Ethics and Agency Theory

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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.


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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.


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+


45/47

( )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


47/47

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 + = = .

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Ethics and Agency Theory