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Ethics and Agency Theory:
Incorporating a Standard for Effort and an Ethically Sensitive Agent
Douglas E. Stevens
Syracuse University
M. J. Whitman School of Management
Syracuse, NY 13244-2130
Phone: 315-443-3587Fax: 315-443-5457
E-mail: [email protected]
Alex Thevaranjan
Syracuse University
M. J. Whitman School of Management
Syracuse, NY 13244-2130
Phone: 315-443-3355
Fax: 315-443-5457E-mail: [email protected]
November 25, 2003
This research was funded through a grant from the Syracuse University School of Management
Research Fund. The authors would like to acknowledge the helpful comments of Anwer S.
Ahmed, Amiya K. Basu, John H. Evans III, Gerald A. Feltham, Paul E. Fischer, David G. Harris,Steven J. Huddart, Gerald J. Lobo, Eric W. Noreen, Brian P. Shapiro, Mary Stanford and
workshop participants at the Sixth Annual Professional and Ethics Symposium, the University of
British Columbia, Syracuse University, and the University of Washington.
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Ethics and Agency Theory:
Incorporating a Standard for Effort and an Ethically Sensitive Agent
We study the implications of introducing ethics into the traditional principal-
agent model. In our model, the principal specifies a standard for effort at the time
of contracting and the agent suffers a utility loss if he chooses not to provide the
standard after agreeing to the contract. The magnitude of the loss depends upon
the agents ethical sensitivity. We demonstrate the emergence of an optimal flat
salary contract. We then examine the interplay between ethical sensitivity and
firm productivity in determining the optimal salary contact, and contrast it with
the traditional incentive solution. Our results are intuitive and help explain a
variety of contracting behavior that is inconsistent with traditional agency
predictions. (JEL: A31, D82, M14)
Researchers in accounting, finance, and economics have frequently used agency theory to
study issues in organizational control (See reviews by Stanley Baiman 1982, John W. Pratt and
Richard J. Zeckhauser 1985, Kathleen M. Eisenhardt 1989, Baiman 1990, and Barry M. Mitnick
1992). Traditional agency models, however, assume that individuals are opportunistic and
motivated solely by economic self-interest. That is, individuals make choices that maximize their
own economic utility independent of the utility of others or abstract values such as honesty, duty
or fairness. Based on this view of human behavior, agency models prescribe complex incentive
schemes and costly monitoring to control opportunistic behavior within the organization.
Employment contracts found in practice, however, bear little resemblance to those
predicted by the theory (Joseph E. Stiglitz 1991). Such contracts are simple and incomplete, and
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the level of monitoring is far less than that required by the theory. This state of affairs has led
researchers to question why agents dont shirk more in the absence of optimal contracts. Herbert
A. Simon (1991) asserts that employees exert effort because they identify with the goals of the
firm, and attributes this to a genetically based propensity for docility. Timothy Besley and
Maitreesh Ghatak (2003) describe workers as mission-oriented agents who work hard when
the goals of the firm match their own. Other researchers, however, see the employment contracts
found in practice as evidence of ethical values at work (Kenneth J. Arrow 1985). Kenneth
Koford and Mark Penno (1992) assert that most people have attitudes toward telling the truth
and providing fair amounts of effort, and agency models neglect a significant element of reality
by failing to incorporate such attitudes.
Researchers have already begun to study the potential effect of ethics on common
economic relationships. Eric W. Noreen (1988) uses an economic framework to show how
ethical behavior makes the formation of markets and organizations possible. Thomas H. Noe and
Michael J. Rebello (1994) demonstrate more formally how ethical norms increase the
profitability of investment opportunities. Koford and Penno (1992) model ethical behavior in
various ways to show how the results could better reflect behavior within the organization.1
Recent experimental studies also support the potential role of ethics in organizational control.
Human subjects have been found to give up some earnings in order to honestly report their
production potential (J. Harry Evans III et al. 2001), reduce budgetary slack (Douglas E. Stevens
2002), or provide higher effort (Jeffrey W. Schatzberg and Stevens 2003).
Despite the potential for enhancing descriptive validity, however, agency theorists have
not explicitly modeled the effect of ethics on the contracting behavior of principals and agents.
Mitnick (1992) conjectures that the mathematical formalism that has developed in the principal-
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agent literature in accounting, finance, and economics has closed it to influences from the ethics
literature.2
This is unfortunate, since the notion of potentially offsetting preferences for ethics
and earnings has existed from the inception of economic theory (Adam Smith 1759) and has
received particular attention in other areas of the literature (Richard H. Thaler and Hersh M.
Shefrin 1981).
To address this void in the literature, we incorporate ethics into the traditional principal-
agent model following the two guidelines offered by Koford and Penno (1992). Koford and
Penno suggest that there be a clear boundary between conformity and violation of an ethical
standard, and that ethics be incorporated by adding a penalty for unethical behavior into the
agents utility function. We incorporate the first guideline by allowing the principal to specify a
standard level of effort to the agent at the time of contracting. If the agent accepts the contract,
he is agreeing to provide the specified level of effort in exchange for the compensation. Thereby,
if he fails to provide the effort he violates the ethical norm that valid-agreements-should-be-
kept (Mitnick 1992). We incorporate the second guideline by assuming that the agent suffers a
disutility in the ethical realm when he chooses to provide less than the agreed level of effort. The
magnitude of the disutility depends upon the ethical sensitivity of the agent, which is zero under
the traditional agency assumption of unconstrained opportunism.
We believe that adding a standard for effort and an ethically sensitive agent is a
meaningful extension of the traditional agency model. A standard for effort is already inherent in
the agency literature through the first-best contract and the concept of shirking (Eisenhardt
1989). Even under unobservable effort, the principal knows the effort she would like to induce
from the agent. While the standard becomes irrelevant in traditional agency models, it remains
relevant in our model because it conveys the principals expectation to an ethically sensitive
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agent. Similarly, we find it reasonable to assume that an ethically sensitive agent would suffer
disutility for violating the standard after agreeing to the contract. This is because individuals tend
to internally monitor themselves and self impose a penalty for behavior that they consider
unethical (Thaler and Shefrin 1981). Moreover, there is a rich literature in ethics examining the
nature of ethical sensitivitywhere it comes from, how it affects behavior, and its impact on
individuals and society. Finally, personal introspection and casual observation persuades us that
experiencing disutility for violating deeply held values such as honesty and duty is as universal
as experiencing utility for wealth or leisure.
We take some level of ethical sensitivity as given, and examine its effect on the
traditional principal-agent model. Our model preserves all other aspects of the traditional agency
framework, including a risk-neutral principal, a risk- and effort-averse agent, unobservability of
effort, and imperfect performance measures. We initially assume that performance measures are
infinitely noisy to make the traditional incentive solution unavailable. This allows us to highlight
the novelty of solutions that emerge when ethics is incorporated into the principal-agent model.
However, after demonstrating the emergence of optimal flat salary solutions, we relax this
assumption and set ethical sensitivity to zero. This allows us to derive the traditional incentive
solution and compare it to the new salary solutions that arise when ethical sensitivity is nonzero.
Introducing a standard for effort and an ethically sensitive agent into the traditional
principal-agent framework generates six main results. The first and fundamental result is the
emergence of a work ethic that controls the opportunism of the agent. We find that the agent
would rather provide the standard level of effort than shirk as long as the standard is below a
critical level and the principal pays him his cost of effort. Intuitively, the critical level of effort
can be interpreted as the maximum effort that the agent perceives to be reasonable or fair.
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Interestingly, the work ethic imposes an employment ethic because the principal knows that
specifying a standard above the critical level will be perceived as unreasonable by the agent and
will result in shirking. This result embodies the old adage, An honest days pay for an honest
days work.
Our second result is that the principal can induce effort beyond the critical level by
paying the agent a salary that more than compensates him for his cost of effort. This salary
premium offers the agent more than his reservation utility and increases what he considers to be
reasonable effort. Accordingly, the salary premium also imposes an employment ethic in that it
requires the principal to share gains from the agents extra effort.
The third result is that the first-best contract is attainable under unobservable effort for
firms with low productivity relative to the agents ethical sensitivity. This is because the first-
best level of effort is below the critical level for these firms. As such, the principal can obtain the
first-best level of effort by simply requesting it and offering the agent his cost of effort. This is
significant because, while salary contracts are common in practice, they are impossible under
unobservable effort and the traditional assumption of zero ethical sensitivity (unconstrained
opportunism).3
With zero ethical sensitivity the agents behavior is not influenced at all by the
effort requested by the principal, and financial incentives are necessary to induce any effort from
the agent (Stephen A. Ross 1973, Joel S. Demski and Gerald A. Feltham 1978).
The fourth result of our model is that the optimal salary contract for firms with high
productivity relative to the agents ethical sensitivity is a salary premium contract. For this
category of firms, the first-best level of effort is significantly above the critical level. Thus, it is
optimal for the principal to pay the agent the salary premium and ask for more than the critical
level of effort. In effect, the willingness of the principal to share the incremental benefits
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motivates the agent to exert the higher effort. The incremental cost, however, makes the optimal
effort lower than the first-best level of effort.
Our fifth result is that the optimal salary contract for firms with medium productivity
relative to the agents ethical sensitivity is an expectation reduction contract. For this category
of firms the first-best level of effort is only marginally above the critical level, and the benefit of
the extra effort does not justify the required salary premium. Accordingly, the principal reduces
her expectation and settles for the critical level of effort. In this case, the work ethic of the agent
restrains the principal from making excessive demands.
The final result of our model relates to comparative statics on ethical sensitivity. We find
that the ethical sensitivity of the agent does not have to reach its upper bound (one) for the first-
best effort to become achievable. In fact, the required level of ethical sensitivity decreases
exponentially with decreases in the firms productivity and the agents risk aversion. Only when
the ethical sensitivity reaches its lower bound (zero), does the flat salary contract lose power to
induce any effort from the agent, making the traditional incentive solution necessary. In general,
however, we show that the traditional incentive solution is more expensive than our flat salary
solution for firms with relatively low and high levels of productivity. Moreover, if the agents
ethical sensitivity is sufficiently high, the flat salary solution dominates the traditional incentive
solution across all firms.
Our results are intuitive and help explain a variety of contracting behavior that is
inconsistent with traditional agency predictions. Take for example the case of not-for-profit
managers. The absence of a bottom-line profit measure makes it difficult to identify suitable
performance measures for incentive contracts. Yet, these managers do not shirk their
responsibility as evidenced by the size and growth of the nonprofit sector in the last two decades.
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As Susan Rose-Ackerman (1996) points out, this behavior cannot be understood within the
standard agency framework. Among her potential explanations for why non-profit firms exist,
she observes that non-profits recruit ideological managers with high ethical motives relative to
profit motives. This recruiting strategy is confirmed in the financial press (See Max Messmer
2002). By incorporating an ethically sensitive agent, our model is able to explain why non-profit
firms recruit ethical managers and why such managers exert reasonable effort in the absence of
traditional incentives.
Consider also the case of professionals within for-profit firms, such as lawyers, engineers
and accountants. Given that they provide support functions and possess expert knowledge,
bottom line profit measures are not very useful in evaluating their performance and external
monitoring may not be possible (Robert N. Anthony and Vijay Govindarajan 2001). Such
professionals, however, are frequently paid a high flat salary and perform at a high level. The
traditional agency framework has no satisfactory explanation for the behavior of these
professionals either. Our model, however, predicts that where the effort of the agent is highly
valued, the principal will pay a salary premium to get the agent to provide a high level of effort.
Our model is in the spirit of Matthew Rabin (1993), who incorporates fairness into
traditional game theory by adding a preference for fairness into each players utility function.
Rabin uses his model to explain experimental results from cooperation games (e.g., public goods,
prisoners dilemma) suggesting that people cooperate to a greater degree than would be implied
by pure self-interest. Similar to our ethics results, Rabin finds that agents trade off their
preference for fairness against their preference for earnings, and one preference may dominate
the other in a given situation. In a special application of his model, Rabin considers a situation in
which a worker chooses an effort level (High or Low) and the firm simultaneously chooses a flat
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salary for the worker that shares a portion of the firms income. Similar to our results, Rabin
finds that flat salary contracting is not possible without some preference for fairness. Our model
is unique, however, in that it incorporates a preference for ethics within the traditional principal-
agent framework. Thus, we are able to provide new and useful insights to augment the extensive
agency literature in accounting, economics, and finance.
The rest of the paper is organized as follows. In the following section we present our
model more formally and demonstrate how we introduce a standard for effort and an ethically
sensitive agent. In section II we present the main results of the model. We compare our results to
the traditional agency model in section III and discuss the implications and directions for future
research in section IV. We conclude in section V.
I. THE MODEL
We begin with the basic single-period, principal-agent framework. The principal is risk
neutral4
and hires a risk- and effort-averse agent to perform a production task that she cannot do
herself. The outcome the principal expects to realize at the end of the period is a multiple of the
firms productivityp and the agents effort a:
(1) [ ] paY =E
A moral hazard problem arises because the agent experiences disutility from effort and the
principal is unable to monitor the agents effort. The traditional agency solution to this problem
is to provide incentives to the agent based on a performance measure X that serves as a noisy
signal of the agents effort:5
(2) X a = + ; where ( )20,N~ .
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The noise term prevents the principal from perfectly inferring the agents effort, and
represents other unobservable factors that affect the performance measure X. This noise term is
assumed to be normally distributed with mean zero and variance 2. The variance captures the
level of inefficiency in Xas an inference tool. We initially assume an infinitely large variance,
characterizing a situation where the performance measure is not a reliable signal of the agents
effort. Thus, the principal can only utilize a flat salary contract.
Figure 1 presents the events in our model. As is true of most agency models, there is no
asymmetry of pre-contract information (Baiman 1982). That is, both the principal and the agent
know the production technology of the firm,6 the characteristics of the performance measure, and
the preferences of each other (including the ethical sensitivity of the agent) before contracting
takes place. At the time of contracting, however, we allow the principal to specify a standard
level of effort, d, in addition to the compensation wage, . Thus, if the agent accepts the
contract, he is explicitly agreeing to exert the standard level of effort in return for the specified
wage, although his choice of effort a is not observable by the principal. If instead the agent
rejects the contract, he receives his reservation utility from the labor market.
[Insert Figure 1 about here]
The economic concepts of opportunism and shirking are based upon some previously
agreed-upon level of effort (Eisenhardt 1989), so a standard for effort is inherent in agency
theory. In the traditional case, however, the existence of the standard is irrelevant because the
agent is opportunistic and suffers no disutility when choosing to deviate from it. In traditional
agency models, therefore, the standard is not an argument in the model even though the principal
knows the effort she would like to induce. Instead, the principal indirectly induces effort from
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the agent through an incentive contract. In our model, however, the standard specified by the
principal is relevant because it raises a moral obligation in an ethically sensitive agent.
We incorporate ethical sensitivity into the model in the following manner. If the agent
accepts the contract, he agrees to provide the standard level of effort d. Therefore, if he provides
a level of effort less than d, he is going against his word and failing to fulfill his obligation to the
principal. We use an indicator variable to capture the agents violation of the standard.
Specifically, is one when the agent violates the standard (a < d) and zero when the agent meets
his obligation under the contract (ad). Moreover, we assume that the agent suffers a utility
loss e when he chooses to violate the standard for effort after agreeing to the contract. Thus, we
incorporate a multiplicative term, e, to the standard utility function to capture the potential
disutility from violating the standard for effort:7
(3) ( ) ( ) eaa = ,U,,U
where ( )U , Ua and 0 e U
We allow the utility loss e associated with failing to meet the standard to vary from 0 to
U , the upper bound of the agents utility from the physical realm. Note that e = 0 corresponds to
the traditional agent who is fully opportunistic and insensitive to the standard specified by the
principal, and e = U corresponds to an agent who will never shirk once he agrees to the contract.
Accordingly, e corresponds directly to the agents ethical sensitivity, i.e., the depth of his
conviction for values such as honesty and duty.
Ethical sensitivity has a variety of potential sources. It could be inborn or genetic (Jack
Hirshleifer 1977 and Gary S. Becker 1976), but is more likely to arise from childhood and school
socialization (Koford and Penno 1992). Religion has also served an important role in
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establishing and maintaining ethical codes and convictions (Noreen 1988). Within the
organization, ethical values can also be attributed to management leadership, company policies,
and government regulations (David J. Cherrington 1980). Although ethical sensitivity is
exogenous to our model, we assume that it varies across agents due to differences in upbringing,
socialization and training. In fact, a potential theme from our model is the considerable benefit of
encouraging ethical sensitivity, and we discuss this at length in a later section.
Our assumption that ethical sensitivity is exclusively in the ethical realm is clearly
reflected in equation 3, as the agents utility loss from violating the standard is independent of
the level of pay and effort. We add to this assumption the standard assumptions contained in
traditional LEN agency models (e.g., Bengt Holmstrom and Paul Milgrom 1991, Feltham and
Xie 1994, Datar, Kulp, and Lambert 2001).8
In particular, we assume that utility is strictly
decreasing in effort (
u
0), and that the agent has constant
absolute risk aversion (r) and finds his work less onerous as his income increases (
>2
0ua
).
The later assumption is present in all LEN agency models, possibly because researchers have
found it reasonable to assume that the agent will be willing to exert more effort if he is given a
higher wage. This willingness to exert more effort could come from the agents increased sense
of prestige in his work, or his increased sense of gratitude and loyalty to the firm because he is
unlikely to get the same high pay from the external labor market.
In keeping with our intent to incorporate ethics into the traditional LEN agency
framework, we utilize the following exponential form for the agents utility:9
(4) ( ) ( ) ( )2
2U , , U , 1 expaa a e r e = =
where ( )U ,a = 1 and 0 1e
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The principals problem in our setting is to specify a wage and a standard for effort that
will maximize her expected utility subject to two constraints. This is formally stated as:
(5)Max:
, d ( )Epa
Subject to:
IR ( ){ }22E 1 exp 0ar e
IC ( ){ }22,
, Arg max E 1 expa
aa r
e
The first constraint represents the assumption of individual rationality (IR), and ensures
that the agent will only contract with the principal if it is in his best interest. Without loss of
generality, we have assumed that the agents reservation utility is zero.10
The second constraint
represents the assumption of incentive compatibility (IC), and ensures that the agent will
maximize his utility in choosing the level of effort and, correspondingly, whether or not to meet
the standard. If the agent chooses to meet the standard, = 0 and he provides effort a = d. But if
the agent chooses not to meet the standard, = 1 and he will provide a level of effort a below d
that maximizes his expected utility. Where only flat salary contracts are available, the level of
effort that maximizes the agents utility is zero once he chooses not to meet the standard.
Note that setting e = 0 makes an irrelevant variable for the IR and IC constraints. In this
case, the principal derives no benefit from specifying a desired level of effort because the agent
suffers no disutility from shirking. This emphasizes again that setting the agents ethical
sensitivity to zero gives us the traditional agency case, which is void of any ethical
considerations.
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II. MAIN RESULTS
We begin our analysis by deriving the first-best contract. Here we assume that the
principal can costlessly monitor the agents effort and inflict a severe penalty if the agent does
not provide the standard level of effort. In this setting, the agent is compelled to provide the
standard level of effort upon contracting (= 0), and the IC constraint is redundant. Substituting
= a2
2from the IR constraint into the principals objective function in equation 5 results in:
(6)Max:
apa a
2
2.
Note that the term pa captures the principals benefit and the term a captures the principals
cost of inducing effort a. The first-order condition of this problem results in:
2
2
(7) a pFB = ,
where aFB
is the first-best effort and is increasing in the firms productivity p. Interestingly,
introducing a standard for effort and an ethically sensitive agent has not altered the first-best
contract from the extant agency literature. It remains a flat-wage contract that pays the agent his
cost of providing the first-best effort:
(8) FBp
=2
2.
The agents ethical sensitivity plays no role in the first-best solution because the threat of a
severe penalty (external monitoring) makes the utility loss from violating the standard (internal
monitoring) redundant. The first-best solution is presented graphically in Figure 2.
[Insert Figure 2 about here]
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When effort is unobservable, however, our results diverge widely from the traditional
principal-agent model. Given traditional agency assumptions, a flat salary contract has no power
to induce effort from the agent in this case (Ross 1973, Demski and Feltham 1978). This changes
when we introduce ethical sensitivity to the model. Specifically, a work ethic emerges that
deters the opportunism of the agent and grants a salary contract the power to induce effort. This
result is stated formally in our first proposition.
PROPOSITION 1:The principal can induce a level of effort d that is below a critical level d1
by simply requesting it from the agent and paying him a flat salary that equals the cost of that
effort,
(9)2
2
d = for 1
2 11
logr ed d = ,
where e and r are the ethical sensitivity and risk aversion of the agent respectively. If the
requested level of effort is above this critical level, however, the agent will shirk completely and
exert no effort (i.e., a = 0).
Proof: All proofs are in an appendix
The intuition behind Proposition 1 is not difficult to see. Upon contracting with the
principal, the agent has two options. He can exert the standard effort and thereby avoid the utility
loss e, or he can violate the standard and provide zero effort. In the latter case, he incurs the
utility loss e but avoids all disutility for effort. Yet, when the standard level of effort is below the
critical level, the agent would rather provide the standard than shirk because the gain from
avoiding the disutility for effort is not large enough to justify the utility loss in the ethical realm.
Intuitively, the critical level of effort d1 represents the maximum level of effort that the
agent finds reasonable or fair. Equation 9 suggests that the critical level of effort is determined
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by the agents ethical sensitivity and risk aversion. In particular, d1 is increasing in ethical
sensitivity and decreasing in risk aversion. When the agent has zero ethical sensitivity, d1 is zero
and the flat wage is incapable of inducing any effort from the agent as in the traditional case. As
ethical sensitivity increases above zero, however, the agent finds a higher level of effort to be
reasonable.
The result that d1 is decreasing in rmay seem surprising given that the agent bears no
financial risk with a flat salary contract. But r plays an important role in our model by
influencing the agents tradeoff between the physical realm and the ethical realm. The greater the
agents risk aversion, the more he values the physical realm relative to the ethical realm.
Therefore, the agent appreciates more the increase in net wealth that comes from shirking (i.e.,
saving on effort). In essence, an increase in risk aversion reduces the effect of ethical sensitivity
by making the ethical realm relatively less important to the agent. This ethics dampening role
of risk aversion is ignored in traditional agency models that assume zero ethical sensitivity.
It is important to distinguish between ethical sensitivity and the emerging work ethic in
our model. As discussed above, ethical sensitivity captures the depth of the agents ethical values
and is exogenous to the model. In contrast, the work ethic captures the agents willingness to
exert effort, which arises endogenously from our model as a result of the agents ethical
sensitivity and the standard for effort. It is also important to note that the work ethic does not
reduce the agents disutility for effort.11
Rather, the work ethic reflects the amount of effort that
the agent is willing to provide despite his disutility because of his sensitivity to ethical
considerations. Thus, the emerging work ethic in our model is consistent with much of the work
ethic literature (See Cherrington 1980 and Irving H. Siegel 1983).
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Interestingly, Proposition 1 suggests that the agents ethical sensitivity also imposes an
employment ethic on the principal. This is because the principal cannot specify a standard for
effort higher than the critical level, or the agent will shirk. Specifically, the principal will never
ask for a level of effort dgreater than d1 for a flat wage of = d2
2. Yet, a second result of our
model is that the principal can induce a level of effort greater than the critical level (d> d1) by
offering the agent a salary premium. This result is stated formally in Proposition 2:
PROPOSITION 2:The principal can induce a level of effort d that is greater than the critical
level d1 by paying the agent a flat salary that includes a salary premium,
(10)2
221
2
1 explog
rd
e
dr
=
+ ford d. 1
Proof: See appendix
To see the intuition behind Proposition 2, recall that an increase in income makes effort
less onerous to the agent and thereby decreases the gain from shirking. At the salary premium
described in Proposition 2, the gain from shirking exactly equals the loss in the ethical realm.
Thus, paying the agent the salary premium in addition to his cost of effort makes him willing to
exert a level of effort dabove the critical level d1. This result suggests, however, that to induce
effort beyond the critical level the principal must share the resulting increase in profit with the
agent. We graph the cost of effort and the salary premium from equation 10 in Figure 3.
[Insert Figure 3 about here]
Figure 3 shows that the cost of the salary premium is concave in d. Initially, the principal
must be willing to share more and more of the increase in profit with the agent to induce
incremental increases in effort. Thereafter, the agent requires less and less to induce effort and
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the salary premium converges to an upper bound equaling 1 logr1e as d goes to infinity.
Interestingly, the cost of the salary premium decreases with the ethical sensitivity of the agent e.
This is because the gain from shirking must exceed a higher threshold, making it less attractive.
Moreover, d1 increases with e, thereby reducing the amount of effort the principal needs to
induce through the salary premium.
Now that we have established that the principal can induce effort from an ethically
sensitive agent through a flat salary, we turn our attention to the optimal flat salary contract. We
first note that at the optimal flat salary, the induced level of effort a always equals the standard
level of effort asked by the principal, d. This is because if a < d, the agent suffers the ethical
disutility e and subsequently has no incentive to exert any positive level of effort. On the other
hand, ifa > dthe contract will not be incentive compatible as the agent can improve his utility by
reducing his effort to d. Thus, the principals problem reduces to finding the d that maximizes
her expected outcome, , net of the wage function[ ] pdY =E da f. We continue our analysis by
deriving the optimal salary contract for firms with different levels of productivity, p.
PROPOSITION 3: The optimal flat salary for firms with relatively low productivity, i.e.,
12 1
1logr ep d = , is the first-best contract. For this category of firms, the principal will
specify a standard level of effort that is equal to the first-best effort, d d 1FB , and pay a flat
salary equal to the cost of that effort,2
2
p = .
d= d
1where d , is a salary premium contract.d2
12 For this category of firms, the
principal will specify a standard level of effort that is between the critical level and the first-best
effort, ( )1 2 2 FBrdd d d p d < =
( ){ }2 22 2Argmax E 1 expa
d aa r
e
0a =
Proof of Proposition 2
If = d2
2satisfies the IR constraint, then > d
2
2clearly does as well. The IC constraint is
satisfied when
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( ){ } ( ){ }2 22 2E 1 exp maximum E 1 expa d
d ar r
e
( ) ( )221 exp 1 expdr r e
( ) ( )22exp expde r r
( ) ( )2 22 2exp 1 expd re r d
( )( )22 2
2
1 expexp
rddr
e
( )22 212
1 explog
rdd
er
+
Proof of Proposition 3
According to Proposition 1, the principal can induce a level of effort without any salary premium
as long as the effort is below d1. We show in the body of the paper that the first-best effort is
d pFB = . Thus, for relatively low productivity firms, the first-best effort could be below the
agents reasonable level, d p dFB = < 1. Thus, the optimal salary contract for these firms is the
first-best contract that pays the cost of the first-best effort.
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Proof of Propositions 4 & 5
According to Proposition 3, when 1p d the principal can induce the first-best effort d pFB =
without any salary premium, but not so when 1p d> . According to Proposition 2, the cost of
inducing effort is:1d d
22
212
1 explog
rd
e
dr
=
+
2 22
2
11 12 2
exp
log exp log
rd
e
d rd
r r
= + +
2
211 explog
rd
er
=
The principals problem then is to
1
Max:
d d
2
211 explog
rd
e
pd r
=
The above objective function is concave in when1d d
( ) ( )2
2 2
2
2
2 2
2
1 11 1
exp exp0
rd rd d
rd
+ =
>
( )22 21 exp rdrd + <
Note that the left hand side of the above inequality increases linearly in d2
while the right hand
side increases exponentially in d2. As such, this inequality holds for large values of d. The
critical question is whether it holds for 1d d= because ( )22
2exp rdrd+
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( )212
1 21 exp
rdrd+
( ) ( )1 11 11 2 log e e + .
Note that the left hand side of the above inequality increases in a concave manner in ( )11 e
while the right hand side increases in a linear manner. As such, this inequality holds for e .
In summary, when e the wage function is convex in the domain , and when e
ce
cece 1d d <
the wage function is initially concave and then becomes convex.
Case 1: e . In this case, the wage function is concave in andce 1d d
( )2
21 exp rdd
dp
=
.
Therefore, the solution is the corner point d1 when
1
1
0d dd
dp
e
=
= <
11d
ed p < .
In contrast, when 1dep > the solution is an interior point characterized by ( )
2*
*
21 exp rd
dp
= .
Case 2: e . In this case, the wage function is initially concave and then convex in d.ce .
Note, however, that when
( )22
2
1
21 exp
rdp
dde
< <
there will be two interior values (a
minimum and a maximum) that will solve( )
2*
*
21 exp rd
dp
= , and the solution is the higher of
the two values.
Proof of Propositions 6
According to Proposition 3, the first-best contract is implementable if 2 11
logr ep . This is
equivalent to (2
21 exp
rp e . If e = 0, then d1 = 0 and the agent will never exert the
standard effort if he is paid only the cost of effort. Yet, if e = 0, then the salary premium goes to
infinity, implying that this solution will also not work. On the other hand, if d1 > 0 or the salary
premium is finite, then it must be that e 0.
)
45
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The Traditional Agency Problem
With ethical sensitivity constrained to zero in our model, the principals problem in
equation 5 becomes the traditional agency problem:
Max:
( )Epa
Subject to:
IR ( ){ }22E 1 exp 0ar
IC ( ){ }22Arg max E 1 expa
aa r
LC A BX = +
The LC constraint represents the traditional LEN assumption that the incentive contract is linear
in the performance measure. In the LEN framework the agents expected utility simplifies to
( )2 22
2 21 exp A B Ba rr a +
.
The IC constraint thus simplifies to Ba = . Substituting for B in the IR constraint results in
( )22 22 21 exp A B 0a ar a r +
22 2
2 2A B a aa r + .
Note that A does not affect the induced effort. As such, the principal will chose A so that there is
no slack in the IR constraint. Therefore,
( )22 2
2 2A B Ea aa r + = = .