. Despite this, a small number of judges have denied ERISA preemption of malpractice claims.49 in




However, the victim can still pursue a claim against the physician(s) under state malpractice law.

4[12], pp. 40-43.

~Corcoran v. United Healthcare, Inc., 965 F.2d 1321 (5th Cir. 1992), p. 13333. 4FMC Corp. v. Holliday, 498 U.S. 52 (1990), p.58
49
For example, Haas v. Group Health Plan, Inc., 875 F. Supp 544 (S.D. Ill. 1994), and Smith v. lMO Great Lakes, 852 F. Supp. 669 (N.D. Ill. 1994).







86

addition, the Supreme Court has recently backtracked somewhat from their accommodating interpretation of the ERISA preemption clause." This may give courts leeway to uphold claims of vicarious liability against HN40s in future rulings.

4.5 Efficiency of the ERISA Preemption Clause The use of the ERISA preemption clause has become an effective tool for HMOs in avoiding vicarious liability. The belief among many is that the use of ERISA in this way could lead to more medical accidents and misdiagnoses.5' The analysis of section 4.3 certainly supports this view. However, the context of HMO liability for malpractice is a bit more complex than that modeled in section 4.3. In section 4.3, the agent's care was the sole factor affecting the likelihood of an accident. In many malpractice cases affecting HMOs, the physician's care is not the only factor contributing to an accident. The HMO often dictates what procedures and tests to use and this can significantly affect the probability of an accident or misdiagnosis. In this more complex context, how does the avoidance of vicarious liability affect accident prevention?

To answer this question, consider a slightly modified version of the model in

section 4.3. Suppose the productive activity referred to in section 4.3) is the diagnosis and treatment of an ailing HMO member. The HM0 specifies the allowed tests and procedures to use in treatment. Let the number of tests and procedures be indexed with the (real) variable s. This variable can also reflect the overall quality of the medical tests and procedures. For example, a very accurate (and possibly very expensive) test for cancer 5' New York Conference of Blue Cross v. Travelers Insurance, 115 S.Ct. 1671 (1995).

51 [ 19],







87

translates into a large value of s. As before, the average level of care exerted by a physician in performing these tests and procedures is denoted x. The probability that malpractice occurs in the diagnosis and/or treatment of the patient is given by p(s,x). p(s,x) is a decreasing, convex function of both s and x." In addition, assume that tests/procedures and care are "compliments" with respect to achieving a mistake-free diagnosis and treatment. In other words, increasing the number or quality of test s/procedures will increase the marginal ability of care to prevent malpractice (p,, < 0).

The H-lMO's profit gross of physician compensation is R(s) = C u~s. C represents the capitation paid by the patient to the HMO. Recall, this is a:lump sum fee independent of the number or quality of services provided. cx represents the constant incremental cost of tests and procedures. The physicians marginal cost of care is assumed to be a constant P3.

The socially optimal number of test s/procedures and level of care are characterized by conditions analogous to those found in section 4.3:


-pS9 =a




where D is the level of damages associated with an incident of malpractice. At the socially optimal number of test s/pro cedures, the marginal cost of increasing s equals the marginal decrease in expected damage associated with increasing s. Likewise, the marginal cost of increasing care equals the marginal decrease in expected damage associated with 12 In other words, p, < 0, p, < 0, p,,,> 0, p,> 0, and pp (pSX)2 > 0.







88

increasing care at the socially optimal care level. Let this socially optimal number of procedures and level of care be denoted by [x*(D), s*(D)].

As before, the HMO pays the physician a wage that can be made contingent on the occurrence of an accident. In addition, it is assumed that the HFEWI can observe and contract upon the physician's quality of medical care. The accuracy of this assumption may, at first, seem uncertain given the myriad of organizational structures which characterize the J-H40-physician relationship. However, I believe this best describes the flow of information between physician and H-MO in all of the HMJVO models. In the "staff' model, physicians are essentially employees of the 1-MO, so the HMO can easily observe and control their physicians' level of care. In the "group" and "IPA" models, the observability and control of the physicians is not as clear cut. Many H-lMO's of this type openly claim that they cannot control the care of their affiliated physicians. As one HMOVI executive recently stated, "U.S. Healthcare does not direct the care furmished by participating health care providers.""3 However, almost all of the group/IPA H-lMOs employ "utilization review"~ and "quality assurance"~ programs which monitor their affiliated physicians.5' In addition, I-HMOs often use advertising which assures potential customers of the highest quality of medical care through rigorous monitoring of their physicians.55 Therefore, despite the claims of lack of control, most of the evidence





5' [ 19], p. 16, col. 6.

54 [12].

S[19].







89

supports the contention that group/IPA model HMOs are able to observe and control the medical care of their physicians.

The contracting problem facing the HMO is the following:

[HP] Max R(s)-p(s,x)w0(x)-(1 -p(s,x))w (x)-p(s',x)Lp
s.t. (i) p(s,x)1+,(x) +(1 -p(s,x))w,(x) Px -p(s,x)L, > 0
(ii) wo(x) >_ -A


As in [P], constraint (i) is the physician's participation constraint and constraint (ii) is the wealth constraint reflecting the fact that the physician's wealth is restricted to A. The liability rule applied by the courts is characterized by LP, the liability the HMO (principal) faces in the event of an accident, and L,,, the liability the physician (agent) faces in the event of an accident. The standard joint liability for malpractice is represented by any [Lp,Ll which satisfies Lp + La = D (provided L, _< A). If the HMO is able to shield itself from liability using the ERISA preemption clause, LP = 0 and L. can be no more than A given the physician's limited wealth.

If the HMO can avoid liability through the ERISA preemption clause, one would naturally expect the HMO to scrimp on the use of costly medical tests and procedures when treating patients. The IMO can save money by reducing procedures without increasing the likelihood of a successful malpractice claim against the 1-1MO. Thus, the ERISA preemption clause clearly gives the HMO an incentive to authorize too few procedures relative to the social optimum, s*(D). However, the ERISA preemption clause also creates another inefficiency. If the HMO avoids liability, this will also result in the provision of an insufficiently low level of care, when the physician is judgement-proof (D







90

> A), Under ERISA, only the physician can be held liable for malpractice, If the physician is judgement-proof, his expected loss due to liability is pA. The FB40 need only compensate the physician for this expected loss and, thus, the FEVO only faces the indirect cost of pA due to malpractice. Since the HMO faces a cost less than the expected damages, pD, the HMO will not only authorize too few procedures, but will require an insufficient level of care from the physician. This result is summarized in the following theorem:

Theorem 4.4: If the physician is judgement-proof (D > A), the exemption of liability for FfMOs under ERISA will result in a level of care less than the social optimum (x*(D)) and too few tests and procedures relative to the social optimum (s*(D)). Proof See Appendix A4.4.

The result in theorem 4.4 can be generalized to contexts other than HMOphysician liability. For instance, s can be interpreted as the number or quality of safety enhancing investments made by the principal (reflected in the production process or the final product or both). Theorem 4.4 then states that escaping vicarious liability will result in too little care by the agent and too few safety enhancing investments. Alternatively, suppose s is interpreted generally as the level of production specified by the principal. In this case, R(s), the profit gross of employee compensation, is an increasing function of s." In addition, p(sx), the probability of an accident, increases with s at a decreasing rate (p, >

0 and p,, < 0) and "reducing production" and care are "compliments" with respect to accident prevention (p,, > 0). The result in theorem 4.4 now takes the following form: 5' For this generalization, assume R is concave in s (R" < 0).







91

Corollary 4.5: If the agent is judgement-proof (D > A), an exemption of liability for the principal will result in a level of care less than the social optimum (x*(D)) and a level of production greater than the social optimum (s*(D)). Proof See Appendix A4.5.

If the agent is judgement-proof and the principal can avoid vicarious liability, the principal saves D-A in the event of an accident since only the agent is liable for damages, With this leeway in expected accident costs, the principal can increase production and compensate the agent with a relaxation of requirements for care. In this fashion, the principal can earn greater expected profits while still giving the agent the same net compensation.

This result, as expressed in corollary 4.5, contradicts a widely-held belief about the possible effects of direct liability on care and production. Some legal scholars argue that a directly liable agent may take excessive care to prevent an accident and thus may be less productive, As Kornhauser (1982) states-.

... there is a conflict of interest between agent and principal in which
the agent prefers, if all else is equal, to take less care, while the
principal cares only about her profit. This rationale assumes that the
agent's exercise of care decreases productivity so that if he takes
more care, enterprise profits fall. However, under a rule of law that assigns liability to the agent, the agent's interests conflict with those
of the enterprise. Thus, in order to avoid liability, he might take
more care than he otherwise would under enterprise liability.
Consequently, from an economic standpoint, too few accidents and
too little profit would be produced under agent liability."


Former Assistant Attorney General William F. Baxter shares this opinion:




5' [131, pp. 1350.







92

Pecuniary responsibility on the part of employees leads to internal inefficiency not because employee behavior is unresponsive to the prospect of such liability but because it is too responsive. Liability
induces the employee to adopt behavior that is suboptimal from the
standpoint of the employer. Pecuniary responsibility forces
employees to choose between protecting their own purses and
executing the programs of their employers with zeal and
imagination. We should not be surprised to find that employees
who face such a choice strike a different balance than would those who had to bear both the costs of harm to outsiders and the costs
of ineffective implementation. 38


Corollary 4,5 states that a wealth-constrained agent will never behave in this manner. A directly liable judgement-proof agent will exert too little preventive care and produce too much at the direction of the principal. However, the previous analysis does not incorporate such factors as the agent's expected future income and reputation which could create an incentive for greater care under direct liability.

4.6 Conclusion

The two tactics employed by principals to avoid vicarious liability--the

Independent Contracting (IC) Rule and the ERISA preemption clause--both lead to inefficiencies in accident prevention. The IC rule is inefficient in two ways. Ex ante, the IC rule gives the principal an incentive to give up control by using an independent contractor to avoid liability. Ex post, after the principal has chosen to use an independent contractor, the IC rule imposes direct liability when vicarious liability would be more efficient in preventing accidents. However, the dangerous activity exception and the





5' [1], pp. 49,







9n

undercapitalization exception eliminate these inefficiencies in those instances in which they are particularly damaging to accident prevention.

When implemented in the case of FMO and physician malpractice, the ERISA preemption clause leads, not only to an inefficiently low number of medical procedures, but also induces an insufficient level of care from the physician. This result can be generalized to dispel the commonly held belief that direct liability induces the agent to take excessive care in avoiding an accident while producing too little output. Direct liability induces too little care and too much production relative to the social optimum when the agent is judgement-proof



A4.0: Legal Definition of a Servant

The legal definition of a servant, found in section 220.2 of the Restatement (Second) of Agency, is the following:



In determining whether one acting for another is a servant or an independent contractor, the following matters of fact, among others, are considered:

(a) the extent of control which, by the agreement, the master may exercise over the details of the work,

(b) whether or not the one employed is engaged in a distinct occupation or business;

(c) the kind of occupation, with reference to whether, in the locality, the work is usually done under the direction of the employer or by a specialist without supervision-,

(d) the skill required in the particular occupation-,




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ESSAYS ON THE ECONOMICS OF VICARIOUS LIABILITY
*
BY
CHRISTOPHER J. GARMON
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
1997

ACKNOWLEDGMENTS
I have benefitted immeasurably from the help and support of many people while
completing this dissertation. It goes without saying that I could not have completed this
dissertation without the help of my advisory committee. Dr. David Sappington made
numerous, valuable suggestions on various drafts, always prodding me to give more
intuitive explanations of my results. Dr. Steven Slutsky was always unselfish with his time,
helping me understand the intuition of complex maximization problems. Most of all, I
would like to thank, my advisor, Dr. Tracy Lewis, for his many illuminating insights, his
constant encouragement throughout (but particularly in the less productive phases of my
research), and his never ending patience with my often stubborn mind. I learned a great
deal under his tutelage. Also, much of my interest in the economic effects of laws and
institutions was gained in the courses I have taken with Drs. Lewis, Sappington, and
Slutsky.
I would like to thank my officemate and friend, Michael Blake, for his support and
encouragement and for lending an ear when the sense of my results was eluding me. I
would also like to thank Dr. Sanford Berg, Dr. Margaret Byrne, Dr Glenna Carr, Dr.
Jonathan Hamilton, and Dr. Jeffery Harrison for their helpful suggestions.
Finally, I would like to thank my parents and Andie for their love and support
which sustained me these past four years.
u

TABLE OF CONTENTS
ACKNOWLEDGMENTS
LIST OF FIGURES
ABSTRACT
CHAPTERS
1 INTRODUCTION
2 VICARIOUS LIABILITY AND BARGAINING POWER
2.1 Introduction
2.2 Vicarious Liability Benchmark Model
2.3 Vicarious Liability with Variable Bargaining Power
2.4 Comparison of Models
2.5 Conclusion
A2.1: Proof of Theorem 2.1
A2.2: Proof of Theorem 2.2
A2.3: Proof of Theorem 2.3
A2.4: Proof of Theorem 2.4
A2.5: Proof of Theorem 2.5
3 VICARIOUS LIABILITY, NEGLIGENCE, AND MONITORING
3.1 Introduction
3.2 Collusion-Proof Negligence and Vicarious Liability
3.3 Monitoring and Vicarious Liability
3.3.1 Benchmark Vicarious Liability Model
3.3.2 Vicarious Liability and Endogenous Monitoring .
3.4 Conclusion
A3.1: Proof of Theorem 3.1
A3.2: Proof of Theorem 3.2
A3.3: Proof of Theorem 3.3
iii
. ii
. v
vi
. 1
. 6
. 6
. 9
17
23
27
28
32
"â– > o
JO
34
35
36
36
38
45
45
49
57
57
58
61

4 AVOIDING VICARIOUS LIABILITY: THE INDEPENDENT CONTRACTING
RULE AND THE ERISA PREEMPTION CLAUSE 67
4.1 Introduction 67
4.2 Vicarious Liability and the Independent Contracting Rule 68
4.3 The Efficiency of the IC Rule and Its Exceptions 71
4.3.1 The Model 71
4.3.2 Observable Care 73
4.3.3 Unobservable Care 74
4.3.4 Efficiency of the IC Rule 78
4.3.5 The Efficiency of the Exceptions to the IC Rule 79
4.4 Vicarious Liability, Medical Malpractice, and the ERISA Preemption Clause
81
4.5 Efficiency of the ERISA Preemption Clause 86
4.6 Conclusion 92
A4.0: Legal Definition of a Servant 93
A4.1 Proof of Theorem 4 1 94
A4.2: Proof of Theorem 4.2 95
A4.3: Proof of Theorem 4.3 95
A4.4: Proof of Theorem 4.4 96
A4.5: Proof of Corollary 4.5 97
5 CONCLUDING REMARKS AND EXTENSIONS 99
REFERENCES 101
BIOGRAPHICAL SKETCH 104
iv

LIST OF FIGURES
Figure 1 16
Figure 2 25
Figure 3 51
v

Abstract of the Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ESSAYS ON THE ECONOMICS OF VICARIOUS LIABILITY
By
Christopher J. Garmon
August, 1997
Chairman: Professor Tracy Lewis
Major Department: Economics
This dissertation, a compilation of three essays, investigates the economic
efficiency of vicarious liability relative to direct liability when the former is used to solve
the judgement-proof problem. The first essay analyzes how the relative bargaining power
of the principal and agent affects vicarious liability's efficiency in preventing accidents
when the agent is judgement-proof. When the agent has no bargaining power, vicarious
liability induces a more efficient level of care than direct liability when the agent is
judgement-proof. In addition, it is shown that the preventive care induced by vicarious
liability increases as the agent's bargaining power increases.
The second essay investigates the accident-preventing efficiency of various liability
rules when the principal can monitor the agent's care. It is shown that strict vicarious
liability induces the same level of preventive care as strict joint liability and collusion-proof
negligence. The paper also investigates the efficiency of vicarious liability when the
principal's level of monitoring is endogenous. It is shown that vicarious liability induces
vi

monitoring if the agent is sufficiently judgement-proof and if monitoring is not too
expensive. In addition, preventive care when monitoring is possible is at least as great (and
often greater) than that induced without monitoring. Finally, it is shown that the principal
does not gain by using ex post investigation instead of ex ante monitoring.
The third essay explores two tactics firms use to avoid vicarious liability: the
Independent Contracting (IC) Rule and the ERISA Preemption Clause. This paper shows
that the use of a judgement-proof independent contractor to avoid liability leads to
insufficient accident-preventing care. It is shown that the exceptions to the IC rule are
justifiable, both ex ante and ex post, on efficiency grounds. This paper also shows that,
under the protection of ERISA, a health maintenance organization will not only authorize
too few medical tests and procedures, but will require an insufficient level of care from the
physician. This result is generalized to dispel the belief that direct liability induces
excessive care in avoiding an accident while producing too little output.
vii

CHAPTER 1: INTRODUCTION
Vicarious liability occurs when one party causes an accident and another party is
held liable for at least a portion of the damages. As a rule for assigning liability and
recovering damages, vicarious liability is used by the courts in many different contexts.
For example, fleet companies may be held liable for accidents caused by their truck drivers
[16] and oil companies may be held liable for accidents occurring at their franchised gas
stations [4],[5], Recently, vicarious liability has been applied in some areas that were
previously exempt. For example, hospitals and health maintenance organizations have been
found liable for the malpractice of independent physicians working on their premises
[11 ],[21 ]. In addition, banks now face an increased threat of liability for environmental
damages caused by their debtors [17],[27]. There is also a trend within state legislatures to
make parents liable for damages caused by their children [6],
When applying vicarious liability, courts usually justify their action using one of
three arguments [10], First, under the "deep pockets theory," vicarious liability is seen as
beneficial because it allows the victim to be fully compensated for the inflicted damages.
Second, vicarious liability is used to induce the principal (e.g., employer) to be more
careful in selecting and monitoring her agents (e.g., employees). Third, the "modern
justification" sees vicarious liability "as a means of allocating to business enterprises the

2
costs of accidents caused by those enterprises"' to induce the efficient amount of accident¬
preventing care.
The first justification highlights a common factor in virtually all vicarious liability
cases: the "judgement-proof problem." Vicarious liability is almost always applied in cases
in which the party responsible for the accident has insufficient assets to fully compensate
the victim for his or her damages. Indeed, if the accident-causing agent has sufficient
assets for compensation, there is no reason for the victim to seek compensation from a
third party. Thus, a feature prevalent in most vicarious liability cases is a judgement-proof
agent.
The second justification highlights the fact that, in many vicarious liability cases,
the behavior of the accident-causing agent is difficult for any party to observe. Vicarious
liability is applied by the courts with the belief that, of all parties, the principal is best able
to monitor the agent. Thus, vicarious liability is seen as a way to induce the principal to
monitor the agent, even when monitoring is difficult and costly.
The third justification highlights the commonly held legal belief that accidents are
an "externality" associated with many business activities. If a principal hires an agent to
complete a productive activity which is potentially damaging to a third party, and only the
agent can be held liable in the event of an accident, then the principal-agent business
enterprise may avoid some of the potential accident costs which are born by society. For
this reason, the principal-agent enterprise may take too little care in preventing an
[10], p. 183.

accident. From this point of view, vicarious liability is seen as a way of assuring that the
total accident costs are born by the principal-agent enterprise in the event of an accident,
so the proper amount of care will be taken to avoid an accident.
This dissertation investigates the accident-preventing efficiency of vicarious
liability relative to direct liability (where the agent alone is liable) when the agent is
judgement-proof and his actions may be difficult to observe. The dissertation proves that
vicarious liability is more efficient in preventing accidents than direct liability in most
contexts in which it is applied. In addition, vicarious liability can sometimes induce the
principal to expend resources to monitor the agent. Finally, common methods of avoiding
vicarious liability are shown to produce various inefficiencies in accident prevention.
In particular, Chapter 2 analyzes how the relative bargaining power of the principal
and agent affects vicarious liability's efficiency in preventing accidents when the agent is
judgement-proof. When the agent has no bargaining power, vicarious liability induces a
more efficient level of care than direct liability when the agent is judgement-proof. In
addition, it is shown that the preventive care induced by vicarious liability increases as the
agent's bargaining power increases. Thus, vicarious liability is more efficient than direct
liability regardless of the principal and agent's relative bargaining power.
Chapter 3 investigates the accident-preventing efficiency of various liability rules
when the principal can (imperfectly) monitor the agent's care. It is shown that strict
vicarious liability induces the same level of preventive care from the agent as strict joint
liability and collusion-proof negligence. The chapter also investigates the efficiency of
strict vicarious liability when the principal's level of monitoring is endogenous. It is shown

4
that vicarious liability induces monitoring of the agent if the agent is sufficiently
judgement-proof and if monitoring is not too expensive. In addition, preventive care when
monitoring is possible is at least as great (and often greater) than that induced when
monitoring is not possible. Finally, it is shown that the principal does not gain by using ex
post investigation instead of ex ante monitoring.
Chapter 4 explores two tactics firms use to avoid vicarious liability: The
Independent Contracting Rule and the ERISA Preemption Clause. The "Independent
Contracting Rule," the general legal rule courts use to impose vicarious liability, states that
principals are vicariously liable for the torts of their "servants," but not those of
independent contractors. This gives principals an incentive to avoid vicarious liability with
the use of an independent contractor. The chapter shows that the use of a judgement-
proof independent contractor to avoid liability leads to insufficient accident-preventing
care. Two categories of exceptions to the Independent Contracting Rule have emerged in
recent court rulings. The chapter shows that these exceptions are justifiable on efficiency
grounds. Ex ante, these exceptions discourage the use of an independent contractor to
avoid liability. Ex post, these exceptions induce the efficient care level in some principal-
independent contractor relationships.
Recently, health maintenance organizations (HMOs) have begun to use a
preemption clause in the Employee Retirement Income Savings Act of 1974 (ERISA) to
avoid vicarious liability for physician malpractice. Chapter 4 shows that, under the
protection of ERISA, the HMO will not only authorize too few medical tests and
procedures, but will require an insufficient level of care from the physician. This result is

5
generalized to dispel the commonly held belief that direct liability induces the agent to take
excessive care in avoiding an accident while producing too little output. Direct liability
induces too little care and too much production relative to the social optimum when the
agent is judgement-proof.
A preliminary comment about the content of subsequent chapters is warranted at
this time. Each substantive chapter is written to be a self-contained analysis of an issue
related to the efficiency of vicarious liability. For this reason, the reader may notice some
interchapter redundancy. In particular, a benchmark model of vicarious liability is
contained in all three chapters as a basic framework for each chapter's analysis of vicarious
liability. This is done because this benchmark model gives the best understanding of the
basic workings of a principal-agent relationship under vicarious and direct liability. Thus, it
serves as the best foundation for the models contained in each chapter.

CHAPTER 2: VICARIOUS LIABILITY AND BARGAINING POWER
2.1 Introduction
Vicarious liability is applied by the courts in many different business contexts: from
HMO liability for physician malpractice to bank liability for environmental damages. Given
the scope of vicarious liability, it is natural to question its efficiency in preventing
accidents. In many circumstances, vicarious liability and direct liability (in which the agent
alone is liable) are identical in their ability to deter accidents. For instance, if both the
principal (e.g., employer, hospital, lender, etc.) and the agent (e g., employee, physician,
firm, etc.) have adequate wealth to cover the damages from an accident, if there are no
information asymmetries, and if contracting costs are negligible, then vicarious liability and
direct liability will induce the same level of preventive care from the agent. Under
vicarious liability, the principal can simply pass along the liability to the agent through the
wage contract and make the agent's incentives identical to those under direct liability. This
equivalence can also be thought of as an application of the famous Coase Theorem [9],
However, vicarious liability is applied most often in cases where the agent does not
have sufficient wealth to satisfy a liability claim (often referred to as the "judgement-proof
problem") and where the agent's preventive care is difficult to monitor. In these cases, the
efficiency of vicarious liability is not as clear. In the last fifteen years, a few articles have
6

7
analyzed the efficiency of vicarious liability in this context. The conclusions of these
studies are mixed. Shavell (1987) [26] shows that under vicarious liability, if the agent is
judgement-proof and the principal cannot observe the agent's care, the agent "may take
suboptimal care, but at least as much as he does when he alone is liable."1 Kornhauser
(1982) [13] reaches a similar conclusion, but with more qualifications: "The agent will
clearly take less care [under direct liability] when the agent is close to risk-neutral, has
limited assets, a small reservation wage, and the damages are greatly in excess of his
assets."2 On the other hand, Sykes (1984) [29] argues that vicarious liability will most
likely induce less preventive care than direct liability in this context. Pitchford (1995) [20]
proves this assertion in the context of a lender liability model.2 Considering the similarities
in these authors’ models and assumptions, the conflicting results are particularly puzzling.
One possible explanation for these opposing results is that the authors adopt
different assumptions about the relative bargaining power of the principal and the agent.
Both Shavell and Kornhauser assume implicitly that the principal can make a take-it-or-
leave-it offer to the agent (i.e., the agent has no bargaining power). However, Syke's
argument that vicarious liability may be less efficient than direct liability is predicated on
the assumption that the agent may have some bargaining power:
In labor markets that are not perfectly competitive, some agents possess
bargaining power or special skills that enable them to obtain a fee in excess
of their reservation wage—an economic rent. Because vicarious liability
1 [26] p. 185
2 [13] p. 1363
3 Other papers which relate to this topic include [8], [15], [18], [25], and [28].

8
reduces the profitability of the enterprise relative to its profitability under
personal liability, principals may succeed in bargaining away some of these
rents . . . Then, because vicarious liability reduces the demand for agents'
services, the market will tend to equilibrate at a lower wage rate and thus
provide smaller incentives to avoid losses. Thus, although potentially
insolvent agents invest inefficiently little in loss avoidance under personal
liability, vicarious liability conceivably aggravates the inadequacy of their
loss-avoidance incentives.4
In a subsequent footnote3, Sykes claims that Kornhauser's opposing result emanates from
the "highly restrictive" assumption that the agent has no bargaining power. In addition,
Pitchford shows that vicarious liability can be less efficient than direct liability in
preventing accidents when the principal has no bargaining power. In his model of lender
liability, Pitchford assumes that the lending industry is perfectly competitive and,
therefore, each lending institution earns zero economic profit. Thus, if vicarious liability is
imposed on a lending institution in the event of an accident, the lending institution will
require an increased premium from the agent in the no-accident state in order to break
even. This increased premium in the no-accident state will reduce the agent's incentives to
avoid an accident by making the no-accident state relatively less attractive to the agent.
Therefore, vicarious liability may be less efficient than direct liability when the principal
has little bargaining power relative to the agent.
While a close reading of the previous literature suggests that bargaining power
plays a role in the efficiency of vicarious liability, no analysis has characterized the nature
of this relationship. This paper will analyze how the relative bargaining power of the
4 [29] pp. 1248-9.
3 ibid, Footnote #50, p. 1249.

9
principal and agent affects vicarious liability's efficiency in preventing accidents.
Specifically, this paper will first present a benchmark principal-agent model describing the
efficiency of vicarious liability when the agent has no bargaining power. In this case, it will
be shown that vicarious liability induces a more efficient level of care than direct liability
when the agent is judgement-proof. A closely related model is then presented in which the
agent's bargaining power is allowed to vary. Contrary to Sykes and Pitchford, it will be
shown that the preventive care induced by vicarious liability increases as the agent's
bargaining power increases. This is because the agent’s share of the enterprise’s joint
profit increases with his bargaining power. An agent with bargaining power therefore has
more to lose in the event of a liability claim on the principal and her business. For this
reason, an agent with bargaining power is apt to be more careful in preventing accidents
than an agent with little bargaining power. Furthermore, this implies that vicarious liability
is more efficient than direct liability regardless of the principal and agent's relative
bargaining power.
The chapter is organized as follows. Section 2.2 presents the benchmark model of
vicarious liability in which the agent has no bargaining power. Section 2.3 contains the
closely related model in which the bargaining power of the agent is allowed to vary
parametrically. Section 2.4 compares the results of these models and discusses the effects
of bargaining power on preventive care when the principal is vicariously liable.
2.2 Vicarious Liability Benchmark Model
In order to understand how bargaining power affects the efficiency of vicarious
liability, it is useful to look first at an extreme case in which the agent has no bargaining

10
power. In this case, it will be assumed that the principal can make a take-it-or-leave-it
offer to the agent (i.e., the agent has no power to negotiate the terms of the contract).
Consider a principal who hires an agent to complete a productive activity. This
activity will produce a revenue of R for the principal. However, there is also a probability
p that the agent, while completing this activity, will cause an accident. The probability of
an accident is a function of the precaution or care x the agent takes when completing the
activity. It is assumed that increasing care decreases the probability of an accident at a
decreasing rate (p'(x)<0 and p"(x)>0). The agent's personal marginal cost (or disutility) of
taking care is assumed to be constant and is normalized to unity. In addition, assume the
agent's initial wealth is limited to A.
The timing of the principal-agent relationship is as follows. First, both the principal
and the agent learn the principal's vicarious liability L in the event of an accident. Second,
the principal offers a contract to the agent that specifies a non-accident wage of wn and an
accident wage of wa. Third, the agent chooses to accept or reject the principal’s contract
offer. If the agent accepts the contract, the agent then chooses his level of care, x, in the
activity. This care cannot be observed by the principal or the courts. Fourth, the state of
the world is realized (either accident or no-accident), the liability payment is collected
from the principal in the event of an accident, and the appropriate wage is paid to the
agent.
In choosing a contract to offer the agent, the principal solves the following
problem:

11
[P] V(L) = K4axxyv^[R-p{x)wa-{\-p{x))wn-p{x)L]
s. i. (/) p(x)wa +(1 -p{x))wn -x > 0
00 P\x\M’a-Wn)-\ = 0
(Hi) wa > -A
Constraint (i) is the agent's participation constraint. The agent will only accept the
principal's offer if the expected wage net of effort costs is at least as great as the agent's
reservation wage (here normalized to zero). Constraint (ii) is the incentive compatibility
constraint which reflects the principal's inability to observe the agent's care. Since the
principal cannot make the wage contract contingent on the agent's care level, the agent
will choose a care level that is personally optimal given the wage contract.6 Constraint (iii)
reflects the agent's limited wealth and the principal's "right to indemnification." When a
principal is found vicariously liable, she has the right to be compensated by the accident-
causing agent [7], However, this compensation cannot exceed the agent's wealth.
Therefore, the agent's accident wage must be at least -A.
In [P], it is implicitly assumed that both the principal and the agent are risk neutral.
Kornhauser (1982) [13] demonstrated that, if the agent is not judgement-proof, vicarious
6 Actually, an additional condition is needed to insure that the stationary point specified by
(ii) is indeed optimal for the agent This condition is:
p"(x)(wa-wn)< 0
for all x. Since p"(x) > 0, this condition is equivalent to (wa - wn) < 0. Yet, since p'(x) < 0,
condition (ii) implies (wa - wn) < 0. Therefore, condition (ii) specifies an optimal care level
for the agent. See [22] for a thorough discussion of the first-order approach in moral
hazard problems.

12
and direct liability have identical efficiency effects regardless of the risk aversion of the
agent. Therefore, to isolate the effects of judgement-proofness on efficiency, this analysis
makes the assumption (common in this literature) that both the principal and agent are risk
neutral.
Before characterizing the solution to [P], it will be useful to characterize the
socially optimal care level. Suppose a revenue-producing activity has a potential accident
damage of D associated with it. The social welfare of this activity is:
SW = R -p(x)D -x
Therefore, the socially optimal care level is given implicitly by:
-p\x)D-1 =0
At the socially optimal care level, the marginal cost of increasing care equals the marginal
decrease in expected damage associated with increasing care. Let this care level be
denoted by x*(D).
For the vicariously liable principal in [P], the profit-maximizing level of care is
x"(L) (i.e., that which is socially optimal if the liability, L, equals the damages, D). The
principal can induce this level of care by setting wn - wa = L. As mentioned before, the
principal simply passes along the liability to the agent through the wage contract by
penalizing the agent L in the event of an accident. However, as the principal's liability
increases, there comes a point (denoted by L = k) at which passing the liability to the
agent becomes costly to the principal. This occurs because of the agent's limited wealth.

13
Recall that the principal can take no more than the agent's wealth through indemnification
(wa > -A). Therefore, in order to induce x*(L) from the agent, the agent's no-accident
wage (wn) must be at least L - A. However, if L - A > x*(L) + p(x’'(L))L, then the principal
can only induce x*(L) from the agent by giving the agent an expected wage above his
reservation wage (see constraint (i) in [P]). Therefore, if L < k, the principal can costlessly
pass on the liability, L, to the agent. If L > k, then the principal faces a tradeoff: she can
maximize the joint surplus only by sacrificing some of her share of the surplus. Faced with
this tradeoff, the principal will sacrifice less profit by inducing a suboptimal care level from
the agent.
To be specific, the principal is faced with the following trade-off for liability levels
greater than k. At one extreme, the principal could continue to pass the full liability onto
the agent through the contract inducing the profit-maximizing care (x’(L)). However, the
principal incurs a cost of L - A - [x*(L) + p(x*(L))L] when pursuing this approach, since
the principal must give the agent a share of the joint profits in order to fully pass the
liability onto him. At the other extreme, the principal could simply offer the contract which
is profit-maximizing for L = k (i.e., freeze the accident penalty at k). This approach allows
the principal to avoid giving the agent an economic rent. However, this will induce a level
of care from the agent that is too low given the principal's vicarious liability of L. The
principal will, therefore, incur an expected cost of [p(x*(K)) - p(x”(L))]L since the
probability of an accident will be too high given this approach.
At first (i.e., for L £ (K,pj), the latter approach is least costly for the principal, so
the principal sets wn - wa = k, even though L > k. Eventually (i.e., for L > p), this

14
approach leads to a probability of an accident that is too great relative to the principal's
liability, L In this case, the principal uses a combination of the two strategies. The
principal gives the agent a share of the joint profits to induce a higher level of care, but not
enough to induce x*(L). (In other words, the accident penalty will fall between k and L.)
Therefore, even though the induced care is inefficient for L > k, it is never less than x*(k).
In particular, it is non-decreasing in L, reflecting the principal’s desire to pass on as much
of the liability as possible while protecting her profits. This is summarized in the following
theorems.
Theorem 2.1: Let k be defined implicitly by x*(k) + p(x*(k))k = k - A, p be defined
implicitly by x(p) + (P+l)"'p(x(p))p = (P+l)_1p - A, and let x be implicitly defined by V(x)
= 0 where V is the maximized value function of [P], (In other words, k is the liability level
at which the agent’s wealth constraint begins to bind, p is the liability level at which the
agent’s participation constraint no longer binds, and x is the liability level at which the
expected gains from trade are no longer positive.) The care x which solves [P] is given
by:7
x(L)=x*(L) for Lg[0,k]
= x*(K)/orZe(K,p)
-x(L) for Le[p,x]
= 0 for L>x
where x(L) is implicitly defined by:
7 (ii) If k > x, then the care x which solves [P] is given by:
x(L)=x*(L)for Lc[0,x]
= 0 for L>x
This occurs when A is large (i.e. the agent has substantial wealth).

15
-p'(x)L-\ =P(x)
and:
P(I)i(wa>8
(p'(*»2
Proof: See Appendix A2.1.
Theorem 2.2: (i) For all L > 0,
x*(L)>x{L)
(ii) For all L > 0,
dXL>o , i*>0
dL dL
In other words, x' and x are both strictly increasing in L. Therefore, the care which solves
[P] is non-decreasing in L.
Proof: See Appendix A2.2.
Theorems 2.1 and 2.2 characterize the care induced by vicarious liability in this
benchmark case in which the agent has no bargaining power. Flow do these care levels
compare with those induced by direct liability? If the agent is directly liable, he will exert
the socially optimal amount of care (x*(L)) as long as the liability is no greater than his

16
wealth (L < A). However, if the agent is potentially judgement proof (L > A), he will exert
just xM(A) since the penalty he receives in the event of an accident is only the loss of his
wealth, A.
In Figure 1, the care levels induced by vicarious and direct liability are juxtaposed
for all liability levels. As mentioned previously, when the agent is not judgement-proof (D
= L < A), vicarious and direct liability lead to the same levels of care. The difference
between these two liability schemes occurs when the agent is judgement-proof (D = L >
A). From Figure 1, it is clear that vicarious liability is more efficient than direct liability in
this case. When the accident damages exceed the agent's wealth by a relatively small
amount (D e [A,k]), vicarious liability equal to the damages will induce efficient care
whereas direct liability will not. In this region, the principal can still costlessly pass on the
total liability to the agent through the wage contract, because the agent’s wealth shortfall

17
(L - A) is less than the no-accident wage required by the agent for participation (x*(L) +
p(x*(L))L). However, direct liability applied in this region results in a penalty (A) that is
less than the damages and, thus, direct liability induces insufficient care.
For D = L > k, vicarious liability will no longer result in efficient care. However,
vicarious liability will still induce a larger, more efficient level of care than that induced by
direct liability. This is because care under vicarious liability is non-decreasing in this region
while care under direct liability is constant at x’(A). Essentially this is due to the principal's
increased incentive to reduce the probability of an accident as her vicarious liability
increases. Thus, she will increase the agent's incentive to take care, although not perfectly.
Under direct liability an increase in liability will not result in an increased penalty for the
agent and, therefore, it will not result in increased care. Therefore, vicarious liability is
more efficient than direct liability in preventing accidents when the agent has no bargaining
power and is judgement-proof.
2.3 Vicarious Liability with Variable Bargaining Power
The previous section illustrates the effects of vicarious liability on preventive care
when the agent has no bargaining power. In this case, vicarious liability is more efficient
than direct liability in preventing accidents. Is this still true when the agent has bargaining
power? How does preventive care under vicarious liability change as the agent's
bargaining power increases? In this section, a model with variable relative bargaining
power is presented to answer these questions.
The model in this section is identical to the model in section 2.2 with the following
exceptions. First, there are many agents, instead of just one. Second, before learning the

18
potential liability she faces, the principal makes a sunk "safety" investment, I This could
be thought of as training in safety procedures for the agent or the purchase of equipment
which assists the agent in taking preventive care. Along with care, the safety investment
reduces the probability of an accident at a decreasing rate (px, p¡ < 0, pxx, pn > 0).
However, the safety investment is specific to one agent (denote him as the primary agent
(PA)). If it is used with any other agent, its effectiveness is equivalent to an investment of
oT (a G [0,1]). Since the safety investment is sunk, a can be considered an exogenous
parameter and I can be normalized to one. In addition, assume p(l,x) = p(x) from Section
2.2.
The third difference between this model and the previous model concerns the
principal's choice of a contracting agent. After the principal and agents learn the principal's
liability, L, the principal chooses whether to contract with PA or with one of the many
other agents. If the principal contracts with PA, it is assumed that the contract is the result
of a bargaining process consistent with Nash's Axioms of Bargaining.8 In other words, it is
assumed that the resulting contract maximizes the product of the principal and agent's net
returns from trade with each other. If the principal contracts with one of the other agents,
it is assumed that the principal can make a take-it-or-leave-it offer. Since there are many
identical alternative agents, each individual agent has no bargaining power with the
principal. As in the previous model, the principal cannot observe the care of any agent, nor
can agents observe each other's care.
See [23],
9

19
Before describing the problem the principal faces in this model, an additional
comment is needed about the sunk safety investment assumption. The safety investment is
assumed to be exogenous to abstract from questions about the principal's optimal safety
investment under vicarious liability and the disincentives for specific investment due to the
agent's possible opportunism. These are important and interesting issues, but they are left
out of this analysis in order to isolate the effects of bargaining power on preventive care
under vicarious liability. In this model, the principal’s investment and, particularly, its
specificity a are used simply to reflect the agent's bargaining power. A specific safety
investment is but one of many means by which an agent can become more productive in
preventing accidents. In general, a can be thought of as a parameter which reflects any
distinctive characteristic of PA relevant to the principal’s expected profits. For instance,
PA could have an acquired or inherent skill that makes it easier for PA to prevent an
accident (e.g., a firm with previous experience disposing hazardous waste or a surgeon
with steady hands). Therefore, the probability of an accident for PA is less than that for his
colleague agents for a given level of care (p(x) < p(a,x) for a < 1). If a = 1, all agents,
including PA, are identical and, thus, PA has no bargaining power. If a = 0, then the
specific investment is completely ineffective with agents other than PA, so PA's bargaining
power is maximized. Therefore, PA's bargaining power is inversely related to a.
If the principal decides to contract with one of the many alternative agents, she can
make a take-it-or-leave-it offer as mentioned before. Therefore, the principal's problem in
this case is identical to that presented in section 2.2, except that p(x) is replaced with
p(a,x):

20
[aP] V(a ,L) = Maxxw¡w[R-p( s.t. (?) p(a,x)wa~( 1 -p(a,x))wn-x> 0
(//') px(a,x)(wa-wn)-\ =0
(Hi) wa > -A
The care level which solves [aP] (denote as xa(L)) is also analogous to that which solves
[P]
xa(L) = xa\L) for Le[0,kJ
= ra*(K«) f°r Zf(VPa)
= xa(L)forLe[ pa,xj
= 0 for L>Ta
where x(t*(L), x(C(L), Ka, p(t, and T;tt have definitions analogous to those in section 2.2. As
in section 2.2, xt[(L) reflects the tradeoff the principal faces when the agent is judgement-
proof. When L > Ka, the principal induces suboptimal care from the agent because of the
principal's tradeoff between maximizing the joint surplus and maximizing the principal's
personal share of the surplus.
If the principal decides to contract with PA, then the principal and PA will
negotiate a contract consistent with the Nash bargaining process. Therefore, the problem
facing the principal and PA is:
BP] Vfaf) =Max.vi,jVi, [/?-(! -p(x))wn-p(x)wa-p(x)L-V(af)][(\-p(x))wn+p(x)wa-x
s.l. (/) p'(x)(wa-wn)~ 1=0
(//) wgi -A

21
The principal and PA negotiate a contract which maximizes the product of their individual
gains from trade net of the opportunity costs of trading with each other. If the principal
chose not to contract with PA, she could receive V(a,L) by contracting with another
agent. As before, PA's opportunity cost/reservation wage is normalized to zero. As in [P],
constraint (i) is the agent's incentive compatibility constraint, which reflects the principal's
inability to observe the agent's choice of care. Constraint (ii) reflects the limited wealth of
the agent, as before.
A comparison of [aP] and [BP] reveals that the principal will always choose to
contract with PA. Since p(x) < p(a,x) for all a 6 [0,1], PA holds a cost advantage over all
of the other agents. Therefore, for a given level of care, the joint surplus with PA is at
least as much as that with any other agent. If the principal chooses to contract with PA,
she can capture some of this extra surplus in the bargaining process. Therefore, she
receives at least as much profit by contracting with PA as she does with any other agent.
The care level induced when the principal contracts with PA is characterized by the
following theorem:
Theorem 2.3: Let Kb be implicitly defined by
^+X*(Kb)+/?(x*(Ki))K6-y(a,K6)_
2 Kb
and let tb be implicitly defined by Vb(a,tb) = 0. (As in Theorem 1, Kb is the liability level at
which the agent’s wealth constraint begins to bind and Tb is the liability level at which the
expected gains from trade are no longer positive). For a E [0,1), the care which solves
[BP] is given by:

22
xb(L)=x\L) for Le[0,Kb]
=xb{L) for LE(Kb,xb\
= 0 for L>xh
where xb(L) is implicitly defined by:
-p'{xb)L-\ =
(0(f6)+nP(fi))
(0 is the lagrange multiplier for the agent's wealth constraint (ii) and IIp is the principal's
net surplus from trade.)
Proof: See Appendix A2.3.
The solution to [BP] is, in many ways, similar to that of [P], As in section 2.2, care
level x*(L) maximizes the joint profits of the principal and agent. Therefore, passing the
principal's liability, L, to the agent through the wage contract is optimal for both the
principal and the agent if this can be done at no cost to either party. Recall, in section 2.2,
the principal faced a tradeoff, in some cases, when deciding how much of the liability to
pass on to the agent. If L > k, the principal could only maximize the joint profit by
sacrificing some of her share of the profit. Therefore, the principal maximized her profits
by penalizing the agent less in the event of an accident, thereby inducing suboptimal care.
A similar tradeoff faces the principal and agent in [BP] when L > Kb. To see this, it is
useful to rewrite condition (1), which implicitly defines Kb, as follows:
R -x *(Ké) -p(x *(k6))k6 - V(a,Kb)
+X*(Kb)+p(x*(Kb))Kb = Kb-A
2

23
In [BP], the principal and agent negotiate a wage contract which maximizes the product of
their net profits. This simply means the principal and agent will write a contract which
splits the expected joint profits in half, if this is feasible. Therefore, if the wage contract
induces the optimal care, x*(L), from the agent, then the agent's no-accident wage will be:
w -
R-x\L)-p{x\L))L-lXa,L)
2
â– x\L)+p{x\L))L
(2)
Recall that, because the agent's wealth is constrained to A, the no-accident wage must be
at least L - A in order to induce x+(L) from the agent. Therefore, if:
L-A> R~x*^ p{x\L))I,-\\a,L) +x+/?(x
the only wage contracts that induces x*(L) from the agent will also give the agent more
than half of the expected joint surplus. So, again the principal faces a tradeoff when L >
Kb. She can negotiate a wage contract with the agent which induces the optimal care only
by accepting a share of net profits which is less than the agent's. Instead, the principal and
agent will negotiate a contract which gives more equitable profit shares to each, while
inducing a suboptimal care level.
2.4 Comparison of Models
Even though they are similar, the solutions to [BP] and [P] differ in two important
ways. First, when the agent has bargaining power, the liability level at which the
previously described tradeoff first occurs is different from the analogous liability level
when the agent has no bargaining power (k * Kb when a * 1). Second, when the agent has
bargaining power, the care induced when this tradeoff is present is different from that

24
induced when the agent has no bargaining power (x(L) * xb(L) when a * 1). These
observations are described in the following two theorems:
Theorem 2.4:
(i) Kb > k for all a £ [0,1),
(ii) Kb increases as the agent’s bargaining power increases:
dKb
da
<0
Proof: See Appendix A2.4.
The agent's share of the expected joint profit increases with his bargaining power (i.e., it
decreases with a). This is because the net surplus (that in excess of what the principal
could earn elsewhere) decreases with a. Thus, the agent's no-accident wage, given by (2),
increases with the agent's bargaining power (decreases with a). Recall, the no-accident
wage must be at least L - A to costlessly induce efficient care from the agent. Therefore,
as the agent's bargaining power increases, this inducement can be made for larger liability
levels. Hence, tcb increases as the agent's bargaining power increases.
Theorem 2.5:
(i) xb(L) >x(L) for all a £ [0,1),
(ii) For L > Kb, the care induced by vicarious liability increases as the agent’s bargaining
power increases:
da

25
Proof: See Appendix A2.5.
Again, as the agent's bargaining power increases, so does the agent's share of the expected
joint surplus. However, for L > Kb, the costless transfer of the liability from the principal to
the agent is not possible. This is because the agent's accident wage can fall no lower than -
A due to the agent's limited wealth. Since wa = -A in this case, the only way for the agent's
profit share to increase with his bargaining power is for the agent's no-accident wage to
increase. However, this will also make the agent's penalty in the event of an accident (wa -
wn) greater. Therefore, the agent will take more care as his bargaining power increases.
Essentially, the agent has more at stake with respect to the success or failure of the

26
enterprise as his bargaining power increases. Hence, the agent has a greater incentive to
prevent an accident as his bargaining power increases.
This increased incentive to prevent an accident and the resulting increased care are
illustrated in Figure 2. Here the care induced when the agent has no bargaining power
(x(L)) is compared with the care induced when the agent has some bargaining power
(xb(L), a < 1). Notice that, with bargaining power, there is a larger range of liability levels
for which the efficient level of care is induced (from Theorem 2.4). In addition, for those
liability levels in which efficient care is not induced, the care associated with bargaining
power is greater than that without bargaining power (from Theorem 2.5). For these
reasons, vicarious liability is more efficient when the agent has bargaining power. In
addition, the presence of bargaining power increases vicarious liability’s superiority over
direct liability. This, of course, is due to the agent's increased incentive to take care when
his bargaining power is non-negligible. With direct liability, his incentive to take care is
capped at a maximum loss of his wealth, A.
Clearly this result contradicts Syke’s reasoning that vicarious liability will reduce
the agent's loss-avoidance incentives when the agent has some bargaining power. With
bargaining power, the agent has a larger stake in the profits of the principal-agent
enterprise If the agent is potentially judgement-proof, vicarious liability exposes more of
this profit to liability claims than does direct liability. Therefore, as shown above, vicarious
liability will induce greater care from the agent, particularly when the agent has some
bargaining power. The result above also suggests that Pitchford's conclusion about the
effectiveness of vicarious liability is not robust to contexts other than lender liability.

27
Pitchford illustrates how vicarious liability can reduce incentives for care when the
principal belongs to a perfectly competitive industry. The analysis above suggests that
Pitchford's result does not hold for other market structures. In particular, if the agent
belongs to a perfectly competitive labor market, or if bilateral monopoly prevails, then
vicarious liability will increase the agent's incentive to take care.
2.5 Conclusion
When the agent is potentially judgement-proof and his actions are difficult to
monitor, vicarious liability and direct liability produce different incentives for the agent to
exert preventive care. In this case, vicarious liability will induce more care from the agent
than direct liability. Although not completely efficient, vicarious liability is more efficient
than direct liability. This relative advantage of vicarious liability is heightened when the
agent has some bargaining power. As the agent's bargaining power increases, so does his
share of the joint profit of the enterprise. Therefore, the agent has more to lose in the
event of an accident under vicarious liability, so the agent will take more care as his
bargaining power increases.
This result implies that vicarious liability can be used by the courts in a variety of
different contexts to reduce the likelihood of accidents while fully compensating the
victims of accidents. Since the effectiveness of vicarious liability increases with the agent's
bargaining power, vicarious liability is particularly appropriate when applied in situations
where the agent is highly skilled (e g., physicians) or where agents have collective
bargaining power (e.g., unions). In addition, the previous analysis suggests one benefit of
employee-owned firms. Employment contracts that incorporate profit-sharing or employee

28
ownership of some kind may induce more preventive care from employees since they have
more to lose if the firm is subject to a liability claim.
A2.1: Proof of Theorem 2.1
Using constraint (ii), [P] can be rewritten as follows:
in [r-w -p{X)l-£¿I]
p O)
(0 Wn+-^~~X>0 (X)
P (x)
(Hi) —i—+w > -A (0)
P'ix) n
The first order necessary conditions for a solution to [P'] and [P] are therefore:9
(a) -p'L- 1+(1-A)i^l-0^1 = 0
(P')2 ip’)2
(b) X+Q = 1
(c) "’„+y-x>0 (=0ifX>0)
(d) — +w +A> 0 (=0 if 6>0)
P1
(e) A,0 > 0
From conditions (b) and (e), it is clear there are three possibilities:
1.0 = 0 (which implies X = 1),
2. X = 0 (which implies 0 = 1), or
3. 0, A e (0,1).
10 These Kuhn-Tucker conditions are indeed necessary since the Jacobian of the
effective constraints has full rank in all of the cases which follow.

29
Case 1: Binding Participation Constraint (0 = 0 and A = 1)
In this case, condition (a) becomes :
-p'L-1=0
so the care which solves [P] is given by x"(L). From conditions (a) and (c):
w=p{x\L))L+x\L)
Therefore, from condition (d):
p(x*{L))L+x\L)iL-A (Al)
(Al) reflects the fact that x*(L) solves [P] as long as the agent’s wealth constraint does
not bind. If, as a result of a binding wealth constraint, the principal cannot set wn - wa = L
without giving the agent an economic rent (wn > p(x“(L))L + x¥(L)), then x*(L) does not
solve [P], Let k equal the liability level L for which (Al) holds with equality. Then x*(L)
solves [P] for all L < k.
Case 2'.Binding Wealth Constraint (A = 0 and 0 =1)
In this case, condition (a) becomes:
-p’l-i-Ai-tíEl (5p)
(p')2
Denote the care which this implicitly defines as x(L). From conditions (a) and (d):

30
(A2)
Therefore, from conditions (c) and (a):
L
P + 1
-A >
p(x(L))L +m
P + 1
(A3)
(A3) characterizes the liability levels in which only the agent's wealth constraint binds. Let
p equal the liability level for which (A3) holds with equality. Then x(L) solves [P] for all L
> P
Case 3: Both Constraints Bind (6, A e (0,1))
In this case, conditions (c) and (d) imply:
p' p'
Therefore, when both constraints bind, the care which solves [P] is constant at x*(k). From
Lemma A2.1.1 (see below), x*(k) solves [P] for L 6 (K,p).
Since dC/dL > 0 (see Lemma A2.1.1), there exists a liability level such that R - C =
0. Therefore there exists a liability level such that V(L) = 0. Denote this level as x. For L >
t, the principal is better off not contracting with the agent. Therefore, for L > t, the
principal and agent will not contract and the induced care equals zero. â– 
Lemma A2.1.1: k and p exist and p > k.
Proof of Lemma A2.1.1: Let C = p(x*(L))L + x*(L). To show that k exists, it is sufficient
to show that

Recall that x*(L) minimizes C, so:
dC
dL
<1
-jr -P(X*(Q)< 1
dL
by the envelope theorem.
p is implicitly defined by:
1 -/?(%))
- A +x(p)
To show that p exists, it is sufficient to show that:
d_ _ 1 -p(x(L))
dL[ p\m)
>-¿-[A+x{L)]
dL
since x(L) is increasing in L.
d_ _ 1 -p(x(L))
dL[ p\x(L))
,, q, dx dx d r . ~/rx.
Max [/'l - w -p(x)L - ]
-v.w„ L „ i p^x)\
s.t. (?) w +PQL-XZ 0
" P'(x)
Consider the problem

Constraint (i) will always bind. Hence, in [P'], constraint (i) will not bind only when
constraint (iii) binds. Constraint (iii) binds when L > k. Constraint (i) binds only when L
p. Therefore, p > k â– 
A2.2: Proof of Theorem 2.2
i) Since (3 > 0,
-p'(x\L))L-\<-p\x{L))L-\
or
pXx-iL^pxm)
Since p" > 0, this implies x*(L) >x(L) for all L.
ü)
— = --E—>0
dl p"L
•&-- P'
dL p"L+H-
since second-order sufficient conditions dictate that the denominator is positive

33
A2.3: Proof of Theorem 2.3
Using constraint (i), [BP] can be rewritten as follows:
s.t. (//) ■J——+W '?. -A (0)
P 0)
Therefore, the first-order necessary conditions for a solution to [BP] and [BP'] are:
(b) n+-^-x)+(R-wn-p(L+^)-V(a.,L))+Q =0
/ ' v 11 '
P P
(c) —+wn+A>0 (=0 if 0>O)
(d) 0 > 0
Case 1: Wealth Constraint does not Bind (6-0)
From (b), this implies that the agent's share of the net surplus from specific trade
(wn+p/p'-x) equals the principal's net surplus from specific trade (R-wn-p(L+l/p')-
V(a,L)). This implies that (wn+p/p'-x) > 0 for a < 1 (i.e. the agent's share of the net
surplus can only equal zero if there is no net surplus, which only occurs when the agent is
identical to all other agents (a = 1)). Therefore, from (a), the care which solves [BP] in
this case is x*(L). From conditions (b) and (c):
R+x-pL-V(a,L) _ p
~ ~P'
P' P'
Therefore, the wealth constraint is not binding when:

34
R +x *(L) +p(x \L))L - VjaJL) > ¿ _A
2
(A4)
Denote Kb as the liability level for which (A4) holds with equality. Then x'(L) solves [BP]
for L < Kb.
Case 2: Binding Wealth Constraint (6 0)
Denote IIp s R-wn-p(L+l/p')-V(a,L). Therefore, from conditions (a) and (b), the
care which solves [BP] for L > Kb is given implicitly by:
Notice that 0/(0+IIp) approaches zero as 0 approaches zero, so x,,(L) is continuous
(although not differentiable) at Kb.
As before, since dC/dL > 0, there exists a liability level such that Vb(a,L) = 0.
Denote this level as xb. For L > tb, the principal and agent are better off' not contracting
and, therefore, the induced care is zero. (If Kb does not exist, the solution to [BP] is given
by footnote 8.) II
A2.4: Proof of Theorem 2.4
i) Kb is implicitly defined by:
R -x *(K6) -p(x *(k/7))k6 - F(a,Kb)
+x *(K/,) +P(X *(Kb))Kb ~ Kb~A
2

35
which implies
x*(K/7)+p(x*(K,,))Kft since R-x*(Kb)-p(x*(Kb))KirV(a,Kb) > 0 for a < 1. Therefore, Kb > k.
ii)
da
Va(a^b)
dC _
— -lL(a,Kh)-2
<0
since V„ > 0, dC/dL < 1 (see Lemma A2.1.1), and V, (a,Kb) = -p(a,xK(Kb)) >-1.0
A2.5: Proof of Theorem 2.5
i) For a e [0,1), IIp > 0. Therefore,
-p\xb{L))L-\<-p'(x{L))L-\
implying xb(L) >x(L) for all L and a e [0,1).
ü)
dx,
0
da
-v„W-) P
p“l( e+n
p dx 0 +n
p
<0
since Vr(c£,L) > 0 and the denominator is positive by second-order sufficient conditions. ■

CHAPTER 3: VICARIOUS LIABILITY, NEGLIGENCE, AND MONITORING
3.1 Introduction
Vicarious liability is applied by the courts in many different business contexts. In
contexts where the principal can easily observe and control her agent's actions, the
principal is almost always found vicariously liable in the event of an accident. Increasingly,
vicarious liability is being applied in contexts where the principal cannot easily observe the
agent's behavior. (See Chapter 4.) In these cases, the courts often justify the use of
vicarious liability as a way to make principals monitor and control their agents. In light of
this, it is surprising how few articles address this justification in the vicarious liability
literature. To my knowledge, no paper has systematically analyzed the principal's
incentive, under vicarious liability, to monitor her agent. Only one paper (Chu and Qian
(1995) [8]) has investigated the efficiency of vicarious liability when the principal is able to
(imperfectly) monitor her agent.10
Chu and Qian (1995) analyze the efficiency of vicarious liability under a negligence
rule. They find that vicarious liability induces the principal to underreport any evidence of
10
Lewis and Sappington (1996) [15] show how vicarious liability can beneficially
supplement an industry-wide liability rule termed the "access principle" if the vicariously
liable party can monitor the agent.
36

37
negligence gathered while monitoring the agent. If the principal is best able to monitor the
agent and the courts only apply liability when the agent is found negligent (i.e., when the
agent has used insufficient care), then both the principal and the agent will benefit if the
principal fails to report any evidence of negligence. However, Chu and Qian assume the
principal's monitoring capability is exogenous. Thus, they do not investigate the principal's
incentive to monitor the agent under vicarious liability. In addition, although Chu and Qian
successfully demonstrate that negligence liability, as currently applied by the courts,
induces the principal to underreport evidence of negligence, they fail to investigate other
"collusion-proof forms of negligence liability which do not give principals this incentive.
The objective of this chapter is twofold. First, this chapter investigates the ability
of collusion-proof negligence liability to prevent accidents. In a collusion-proof liability
scheme, the total amount paid by the principal-agent enterprise does not vary with the
agent's negligence, while the agent's share of this liability is greater if he is found negligent.
Under collusion-proof schemes the principal will report all evidence of the agent's
negligence. Failure to do so would only increase the principal's share of the liability
payment. In this chapter, it is shown that the preventive care induced by collusion-proof
negligence liability is the same as that induced by strict vicarious liability. Furthermore, it
is shown that any liability scheme which fully compensates the victim in the event of an
accident will induce the same level of preventive care as strict vicarious liability.
Second, this chapter investigates whether vicarious liability gives the principal an
incentive to monitor the agent when monitoring is costly and whether preventive care is
more efficient under vicarious liability when monitoring is possible. This chapter will show

38
that vicarious liability induces monitoring of the agent if the agent is sufficiently
judgement-proof When the principal monitors the agent, the level of monitoring increases
as the principal’s liability increases and decreases as the cost of monitoring increases. In
addition, this chapter will show that preventive care when monitoring is possible is at least
as great (and often greater) than that induced when monitoring is not possible.
The chapter is organized as follows. Section 3.2 presents a model of collusion-
proof liability when the principal can monitor the agent for negligence. Section 3.3
investigates the principal's incentive to monitor under vicarious liability. Section 3.3.1
presents a benchmark vicarious liability model in which the principal cannot monitor the
agent. Section 3.3.2 contains a closely related model in which the principal can monitor
and choose the monitoring intensity.
3.2 Collusion-Proof Negligence and Vicarious Liability
Consider a principal who hires an agent to complete a productive activity. This
activity will produce a revenue of R for the principal. However, there is also a probability
p (e (0,1]) that the agent, while completing this activity, will cause an accident. The
probability of an accident is a function of the precaution or care x the agent takes when
completing the activity. It is assumed that increasing care decreases the probability of an
accident at a decreasing rate (p'(x)<0 and p"(x)>0). The agent's personal marginal cost
(or disutility) of taking care is assumed to be constant and is normalized to unity. In
addition, the agent's initial wealth is A.
The principal cannot directly observe the agent's care. However, with probability q
(e [0,1]), the principal can observe verifiable evidence that the agent was negligent in

39
completing the productive activity. As with p, it is assumed that increasing care decreases
the probability of observing negligence at a decreasing rate (q'(x)<0 and q"(x)>0).n The
principal's ability to possibly observe negligence is assumed to be exogenously given. This
assumption will be relaxed in subsequent sections of this chapter.
The timing of the principal-agent relationship is as follows. First, both the principal
and the agent learn the relevant liability rule. Second, the principal offers a contract to the
agent that specifies accident and non-accident wages of va and vn, respectively, when
evidence of negligence is found and accident and non-accident wages of wa and wn when
no evidence of negligence is found.12 Third, the agent chooses to accept or reject the
principal's contract offer. If the agent accepts the contract, he then chooses his level of
care, x, for the activity. The courts cannot observe this choice of care. Fourth, the state of
the world is realized (either accident or no-accident, evidence of negligence or no
evidence), the liability payments are collected from the principal and the agent in the event
of an accident, and the appropriate wage is paid to the agent.
If the liability rule applied by the courts is based on a report of negligence, there is
an incentive for the principal and agent to collude to avoid liability. For instance, if the
agent is found liable when an accident occurs only when evidence of negligence is
11
Notice, this allows for the possibility of "framing" (i.e., the principal could present
evidence of negligence even when the agent has taken due care: q(x) > 0 for x > x', where
x' is the established due care level set by the courts). In addition, it is assumed that p and q
are independent.
12
Notice this allows for the possibility that wn * vn (i.e., the verifiable evidence of
negligence could be used in contracting even if it is not used in a tort proceeding).

40
reported, both the principal and agent can gain if the agent bribes the principal to withhold
evidence of negligence. If the courts stipulate vicarious liability in the event of negligence,
the principal's incentive to withhold evidence of negligence is magnified.
For this reason, the liability scheme applied by the courts is assumed to be a
"collusion-proof scheme.13 In other words, the scheme provides the agent with no
incentive to bribe the principal with an amount sufficient for the principal to withhold
evidence of negligence.14 Specifically, the total liability assigned to the principal and the
agent in the event of an accident does not vary with the agent's negligence, although the
agent's share of this liability may vary with negligence.12 In this way, the agent's gain from
avoiding negligent liability is exactly the principal's loss. Therefore, on net, the principal
cannot gain through any bribe the agent would be willing to offer to avoid negligent
liability. Hence, a collusion-proof liability scheme can be summarized by the total liability
of the principal and agent (L), the agent's share of this liability when there is no evidence
of negligence (P), and the agent's share when there is evidence of negligence (Pn). Besides
negligence (Pn * p), this specification allows for other types of liability schemes including
strict vicarious liability (Pn = P = 0) and strict joint liability (Pn = P > 0).
13
Tiróle (1992) [31] has shown that there is no loss of welfare associated with the use of
collusion- proof contracts.
14
For this reason, in the event of an accident, the principal will present the court with
evidence of negligence if she observes such evidence.
13
In addition, the total liability could also vary with the damages inflicted upon the victim as
we would expect.

In choosing a contract to offer the agent, the principal solves the following
problem:
m Maxx w w v v ELI
n u n a 1
s.t.{a) EUa> 0
(c) vn > -A
(d) (:/_ ¿ -a
«0 vP/>-/i
where the principal's objective (EUp) is:
EUp = R-q[p(va+(\-P)L)+( 1 -p)>’J-(l -q)\p{wa+{ 1 -p)A)+(l ~P)wn]
and the agent's objective (EUa)16 is:
EUa = q\p[ya-§¿)+{\~p)v J+(l -q)\p(wa-$L)+(\-p)wn]-x
Constraint (a) is the agent's participation constraint. The agent will only accept the
principal's offer if the expected wage, net of effort costs, is at least as great as the agent'
reservation wage (here normalized to zero). Constraint (b) is the incentive compatibility
constraint which reflects the principal's inability to observe the agent's care. Since the
principal cannot make the wage contract contingent on the agent's care level, the agent
16
The principal and the agent are both assumed to be risk neutral. This is a standard
assumption found in most of the previous vicarious liability literature. See [13] for
implications of general risk aversion.

42
will choose a care level that is personally optimal given the wage contract.17 Constraints
(c), (d) and (e) reflect the agent's limited wealth and the principal's "right to
indemnification." When a principal is found partially or completely liable, she has the right
to be compensated by the accident-causing agent [7], However, this compensation plus
the agent's assigned liability cannot exceed the agent's wealth. Therefore, the agent's
accident wage (with or without negligence) plus the agent's assigned liability must be at
least -A.18
The main result of this section is the following:
Theorem 3.1: The care (x) which solves [NP] is independent of P and Pn.
Proof: See Appendix A3.1.
In other words, collusion-proof negligence, strict vicarious liability, and strict joint liability
all induce the same level of accident-preventing care. In fact, theorem 3.1 implies that all
liability schemes in which the principal and agent fully compensate the victim (i.e. L = the
total accident damages) will induce the same level of preventive care.
17
Constraint (b) assumes the use of the "first-order approach" is valid in this case.
Normally, the use of the "first-order approach" requires that the cumulative distribution
function be convex and exhibit the monotone likelihood ratio property (MLRP). However,
MLRP is meaningless in this context since the potential states of the world (no accident
w/o negligence, accident w/o negligence, no accident w/ negligence, and accident w/
negligence) cannot be ordered, a priori, from best to worst from the point of view of the
principal. See [22] for a thorough discussion of the validity of the first-order approach in
moral-hazard problems and its relation to MLRP and convexity of the distribution function
(CDFC).
18
Constraint (a) implies that wn is non-negative, so a separate wealth constraint for wn is
not needed.

43
To understand how this result comes about, it is useful to rewrite the agent's
objective as follows:
EUa = w„ +P[^ü~Wn - + Expression (3) highlights an alternative interpretation of the contract between the principal
and the agent. In addition to the penalties the government specifies in its liability rule, the
principal offers the agent a contract characterized by a base wage (wn) and three penalties:
a penalty if an accident occurs without negligence (wa - wn), a penalty if no accident
occurs but the agent is found negligent (vn - wn), and an additional penalty when an
accident occurs and the agent is found negligent ((va - vn) - (wa - wn)). These penalties are
the principal's tools for inducing the profit-maximizing level of care from the agent, given
the total liability, L. However, the government also penalizes the agent and these penalties
also affect the agent's choice of care. Therefore, if the government changes its distribution
of liability between the principal and agent (i.e., changes P or pn), the principal will
compensate for this change by altering the penalties in the wage contract. In this way, the
principal ensures that the agent will continue to exert the profit-maximizing level of care
given the total liability. For instance, if the agent's share of liability (p) is increased, then
the agent's accident wage (wa) will increase to compensate for this change. If the agent's
additional liability for being negligent in causing an accident (Pn - P) is increased, then the
agent's negligent accident wage (va) will increase to compensate for this change. In both

44
cases, the total penalties the agent is subject to will not change with (3 or pn. Therefore,
the agent's choice of care will not vary with P or pn.19
The intuition of this result resembles the well-known theoretical macroeconomic
result of "Ricardian equivalence." Ricardian equivalence states that a change in the mix of
public debt and taxes will not result in any change in most real macroeconomic variables,
including consumption and interest rates. The logic behind this is the following. If
government expenditures remain the same while taxes fall, disposable income will
increase. However, individuals recognize that the increase in debt implied by lower taxes
in the present implies higher taxes in the future. Therefore, individuals will increase their
current savings to compensate for the increased debt and future tax obligations. Hence,
consumption will not change. Likewise, in the present liability model, preventive care does
not change with changes in the principal and agent's liability mix because the contract
between the principal and agent will exactly compensate for any changes in the liability
• 20
mix.
The accident-preventing care induced by any collusion-proof liability scheme is the
same as that induced by strict vicarious liability, even when the principal can monitor the
agent for negligence. Therefore, negligence liability rules offer no improvement in
19
Another way to explain Theorem 1 is by using constraints (a), (c), (d), and (e) in [NP], If
P or (Pn - P) is increased and the participation constraint (a) binds, then the agent's wages
must increase in order for the agent to still receive his expected reservation wage. If P or
(Pn - P) is increased and the wealth constraints bind, then the agent's wages must increase
so that the total penalty is not greater than the agent's wealth (i.e., there is less left over
for the principal to collect in indemnification).
20 For a thorough review of the literature on Ricardian equivalence, see [24],

45
accident-prevention over strict vicarious liability. As Chu and Qian detail, when negligence
rules are not collusion-proof, they can often lead to inefficiencies.
Still, these results assume the principal's monitoring ability is given exogenously. If
the principal can choose her level of monitoring, will strict vicarious liability induce more
monitoring than direct liability (in which the agent alone is liable)? If so, does this
increased monitoring lead to improvements in accident prevention? These questions will
be addressed in the following section.
3.3 Monitoring and Vicarious Liability
3.3.1 Benchmark Vicarious Liability Model
In order to understand how vicarious liability affects the principal's monitoring
choice, it is useful to look first at a benchmark case in which the principal cannot monitor
the agent's care.21
The model in this section is the same as that in section 3.2 except that the principal
is unable to observe the agent's care or any evidence of negligence. Therefore, the contract
between the principal and agent is made contingent only on the observation of an accident
or no accident. In addition, since preventive care does not change with the liability mix, it
is assumed that strict vicarious liability holds (i.e., (3 = 0).
In choosing a contract to offer the agent, the principal solves the following
problem in this case:
21
A complete description of this subsection's model and results can be found in Chapter 2,
section 2.2.

46
[P] Maxx Wn Wa [7?-p(x)wa-( 1 ~p(x))wn-p(x)L]
s.t. (a) p{x)wa+(\ -p(x))wn-x> 0
(b) p'(x)(wa-wn)-\ =0
(c) wa > -A
As before, constraint (a) is the agent's participation constraint. Constraint (b) is the
incentive compatibility constraint which reflects the principal's inability to observe the
agent's care. Constraint (c) reflects the agent's limited wealth and the principal's right to
indemnification.
Before characterizing the solution to [P], it is useful to characterize the socially
optimal care level. Suppose a revenue-producing activity has a potential accident damage
of D associated with it. The social welfare of this activity is:
SW=R-p(x)D-x
Therefore, the socially optimal care level is given implicitly by:
-p\x)D-1=0
At the socially optimal care level, the marginal cost of increasing care equals the marginal
decrease in expected damage associated with increasing care. Let x"'(D) denote this care
level.
For the vicariously liable principal in [P], the profit-maximizing level of care is
x*(L) (i.e., that which is socially optimal if the liability, L, equals the damages, D). The

47
principal can induce this level of care by setting wn - wa = L. The principal simply passes
along the liability to the agent through the wage contract by penalizing the agent L in the
event of an accident. However, as the principal's liability increases, there comes a point
(denoted by L = k) at which passing the liability to the agent becomes costly to the
principal.22 This occurs because of the agent's limited wealth. Recall that the principal can
take no more than the agent's wealth through indemnification (wa 2: -A). Therefore, in
order to induce x*(L) from the agent, the agent's no-accident wage (wn) must be at least L
- A. However, if L - A > x*(L) + p(x*(L))L, then the principal can only induce x*(L) from
the agent by giving the agent an expected wage above his reservation wage (see constraint
(a) in [P]). Therefore, if L < k, the principal can costlessly pass on the liability, L, to the
agent. If L > k, then the principal faces a tradeoff: she can maximize the joint surplus only
by sacrificing some of her share of the surplus. Faced with this tradeoff, the principal will
sacrifice less profit by inducing a suboptimal care level from the agent.
To be specific, the principal is faced with the following trade-off for liability levels
greater than k. At one extreme, the principal could continue to pass the full liability onto
the agent through the contract inducing the profit-maximizing care (x*(L)). However, the
principal incurs a cost of L - A - [x*(L) + p(x'(L))L] when pursuing this approach, since
the principal must give the agent a share of the joint profits in order to fully pass the
liability onto him. At the other extreme, the principal could simply offer the contract which
is profit-maximizing for L = k (i.e., freeze the accident penalty at k). This approach allows
22
k (the point at which the wealth constraint first binds) is implicitly defined by x"(k) +
P(x*(k))k = k - A.

48
the principal to avoid giving the agent an economic rent. However, this will induce a level
of care from the agent that is too low given the principal's vicarious liability of L. The
principal will, therefore, incur an expected cost of [p(x*(K)) - p(x*(L))]L since the
probability of an accident will be too high given this approach.
At first (i.e., for L £ (K,p]23), the latter approach is least costly for the principal, so
the principal sets wn - wa = k, even though L > k. Eventually (i.e., for L > p), this
approach leads to a probability of an accident that is too great relative to the principal's
liability, L. In this case, the principal uses a combination of the two strategies. The
principal gives the agent a share of the joint profits to induce a higher level of care, but not
enough to induce x*(L). (In other words, the accident penalty will fall between k and L.)
Therefore, even though the induced care is inefficient for L > k, it is never less than x*(k).
For this reason, vicarious liability is at least as efficient as direct liability in
preventing accidents and more efficient when the agent is judgement-proof (L > A). If the
agent is directly liable, he will exert the socially optimal care (x’XL)) as long as the liability
is no greater than his wealth (L < A). However, if the agent is potentially judgement-proof
(L > A), he will exert just x*(A) since the penalty he receives in the event of an accident is
only the loss of his wealth, A. As shown above, when the principal is vicariously liable, she
induces the efficient level of care from the agent not only when L < A, but also when L e
[A,k], In addition, when L > k, the inefficiently low level of care induced under vicarious
liability is never less than x¥(k)(> x" (A)). Hence, when the agent is judgement-proof,
vicarious liability is more efficient than direct liability.
23 p is the liability level at which the participation constraint no longer binds.

49
3.3.2 Vicarious Liability and Endogenous Monitoring
Now, suppose the principal has access to a (costly) means of monitoring the
agent's care. Specifically, the principal can invest in a monitoring technology which gives
the principal the ability to observe the agent's care perfectly with probability q (e [0,1]).
The cost of this technology is assumed to be c(q) where c is an increasing, convex
function of q, c(0) = 0, and limq .]C'(q) = For the purpose of calculating comparative
static derivatives, c(q) = aq/(l-q) where a is a cost parameter.
The timing of the principal/agent relationship is now the following. First, the
principal and agent both learn of the principal's strict vicarious liability, L, in the event of
an accident. The principal then invests in the monitoring technology by choosing q and the
agent observes this choice. Next, the principal offers the agent a contract contingent on
both the possible observation of the agent's care and the observation of an accident or no
accident. In particular, the contract specifies a wage schedule of [va(x),vn(x)] if the
principal can observe the agent's care and a wage schedule of [wa,wn] if the principal can
only observe the occurrence of an accident, where the subscripts a and n denote the
"accident" and "no-accident" states of the world, respectively. The agent then chooses to
accept or reject the contract. If the agent accepts the contract, the agent chooses his care
in completing the activity knowing q, but not knowing whether the principal can observe
his care or not. Finally, the state of the world is realized (care can or cannot be observed,
accident or no accident) and the appropriate payments are made.
In choosing a contract to offer the agent, the principal solves the following
problem:

50
[MP]
Max
X4’*’n,wa,vn(x),va(x)
EU„
s.t.(a) EUa> 0
(b) x = argmax[EUa]
(c) wa> -A
(d) v;(x)> -A Vx i-aqi
(e)c/e[0,l]
where the principal's objective (EUp) is:
EUp = R-pL-q\pva(x)+(\-/?)vn(x)]-( 1 -q)\pwa+(\ -p)wn]-c(q)
and the agent's objective (EUa) is:
EUa = q\pva(x) +(1 -/?)vn(x)] +(1 ~q)\pwa+{ 1 ~p)wj -x
As in sections 3.2 and 3.3.1, constraint (a) is the participation constraint which assures
that the agent's expected wage, net of effort costs, is at least as great as his reservation
wage and constraint (b) is the incentive compatibility constraint reflecting that the agent's
choice of care will be that which maximizes the agent's expected wage, net of effort
costs.24 Likewise, constraints (c) and (d) reflect the agent's limited wealth.
Let the care level which solves [MP] (i.e. the care level which the principal wishes
to induce from the agent) be denoted as %. Notice that, given the wage schedule
{va(x),vn(x)}, only the payments va(%) and vn(x) enter the principal's objective. va and vn
for values of x other than x only enter the incentive compatibility constraint (b).
24
The first-order approach is not used in this case since the agent’s objective may not be
differentiable.

51
Therefore, it is in the principal's interest to set va and vn as low as possible for any values
of x * X- Hence, v¡(x) = -A for all x * % and i = a,n.
Figure 3
The following change of variables simplifies the analysis significantly. Let K = wa -
wn (the penalty inflicted upon the agent in the event of an accident if the principal cannot
observe the agent). Let v(x) = p(x)va(x) + (l-p(x))vn(x) (the agent's expected wage if the
principal can observe the agent and his care is x). Since only v(x) is present in [MP] (and
not va(x) or vn(x) separately), the principal does not gain by paying different accident and

52
no-accident wages when she can observe the agent's care. Therefore, when the principal
can observe the agent's care, the wage contract can be characterized completely by v(x).
With these variable changes, the agent's objective can be expressed as:
EUa = qv{x) +(1 -q)(wn +pK) -x (4)
One example of EUa is graphed in Figure 3. Let:
x = argmax[{ 1 -q){wn +pK) -x] (= x(q.K))
In other words, x (a local maximizer of EUa) is the agent’s best alternative level of care
apart from x, the care the principal would like to induce. Therefore, in order to induce x
from the agent, the principal must set v(x), q, wn, and K so that:
or:
qv(x) > -qA +(1 -q)(p-p(x))K-(x-x) (5)
where, for simplicity, p = p(x). Expression (5) replaces constraint (b) in [MP], Likewise,
constraint (a) can be expressed as:
qv(x) > -(1 -q)(wn +pK) +x (6)
Therefore, using (5) and (6), constraints (a) and (b) in [MP] can be expressed as:

53
qv(x) >Max[-qA +(1 -q)(p-p)K-(x-x),-( 1 -q)(wn+pK)+x]
or:
qv(x) > -(1 ~q)(wn +pK) +x +Max[-qA +(1 ~q){wn +pK) -x, 0] (7)
Without an additional constraint on the principal's wealth, [MP] has only a trivial
limiting solution in which the principal sets v(x) = °° and sets q arbitrarily close to zero in
the limit. (See [2] p. 183) Let v(x) < B, where B is a parameter reflecting the principal's
wealth. In this problem, the principal is considered a "deep pocket." Her wealth, while
finite, is an order of magnitude greater than the vicarious liability. To be specific, suppose
all plausible liability levels fall in the interval [L,, L2], Let B = 2L2.
Now the principal's problem can be expressed as follows25:
[MP'] McixxqJ. w Ax) [R-pL -qv(x) -( I -q)(wn +pK)-c(q)\
s.t. (i)qv(x)z -q)(wn+pK)+x+Mctx[-qA+{\ -q)(wn+pK)-x,0]
(ji)wn+K> -A
(.iii)q> 0
(iv)v(x) Although written differently, this problem is equivalent to [MP] (with the exception of the
added constraint (iv)). First, v(x) replaces va and vn and K replaces wa. Second, constraints
(a) and (b) in [MP] are expressed in constraint (i) and constraint (ii) replaces (c) in [MP].
Finally, the q < 1 portion of constraint (e) in [MP] is not needed since limt| ^c'(q) - 00.
251 am thankful to Tracy Lewis and Steve Slutsky for suggesting this approach.

54
Since qv(x) enters the principal's objective negatively in [MP'J, constraint (i) will
bind in equilibrium. Therefore, if both sides of (iv) are multiplied by q (>0) and qv(x) from
(i) is substituted into (iv) and the principal's objective, then the principal's problem can be
expressed as:
[MP "] MctxxqJCw [R -pL -x-Max[-qA +(1 ~q){wn +pK) -x, 0] ~c(q)]
s.t. (iv)qB> -(1 -q)(\v n+pK)+x+Max[-qA +(1 -q)(w n+pK)-x ,Qi\
(ii)wn+K> -A
(Hi) q> 0
If, at the solution to [MP"], -qA+(l-q)(wn+pK)-x < 0, then an equivalent solution exists in
which -qA+(l-q)(wn+pK)-x = 0. If -qA+(l-q)(wn+pK)-x < 0, then wn can be increased
without affecting the principal's objective while still satisfying all of the constraints.
Therefore, [MP"] is equivalent to:
[MPm] MaxxqJíw¡[R-pL-x-c(q)-(-qA +(1 -q)(wn +pK)-x)]
s.t. (ci)qB > -qA +(1 -q)(p-p)K-(x-x)
(b) -qA +(1 -q)(wn+pK)-x> 0
(c)wn+K> -A
(d)q> 0
Unlike [MP], traditional methods of non-linear programming can be used to solve [MP1"]
for induced levels of monitoring and care. Solving [MP'"] produces the following results:
Theorem 3.2: (i) For L < k (the liability level at which the wealth constraint (c) begins to
bind), the solution of [MP"'] is q = 0, x - x*(L), K = -L, and wn = x“(L) + p(x*(L))L.
(ii) For L > k, the solution of [MP"'] is q > 0, x < x*(L), wn = -A-K, and v(x) = B.
Proof: See Appendix A3.2.

55
Theorem 3.2(i) states that the principal will never monitor when L < k. To
maximize her expected profits given a potential vicarious liability of L, the principal would
like the agent to exert x*(L). When L < k, the principal can induce this level of care
costlessly. She can set wn - wa = L without sharing any of the joint profits with the agent.
Therefore, investing in monitoring will not produce any benefits for the principal. It will
only serve to decrease profits by c(q). Therefore, when L < k, the principal will choose q
= 0.
Theorem 3.2(ii) shows that, when it is costly for the principal to pass the vicarious
liability onto the agent (i.e., when it is costly to set K = -L), the principal will employ
monitoring as an additional means to induce care from the agent. As mentioned in section
3.3.1, when L > k, the principal can no longer pass the full liability to the agent costlessly.
To make the agent's penalty in the event of an accident equal to the principal's vicarious
liability, the principal must give the agent a share of the expected profits from the activity.
Therefore, the principal only passes a portion of the liability to the agent, resulting in
suboptimal care. However, with monitoring, the principal has another option. When L > k,
the principal can induce a level of care x > x*(k) from the agent, without giving the agent
an expected economic rent, by investing in the monitoring technology. Essentially, this is
because monitoring gives the principal another means by which to punish the agent for
suboptimal care. With monitoring, if the agent chooses a suboptimal level of care, the
principal can penalize the agent after observing the suboptimal care. Therefore, the
principal can use monitoring (q) as a substitute for the accident penalty (K) to induce care.
This is particularly useful when L > k and any increase in the accident penalty is costly to

56
the principal. Notice this implies that vicarious liability with monitoring induces at least as
much preventive care as vicarious liability without, because the principal has one more
tool with which to control the agent's behavior.
Theorem 3.3: For L > k, the principal's monitoring (q) will decrease as the cost of
monitoring increases (i.e., dq/da < 0) and the principal's monitoring will increase with the
principal's vicarious liability (L) (i.e., dq/dL > 0).
Proof: See Appendix A3.3.
When the principal employs monitoring, the level of monitoring used is inversely
proportional to the cost of monitoring, as one would expect. A less obvious implication is
that monitoring will increase as the principal's vicarious liability increases. When L > k, it
becomes increasingly costly for the principal to fully penalize the agent as the principal's
vicarious liability increases. Therefore, the benefits of monitoring (q) to induce care,
relative to the use of the accident penalty (K), increase as the principal's vicarious liability
increases. Flence, when accident damages are large and the agent is severely judgement-
proof, a principal faced with potential vicarious liability will employ a higher level of
monitoring than that used when damages are relatively small.
In summary, a principal facing vicarious liability for a judgement-proof agent will
not monitor the agent when the liability is relatively small (Le (A,k]). In these cases, the
accident penalty (K) in the wage contract is sufficient to induce the profit-maximizing
care, and can be employed by the principal without sacrificing any of her profits. When the
principal’s liability is relatively large (L > k), the accident penalty in the wage contract can

57
no longer be used without cost. Therefore, the principal will use monitoring to supplement
this accident penalty.
3.4 Conclusion
Although vicarious negligence liability, as it is currently applied by the courts, can
lead to inefficiencies in monitoring, collusion-proof negligence liability avoids this
weakness. In addition, collusion-proof liability (and any other liability scheme in which the
principal and agent fully compensate the victim) induces the same amount of preventive
care as strict vicarious liability. This result resembles the famous theoretical
macroeconomic result of "Ricardian Equivalence" in which changes in the debt-tax mix do
not change real macroeconomic variables such as consumption and the real interest rate.
When the government does employ strict vicarious liability, this gives the principal
an incentive to monitor the agent when the agent is sufficiently judgement-proof (L > k).
This incentive is heightened when monitoring is inexpensive and when the principal’s
liability is large. In all cases, the efficiency of vicarious liability in preventing accidents is
not diminished, and sometimes enhanced, by the ability of the principal to monitor.
A3.1: Proof of Theorem 3.1
Using expression (3), constraint (b) in [NP] becomes:
dEU
a „ /r
dx
P'\.Wa~Wn~^+il ^Vn~W J+(<2P +C1 P)\-V a~V n“(MV~WH) "(P M “ 1 =0 (A5)

58
Solving (A5) for va and plugging it into EUp, EUa, and constraint (e) of [NP] produces the
following equivalent problem:
[NP'] Maxx ^Wa ^ R-pL-wn -6[qp +q p \wa~Wn-PL) +p 'q 2{\’n-wn)\
s t {a) wn +8 [qp +q 'p \wq -wn - PL) +p 'q\vn-wn)] -x > 0
(c) v„>0
(d) wa-$L>-A
(?) S ['1 -P '(^a ~Wn -$L)-Cl '(Vn ~Wr)1 +Vn+(Wa ~W n ~ P7-) * _/l
where 8 = l/(qp'+q'p). Let y = wa - wn - PL. [NP'] can now be rewritten as follows:
[NP "] MaxX'W" R-pL -wn-8[qp +q 'p 2y +p 'q\vn-wfl)]
st.(a) wn+8[c¡p+q'p2q +p 'q\vn- w„)]-x> 0
(c) L,>0
(d) w„+y > -A
(?) Sfi-p7y-q'(vn-wn)\+vn+y>-A
Therefore, the x which solves [NP] is independent of P and Pn. â– 
A3.2: Proof of Theorem 3.2
The lagrangian for [MP'"] is:
+\1[qB+qA -(1 -q)(p-p)K+(x-x)]
+X2[-qA+(l-q)(wH+pK)-x]
+Q[w n+K+A]+Ti[q]

59
Using the fact that (l-q)p'(x)K-l=0, the first-order necessary conditions for the solution
to [MP'"] can be written as:
(1) v =-p'L-\+\l[p X \-q)K-\] = 0
(2) $Zt¡=-c,(q)-(\-X2)[-A-(wñ+pK)]+Xl[B+A+(p-p)K\+n = 0
(3) <£k= -(1 -r/)[(l-X2)p+Xl(j?-p)]+Q = 0
(4) S£H. =-(l-i/)(l-A2)+e=0
(5) ^x =q(B+A)-(\~q)(p-p)K+(x-x)^0 ( = 0 if Xy>0) (A6)
(6) ^=-qA+(\-q)(wn+pK)-x>0 (=0 if X2>0)
(7) <£6=wh+K+Az 0 (-0 if 0>O)
(8) S£Tt = i/> 0 ( = 0 if k>0)
(9) A,,A2,0,Tt > 0
Conditions (3) and (4) in (A6) can be combined to produce:
(1 - Case 1: A, = 0.
From (1) in (A6), this implies x = x*(L). In addition, from (A7), this implies A2 = 1 since q
< 1. Therefore, (2) in (A6) becomes -c'(q) + it = 0 which, from (8), implies q = 0.
(5) in (A6) now becomes -(p-p)K+(x-x)>0 or -pK+x>-pK+x or:
pK-x i pK-x (A8)
From the definitions of x and x*, if q = 0, then x = x'(-K), which implies pK-x>pK-x for
all x. Therefore, pK-x=pK-x which implies x = x and K = -L.
Hence, from (6) in (A6), wn = p(x+(L))L + x*(L) and (7) becomes p(x*(L))L +
x’(L) > L - A. Recall, p(x‘(k))k + x*(k) = k - A, Therefore, (7) cannot hold when L > k.

60
Case 2: A, > 0 and A2 = 0.
First, notice Xl > 0 implies 0 > 0 from (A7) and (4) of (A6). Therefore, wn = -A-K from
(7).
Case 2.1: q = 0. From (5) and (6) of (A6), this leads to the solution found in case 1.
Case 2.2: q > 0. Since A, = (1 -p)/(p-p) from (A7), x, q, and K are given implicitly by:
Fx =q(B+A)-( 1 -q)(p-p)K+(x-x) = 0
F2= -p/L-] + (}=-Pl[pX\-q)K-\]=0
(P~P)
(A9)
(p-p)
where F, is from (5) of (A6), F2 is from (1), and F3 is from (2) and (8). Notice, F2 implies
x < x*(L).
Case 3: A, > 0 and A2 > 0.
Again, this implies wn = - A-K as in case 2.
Case 3.1: q = 0.
Again, this leads to the solution in case 1, except that it only holds for L = k.
Case 3.2: q > 0. Since A2 = c'(q)/(B+A) from (A7) and (2) of (A6), x, q, and K are given
implicitly by:
Gx = q{B+A) - (1 -q)(p-p)K+(x ~x) = 0
C3 = -A-(\-q)(\-p)K-x = 0
(A10)

61
where Gj is from (5) of (A6), G2 is from (1), and F3 is from (6). Notice, G2 implies x <
x*(L).
Therefore, when L p(x*(L))L + x*(L) since this is the first-best solution of the unconstrained problem. (Since
q=0, v(x) is irrelevant.) However, when L>k, there are two candidate solutions, from case
2.2 and case 3.2. It cannot be determined which is optimal for the principal in this case.
However, in both cases, q > 0, wn = -A-K, and x < x*(L). In addition, since Aj > 0 in both
cases, v(x) = B. (See problems [MP'] and [MP"].) â– 
A3.3: Proof of Theorem 3.3
If the solution to [MP'"] when L > k is given by (A9), the principal solves the
following problem:
Max [R-pL-x--^-+A +(1 -q)( 1 -p)K+x\
1 ~q
s.t. q(B+A)-( 1 -q)(p~p)K+(x-x) = 0
where c(q) = aq/(l-q) has been employed. The lagrangian for this problem is:
-R-pL-x--^L+A +(1 -q)(l-p)K+x+X[q(B+A)-( \ -q)(p-p)K+(x-x)]
i -q
and the necessary first order conditions are:

62
gx = q{B+A)-{ 1 -q)(p-p)K+(x-x) = 0
^A.= -p/¿-l+A[p/(l-íir)A:-l]=0
a = í-+x[i(^]-jc[(i -p)-x(p-p)]=o
(l-?)2 _
&K = ( 1 '?)[(1 “P) “^(P-P)] = 0
Let H denote the bordered Hessian matrix of this problem. Using the implicit function
theorem and Cramer’s Rule:
dq
da
0
0
**
0
^.vX
%x
si
(l-<7)~2
cP
31 ?X
^â– KX
si
0
CP
3XX
W\
where:
%=2qk=B+A+K(p-p)
^M = ^n=-(l-cl)(P-P)
^Kx = ^XK = XP'^-Cl)
Cf =Cg -- (1+A)
*Kq 2 2-
K\\-qYp
<£=-p"[L-l{\-q)K\
//
SÍ =
1
0+A)
(W/)3
KY"
~2a
CP = .
(1U)
*30-?)/>'

Therefore:
0
31XK
CP
.vA'
dq _ 1
^â– KX
**
CP
^-KK
da (1 -qf
\H\
The sign of dq/da follows from second order sufficient conditions which imply that |H
0 and the numerator matrix is positive. Likewise:
0
**
0
^XK
p'
^-qX
^-qx
0
CP
aqK
^KX
x
0
CP
^KK
dL I //
or:
-p '{B+A)
(1 -qfip-p^p'-ip'Q-q^-l)
(1+X)
dq _
{K{\-q)p")
H
Hence, dq/dL > 0 since x > x, K < 0 (since wn > 0 from the agent's participation
constraint), and p'(l-q)K-l < 0.
If the solution to [MP'"] when L > k is given by (A10), the principal solves the
following problem:

64
Maxx qj: \-R ~PL ~x ~ +A +(1 - 1 -q
s.t. q(B+A)-( 1 -q){p-p)K+(x-x) = 0
-A-{\-q)(\-p)K-x = 0
The lagrangian for this problem is:
<£=R-pL -x -^L+A+( 1 -q){ 1 -p)K+x
i -q
+lx[q(B+A)-( 1 -r/)(p-/?)^+(x-x)]
and the necessary first order conditions are:
=q{B+A)-( 1 -q){p-p)K+(x-x) = 0
i^2 = -/I-(1 -¿7)( 1 -p)K-x = 0
$£x=-p/L-l+Xl[p/(l-q)K-l]=0
a,=^ [b+^] -*[(i-a2x i -d-xtf-p)}=o
(I ~ aA. = (l-r/)[(l-A2)(l-p)-A1(p-^)]=0
where = 6^/6Aj for i=l,2. Let H denote the bordered Hessian matrix of this problem.
Using the implicit function theorem and Cramer’s Rule:
0
0
eg
0
^1K
0
0
eg
^2x
0
eg
‘Rv i
eg
â– s-.x2
0
eg
axA'
eg
ai/i
eg
aq2
^ o
- eg
dq _
eg
S-A'l
eg
^A'2
sk
0
eg
SAA'
da
\H\

where:
Therefore:
2lq = 2q,=B+A+K(p-p)
^ia' = ^x-i = -i}-R)ip-p)
^2x ®
^q-^-Kd-p)
^ = %q=-\P'K
&Kx = &xK=XPlV-(Í)
eg - -
(i+V*2)
A
K\\-qfp
1
(1 +Aj-A2)
(l-<7)3
Kp"
0+V*2)
K\l~q)p
0
0
eg
31 lx
eg
^ 1Á'
0
0
C^2x
eg
S-2A'
CP
axi
CP
Sx2
se„
CP
^â– xK
dq _ 1
CP
aA'l
eg
3h
se&
CP
AX
(1 -<7)2 |//|
<0
The sign of dq/da follows from second order sufficient conditions which imply that |H|
0 and the numerator matrix is positive. Likewise:

66
0
0
eg
0
eg
°L1 K
0
0
a2.v-
0
^2K
CP
.t1
eg
ax2
XX
P'
eg
CP
^q2
eg
agx
0
eg
CP
aA'l
eg
aA2
eg
^Kx
0
eg
aKK
dL \H
or:
dq _ -p '{B +A){\-q)\\ -pf(p'{\-q)K~\)
dL $
Hence, dq/dL > 0 since p'(l-q)K-l < 0.
Therefore, dq/dL > 0 and dq/da < 0, regardless of which solution is optimal for
the agent when L > k. â– 

CHAPTER 4: AVOIDING VICARIOUS LIABILITY: THE INDEPENDENT
CONTRACTING RULE AND THE ERISA PREEMPTION CLAUSE
4.1 Introduction
The recent trend of the courts to expand the scope of vicarious liability has left
newly afflicted third parties searching for ways to avoid this liability. Some, such as banks
threatened with liability for environmental damages, appeal to established principles of tort
law in their attempt to avoid liability. Others, such as HMOs threatened with liability for
physician malpractice, use new and creative methods to avoid liability. The goal of this
chapter is to survey vicarious liability avoidance strategies, both old and new, and
investigate the effect their success has on accident prevention. In particular, two avoidance
tactics will be explored: one based on the "Independent Contracting Rule" and the other
based on the "ERISA Preemption Clause."
The "Independent Contracting Rule," the general legal rule courts use to impose
vicarious liability, states that principals are vicariously liable for the torts of their
"servants," but not those of independent contractors. This gives principals an incentive to
avoid vicarious liability with the use of an independent contractor. The chapter shows that
the use of a judgement-proof independent contractor to avoid liability leads to insufficient
accident-preventing care. Two categories of exceptions to the Independent Contracting
Rule have emerged in recent court rulings. This chapter shows that these exceptions are
67

68
justifiable on efficiency grounds. Ex ante, these exceptions discourage the use of an
independent contractor to avoid liability. Ex post, these exceptions induce the efficient
care level in some principal-independent contractor relationships.
Recently, health maintenance organizations have begun to use a preemption clause
in the Employee Retirement Income Savings Act of 1974 (ERISA) to avoid vicarious
liability for physician malpractice. This chapter shows that, under the protection of
ERISA, the HMO will not only authorize too few medical tests and procedures, but will
require an insufficient level of care from the physician. This result is generalized to dispel
the commonly held belief that direct liability induces the agent to take excessive care in
avoiding an accident while producing too little output. Direct liability induces too little
care and too much production relative to the social optimum when the agent is judgement-
proof.
The chapter is organized as follows. Section 4.2 describes the Independent
Contracting (IC) Rule and its use by the courts. Section 4.3 investigates the efficiency, in
accident prevention, of the IC rule and its exceptions. Section 4.4 surveys the history of
third party liability for physician malpractice and describes the evolution of the ERISA
preemption clause as a tool used by HMOs to avoid liability. Section 4.5 explores the
efficiency implications of the ERISA preemption clause.
4.2 Vicarious Liability and the Independent Contracting Rule
The general legal rule for the application of vicarious liability is the following: "A
master is vicariously liable for the torts of his servants committed while the latter are

69
acting within the scope of their employment."26 There are two key parts to this general
rule. First, in order for the principal to be held liable for an agent's damaging conduct, the
conduct must fall within the scope of employment. For example, if an agent commits a
crime unrelated to his work for the principal, the principal usually escapes any criminal or
civil liability. Unfortunately, determining whether an agent's conduct falls within the scope
of his employment is often difficult and many controversial court rulings are based on this
determination. For example, there are some cases in which the courts have held firms
vicariously liable for damages resulting from assaults between employees, even when the
motive for the assault is personal and unrelated to the firm's business.27 Following much of
the previous literature, the models described subsequently assume that all of the agent's
torts are directly related to the principal-agent enterprise to avoid the "scope of
employment" complication.28
The second key part of the general vicarious liability rule is the requirement that
the principal-agent relationship be one of master and servant. The level of control the
principal exercises over the agent is the primary factor courts use to determine whether a
business relationship is a master-servant relationship29. If the principal can easily observe
26 [10] p. 176.
27
Carr v. Wm. C. Crowell Co., 28 Cal 2d 652, 171 P.2d 5 (1946); Lebrane v. Lewis, 292
So.2d 216 (La. 1974).
28
[30] analyzes the economic effects of the scope of employment rule in vicarious liability
law.
29 The exact legal definition of servant can be found in Appendix A4.0.

70
and control the agent's level of care, then the courts usually find the principal to be
vicariously liable for any accidents caused by the agent. For example, the courts usually
determine that the principal has adequate control if the principal has a good understanding
of the technology used by the agent, if the principal and agent work in the same location, if
the principal supplies the necessary equipment to the agent, if the principal and agent are
engaged in a long-term business relationship, etc. If the principal cannot readily observe or
control the agent's level of care, then the courts usually will assign the liability for an
accident to the agent who caused it whether or not the agent has enough wealth to cover
the damages. For example, the courts will usually find the agent solely liable if the
principal has little knowledge of the agent's technology, or if the agent is an independent
contractor with which the principal has no long-term business relationship. Therefore, in
general, a principal is held vicariously liable for the torts of his employees, but not for the
torts of independent contractors which she has hired. This is commonly referred to as the
"Independent Contracting Rule." Thus, if the principal wishes to avoid vicarious liability,
she can do so by hiring an independent contractor, although this may result in lack of
complete control over the work to be accomplished.
There are, however, many exceptions to the general independent contracting rule.
In fact, the exceptions are so numerous that, as one judge put it, "it would be proper to
say that the rule is now primarily important as a preamble to the catalog of its
exceptions."30 Yet, as stated in the Restatement (Second) of Torts (Sect. 409),
30 Pacific Fire Ins. Co. v. Kenny Boiler & Mfg. Co., 210 Minn. 500, 277 N.W. 226 (1937).

71
In general, the exceptions may be said to fall into three very broad
categories:
1. Negligence of the employer in selecting, instructing, or
supervising the contractor.
2. Non-delegable duties of the employer, arising out of some
relation toward the public or the particular plaintiff.
3. Work which is specially, peculiarly, or inherently dangerous.
Included in (1) are some cases in which the contractor chosen by the principal was
underinsured or undercapitalized.
4.3 The Efficiency of the IC Rule and Its Exceptions
One commonly used justification of vicarious liability is the argument that it helps
to deter the carelessness which leads to damaging accidents. Is this justification correct?
Does the use of vicarious liability (as opposed to direct liability) increase the accident¬
preventing care of the agent9 How does the Independent Contracting (IC) Rule affect the
relative efficiency of vicarious liability in preventing accidents? This section will examine
the efficiency of vicarious liability in preventing accidents, particularly when it is applied
by the courts using the IC rule and its exceptions.
4,3,1 The Model
Consider a principal who hires an agent to complete a productive activity. This
activity will produce a revenue of R for the principal. However, there is also a probability
p (e (0,1]) that the agent, while completing this activity, will cause an accident. The
probability of an accident is a function of the precaution or care x the agent takes when
completing the activity. It is assumed that increasing care decreases the probability of an
accident at a decreasing rate (p'(x)<0 and p"(x)>0). The agent's personal marginal cost

72
(or disutility) of taking care is assumed to be constant and is normalized to unity. In
addition, assume the agent's initial wealth is A, while the principal's wealth is unlimited.31
Suppose a revenue-producing activity has a potential accident damage of D
associated with it. The social welfare of this activity is:
SW - R-p(x)D-x
Therefore, the socially optimal care level is given implicitly by:
-p'(x)D- \ = 0
At the socially optimal care level, the marginal cost of increasing care equals the marginal
decrease in expected damage associated with increasing care. Let x*(D) denote this care
level.
The IC rule essentially applies vicarious liability when the principal can observe the
agent's care and applies direct liability when the principal cannot observe the agent's care.
Therefore, to investigate the efficiency of the IC rule, the relative efficiency of vicarious
and direct liability must be determined when the principal can and cannot observe the
agent's preventive care.
31
In addition, the principal and the agent are both assumed to be risk neutral. This is a
standard assumption found in most of the previous vicarious liability literature. See [13]
for implications of general risk aversion

73
4.3.2 Observable Care
When the principal can observe the agent's care, the principal can dictate what care
the agent will exert.32 Therefore, concerning preventive care, the principal and agent will
behave as if they are a united enterprise. The principal will dictate that the agent exert a
level of care appropriate considering the potential losses the enterprise may face in the
event of an accident.
For instance, when the principal faces a vicarious liability of L, the principal would
like to maximize her expected profits of:
LTÍ = R -p{x)L -x
where the last term in this expression reflects the fact that the principal must compensate
the agent for his exertion of care and its associated cost. (Otherwise, the agent will not
participate in the productive activity.) Notice, Eli is simply the expected profits of the
principal-agent enterprise. Therefore, to maximize her profits, the principal will dictate
that the agent exert x^L). Hence, vicarious liability will lead to the socially efficient level
of care if the assigned liability equals the damages (L = D).
When the agent faces a direct liability of L, the principal not only has to
compensate the agent for the cost of care, but also has to compensate the agent for his
potential liability. Therefore, the principal must pay the agent an expected wage of p(x)L-x
32
This assumes the principal can make a take-it-or-leave-it offer to the agent (i.e., the agent
has no bargaining power). See Chapter 2 for the implications of an alternative
assumption.

74
if the principal dictates a level of care equal to x. Again the principal would like to
maximize expected profits of R-p(x)L-x and will dictate a care of x*(L) for the agent to
exert. However, if the liability is greater than the agent's wealth (L > A), the agent will
only lose his wealth (A) in the event of an accident. In this case, the principal would only
need to compensate the agent with an expected wage of p(x)A-x and, thus, would dictate
a care of x*(A) for the agent to exert. This is the crux of the judgement-proof problem.
When an agent is judgement-proof and the accident damages exceed his wealth (D > A),
direct liability (with L = D) will lead to an inefficiently low level of care (x“(A) < x*(D)).
When the principal can observe the agent's care, both vicarious and direct liability
lead to efficient care if the agent is not judgement-proof. However, if the agent is
judgement-proof, only vicarious liability insures that the agent will exert the socially
efficient level of care. Thus, the IC rule, which requires vicarious liability when the
principal can observe the agent, will lead to efficient care in this case.
4,3.3 Unobservable Care
When the principal cannot observe the agent's care, the principal cannot effectively
dictate to the agent the care he will exert. In this case, the principal can only induce
preventive care from the agent through provisions in the contract signed between the
principal and the agent.
To be specific, if the principal is vicariously liable, the nature and timing of the
principal-agent relationship is as follows. First, both the principal and the agent learn the
principal's vicarious liability L in the event of an accident. Second, the principal offers a
contract to the agent that specifies a non-accident wage of wn and an accident wage of wa.

75
Third, the agent chooses to accept or reject the principal's contract offer. If the agent
accepts the contract, he then chooses his level of care, x, in the activity. This care cannot
be observed by the principal or the courts. Fourth, the state of the world is realized (either
accident or no-accident), the liability payment is collected from the principal in the event
of an accident, and the appropriate wage is paid to the agent.
In choosing a contract to offer the agent, the principal solves the following
problem:
[/"] V(L) = Max [R -p(x)w -(1 ~p(x))w -p(x)L\
' ' i'P ti
s.t. (/) p(x)wa+i 1 -p{x))wn-x > 0
(77) p'(x){wa-wn)-\ -0
(Hi) wa > -A
Constraint (i) is the agent's participation constraint. The agent will only accept the
principal's offer if the expected wage net of effort costs is at least as great as the agent's
reservation wage (here normalized to zero). Constraint (ii) is the incentive compatibility
constraint which reflects the principal's inability to observe the agent's care. Since the
principal cannot make the wage contract contingent on the agent's care level, the agent
will choose a care level that is personally optimal given the wage contract.33 Constraint
34 Actually, an additional condition is needed to insure that the stationary point
specified by (ii) is indeed optimal for the agent. This condition is:
p"(x)(wa-wn)<0
for all x. Since p"(x) > 0, this condition is equivalent to (wa - wn) < 0. Yet, since p'(x) < 0,
condition (ii) implies (w., - wn) < 0. Therefore, condition (ii) specifies an optimal care level
for the agent. See [22] for a thorough discussion of the first-order approach in moral
hazard problems.

76
(iii) reflects the agent's limited wealth and the principal’s "right to indemnification." When
a principal is found vicariously liable, she has the right to be compensated by the accident-
causing agent [7], However, this compensation cannot exceed the agent's wealth.
Therefore, the agent's accident wage must be at least -A.
For the vicariously liable principal in [P], the profit-maximizing level of care is
x*(L) (i.e., that which is socially optimal if the liability, L, equals the damages, D). The
principal can induce this level of care by setting wn - wa = L. The principal simply passes
along the liability to the agent through the wage contract by penalizing the agent L in the
event of an accident. However, as the principal's liability increases, there comes a point
(denoted by L = k) at which passing the liability to the agent becomes costly to the
principal. This occurs because of the agent's limited wealth. Recall that the principal can
take no more than the agent's wealth through indemnification (wa £ -A). Therefore, in
order to induce x*(L) from the agent, the agent's no-accident wage (wn) must be at least L
- A. However, if L - A > x*(L) + p(x*(L))L, then the principal can only induce x*(L) from
the agent by giving the agent an expected wage above his reservation wage (see constraint
(i) in [P]). Therefore, if L < k, the principal can costlessly pass on the liability, L, to the
agent. If L > k, then the principal faces a tradeoff; she can maximize the joint surplus only
by sacrificing some of her share of the surplus. Faced with this tradeoff, the principal will
sacrifice less profit by inducing a suboptimal care level from the agent. Even though this
care level is suboptimal, it is non-decreasing in L, reflecting the principal’s desire to pass
on as much of the liability as possible while protecting her profits.

77
To be specific, the principal is faced with the following trade-off for liability levels
greater than k. At one extreme, the principal could continue to pass the full liability onto
the agent through the contract inducing the profit-maximizing care (x*(L)). However, the
principal incurs a cost of L - A - [x*(L) + p(x*(L))L] when pursuing this approach, since
the principal must give the agent a share of the joint profits in order to fully pass the
liability onto him. At the other extreme, the principal could simply offer the contract which
is profit-maximizing for L = k (i.e., freeze the accident penalty at k). This approach allows
the principal to avoid giving the agent an economic rent. However, this will induce a level
of care from the agent that is too low given the principal's vicarious liability of L. The
principal will, therefore, incur an expected cost of [p(x¥(K)) - p(x"(L))]L since the
probability of an accident will be too high given this approach.
At first (i.e., for L e (K,p]34), the latter approach is least costly for the principal, so
the principal sets wn - wa = k, even though L > k. Eventually (i.e., for L > p), this
approach leads to a probability of an accident that is too great relative to the principal's
liability, L. In this case, the principal uses a combination of the two strategies. The
principal gives the agent a share of the joint profits to induce a higher level of care, but not
enough to induce x*(L). (In other words, the accident penalty will fall between k and L.)
Therefore, even though the induced care is inefficient for L > k, it is never less than x*(k).
For this reason, vicarious liability is at least as efficient as direct liability in
preventing accidents and more efficient when the agent is judgement-proof (L > A). If the
34
where p is the liability level at which the participation constraint no longer binds.

78
agent is directly liable, he will exert the socially optimal care (x*(L)) as long as the liability
is no greater than his wealth (L < A). However, if the agent is potentially judgement proof
(L > A), he will exert just x*(A) since the penalty he receives in the event of an accident is
only the loss of his wealth, A. As shown above, when the principal is vicariously liable, she
induces the efficient level of care from the agent not only when L < A, but also when L e
[A,k], In addition, when L > k, the inefficiently low level of care induced under vicarious
liability is never less than x*(k)(> x*(A)). Hence, when the agent is judgement-proof and
the principal cannot observe the agent's care, vicarious liability is more efficient than direct
liability.35
4,3,4 Efficiency of the IC Rule
The previous analysis illustrates one shortfall of the IC rule. In general, the IC rule
dictates direct liability when the principal cannot observe the agent. However, if the agent
is judgement-proof, vicarious liability is more efficient than direct liability regardless of
whether the principal can or cannot observe the agent's care. Therefore, if the prevention
of accidents is the courts' primary goal, the application of vicarious liability should not be
made contingent on the agent's status as a servant or independent contractor as in the IC
rule.
The IC rule has an additional drawback. It gives the principal an incentive to avoid
vicarious liability with the use of an independent contractor. If the agent is judgement-
proof (L > A), the principal earns greater profits by using an independent contractor which
she cannot observe than by using an employee which she can observe. Under the IC rule,
33 The preceding model is discussed in more detail in Chapter 2.

79
independent contractors are directly liable, so the principal need only compensate the
independent contractor for his potential loss of wealth in the event of an accident (p(x)A).
If an employee is used, the principal is vicariously liable and faces a greater expected loss
(p(x)L). Therefore, under the IC rule, the principal prefers to use an independent
contractor to avoid vicarious liability, even though this involves a loss of direct control
over operations. This result is summarized in the following theorem:
Theorem 4.1: If the agent is judgement-proof, the principal earns greater profits when she
cannot observe the agent and the agent is directly liable than when she can observe the
agent and the principal is vicariously liable.
Proof: See Appendix A4.1.
The IC rule, thus, creates both ex ante and ex post inefficiencies. Ex ante, the IC
rule gives the principal an incentive to give up control by using an independent contractor
to avoid liability. Ex post, after the principal has chosen to use an independent contractor,
the IC rule imposes direct liability when vicarious liability would be more efficient in
preventing accidents.
4.3.5 The Efficiency of the Exceptions to the IC Rule
In light of this, it is useful to note again the presence of many exceptions to the IC
rule. As shown above, any exception to the IC rule could be justified on efficiency
grounds, since vicarious liability is at least as efficient as direct liability and more so when
the agent is judgement-proof. Still, some exceptions, such as those for severely
undercapitalized contractors and inherently hazardous activities, may be particularly
justifiable on efficiency grounds.

80
To investigate the efficiency of these exceptions, consider a specific form of the
previous model. Suppose p(x) = e'ax. This functional form allows the introduction of a
parameter (a) which reflects the inherent danger of an activity. For example, for a given
level of preventive care, activity 1 (e.g., driving) is more dangerous (i.e., the probability of
an accident is higher) than activity 2 (e.g., flying) when a, < a2. This leads to the following
result:
Theorem 4.2: If the principal cannot observe the agent and the liability level is relatively
large (L > p), then the difference between the care induced under vicarious liability and
that induced under direct liability increases as the activity becomes more dangerous.
Proof: See Appendix A4.2.
As we have seen, when the agent is judgement-proof, vicarious liability is more efficient in
preventing accidents than direct liability. Theorem 4.2 illustrates that the difference in the
preventive care induced by the two schemes grows as the productive activity becomes
more hazardous. Therefore, the use of the IC rule when an activity is inherently dangerous
is particularly detrimental to accident prevention. While any exception to the IC rule is
justified, this shows that an exception based on an inherently hazardous activity is
particularly justifiable on efficiency grounds.
The exception for severely undercapitalized contractors can also be justified on
efficiency grounds:
Theorem 4.3: If the principal cannot observe the agent and the agent is judgement-proof,
then the difference between the care induced under vicarious liability and that induced
under direct liability is non-decreasing in the agent's wealth shortfall (L - A).

81
Proof: See Appendix A4.3.
Theorem 4.3 simply states that the relative efficiency of vicarious liability grows as the
agent becomes more judgement-proof. Therefore, an exception to the IC rule when
contractors are severely judgement-proof is warranted in promoting accident prevention.
In summary, the IC rule is inefficient on two grounds. Ex ante, the IC rule gives
the principal an incentive to give up control by using an independent contractor to avoid
liability. Ex post, after the principal has chosen to use an independent contractor, the IC
rule imposes direct liability when vicarious liability would be more efficient in preventing
accidents. However, the dangerous activity exception and the undercapitalization
exception eliminate these inefficiencies in those instances in which they are particularly
damaging to accident prevention.
4.4 Vicarious Liability, Medical Malpractice, and the ERISA Preemption Clause
Traditionally, third parties have not been held vicariously liable for medical
malpractice. For instance, hospitals were often immune from vicarious liability for the
malpractice of their physicians because hospital physicians and other professional hospital
personnel were considered independent contractors. In the first half of this century, this
legal tendency sometimes lead to bizarre and self-contradictory rulings. For example, "in
Bernstein v. Beth Israel Hospital, a nurse was considered an independent contractor when
she scalded a patient, yet an employee for the purpose of receiving compensation when
she scalded herself in the process."36
36 [12], p.28; Bernstein v. Beth Israel Hospital, 140 N.E. 694 (N.Y. 1923).

82
Courts soon began to realize that the use of the independent contracting rule for
hospitals and physicians was often inappropriate. It became clear that hospitals have
significant control over the quality of the medical care provided by their physicians and
nurses. In addition, many competing hospitals made claims concerning the quality of their
care which suggested that their physicians were employees, not independent contractors.
So, in the late 50's and early 60's, courts began to hold hospitals liable for the malpractice
of their physicians.37
In recent years, a new type institution—the health maintenance organization
(HMO)—has emerged as a dominant form of health care provision. In 1996, 77 percent of
U.S. workers belonged to an HMO (up from 49 percent in 1992).38 The term "health
maintenance organization" has actually come to describe many different types of health
care institutions, some which resemble hospitals and others which more closely resemble
insurance companies. However, all HMO's have one thing in common. Participants of
HMOs, instead of paying a fee for each medical service they require, pay an up-front lump
sum fee for their complete medical coverage.
The vicarious liability of HMOs for medical malpractice is far more complex than
that of hospitals. One reason for this is the heterogeneity of organizational structures
which fall under the title of HMO. The "staff model" HMOs, which directly employ their
physicians and staff and own the hospitals, clinics, and laboratories in which their staff
37 One landmark case in this area is Bing v. Thunig, 143 N.E. 2d 3 (N.Y. 1957).
38 [14],

83
work, are generally held vicariously liable for malpractice.39 The vicarious liability of
"group" and "IPA model" HMOs is not as clear cut. Group and IPA model HMOs
contract with independent physicians groups to provide medical care for the HMO's
members. These physicians take fee-for-service customers in addition to their HMO
customers, so they are sometimes seen as independent contractors in the eyes of the law.
For this reason, group and IPA model HMOs are sometimes found immune from vicarious
liability for physician malpractice.40 But, more often than not, group and IPA model
HMOs cannot escape vicarious liability on these grounds.41
Recently, HMOs have begun to use a creative approach to avoid much of the
vicarious liability they face. This strategy involves the use of a clause in the federal
"Employee Retirement Income Savings Act" (ERISA) of 1974. Prior to 1974, pensions
and other employee benefit plans were regulated by a patchwork of state laws. This often
created problems for firms wishing to design benefit plans for employees in different
states. In addition, some state regulations were inadequate and allowed abuses in pension
administration and disclosure of pension funding and vesting. Congress responded to these
inadequacies by passing ERISA to make the regulation of employee benefit plans a federal
39
One example is Sloan v. Metropolitan Health Council, 516 N.E.2d 1104 (Ind. Ct. App.
1987).
40
Two examples are Raglin v. HMO Illinois, 595 N.E.2d 153 (Ill. App. Ct. 1992) and
Chase v. Independent Practice Association, 583 N.E.2d 251 (Mass. App. Ct. 1991).
41
Two examples are Schleier v. Kaiser Foundation Health Plan, 876 F.2d 174 (D.C. Cir
1989) and Boyd v. Albert Einstein Medical Center, 547 A.2d 1229 (Pa. Super. Ct. 1988).

84
responsibility. To supersede the patchwork of state laws regulating benefit plans, section
514 of ERISA contains a preemption clause which states that ERISA "shall supersede any
and all State laws insofar as they may now or hereafter relate to any employee benefit
plan."42 It is this preemption clause that HMOs have used, somewhat successfully, to
avoid much of the vicarious liability they would normally face.
HMOs can use the ERISA preemption clause because most of their members join
through employee health insurance. In particular, many large companies fully fund their
employee health benefits and contract with an HMO to administer these health plans.
Approximately half of all American workers receive their health benefits through
employer-funded health plans.43 In addition, medical malpractice traditionally falls under
the jurisdiction of the state courts. HMOs argue that they simply administer these
employer-funded health benefit plans and, therefore, medical malpractice claims made in
connection with these plans in state courts are superseded by ERISA. As a lawyer for U.S.
Healthcare recently stated, “ERISA pre-empts state law medical malpractice claims
against entities involved in the administration or delivery of health care benefits under an
ERISA plan.”44
One may wonder, why is this significant9 If ERISA preempts state medical
malpractice claims against HMOs, why can’t a victim bring his or her claim against an
HMO in federal court9 The problem with this approach is that ERISA has no provisions
42 [3], p. 1023; 29 U.S.C. § 1144(a).
43 [12], p.9.
44 [19], p. 16.

85
relating to medical malpractice. If a victim’s medical malpractice suit is moved from state
to federal court, this leaves the victim with no means of recovering damages from the
HMO.43 Therefore, if an HMO is successful in moving a medical malpractice suit from
state to federal court, it effectively avoids all vicarious liability.
HMOs generally have been successful in their use of the ERISA preemption
clause. In the majority of cases in which HMOs have claimed immunity from liability
through ERISA, the federal appeals courts have invoked the preemption.46 The courts
have done so despite the knowledge that victims have no recourse under ERISA. As one
judge stated, "the lack of an ERISA remedy does not affect a preemption analysis."47 In
this reasoning, the courts have followed the example of the Supreme Court, which has
broadly interpreted the "relate to" verb in the preemption clause. The Supreme Court has
asserted that "a law relates to an employee welfare plan if it has a 'connection with or
reference to such a plan.1"48 This leaves federal appeals courts little room to uphold a
malpractice claim against an HMO administering an employer-funded health plan. Despite
this, a small number of judges have denied ERISA preemption of malpractice claims.49 In
45
However, the victim can still pursue a claim against the physician(s) under state
malpractice law.
46 [12], pp. 40-43.
47 Corcoran v. United Healthcare, Inc., 965 F.2d 1321 (5th Cir. 1992), p. 1333.
48 FMC Corp. v. Holliday, 498 U.S. 52 (1990), p.58
49
For example, Haas v. Group Health Plan, Inc., 875 F. Supp 544 (S.D. Ill. 1994), and
Smith v. HMO Great Lakes, 852 F. Supp. 669 (N.D. Ill. 1994).

86
addition, the Supreme Court has recently backtracked somewhat from their
accommodating interpretation of the ERISA preemption clause.50 This may give courts
leeway to uphold claims of vicarious liability against HMOs in future rulings.
4.5 Efficiency of the ERISA Preemption Clause
The use of the ERISA preemption clause has become an effective tool for HMOs
in avoiding vicarious liability. The belief among many is that the use of ERISA in this way
could lead to more medical accidents and misdiagnoses.51 The analysis of section 4.3
certainly supports this view. However, the context of HMO liability for malpractice is a bit
more complex than that modeled in section 4.3. In section 4.3, the agent's care was the
sole factor affecting the likelihood of an accident. In many malpractice cases affecting
HMOs, the physician's care is not the only factor contributing to an accident. The HMO
often dictates what procedures and tests to use and this can significantly affect the
probability of an accident or misdiagnosis In this more complex context, how does the
avoidance of vicarious liability affect accident prevention?
To answer this question, consider a slightly modified version of the model in
section 4.3. Suppose the productive activity referred to in section 4.3 is the diagnosis and
treatment of an ailing HMO member. The HMO specifies the allowed tests and procedures
to use in treatment. Let the number of tests and procedures be indexed with the (real)
variable s. This variable can also reflect the overall quality of the medical tests and
procedures. For example, a very accurate (and possibly very expensive) test for cancer
50 New York Conference of Blue Cross v. Travelers Insurance, 115 S.Ct. 1671 (1995).
51 [19].

87
translates into a large value of s. As before, the average level of care exerted by a
physician in performing these tests and procedures is denoted x. The probability that
malpractice occurs in the diagnosis and/or treatment of the patient is given by p(s,x).
p(s,x) is a decreasing, convex function of both s and xf2 In addition, assume that
tests/procedures and care are "compliments" with respect to achieving a mistake-free
diagnosis and treatment. In other words, increasing the number or quality of
tests/procedures will increase the marginal ability of care to prevent malpractice (psx < 0).
The HMO's profit gross of physician compensation is R(s) = C - as. C represents
the capitation paid by the patient to the HMO. Recall, this is a lump sum fee independent
of the number or quality of services provided, a represents the constant incremental cost
of tests and procedures. The physicians marginal cost of care is assumed to be a constant
P-
The socially optimal number of tests/procedures and level of care are characterized
by conditions analogous to those found in section 4.3:
-p p - a
-pP = p
where D is the level of damages associated with an incident of malpractice. At the socially
optimal number of tests/procedures, the marginal cost of increasing s equals the marginal
decrease in expected damage associated with increasing s. Likewise, the marginal cost of
increasing care equals the marginal decrease in expected damage associated with
32 In other words, px < 0, ps < 0, p^ > 0, pss > 0, and p^pss - (p J2 > 0.

88
increasing care at the socially optimal care level. Let this socially optimal number of
procedures and level of care be denoted by [x"(D), s*(D)].
As before, the HMO pays the physician a wage that can be made contingent on the
occurrence of an accident. In addition, it is assumed that the HMO can observe and
contract upon the physician's quality of medical care. The accuracy of this assumption
may, at first, seem uncertain given the myriad of organizational structures which
characterize the HMO-physician relationship. However, I believe this best describes the
flow of information between physician and HMO in all of the HMO models. In the "staff
model, physicians are essentially employees of the HMO, so the HMO can easily observe
and control their physicians' level of care. In the "group" and "IPA" models, the
observability and control of the physicians is not as clear cut. Many HMO's of this type
openly claim that they cannot control the care of their affiliated physicians. As one HMO
executive recently stated, "U.S. Healthcare does not direct the care furnished by
participating health care providers. 1,33 However, almost all of the group/IPA HMOs
employ "utilization review" and "quality assurance" programs which monitor their
affiliated physicians.34 In addition, HMOs often use advertising which assures potential
customers of the highest quality of medical care through rigorous monitoring of their
physicians.33 Therefore, despite the claims of lack of control, most of the evidence
33 [19], p. 16, col. 6.
54 [12].
55 [19].

89
supports the contention that group/IPA model HMOs are able to observe and control the
medical care of their physicians.
The contracting problem facing the HMO is the following:
[HP] Max R(s) -/?0,x>r (x)-(l -p(s,x))w (x) -p(s,x)L
’ * n? a t
s t. (0 /?(yx)wa(x)+(l -p(5,x))w„(x)-px-^(5',x)Za > 0
(H) wa(x) > -A
As in [P], constraint (i) is the physician's participation constraint and constraint (ii) is the
wealth constraint reflecting the fact that the physician's wealth is restricted to A. The
liability rule applied by the courts is characterized by Lp, the liability the HMO (principal)
faces in the event of an accident, and La, the liability the physician (agent) faces in the
event of an accident. The standard joint liability for malpractice is represented by any
[Lp,LJ which satisfies Lp + La = D (provided La < A). If the HMO is able to shield itself
from liability using the ERISA preemption clause, Lp = 0 and La can be no more than A
given the physician's limited wealth.
If the HMO can avoid liability through the ERISA preemption clause, one would
naturally expect the HMO to scrimp on the use of costly medical tests and procedures
when treating patients. The HMO can save money by reducing procedures without
increasing the likelihood of a successful malpractice claim against the HMO. Thus, the
ERISA preemption clause clearly gives the HMO an incentive to authorize too few
procedures relative to the social optimum, s*(D). However, the ERISA preemption clause
also creates another inefficiency. If the HMO avoids liability, this will also result in the
provision of an insufficiently low level of care, when the physician is judgement-proof (D

90
> A). Under ERISA, only the physician can be held liable for malpractice. If the physician
is judgement-proof, his expected loss due to liability is pA. The HMO need only
compensate the physician for this expected loss and, thus, the HMO only faces the indirect
cost of pA due to malpractice. Since the HMO faces a cost less than the expected
damages, pD, the HMO will not only authorize too few procedures, but will require an
insufficient level of care from the physician. This result is summarized in the following
theorem:
Theorem 4.4: If the physician is judgement-proof (D > A), the exemption of liability for
HMOs under ERISA will result in a level of care less than the social optimum (x*(D)) and
too few tests and procedures relative to the social optimum (s*(D)).
Proof: See Appendix A4.4.
The result in theorem 4.4 can be generalized to contexts other than HMO-
physician liability. For instance, s can be interpreted as the number or quality of safety
enhancing investments made by the principal (reflected in the production process or the
final product or both). Theorem 4.4 then states that escaping vicarious liability will result
in too little care by the agent and too few safety enhancing investments. Alternatively,
suppose s is interpreted generally as the level of production specified by the principal. In
this case, R(s), the profit gross of employee compensation, is an increasing function of s.56
In addition, p(s,x), the probability of an accident, increases with s at a decreasing rate (ps >
0 and pss < 0) and "reducing production" and care are "compliments" with respect to
accident prevention (psx > 0). The result in theorem 4.4 now takes the following form:
36 For this generalization, assume R is concave in s (R " < 0).

91
Corollary 4.5: If the agent is judgement-proof (D > A), an exemption of liability for the
principal will result in a level of care less than the social optimum (x\D)) and a level of
production greater than the social optimum (s*(D)).
Proof: See Appendix A4.5.
If the agent is judgement-proof and the principal can avoid vicarious liability, the principal
saves D-A in the event of an accident since only the agent is liable for damages. With this
leeway in expected accident costs, the principal can increase production and compensate
the agent with a relaxation of requirements for care. In this fashion, the principal can earn
greater expected profits while still giving the agent the same net compensation.
This result, as expressed in corollary 4.5, contradicts a widely-held belief about the
possible effects of direct liability on care and production. Some legal scholars argue that a
directly liable agent may take excessive care to prevent an accident and thus may be less
productive. As Kornhauser (1982) states:
...there is a conflict of interest between agent and principal in which
the agent prefers, if all else is equal, to take less care, while the
principal cares only about her profit. This rationale assumes that the
agent's exercise of care decreases productivity so that if he takes
more care, enterprise profits fall. However, under a rule of law that
assigns liability to the agent, the agent's interests conflict with those
of the enterprise. Thus, in order to avoid liability, he might take
more care than he otherwise would under enterprise liability.
Consequently, from an economic standpoint, too few accidents and
too little profit would be produced under agent liability.57
Former Assistant Attorney General William F. Baxter shares this opinion:
[13], pp. 1350.
57

92
Pecuniary responsibility on the part of employees leads to internal
inefficiency not because employee behavior is unresponsive to the
prospect of such liability but because it is too responsive. Liability
induces the employee to adopt behavior that is suboptimal from the
standpoint of the employer. Pecuniary responsibility forces
employees to choose between protecting their own purses and
executing the programs of their employers with zeal and
imagination. We should not be surprised to find that employees
who face such a choice strike a different balance than would those
who had to bear both the costs of harm to outsiders and the costs
of ineffective implementation.58
Corollary 4.5 states that a wealth-constrained agent will never behave in this manner. A
directly liable judgement-proof agent will exert too little preventive care and produce too
much at the direction of the principal. However, the previous analysis does not
incorporate such factors as the agent's expected future income and reputation which could
create an incentive for greater care under direct liability.
4.6 Conclusion
The two tactics employed by principals to avoid vicarious liability—the
Independent Contracting (IC) Rule and the ERISA preemption clause—both lead to
inefficiencies in accident prevention. The IC rule is inefficient in two ways. Ex ante, the IC
rule gives the principal an incentive to give up control by using an independent contractor
to avoid liability. Ex post, after the principal has chosen to use an independent contractor,
the IC rule imposes direct liability when vicarious liability would be more efficient in
preventing accidents. However, the dangerous activity exception and the
[I], pp. 49.
58

93
undercapitalization exception eliminate these inefficiencies in those instances in which they
are particularly damaging to accident prevention.
When implemented in the case of HMO and physician malpractice, the ERISA
preemption clause leads, not only to an inefficiently low number of medical procedures,
but also induces an insufficient level of care from the physician. This result can be
generalized to dispel the commonly held belief that direct liability induces the agent to take
excessive care in avoiding an accident while producing too little output. Direct liability
induces too little care and too much production relative to the social optimum when the
agent is judgement-proof.
A4.0: Legal Definition of a Servant
The legal definition of a servant, found in section 220.2 of the Restatement
(Second) of Agency, is the following:
In determining whether one acting for another is a servant or an independent contractor,
the following matters of fact, among others, are considered:
(a) the extent of control which, by the agreement, the master may exercise over the details
of the work;
(b) whether or not the one employed is engaged in a distinct occupation or business;
(c) the kind of occupation, with reference to whether, in the locality, the work is usually
done under the direction of the employer or by a specialist without supervision;
(d) the skill required in the particular occupation;

94
(e) whether the employer or the workman supplies the instrumentalities, tools, and the
place of work for the person doing the work;
(f) the length of time for which the person is employed;
(g) the method of payment, whether by the time or by the job;
(h) whether or not the work is a part of the regular business of the employer;
(i) whether or not the parties believe they are creating the relation of master and servant;
and
(j) whether the principal is or is not in business.
A4.1: Proof of Theorem 4.1
As shown earlier, when the agent is judgement-proof, direct liability leads to care
of x*(A) and profits for the principal of Elld = R-p(x*(A))A-x*(A). Recall, that the care
induced when the principal is vicariously liable and can observe the agent is x*(L). The
associated profits for the principal are EIIV = R-p(x‘(L))L-x*(L).
Eñd = R~p(x *(A))A -x *(A)>R-p(x *(L))A -x*{L)
since x*(A) is the maximizer of SW(A) by definition.
R -p(x \L))A -x ’(/.)>R-p(x \L))L -x *(I) = EUv
since the agent is judgement-proof (L > A). Therefore, Elld > EIIV.H

95
A4.2: Proof of Theorem 4.2
Using p(x)=e'“ the care induced under direct liability when L > p > A is:
x*(A) = )H2d. far all L
a
From Theorem 1, the care induced under vicarious liability when L > p is:
x(L) =
In aL
2a
Therefore, the difference between these two care levels is A = x(L) - x’(A) or:
A
2 a
Taking the derivative of A with respect to a:
(A10)
6/A
da
1
In
/ \
L
2 a1
{ aA1)
+
1 <0
since A > 0 for L > p. Therefore, since smaller a's denote more dangerous activities, the
difference between the care levels increases as the activity becomes more dangerous. â– 
A4.3: Proof of Theorem 4.3
When L e (A,k), the difference between the care induced under vicarious liability
and that induced under direct liability is A = x*(L) - x*(A), which is increasing in L since
x*(L) is increasing in L. When L c [K,p], A = x¥(k) - x*(A), which is constant in L. When

96
L > p, A is given by (A10) which is increasing in L. Therefore, A is non-decreasing in L
and, thus, non-decreasing in (L - A). â– 
A4.4: Proof of Theorem 4.4
When the HMO cannot avoid liability (Lp + La = D), the first order conditions
characterizing the [s,x] which solve [HP] are given by:
-p.D = a
-p.P = p
When the HMO can avoid liability through ERISA (Lp =0, La = A), the first order
conditions characterizing the [s,x] which solve [HP] are given by:
-p A = a
-pA= P
Both sets of first order conditions can be thought of as first-order conditions for the
maximization of:
Illv=R(s)-p(s,x)W-fix
where s and x are endogenous variables and W is an exogenous parameter. With the
ERISA preemption, W = A, while without the preemption, W = D. Totally differentiating
the maximized first-order conditions produces the matrix equation:

97
ds
-P»V -Ps*W
dW
Ps
-pjr ~pjr
dx
Px
dW
Therefore:
A- _ 0
dw~ IV2(plsP„-(fiJ)
and
dx _ (-PJ>X*PJ>„W
dW ^.Pxx-fPj)
In other words, a reduction in W from D to A will cause tests and procedures (s) to
decrease and care (x) to decrease. Therefore, the ERISA preemption leads to
tests/procedures and care which are both below the social optimum.â– 
A4.5: Proof of Corollary 4.5
The proof is the same as in appendix A4.4, except that in this case, totally
differentiating the maximized first-order conditions produces the matrix equation:

98
r
_
ds
(R"-PSSW)
-pjr
dW
Ps
-P«w
-pjr
dx
px
dW
Therefore:
ds _ ( PJ^~PJ>JW
dW -(Rf'-pssW)PxxW-(psxW)2
and
dx _ tRl/~PsF)PSPPsF
dW -(R"-PtsW)PxxW-{psxW?
since second order sufficient conditions for a maximum dictate that -(R"-pssW)pxxW >
(psxW)2 and (R"-pssW) < 0. In other words, a reduction in W from D to A will cause
production (s) to increase and care (x) to decrease. Therefore, when the principal is able
to avoid liability, production is greater than the social optimum and care is less than the
social optimum.â– 

CHAPTER 5: CONCLUDING REMARKS AND EXTENSIONS
One theme common to the preceding chapters is the relative efficiency of vicarious
liability in preventing accidents when the accident causing agent is potentially judgement-
proof. In chapter 2, it was shown that vicarious liability will not always induce the socially
optimal level of care. However, when the agent is judgement-proof, vicarious liability is
more efficient than direct liability in preventing accidents. Furthermore, the superiority of
vicarious liability is enhanced when the bargaining power of the agent is increased. In
chapter 3, it was shown that strict vicarious liability induces as much preventive care as
any liability scheme which fully compensates the victim, even those employing negligence.
In addition, the superiority of vicarious liability over direct liability is enhanced if the
principal is able to invest in a monitoring technology. Chapter 4 illustrates that accident
prevention is only harmed by the principal's ability to avoid vicarious liability.
As in all economic modeling, this dissertation has utilized simplifying assumptions
to gain insights into a complex economic relationship. Yet, by using alternative sets of
assumptions, there is the potential to deduce equally valuable insights about the efficiency
of vicarious liability. For instance, in section 2.3, the principal can make safety enhancing
specific investments, but these investments are assumed to be sunk to isolate the effect of
bargaining power on accident prevention under vicarious liability. In section 4.5, it is
99

100
shown that avoiding vicarious liability will lead to a suboptimal number of safety
enhancing investments, but these investments were assumed to be nonspecific to avoid the
complications of bargaining power and opportunism. I believe it would be fruitful to
investigate the accident preventing ability of vicarious liability when the principal can make
potentially specific safety enhancing investments which improve the agent's bargaining
power.
This dissertation also did not consider issues related to the enforcement costs of
vicarious liability. In particular, it was implicitly assumed throughout the dissertation that
the courts could accurately and costlessly determine the amount of accident damages (D).
In some cases, the victim of an accident may be privately informed about the damages
suffered and it may be difficult to elicit this information from the victim. If vicarious
liability is used by the courts, the victim may have an incentive to overstate his or her
damages in hopes of a larger settlement. If the court is unable to determine the actual
damages, this may lead to a liability award that is greater than the actual damages. This, in
turn, would induce a superoptimal level of preventive care from the principal-agent
enterprise. 1 believe it would be useful to investigate when the victim is most likely to have
private information about damages and what mechanisms can be employed to elicit this
information at least cost. In addition, the relative efficiency of vicarious liability should be
determined in these contexts in which the victim is privately informed.

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BIOGRAPHICAL SKETCH:
Christopher Garmon was born in Uvalde, Texas, on October 30,1969. He has lived
in 14 states. He graduated from Northfield Mount Hermon School in Mount Hermon,
Massachusetts and received a B.A. in economics from New College of the University of
South Florida. He is currently a Ph.D candidate in economics at the University of Florida
and is the assistant director of the Center for Economic Education at the University of
Florida. After receiving his degree, he will work in the Bureau of Economics of the
Federal Trade Commission in Washington, D.C.
104

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
TracyJEUdfewis
James W. Walter Eminent Scholar of
Entrepreneurship/ Economics
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully acféquate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
M. jkippington
izillotti-McKethan Eminent
Scholar of Economics
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in ¡poye and quality,
as a dissertation for the degree of Doctor of Philosophy/
Steven M. Slutsky
Professor of Economics
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
a
ley Harrison
Chesterfield Smith Professor of
Comparative Law
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.
August, 1997
Dean, Graduate School