Total Compensation in Moral Hazard Settings
Pattarin Adithipyangkul*
Sauder School of Business
University of British Columbia
pattarin@interchange.ubc.ca
Current Draft: December, 2004
Preliminary and comments welcome.
Please do not quote without the author’s permission.
* The author is greatly indebted to Jerry Feltham, Dan Simunic, and Gilles Chemla for their kind
support and valuable comments. Comments from participants in the workshop at the University of
British Columbia are also very much appreciated. The author is responsible for any errors.
Abstract
Prior literature has focused on the use of formal cash compensation to solve agency
problems. In practice, employees are also paid in terms of fringe benefits, perks, etc. Some
receive informal compensation, which includes any cash or other resources employees obtain
or appropriate for personal use without proper approval from authorized personnel. This
paper considers two aspects of compensation decisions: the composition of pay and the
method of payment. In part one, I examine the use of non-cash compensation to reduce the
total compensation cost in moral hazard settings. The main findings are that (i) for given
reservation utility and disutility of effort, the optimal compensation portfolio includes a noncash item with greater value to the agent (in the sense that the slope of the utility function
with respect to the dollars spent on that non-cash item is higher, while the degree of
concavity is lower) or a non-cash item with higher productivity; and (ii) when the agent’s
utility function is strictly concave in cash and non-cash compensation, the number of noncash items included in the compensation portfolio increases, as the agent’s reservation utility
and cost of effort rise.
In part two, I examine the use of informal compensation to benefit from greater flexibility.
Informal compensation is often paid to a small number of employees and is not covered by a
collective bargaining agreement. It sometimes involves “illegal” or “immoral” activities so
that the payees generally prefer the payment to be secretive. As a result, it is less rigid and
easier to change than formal compensation. I formulate a two-period model where the
principal optimally adjusts the compensation schemes from period to period, according to
the change in the value of non-cash compensation to the agent, and to the change in its cost
to the principal. The agent may find herself better off with the preceding period’s scheme, so
that she wants to resist the change in compensation. I show that when the agent can resist the
changes in compensation schemes, the principal can avoid the problem by paying part of the
compensation informally. Subsequently, I examine the use of illegal or immoral informal
compensation to deter employee litigation. I consider a setting in which the performance
measure is not verifiable by the courts so that opportunistic discrimination litigation is a
problem. By paying illegal or immoral informal compensation, the principal subjects the
agent to prosecution or reputation loss, which can deter the agent from suing the principal.
To make the agent accept the informal pay, the informal pay must be such that if not sued,
the principal will not prosecute the agent.
1
I. Introduction
The compensation decision is multi-dimensional. In addition to the amount of pay based on a
realized performance measure, the principal can choose the composition of the pay – cash or
non-cash; the way to pay it – formal or informal; and the timing of the pay – immediate or
deferred (e.g. retirement benefit, etc.). This paper addresses the optimal composition of the
pay and the method of payment in moral hazard settings. In the term ‘cash compensation’, I
also include cash-equivalents like stocks. Non-cash compensation includes fringe benefits,
an office, secretarial service, etc. By ‘formal compensation’, I mean such pay as is specified
in the employment contract, the company’s compensation policies, the company’s charters,
or any other pay that is formally approved by authorized personnel. By ‘informal
compensation’, I mean any cash or other resources employees receive or appropriate for
personal use without proper approval from higher authorities. For example, health benefits
specified in compensation packages are formal compensation. The money an employer pays
to an ill employee to assist her with the health care expenses on case by case basis is
informal compensation.
The motivation for this paper stems from the lack of agency literature on non-cash and on
informal compensation. Previous theoretical or empirical accounting literature focuses
almost exclusively on formal cash compensation when non-cash and informal compensation
can be significant parts of total compensation, both in terms of the amounts and in terms of
their effects on employees’ behaviour. For example, in the military, non-cash compensation
constitutes about 57% of total military compensation (Murray, 2004)1. Hashimoto (2000)
finds that the proportion of (formal) non-cash compensation (of the total (formal)
compensation) across industries has increased by 46.1% from 1966 to 1994. From casual
observation, we observe the use of productive non-cash compensation like an office, a
secretary (who may often be asked to help with her boss’s personal matters), a training
program, a company car, a laptop computer, an insurance policy, meals, etc. We also observe
the use of non-productive non-cash compensation like a paid leave, subsidy for children’s
education, etc.
1
Examples of the non-cash compensation paid include “subsidized goods and services that can be used
immediately--such as medical care, groceries, housing, and child care … other deferred benefits that service
members receive after they leave active duty--including health care for retirees and veterans' benefits.”
(Murray, 2004: 1)
2
I know of only one empirical accounting work addressing non-cash compensation. Lee,
Matolcsy, and Wells (2004) study the compensation-performance relation for State
Dominated Enterprises (SDE) and Non-State Dominated Enterprises (NSDE) in China. They
find no difference in accounting performance measures, which are tied to monetary
compensation, between SDE and NSDE, and no difference in the monetary pay-performance
relation. They also find that the level of monetary compensation is lower for SDE. They
anticipate that the amount of non-cash fixed compensation paid is higher for SDE, while the
amounts of cash bonuses are similar between SDE and NSDE. This possibly explains why
they do not find a difference in measured performance, despite the lower cash pay for SDE.
Other empirical work on non-cash compensation can be found in the macro-economics field
(Rosen, 2000).
As to theoretical work on non-cash compensation, I only know of Marino and Zábojník
(2003), who study the use of employee discounts and non-cash compensation in adverse
selection models. They first formulate a model in which a monopolist-employer determines
the optimal price to charge his employee and other customers. There are two types of
customers; one type has a greater preference for the firm’s product. The monopolistemployer wants to hire an employee from a pool of customers. Assume that the pool is large
so that the employer can choose which type to hire. Marino and Zábojník (2003) find that it
is optimal to charge the employee at marginal cost to induce the employee to purchase as
much as possible, and then extract the surplus the employee receives by decreasing the
amount of cash salary. Since a customer with high preference has a larger surplus the
employer can extract, it is optimal to hire her. The principal then designs a contract to induce
only the high-preference type to participate. There is price discrimination: the price charged
to outside customers is higher than the price charged to employees. Subsequently, the
authors also consider the use of perks in a setting where there are, again, two types of
workers, high-preference and low-preference, and the principal wants to hire both types. In
addition to their preferences, the two types also have different reservation utilities. Marino
and Zábojník show that the principal can wage-discriminate to minimize the amount of rent
paid the employee. Generally, the high-type is over-supplied, while the low-type is undersupplied, compared with the efficient levels.
Concerning informal pay, the empirical or field evidence in accounting barely exists. Some
evidence from the field exists in organizational behaviour (Greenberg and Scott, 1996).
3
Researchers describe controlled theft systems, where a certain employee is occasionally
allowed to “steal” a certain amount of a certain item as part of her compensation. As further
evidence, in Appendix 1, I include my findings on the use of informal compensation in a
pharmaceutical business in Thailand.
In this paper, I study moral hazard settings, rather than adverse selection settings. Part one
examines the use of non-cash compensation, while part two considers the use of informal
compensation. In part one, I show that the characteristics of the optimal contract are
determined by the agent’s utility function, her reservation utility, her cost of effort, and the
characteristics of the non-cash item considered. Section 2 describes a single-period moral
hazard model. Section 3.1.1 considers the use of non-cash compensation when it is not
productive and not available from the market. Section 3.1.2 assumes instead that the noncash compensation is productive. Section 3.2 examines the optimal contract when the noncash compensation is available from the market. The main results are: (i) for given
reservation utility and cost of effort, a non-cash item included in the optimal compensation
portfolio is a non-cash item with greater value to the agent (in the sense that the slope of the
utility function with respect to a dollar spent on that non-cash item is higher, while the
degree of concavity is lower) or a non-cash item with higher productivity; and (ii) when the
agent’s utility function is strictly concave in cash and non-cash items, the number of noncash items included in the compensation package increases, as the agent’s reservation utility
or cost of effort increase. Based on the assumption that the non-cash items which satisfy
basic needs have higher value to the agent, the theory explains why we often observe
employees being paid more in terms of non-cash items like food, lodging, health care, etc.,
which are both productive and necessary for survival. For an executive with high reservation
utility, other non-cash items (possibly luxurious items) are added into the compensation
portfolio.
Section 4 in Part 2 discusses a multi-period setting, where the principal optimally adjusts the
compensation schemes from period to period according to the changes in the agent’s utility
function with respect to non-cash compensation, and to the changes in its cost to the
principal. When the agent can resist the change in compensation plan from period to period,
the principal is weakly worse off. I introduce informal compensation, which is less rigid and
easier to change than formal compensation for several reasons. Informal compensation is
often paid to a small number of employees and is not covered by a collective bargaining
4
agreement. Informal payment methods like allowed “theft” systems involve “illegal” or
“immoral” activities so that the payees prefer the payment to be secretive. I show that the
principal can solve the resistance problem by paying part of the compensation informally.
The formal compensation is then designed such that the agent has no incentive to resist the
changes in formal compensation. Consequently, the principal has greater flexibility in
changing the compensation schemes from period to period, with an option to pay informally.
Section 5 discusses the use of informal compensation to gain some power over the agent,
possibly to induce more cooperation or to deter undesirable actions. In particular, I consider
the setting in which the principal wants some power to deter costly employee litigation,
specifically the situation in which a performance measure is not verifiable to the courts. In
such a setting, when the agent is not paid a bonus because the realized performance measure
is not good, the agent can opportunistically sue the principal, claiming discrimination in
performance evaluation – the most “popular” employee lawsuits in the US courts. The
principal cannot defend himself very effectively, since he has no evidence to show the courts
that the agent is actually not paid a bonus due to inadequate performance. To deter the agent
from suing him, the principal can pay informal compensation which is illegal or immoral.
Examples include the controlled theft systems described above. With this illegal or immoral
informal pay, it is possible for the principal to punish the agent for opportunistic litigation by
prosecuting the agent for “misappropriation” or by revealing the agent’s “misappropriation”
to the public. The amount of informal pay is determined by the expected gain to the agent
from the lawsuit and the expected gain to the principal from the prosecution. The control
issues associated with informal compensation are discussed at the end of the section.
In explaining fraud, the most important theory in organizational behavior (which is adopted
for accounting – see, for example, Wells (1997)) seems to be the so-called triangle model of
fraud. According to this theory, fraud occurrence is determined by three factors: an
employee’s motives; her attitudes; and the opportunity to perpetrate fraud. The motives
include greed (which is assumed to be the only motive in the economics literature); personal
financial difficulties; and other psychological factors such as job dissatisfaction, the feeling
of being treated unfairly and the desire to retaliate, etc. Once the employee has a motive to
commit fraud, whether she really does so is determined by her attitude toward fraud (i.e., her
levels of honesty, risk aversion, possible guilt over fraud, etc.), and by whether the
opportunities to perpetrate fraud exist (i.e., whether the internal control is effective or not).
5
This theory explains from the employee’s perspective whether fraud will occur. It delineates
how the employee’s attitudes and the situational factors (e.g. whether the internal audit is
effective, whether the employee gets compensated fairly, etc.) affect her decision to
perpetrate fraud. From an employer’s perspective, the economic literature usually explains
the choice of control as a cost-benefit analysis. With costless control, an employer wants to
implement the perfect control to deter all fraud incidents. When control is costly, he
optimally chooses less than perfect control because perfect control is too costly, compared
with the benefit. Consequently, in equilibrium, we observe fraud.
Here, I argue that some of the fraud incidents we observe may be virtual fraud, which is
allowed as a way to pay employees informally, rather than the unwanted fraud which occurs
because the perfect control is too costly. Even when perfect control is costless, an employer
may not implement the perfect control to deter all fraud because he wants to pay the agent
informally to gain some power over the agent.
In summary, this paper contributes to the accounting literature by extending our knowledge
on use of non-cash and informal compensation. My research also suggests that the control
decision is not just a simple cost-benefit analysis. The principal may strategically impose
weak control somewhere to facilitate informal compensation, but stronger control elsewhere
to prevent unwanted appropriation of valuable organizational resources. Also, in addition to
prevention and detection of errors or fraud, we need to determine the degree to which the
control system can produce convincing evidence for successfully prosecuting the “thieving”
employees (or to support the claim that the employees have embezzled, when the employer
chooses to condemn the employees rather than prosecute them), if this becomes necessary.
Part 1: Cash vs Non-cash Compensation
Prior macroeconomic literature discusses various benefits of non-cash compensation: an
economy of scale from providing the non-cash compensation to a large number of
employees; its productivity; and tax benefits (Rosen, 2000; Long and Scott, 1982). In this
paper, I examine the effects of the productivity of non-cash compensation, the existence of
economies of scale, and the agent’s utility function on the optimal use of non-cash as
compensation. Below, I first examine a simple setting in which there is only one non-cash
item to be used. Subsequently, to analyze the choice of non-cash items to include in a
6
compensation portfolio, two non-cash items are considered. (The results are similar when
there are more than two non-cash items the principal can use.)
II. Model Description
I consider a moral hazard setting where the principal (P, later referred to as he) has a linear
utility function with respect to cash. The agent (A, subsequently referred to as she) is strictly
work-averse. At the beginning of the period, the principal offers a contract to the agent. The
contract specifies the amounts of cash and non-cash compensation as functions of a
performance measure. If the agent accepts the offer, she chooses an action a, which
stochastically determines the benefit of her effort to the principal. An additive disutility of
effort is denoted by v(a); v' > 0 and v" > 0. The agent’s action is not observable to the
principal. If not properly motivated, the agent will not supply the costly effort. Assume that
the agent has limited liability or has inadequate wealth, so that it is not possible for the
principal to sell the firm to the agent to solve the moral hazard problem, even when the agent
is risk-neutral.
Production Technology
The benefit of the agent’s effort to the principal (or the outcome) measured in monetary
terms is denoted by x. Since the focus of the model is on the compensation rather than on the
optimal action to induce, I consider a binary model where a  {0, 1} and x  {xL, xH}, xH =
xL + x > xL, and assume that the principal wants to induce a = 1. If the agent chooses a = 0,
then the outcome is xL, i.e. pr(xL| a = 0) = 1. If the agent chooses a = 1, then the outcome
realized is xH with probability p, i.e. pr(xL|a = 1) = 1 - p and pr(xH| a = 1) = p. Assume that
p  (0, 1), i.e., that the outcome is an imperfect signal informing the principal of the agent’s
action. Let x = xL + px.
If the non-cash compensation is productive, assume that the productive benefit of the noncash pay is weakly concave, i.e. x  {g(n)xL, g(n)xH}, g > 0, and g  0, where n is the noncash compensation provided during the production process.
The Agent’s Preferences
The agent’s utility function is denoted by ua(c, n, a) = u(c, n) – v(a), where c  R+ is cash
compensation, n R+ represents the quantity of the non-cash compensation, and a  {0, 1} is
7
the action taken. Let v = v(a=1) – v(a=0). I assume that n is a continuous variable. Let U
denote the agent’s reservation utility. The agent’s expected utility is denoted by Ua(a) ≡
E[u(c, n)|a] – v(a). Assume that the principal knows the agent’s preferences with respect to
cash and non-cash.
Note that it is difficult to capture the characteristics of all types of non-cash compensation
mathematically. This is especially true for non-cash compensation like an office, a company
car, or a paid vacation. In this case, it seems more appropriate to think about n as quality
rather than quantity. The higher the amount of cash spent, the higher the quality of the noncash compensation received.2
Compensation
At the beginning of the period, the principal offers a contract specifying fixed cash and noncash wages, and cash and non-cash bonuses. Let fc denote the fixed cash wage; fn denote the
quantity of fixed non-cash wage; c denote the cash bonus; and n denote the quantity of the
non-cash bonus paid if x = xH. The principal’s expected utility is denoted by UP(a, f, ). Note
that the non-cash bonus is paid after the production is finished and the outcome is known.
Therefore, the non-cash bonus is not productive.
The cost of the non-cash compensation to the principal is denoted by KP(n), KP(0) = 0, KP >
0. Below, I first assume that the non-cash is not available from the market. Subsequently, I
assume that the non-cash is also available from the market, and let Ka(n), Ka(0) = 0, Ka > 0
denote the agent’s cost of acquiring the non-cash from the market. Whether the non-cash is
available from the market or not, assume that the agent cannot sell the non-cash she receives
as compensation (or does not find it optimal to do so because of high transaction costs).
III. The Optimal Compensation When the Performance Measure Is Verifiable
Assuming that the outcome x is contractible, in Section 3.1.1, I first consider a simple setting
in which the non-cash is not productive and is not available from the market. Next, in section
2
In this case, n represents the level of non-cash compensation above some base level that the principal needs
to provide. If the principal has an option not to pay in terms of that non-cash item, we need to consider a corner
solution.
8
3.1.2, I consider a setting in which the non-cash is productive but still not available from the
market. In Sections 3.1.1.1 and 3.1.2.1., I consider the setting with only one non-cash item
available to compensate the agent. To study the selection of non-cash items to include in the
compensation portfolio, I consider the setting with two non-cash items in Sections 3.1.1.2
and 3.1.2.2. The results are similar when the principal has more than two non-cash items to
choose from. Then in Section 3.2, I examine the setting in which there is only one non-cash
item under consideration and the non-cash is available from the market. (The results when
there are many non-cash items – which are not shown in this paper – are similar to the
results when only one non-cash item is available for use.)
3.1 The Non-cash Is Not Available from the Market
When the agent cannot purchase the non-cash from the market, the principal’s optimization
problem is as follows:
Max
f ,
U P ( f ,  , a  1)  g ( f n ) x  (1  p )[ f c  K P ( f n )]  p[ f c   c  K P ( f n   n )]
subject to
( PC a )
U a (a  1)  (1  p ) u ( f c , f n )  p u ( f c   c , f n   n )  v(a  1)
( IC a )
U a (a  1)


U
U a ( a  0)  u ( f c , f n )  v ( a  0 )
The participation constraint (PCa) is to guarantee that the compensation contract pays the
agent at least her reservation utility, and the incentive compatibility constraint (ICa) is to
ensure that the agent is weakly better off choosing a = 1.
To simplify the analysis, I rewrite the utility function u(c, n) and the productivity function
g(n) as functions of the dollars spent on non-cash compensation n$, rather than of the
quantity of non-cash compensation n, i.e.,
u (c, n $ )

u(c, K P 1 (n $ )) , and
gˆ (n $ )

g ( K P 1 (n $ )) ,
where KP -1 is the inverse of the cost function KP.
Let fn$ = KP(fn)and n$ = KP(n) denote the dollar amount of non-cash fixed wage and bonus
respectively. To be able to use the first-order approach, I assume that u (c, n $ ) and gˆ (n $ ) are
9
continuous and weakly concave in c and n$. The rewritten optimization problem is as
follows:
Max
f ,
$
$
$
U P ( f ,  , a  1)  gˆ ( f n ) x  [ f c  f n  p c  p n ]
subject to
( PC a ) U a (a  1)  (1  p) u ( f c , f n )  p u ( f c   c , f n   n )  v(a  1)  U
$
U a (a  1) 
( IC a )
$
$
U a (a  0)  u ( f c , f n )  v(a  0).
$
With this simplified problem, the principal basically decides how to spend each additional
dollar to compensate the agent for her cost of effort – simply pay $1 or use that $1 to acquire
the non-cash to pay the agent, with (PCa) and (ICa) specifying the amounts of fixed wage and
bonus he needs to pay.
The Lagrangian function is as shown below.
L
$
$
$
gˆ ( f n ) x  [ f c  f n  p c  p n ]

  { (1  p) [u ( f c , f n )]  p [u ( f c   c , f n   n )]  v(a  1)  U}
$
$
$
  { p [u ( f c   c , f n   n )  u ( f c , f n$ )]  [v(a  1)  v(a  0)]}
$
$
Differentiate the Lagrangian function with respect to each choice variable. Let
ĝ  ( ) represent the first derivative of gˆ (n $ ) with respect to n$, and ui( ), i = c, n denote the
first derivative of u (c, n $ ) with respect to c or n$ respectively. When the non-cash
compensation is not productive, the optimal interior solution is such that
1
u c ( f c , f
*
and
$*
n
)
uc ( f c   c , f n$*   n$* )
*
u n ( f c , f )

*
*

$*
n

p 
   
 ,
1  p 

un ( f c  c , f n$*   n$* )

*
*

(   ) 1 .
When the non-cash compensation is productive, the optimal interior solution is such that
u c ( f c , f
*
and
$*
n
)

u n ( f c , f ) 
uc ( f c   c , f n$*   n$* )
*
*
*

$*
n
gˆ  ( f n$* ) x
(1  p)   p
1
=
un ( f c  c , f n$*   n$* )
*
*

p 
   
 ,
1  p 


(   ) 1 .
To obtain further results, in this section and Section 4, I simplify the analysis by assuming
that the agent’s utility u(c, n) is additively separable in c and n, i.e. u(c, n) = uc(c) + un(n),
10
uc > 0, uc  0, un > 0, and un 0. The main characteristic of this additively separable form
is that c and n are additively independent (Keeney and Raiffa, 1993: Theorem 5.1), i.e. that
the agent is indifferent between the following two lotteries3:
Lottery A:
½
½
Lottery B:
(ch, nh)
(cl, nl)
½
(ch, nl)
½
(cl, nh)
Then, I rewrite the utility function with respect to non-cash compensation un(n) and the
productivity function g(n) as functions of the dollars spent on the non-cash compensation n$,
i.e., uˆ n (n $ )  u n ( K P 1 (n $ )) , and gˆ (n $ )  g ( K P 1 (n $ )) .4
Let wc denote the inverse of uc, i.e., wc ≡ uc-1. With both (PCa) and (ICa) binding, we can
rewrite the two constraints as shown below: 5
fc
fc +  c
$
= wc(U + v(a=0) – uˆ n ( f n ))
(3.1.1)
= wc(U + v(a=0) + v/p – uˆ n ( f n$   n$ ))
(3.1.2)
Substitute the above into the objective function and differentiate the objective function with
respect to fn$ and n$. The first-order derivatives are the following:
3
If the cash and non-cash compensation are complements, the agent’s utility can be represented by u(c, n)
= uc(c) + un(n), +  uc(c) un(n),  > 0, uc > 0, uc  0, un > 0,and un 0. When c and n are complements, the
agent strictly prefers Lottery A to Lottery B.
4
For instance, let un(n) = 2n1/2,
g(n) = bpn, where bp is marginal product of n, and KP(n) = Pn, where P
is the cost per unit of n to the principal. Then, uˆ (n $ )  2 1 n $ 
n
P


5
1/ 2
and gˆ (n $ )   b p n $  .
 P



We can rewrite (ICa) as p [u c ( f c   c )  u c ( f c )  uˆ n ( f n $   n $ )  uˆ n ( f n$ )  v . Substitute the
rewritten (ICa) into (PCa) and we have the rewritten (PCa), u c ( f c )  uˆ n ( f n $ )  U  v(a  0) , which leads to
(3.1.1). Finally, substitute the rewritten (PCa) back into the rewritten (ICa), and we have the following equation,
which leads to (3.1.2): u c ( f c   c )  uˆ n ( f n $   n $ )  U  v(a  0)  v / p .
11
U p (a  1)
 fn
$
$

$

 gˆ ( f n ) x  (1  p) [ wc (U  v(a  0)  uˆ n ( f n )) uˆ n ( f n$ ) ]
v

$
$

 p [ wc (U  v(a  0) 
 uˆ n ( f n   n )) uˆ n ( f n$   n$ )]  1
p
U p (a  1)
v


 p [ wc (U  v(a  0) 
 uˆ n ( f n$   n$ )) uˆ n ( f n$   n$ ) 1]
$
p
 n
(3.1.3)
(3.1.4)
Below, I first analyze the case when the non-cash compensation is not productive. The
benefit of the non-cash comes from two sources: first, the difference between its value to the
agent and to the principal; and second, from the use of non-cash bonuses to minimize the
risk premium when the agent’s marginal utility with respect to cash is diminishing. Next, I
assume an additional benefit of the non-cash: its productivity.
3.1.1 The Non-cash Compensation Is Non-Productive
3.1.1.1 One Type of Non-cash Compensation under Consideration
In this section, assume that there is only one type of non-cash compensation item for the
principal to use and it is not productive, i.e. gn(n) = 1, g(n) =0  n.
From the first-order derivatives, when both uc and û n are linear, we have a corner solution, in
which the principal pays either in cash or in non-cash terms. Let uc(c) = c and uˆ n (n $ ) =
ban$. With linear utilities, the solution depends on the slopes of uc and û n . When $1 spent
purchasing the non-cash for compensation has the value ba > 1 to the agent, the principal is
better off spending $1 to acquire the non-cash to pay the agent than simply paying her
$1.The solution is as follows:
(i)
when ba > 1,
fc* = c* = 0, fn$* = (U + v(a=0))/ba, and n$* = v/pba;
(ii)
when ba  1,
fc* = U + v(a=0), c* = v/p, and fn$* = n$* = 0.
Next I consider interior solutions, when the two utility functions uc and û n are weakly
concave. From the first-order conditions (note that gˆ (n $ ) 1  n $  R  ) and the fact that
wc (u c (c))  1 / u c (c) , the optimal interior solution must be such that
uˆ n ( f n$* ) = uc(fc*)
and
uˆ n ( f n$*   n$* ) = uc(fc*+c*)
(3.1.5),
(3.1.6).
12
For example, when the agent’s utility with respect to cash uc is linear while her utility with
respect to non-cash û n is concave, the optimal interior solution is as follows:
fn$*
such that uˆ n ( f n$* ) = uc(fc*) = 1 ,
fc*
=
U + v(a=0) - uˆ n ( f n$* ) , and
n$*
=
0,
c*
=
v/p.
The fixed non-cash compensation fn$* is chosen such that the marginal utility from the
dollars spent on non-cash compensation is equal to the marginal utility from cash
compensation. Paying a non-cash bonus is not optimal, since for n$ > fn$*, the incremental
benefit from $1 paid to acquire the non-cash compensation is less than the incremental
benefit from paying $1 to the agent, due to the concavity of û n . Similarly, the principal
cannot improve her payoff by choosing fn$ < fnS* and n$ > 0, due to the concavity of û n .
If the principal is limited to cash compensation, his payoff is x - U – v(a=1). When he can
pay non-cash compensation as well, his payoff increases to x - U – v(a=1)+ ( uˆ n ( f n$* ) - fn$*),
i.e., he can reduce the total compensation by the amount of the agent’s surplus from noncash compensation. When the agent’s preference is concave in cash, the principal can also
benefits from the reduction in risk premium, as discussed below.
The interior solution when the agent’s utility with respect to cash uc is concave but her utility
with respect to non-cash û n is linear, i.e., uˆ n (n $ ) = ban$, is as follows:
fn$*
such that uc(fc*) = uˆ n ( f n$* ) = ba ,
fc*
=
U + v(a=0) - uˆ n ( f n$* ) , and
n$*
=
v/pba,
c*
=
0.
If the principal is limited to paying cash as compensation, he has to pay risk premium when
uc is concave. When the non-cash compensation is introduced and û n is linear, the principal
is better off, since he does not have to pay risk premium any more. (Even when û n is
concave, the principal can reduce the risk premium by paying some non-cash bonus when
the slope of û n is adequately high.)
13
When either one of the two utility functions is linear, we have a corner solution, where the
slope of the two utility functions differs greatly. For example, when uc is linear and û n is
concave, the principal only pays in cash when uc(m) > uˆ n (m) for all m  R+.
When both the agent’s utility with respect to cash uc and her utility with respect to non-cash
û n are concave, the optimal solution is determined by the slopes and the concavity of uc and
û n . To simplify the analysis, I assume that either uc(m) > uˆ n (m) for all m  R+ or vice versa
- the two utility functions do not cross. When the slopes of uc and û n differ vastly, the
principal pays either cash or non-cash compensation. From (3.1.1) and (3.1.2), if the
principal has to pay only in cash, the cash pay must be such that uc(fc) = U + v(a=0) and
uc(fc+c) = U + v(a=0) + Δv. Consider Figure 1a. The slope of uc at fc + c for uc(fc + c) =
U + v(a=0) + v/p is still greater than the slope of û n at the origin. In other words, the
marginal benefit from spending money as cash compensation is higher than the marginal
benefit from purchasing the non-cash to pay as compensation. Therefore, the principal only
pays in cash. The opposite is true when the slope of û n is much higher than the slope of uc.
Figure 1a
uc
U + v(a=0) +v/p
U+v(a=0)
û n
fc
(fc + c)
When the slopes of uc and û n differ rather greatly, the principal pays either a cash or a noncash fixed wage, and pays both cash and non-cash bonuses. Consider Figure 1b. The slope of
uc at fc for uc(fc) = U + v(a=0) is greater than the slope of û n at the origin, but the slope of uc
at fc + c for uc(fc + c) = U + v(a=0) + v/p is less than the slope of û n at the origin.
Therefore, the principal pays a fixed wage only in cash but pays both cash and non-cash
14
bonuses. The fixed cash wage, the cash and non-cash bonuses are such that (3.1.6) is true.
Again, the opposite is true when the slope of û n is much larger than the slope of uc.
Figure 1b
uc
U + v(a=0) +v/p
U+v(a=0)
û n
n$ fc (fc+c)
When the slopes of uc and û n do not differ greatly, we have a truly interior solution in which
the principal pays fixed wages and bonuses both in cash and non-cash terms. The interior
solution is characterized by conditions (3.1.5) and (3.1.6). See Figure 1c. The amounts of
cash and non-cash compensation are determined by both the slopes and the degrees of
concavity of the two utility functions, with the marginal utilities from cash fixed wage and
from non-cash fixed wage being equal, and the marginal utility from (fc*+c*) equal to the
marginal utility from (fn$* + n$*).
Figure 1c
uc
U + v(a=0) +v/p
U+v(a=0)
û n
fn$ fc (fc+c)
(fn$+n$)
The results from the analysis above are summarized in Proposition 1.
15
Proposition 1: Assume that the agent’s utility with respect to cash and non-cash is
additively separable.6 When the non-cash compensation is non-productive and is not
available from the market, the principal pays a non-cash fixed wage when the slope of û n is
sufficiently high, and he pays a non-cash bonus when the slope of û n is sufficiently high and
the degree of concavity of û n is sufficiently low.
Exponential Utility Example
Let uc(c) = – exp[-rcc], un(n) = – exp[-rnn], where rc and rn are the degrees of risk aversion
with respect to cash and non-cash compensation respectively. Let ri = 1/i, i = c, n represent
the degree of risk tolerance with respect to cash and non-cash compensation. The cost of
non-cash compensation to the principal is represented by KP(n) = Pn, P > 0. We can
rewrite un(n) as uˆ n (n $ )   exp[ rˆn n $ ], where rˆn  rn /  P ; ˆn  1 / rˆn . In addition, assume that
(- U - v(a=0))  (0, 1] and (- U - v(a=0) - v/p)  (0, 1]. The interior solution is as follows:
*

 c

 U  v(a  0) ,
 c ln 
 c  ˆn

$*

 n

 U  v(a  0) ,
ˆn ln 
  c  ˆn

c*

  c
 c  ln 
  c  ˆn
 
 c


v 
  U  v(a  0) 
  ln 
 U  v(a  0)   ,
p 

  c  ˆn

 n$*

  ˆn
ˆn  ln 
   ˆ
n
  c
 ˆn


v 
  U  v(a  0) 
  ln 
 U  v(a  0)   .
p 

  c  ˆn

fc
fn
From the above, c* is decreasing, while fc* is increasing in rc, the degree of concavity of uc.
Similarly, n$* is decreasing, while fn$* is increasing in r̂n , the degree of concavity of
6
If the cash and non-cash compensation are complements, as discussed in footnote 3, the optimal contract is
still such that the marginal utility from cash and the marginal utility from the dollars spent on non-cash are
equal (but the functional forms of the marginal utilities now differ.) The significant change is in the optimal
contract, when the agent’s utility with respect to cash is linear but the utility with respect to the dollars spent on
non-cash is concave. When the utilities are additively separable, the principal does not pay a non-cash bonus.
When the utilities are not additively separable, e.g. when the cash and non-cash are complements, the principal
also pays a non-cash bonus, to increase the utility the agent receives from the cash bonus.
16
uˆ n (n $ ) , i.e. n$* is increasing in P but decreasing in rn, while fn$* is decreasing in P but
increasing in rn.
3.1.1.2 Two Types of Non-cash Compensation under Consideration
As before, I assume additively separable utility function, i.e., u(c, n1, n2) = uc(c) + un1(n1) +
un2(n2) , uc > 0, uc  0, uni > 0, and uni 0, for i = 1, 2. Assume also that the three utility
functions do not cross, and their slopes can be ordered, i.e., uc(m) > uˆ ni (m) > uˆ nj (m) for all m
 R+, i, j = 1, 2, i  j, or any other orders. I repeat the analysis above and find that the
optimal interior solution is characterized by
uˆ n1 ( f n$1* ) = uˆ n 2 ( f n$2* ) = uc(fc*)
and
uˆ n 1 ( f n$1*   n$1* ) = uˆ n 2 ( f n$2*   n$2* ) = uc(fc*+c*)
(3.1.7),
(3.1.8).
Similar to the results in Section 3.1.1.1, when the slopes of uc , uˆ n1 , and uˆ n 2 differ greatly, we
have a corner solution where the principal does not pay the fixed wage or bonus in all
possible forms. The principal optimally pays an additional $1 in the form that creates the
highest incremental utility for the agent. For a given value of (U, v(a=0), v), as the slope of
û ni increases, the incremental benefit from paying $1 as a non-cash item i increases. The
non-cash item to be selected first is the one that exhibits the greatest slope. Given an
adequately high slope, the principal pays a bonus in terms of the non-cash item i when û ni is
not very concave.
Proposition 2: Assume that the utility with respect to cash is strictly concave. When there
are many non-cash items to choose from, the principal optimally includes in the
compensation portfolio the non-cash item for which the utility function exhibits a higher
slope and a lower degree of concavity.
Now we hold constant the slopes and degrees of concavity of uc, uˆ n1 , and uˆ n 2 . If U + v(a=0)
and v are large, the amount of cash compensation needed to induce the agent to accept the
contract and to choose a = 1 is large, especially when uc is concave so that the marginal
utility from cash compensation is decreasing. As a result, if the slope of the non-cash utility
17
function is sufficiently high, the principal is better off paying a non-cash fixed wage and
bonus to complement cash compensation. To illustrate, consider Figure 1a. If U + v(a=0) or
U + v(a=0) + v/p increases to, say, the highest dotted horizontal line, the principal is better
off paying a fixed wage and bonus both in terms of cash and non-cash, rather than only in
cash as he does when the reservation utility and disutility from work are low.
Proposition 3: Assume that the utility with respect to cash and the utility with respect to
each non-cash item are strictly concave. As the reservation utility or the disutility of effort
increases, the number of non-cash items included in the optimal compensation portfolio
increases.
In practice, it seems most reasonable to assume that the agent’s marginal utility from cash
and that from the dollars spent on non-cash compensation are diminishing. Also, the slope of
the utility with respect to cash should be high, since we definitely need some cash to buy
goods or services necessary for survival today and in the future, for both ourselves and our
families. The slopes of utility functions for goods or services that satisfy basic needs (like
food, lodging, health care) should be high as well. I anticipate that these necessary non-cash
items will be provided to employees at all organizational levels, especially in a setting where
production occurs in a remote area without a well-developed market for food,
accommodation, and supplies (e.g., a military base). When the reservation utility or the cost
of effort is large, I anticipate the inclusion of more non-necessary goods or services in the
compensation portfolio. For instance, we observe that executives (who have higher
reservation utility) are paid more in terms of some luxurious non-cash items, e.g. a better
office, an expensive car, etc. Some of the items paid are not only paid because an employee
has diminishing marginal utility with respect to cash, but also because those items are
productive, as discussed in Section 3.1.2 below.
3.1.2 The Non-cash Is Productive and Is Not Available from the Market
3.1.2.1 One Type of Non-cash Compensation under Consideration
In this section, the agent cannot purchase the non-cash from the market and the non-cash is
productive. The first-order derivatives are as shown by (3.1.3) and (3.1.4). In addition to the
slopes and the degrees of concavity of uc and û n , the solution is determined by the slope and
the degree of concavity of the productivity function ĝ .
18
From the first-order derivatives, we have a corner solution when uc, û n , and ĝ are linear. Let
uc(c) = c, uˆ n (n $ ) = ban$, where ba is marginal utility to the agent from the dollars spent on
the non-cash compensation, and gˆ (n $ ) = bPn$, where bP is marginal product of the dollars
spent on the non-cash compensation. The solution is as follows:
fc* = c* = 0 , fn$* = (U + v(a=0))/ba, and n$* = v/pba;
(i)
when ba > 1,
(ii)
when ba  1 but ba + bP > 1,
fn$* = (U + v(a=0))/ba, n$* = fc* = 0, and c* = v/p;
when ba + bP  1,
(iii)
fc* = U + v(a=0), c* = v/p, and
fn$* = n$* = 0.
When the principal spends $1 to acquire the non-cash compensation, the value to the agent is
ba. If ba > 1, then the principal optimally pays only in non-cash terms. If ba  1, but the
marginal utility to the agent plus the marginal product is greater than 1, i.e., ba + bP > 1, the
principal pays all the fixed wage in non-cash terms but pays all the bonus in cash. This is
because the bonus is paid after the production ends, and hence is not productive. If the
incremental utility plus the incremental production outcome of $1 spent to buy non-cash
compensation is less than $1, the principal does not pay non-cash compensation at all.
Next I consider interior solutions, when the two utility functions uc and û n are weakly
concave. From the first-order conditions and the fact that wc (u c (c))  1 / u c (c) , the interior
optimal solution must be such that
and
$*
uc(fc*) gˆ ( f n ) x /(1  p)  uˆ n ( f n$* )  uc(fc*)
(3.1.9),
uˆ n ( f n$*   n$* ) = uc(fc*+c*)
(3.1.10).
For instance, when the agent’s utility with respect to cash uc is linear while her utility with
respect to non-cash û n is concave, and ĝ is weakly concave, the optimal interior solution is
as shown below.
$*
fn$* such that gˆ ( f n ) x /(1  p)  uˆ n ( f n$* )  uc(fc*) = 1,
fc*
=
U + v(a=0) - uˆ n ( f n$* ) , and
n$*
=
0,
 c*
=
v/p.
Compared with the case where the non-cash is not productive, the optimal fixed non-cash
wage fn$* is now higher, since the marginal benefit of the fixed non-cash compensation
19
increases by the amount of the marginal product of the non-cash. The non-cash bonus
remains zero.
Similarly, when the agent’s utility with respect to cash uc is concave but her utility with
respect to non-cash û n is linear, and ĝ is weakly concave, the interior solution is such that
the fixed non-cash wage is higher than when non-cash is not productive, while the non-cash
bonus remains the same.
When both the agent’s utility with respect to cash uc and her utility with respect to non-cash
û n are concave (and ĝ is weakly concave), the optimal interior solution is characterized by
conditions (3.1.9) and (3.1.10). When the slopes of uc and û n differ greatly, the principal
may not pay in all forms possible, as discussed in Section 3.1.1.1 above.
Compared with the setting where the non-cash is not productive, the fixed non-cash wage
increases, while the non-cash bonus decreases. (See the proof in Appendix 3.) Intuitively,
this is because the amount of non-cash fixed wage - which is essentially chosen so that the
marginal benefit to the principal (the marginal product plus the marginal benefit to the agent)
equals the marginal cost - is already so large that it is “more expensive” to pay a large
additional non-cash bonus (in the sense that an additional dollar spent on the non-cash to be
paid as a bonus will not create very large incremental utility to the agent).
Proposition 4: Assume that the slope of û n is sufficiently high. Compared with the setting
where the non-cash compensation is not productive, the principal pays a higher fixed noncash wage when the non-cash compensation is productive. The principal also pays a lower
non-cash bonus if the agent’s utility with respect to cash uc and the utility with respect to the
dollars spent on the non-cash û n are both strictly concave.
Are Agency Costs a Form of Compensation?
When the non-cash is productive, the principal essentially chooses the level of non-cash such
that the marginal productivity (MP) plus the marginal benefit from paying non-cash
compensation (MB) equals the marginal cost (MC), as opposed to the level where MP = MC,
which seems to be an efficient level. This explains why we observe a luxurious executive
office rather than a budget one, a corporate jet rather than business-class airfares, etc. This
20
apparent abuse of shareholders’ money may be part of the compensation. It is paid because
the employee’s marginal utility with respect to cash is diminishing and because the cost of
the non-cash compensation to the employer is lower than the benefit to the employee (i.e.,
uˆ n (n $ ) > n$ at least for some small n$).
3.1.2.2 Two Types of Non-cash Compensation under Consideration
Assume that the production outcome is represented by x  {[g1(n1)+ g2(n2)] xL, [g1(n1)+
g2(n2)] xH}, with gi > 0, gi  0, where ni, i = 1, 2 is the non-cash compensation provided
during production. The optimal interior solution is such that
uc(fc*) =
=
and
uc(fc*+c*)
$*
uc(fc*) gˆ1 ( f n1 ) x /(1  p)  uˆ n1 ( f n$1* )
$*
uc(fc*) gˆ 2 ( f n 2 ) x /(1  p)  uˆn 2 ( f n$2* )
=
uˆ n 1 ( f n$1*   n$1* ) =
uˆ n 2 ( f n$2*   n$2* )
(3.1.11),
(3.1.12).
Consider the analysis used to derive Proposition 2. With a similar analysis, I find that, given
that uˆ n1  uˆ n 2 , the principal will choose to pay a fixed wage in terms of the non-cash item for
which the productivity function exhibits a higher slope and a lower degree of concavity first.
3.2 The Non-cash Compensation is Available from the Market
The objective of this section is to determine when the agent’s access to the non-cash market
alters the characteristics of the optimal contract, compared with situations where the agent
has no access to the non-cash market. For simplicity, assume that the agent’s cost of
purchasing n from the market is Ka(n) = (1 + ) KP(n),  > -1. When the economy-of-scale
parameter  is greater than zero, the cost to the principal is lower than that to the agent and
vice versa.
3.2.1 The Model When the Agent Has Access to the Non-cash Market
Let q = (qf, q) denote the amount of the non-cash the agent purchases from the market; qf
[q] is the non-cash bought when the outcome realized is xL [xH] and the compensation paid
is (fc , fn) [(fc + c, fn + n)]. Note that when n is not productive, g(n) = 1 for all n.
The principal’s optimization problem is as follows:
21
U P ( f ,  , a  1)  g ( f n ) x  (1  p)[ f c  K P ( f n )]  p[ f c   c  K P ( f n   n )]
Max
f , ,q
subject to
( PC a ) U a (a  1, q)  (1  p) u ( f c  K a (q f ), f n  q f )
 p u ( f c   c  K a (q  ), f n   n  q  )  v(a  1)  U
( IC a 1 ) U a (a  1, q)
 U a (a  1, qˆ*) where qˆ*  arg max U a (a  1, qˆ )
( IC 2 ) U (a  1, q)
 U (a  0, qˆ * *)  u ( f c  K (qˆ * *), f n  qˆ * *)  v(a  0)
qˆ
a
a
a
a
where qˆ * *  arg max U a (a  0, qˆ ).
qˆ
Note that qˆ * *  qˆ f * . (ICa1) and (ICa2) can be rewritten as follows:
( IC a 1 ) q  (q f , q  )  arg max U a (a  1, qˆ )
qˆ
( IC a 2 ) u ( f c   c  K a (q  ), f n   n  q  )  u ( f c  K a (q f ), f n  q f )

v
p
When the cost of the non-cash to the agent is lower than the cost to the principal, or the cost
functions KP and Ka are convex, the principal will want to use an agent as both worker and
supplier. In addition to paying the agent for her productive effort, the principal also needs to
pay her some commission for arranging the deal with the low-cost manufacturer. The
amount of commission paid should be determined by the bargaining power between the two
parties, the characteristics of the non-cash market, etc. Here I only characterize the
compensation contract for work effort. If the principal also wants the agent to be his
supplier, he offers another buyer-supplier contract, which is not discussed in this paper. In
other words, below, I rule out the employee-supplier solutions where the principal basically
asks the agent to purchase some of the non-cash compensation to be used in production or to
be used as compensation (because the agent can purchase the items at a lower price or
because the cost functions are convex), without paying her the commission.
As in the previous sections, I simplify the analysis by assuming that that the agent’s utility
u(c, n) is additively separable in c and n, i.e. u(c, n) = uc(c) + un(n).
3.2.2 The Optimal Contract When the Agent Has Access to the Non-cash Market
The main objective in this section is to compare the optimal contract when the agent has
access to the non-cash market and when she does not. Intuitively, we must first answer the
following questions:
22
(i)
Given the optimal contract derived assuming the agent does not have access to the
non-cash market, does the agent have an incentive to purchase additional non-cash
from the market? (If not, then the optimal contract derived assuming no access is
still optimal when there is access to the market.)
(ii)
If so, the purchase will lead to a different consumption bundle from the one when
the agent has no access to the non-cash market. Do the slopes and concavities of
the cash and non-cash utility functions associated with the new consumption
bundle differ from the ones at the consumption bundle derived in the last section?
(If not, then the optimal contract derived assuming no access is still optimal with
access to the non-cash market.)
(iii) If so, how does the principal react?
First, consider a simple linear setting where the agent’s utilities with respect to cash and noncash are linear, i.e., uc(c) = c and uˆ n (n $ ) = ban$. The optimal solution, assuming no access to
the market, is such that the principal pays non-cash compensation if the marginal benefit
(marginal value to the agent plus marginal product to the principal) is greater then the
marginal cost to the principal. Given such a contract, the agent will purchase more of the
non-cash if the marginal utility of the dollars spent on the non-cash is greater than her
marginal cost. However, the purchase does not change the slope of û n at the consumption
point, i.e. uˆ n ( f n$* )  uˆ n ( f n$*  q $ ) ,  q$  R+ due to the linearity. Therefore, the optimal
contract remains similar to the one derived when the agent has no access to the non-cash
market.
Second, consider the setting where the agent’s utility with respect to cash uc is concave, and
her utility with respect to the non-cash û n is linear. Again, uˆ n ( f n$* )  uˆ n ( f n$*  q $ ) ,  q$ 
R+. Therefore, the optimal contracts are similar whether the agent has access to the non-cash
market or not. Whether the agent will purchase additional non-cash from the market depends
on the degree of productivity and the cost saving parameter. For simplicity, assume that the
productivity function is linear, i.e., gˆ n (n $ ) = bPn$, bP  (0, 1). If the cost to the agent is
23
higher than the cost to the principal, or  > 0, the agent will not purchase more non-cash
from the market. For  < 0, the agent will purchase more of the non-cash when || > bP.7
Proposition 5: Whether the agent’s utility with respect to cash uc is linear or concave, when
her utility with respect to the dollars spent on non-cash û n is linear, the optimal contract
when the agent has access to the non-cash market is similar to that when she does not.
Third, consider the setting where the agent’s utility with respect to cash is linear, i.e., uc(c) =
c, and her utility with respect to the non-cash û n is concave.8 Assume that the cost function
KP is linear or mildly convex. The agent will not purchase additional non-cash if the cost to
the agent is higher than the cost to the principal or  > 0. Intuitively, this is because the
principal optimally selects the non-cash fixed wage such that u(fn*) = KP(fn*) < Ka(fn*) =
(1+ )KP(fn*) for  > 0. For  < 0, when the non-cash is adequately productive, the non-cash
fixed wage chosen will be large such that u(fn*) < Ka(fn*). (See the proof in Appendix 3.)
7
Note that û n is linear if both un(n) and KP(n) are linear. Let un(n) = bn, and P denote the cost per unit to
$
the principal. Therefore, uˆ n (n $ )  b n  b a n $ , b a  b . With $1, the principal can purchase 1/P unit of
P
P
the non-cash, while the agent can buy 1/(1+ )P unit. Let w
ˆ n  uˆ n 1  u n / b a . Assuming that (ICa2) and (PC)
are binding, we can rewrite the two constraints as follows:
fn$
=
wˆ n (U  v(a  0)  u c ( f c )) , and
 n$
=
wˆ n (U  v(a  0)  v / p  u c ( f c   c ))  f n$ .
Substitute the above into the objective function and differentiate with respect to fc and c. Using the result from
the last section that c* = 0, the fixed cash wage fc* is chosen such that uc(fc*)(1 – bP) = ba, i.e. uc(fc*) =
ba/(1-bP), and the non-cash bonus is v/pba. Let the marginal utilities with respect to cash and non-cash
approximately represent the incremental utility the agent receives from $1 cash and from $1 spent to acquire
non-cash compensation, respectively. If the agent spends $1 to buy additional non-cash, the incremental utility
is approximately b/(1+)P = ba/(1+). The incremental “cost” is approximately uc(fc*–1)> uc(fc*) = ba/(1-bP).
Therefore, if the cost to the agent is higher than the cost to the principal, or  > 0, the incremental benefit is
less than the incremental cost, so that the agent will not purchase more non-cash from the market. For  < 0,
the agent will purchase more of the non-cash when || > bP.
8
Note that a concave û n is generally possible when (i) un is linear and KP convex, and (ii) un is concave
and KP linear or convex.
24
Proposition 6: Assume that the agent’s utility with respect to cash uc is linear and her utility
with respect to the dollars spent on non-cash û n is concave. Also assume that the cost
function KP is linear or mildly convex. The optimal contract when the agent has access to the
non-cash market is similar to that when she does not if (i) the cost of the non-cash
compensation to the principal is lower than the cost to the agent or (ii) the cost to the
principal is not much higher than the cost to the agent, and the non-cash compensation is
adequately productive. Otherwise, the principal optimally pays a lower non-cash fixed wage
(and a higher cash fixed wage) than when the agent does not have access to the market, and
the agent will purchase some non-cash from the market.
The analysis when both the agent’s utility with respect to cash uc and her utility with respect
to the dollars spent on non-cash û n are concave is more complicated and not tractable.
However, I anticipate the results above to be valid. To be specific, I conjecture that the
optimal contract remains the same if the cost to the principal is lower than the cost to the
agent ( > 0), or when  < 0 and the non-cash is very productive. Otherwise, the agent has
an incentive to purchase the non-cash from the market. The principal optimally pays less
non-cash compensation (and more cash compensation), compared with the situation when
the agent does not have access to the non-cash market.
Part 2: Formal vs Informal Compensation
In this part, I study another dimension of the compensation decision: formal vs informal.
While the previous accounting research on informal compensation does not seem to exist,
employee thefts and informal compensation have been topics of interest for researchers in
organizational behavior. Mars (1982), for instance, remarks that the total compensation from
work consists of the formal, legal rewards (e.g. wages, salaries, etc.); the informal, legal
rewards (e.g. tips, perks, etc.); and the hidden economy rewards (e.g. pilfering, overcharged
expenses, etc.) He reports a custom of compensating journalists informally for the quality of
the articles submitted. The journalist handing in a better article can submit a more inflated
expense list for reimbursement. Another vivid real-world case is reported by Zeitlin (1971:
22).
A close friend of mine, an accountant, told me of an experience he had recently when
he audited the books of a corporation. It became apparent that the office manager was
dipping into petty cash to the extent of about $2,000 a year. He reported this fact to the
25
president. The president responded, “How much are we paying him?” “Ten thousand a
year,” replied the accountant. “Then keep quiet about it,” said the president. “He’s
worth at least $15,000.”
Greenberg and Scott (1996) argue that employers pay informally rather than formally
because this is a more a flexible and timely way to reward an employee. In Appendix 1, I
report the compensation practices of a pharmaceutical manufacturer in Thailand. I find that,
consistent with the main idea in this paper, the executive pays informally both because that
method is more flexible and the informal pay helps him maintain some influence over his
employees.
For formal compensation, we generally focus on the amount of pay. For informal
compensation, in addition to the amount, an employer also needs to decide how the pay can
be transferred to an employee. The control system in an organization must be designed to
allow the informal pay. For example, Greenberg and Scott (1996) describe the controlled
theft system, where the employer allows the employee to take a certain amount of a certain
item from the workplace as part of compensation. By the word “allow”, I mean the firm
chooses not to implement an adequate control system to protect certain organizational
resources at risk. The control is weak enough to facilitate the permitted asset appropriation,
but strong enough to prevent unwanted misappropriation. Consider an example of the
inflated expense account discussed earlier. With a weak policy as to what and how much is
allowed for reimbursement, the editor has some leeway to compensate the journalist for
good work. However, the business can prevent the unwanted abuse of the expense account
by requiring management’s authorization for a large reimbursement. To change the amount
of informal pay, the employer adjusts the control system accordingly. While employees can
negotiate formal compensation, they generally cannot negotiate internal control practices. As
a result, informal compensation is less rigid and easier to change.
One of the explanations for why misappropriation is observed in workplaces, as suggested
by the “fraud” triangle theory, is that a control system effective in eliminating all
misappropriation would be too expensive. Here, I assume that any level of control is
available to the principal at no cost. I propose an explanation why the principal may choose
not to implement the costless perfect control system to eliminate all “misappropriation”.
What seems to be theft may actually be informal compensation. The control, as a result, is
weaker somewhere but stronger elsewhere.
26
In addition to control, another important issue is the “shade” of the informal pay. The
informal pay can be “white” – legal and moral (e.g. a boss paying for a birthday gift or a
party for a certain employee); “black” – illegal or immoral (e.g., “employee theft”); or
“grey” – perhaps illegal or immoral, depending on the context and the individual critics (e.g.
the “abuse” of an expense account). If the objective of the informal pay is to gain some
power over the agent, the business uses dark (grey or black) informal pay. By accepting the
pay, the employee is subject to being prosecuted for “misappropriation” or to being
condemned, if the employer discloses the “misappropriation” to the public.
Below, in Sections 4 and 5, I examine the settings where the employer pays informally due
to flexibility and power motives respectively. Section 4 focuses more on the amount of
informal compensation, while Section 5 concentrates on the “shade” of the informal
compensation and control issues.
IV. The Optimal Two-period Contract When the Performance Measure Is Verifiable
In this section, I consider the use of informal compensation due to its greater flexibility. In
the real world, the agent’s preference with respect to the non-cash compensation or even to
cash compensation may change over time. For example, the value of health insurance and
health care benefits to an employee who is diagnosed with a certain disease may increase
until the disease is cured. Cash may become more valuable to an employee who has financial
troubles. The tax law may change so that an employee may prefer one form of compensation
over the others. In addition, the cost of the non-cash compensation to the principal can
fluctuate from period to period (whether it is an opportunity cost of those resources or the
purchase price). As a result, the slope and the concavity of the utility function from the
dollars spent on the non-cash û nt change over time. The principal then optimally adjusts the
compensation scheme in each period accordingly.
In a friction-free world, the principal can change compensation schemes from period to
period according to changes in the functional form of û nt without resistance from
employees. In the real world, as time passes, the agent gathers skills and knowledge which
increase her productivity. This greater productivity then gives her some bargaining power
with respect to compensation. In practice, one way employees use their power is to resist
27
unsatisfactory changes in cash compensation or fringe benefits. In particular, it can be
difficult to decrease any component of the formal compensation (even when another
component is increased).
Theoretically, the principal can design a long-term compensation contract to avoid the
problem of the agent’s resisting changes in the compensation scheme, as discussed in
Appendix 2. However, sometimes the long-term resistance-proof contract involves paying
the agent less than her reservation utility in some periods and more than her reservation
utility in other periods. This will work only when both the principal and the agent can
commit to staying in a long-term relationship and the principal can commit to the contract
which pays more than the reservation utility in the latter period. If the agent anticipates that
the principal cannot commit to pay her more than the reservation utility in some period, she
will not accept the long-term resistance-proof contract. Also, in practice, an employer and an
employee may not be able to commit to a long-term relationship for various reasons. A
future economic recession may require the firm to lay off its employees or even to
discontinue a certain operation. In subsequent periods, production technology may change so
that the skills or knowledge the agent has acquired are no longer useful. If this is the case,
the principal is then better off firing the old agent (who will be paid more than the
reservation utility under the long-term resistance-proof contract) and hiring the new one (and
paying the new agent only at her reservation utility). On the other hand, the agent may not be
able to stay with the current employer because of a family emergency, the discovery of a
new career path, etc.
In this section, I consider a two-period setting where the principal and the agent cannot
commit to a long-term relationship. The principal can only offer a spot contract. I assume
that after working for one period, the agent gains some firm-specific skills and knowledge
that increase the expected level of productivity from x1 to x 2 , x 2  x1 . As a result, the
principal prefers to hire the same agent to work in the second period rather than the
inexperienced one, given that they are paid the same amount. In reality, in addition to the
firm-specific skills and knowledge, the agent may also gain general skills and knowledge
that can be used elsewhere, which consequently increases her reservation utility in the
second period. In the model below, for simplicity, I assume that the agent does not gain any
general skills and knowledge. (The results presented below are valid, given that the increase
28
in the reservation utility from the general skills and knowledge acquired is not very large
compared to the degree of change in unt.)
The main results are that when the difference in productivity between the experienced and
the inexperienced agent is large, and the agent’s utility with respect to cash or to the unit of
non-cash compensation shifts up so that the agent has an incentive to resist the change in
compensation plan, the principal can solve the resistance problem by paying informally. (In
fact, even when the agent does not have bargaining power in the subsequent periods, the
principal can still benefit from the use of informal compensation if the communication costs
to inform and justify the changes in formal pay are higher than those to inform and justify
the changes in informal pay.)
4.1 The Agent Cannot Resist the Change in Compensation Contracts
In this section, I make the following assumptions to simplify the analysis. First, the agent’s
utility with respect to cash is linear, but her utility with respect to the dollars spent on noncash is concave. Both the principal’s and the agent’s utilities are time-additive, and there is
no discounting. Borrowing and lending cash is thus not an issue here. Second, the non-cash
is not productive and is not available from the external market. The agent cannot save the
non-cash from one period to consume in another. Third, the unit cost of non-cash
compensation to the principal is constant and is denoted by tP, t = 1, 2. Fourth, the two
periods are independent in the sense that the period-one action does not affect the period-two
outcome, and there is no correlation between the two periods’ outcomes.
From the analysis in Section 3.1.1, the optimal spot contracts for the first and second periods
are as shown below. For, t = 1, 2,
fnt$*

such that uˆ nt ( f nt$* ) = uct(fct*) = 1 ,
fct*
=
U + v(a=0) - uˆ n ( f n$* ) , and
nt$*
=
0,
ct*
=
v/p.
The interior solution above is such that no risk premium is paid. Therefore, there is no room
for ex-post beneficial renegotiation to increase the total welfare of the two contracting
parties by removing the incentive risk after the action is taken. The principal receives the
first-best payoff in both periods. In Section 4.2 below, I relax the assumption that the agent
cannot resist the change in compensation contracts. Note that as opposed to renegotiation
29
which is beneficial ex post, resistance allows the agent to extract some wealth from the
principal. It does not increase the total welfare.
4.2 The Agent Can Resist the Change in Compensation Contracts
In this section, I examine the conditions under which the agent will resist the change in
compensation plans, if the optimal spot contracts derived in Section 4.1 are used. Then in
Section 4.3, I show how the principal can overcome resistance problems with informal
compensation.
Consider a game between the principal and the agent. At the beginning of the second period,
the principal offers a period-two spot contract specifying (fc2, 
c2, fn2
$
) to the agent. The
agent then decides whether to accept the contract or to bargain. The wage bargaining is in
practice complicated, and may involve many rounds of offers and counter-offers, or even a
strike. Since we often observe employees using the preceding formal compensation practice
as a fall-back position in wage bargaining - the new compensation packages proposed should
be at least as good as the previous one - I consider a simplified strategy where the agent can
choose whether to accept the contract or to fight by pressing the principal to switch back to
the first-period contract. If the agent chooses to fight, the principal chooses whether to
accommodate by switching to the first-period contract as requested, or to fight back by firing
the old agent and hiring a new agent. The bargaining game between the principal and the
agent is as shown in Figure 2 below.
Accomodate
[ x 2 -fc1 - pc1 – 2P( fn1$/P1),
fc1 + pc1 + un2(fn1$/ 1P)]
Fight
Offer
P1
P2
Fight
[ x1 -fc2 - pc2 –fn2$- R,
U - J]
A1
Accept
[ x 2 -fc2 - pc2 – fn2$,
fc2 + pc2 + un2(fn2$/ 2P)]
Figure 2: The Wage Bargaining Game in Period 2
30
At node P2, if the principal accommodates by using the period-one spot contract, he receives
the expected outcome of x 2 , and pays the expected cash payment fc1 + pc1. Also, he
provides non-cash compensation of fn1$/P1 unit, which costs him $2P( fn1$/P1). If the
principal decides not to accommodate, he fires the experienced agent, and then hires a new
one, paying R as a recruitment cost. He receives the expected outcome of only x1  x 2
because the new agent is inexperienced. The expected amount of cash compensation paid is
fc2 + pc2. In addition, he pays non-cash compensation of fn2$/ 2P unit, which costs him $
fn2$.
Consider the optimal spot contracts derived in Section 4.1. If the principal hires another
agent, his payoff is x1 - U – v(a=1). If the principal accommodates, his payoff is x 2 - [fc1 +
pc1 + 2P( fn1$/P1)]. The principal chooses to accommodate when
  2P
( x2  x1 )  R  f 1  P
 1
$*
n1




[uˆ n 2 ( f n$2* )  f n$2* ]  [uˆ n1 ( f n$1* )  f n$1* ]
(4.1).
In other words, the principal accommodates when the difference in productivity between the
experienced and inexperienced agent and the recruitment cost are sufficiently large, and
when the cost of non-cash to the principal is decreasing, i.e., 1P > 2P.
At node A1, if the agent accepts the offer, her expected payoff is fc2 + pc2 + un2(fn2$/ 2P). If
the agent fights and the principal accommodates, her payoff is fc1 + pc1 + un2(fn1$/ 1P). If
the agent fights and the principal fires her, she finds a job which pays at her reservation
utility elsewhere. She also incurs the cost of job-finding J. The optimal contract derived in
Section 4.1 is such that the agent receives her reservation utility with (fc2*, c2*, fn2$*).
Therefore, if the agent anticipates that the principal will fight, she will not fight. If she
anticipates that the principal will accommodate, she will fight when her payoff from the
period-one spot contract is greater than that from the period-two spot contract offered, i.e.,
when
un2(fn1$*/ 1P) - un1(fn1$*/ 1P) >
0
(4.2).
Intuitively, the period-one contract pays the agent equal to her reservation utility in the first
period. In the second period, if her utility function un2 shifts up, the same quantity of noncash compensation fn1 = fn1$*/ 1P will result in higher utility. If the amount of cash payment
31
remains the same, she receives more than her reservation utility by the amount un2(fn1*) un1(fn1*). Therefore, she prefers the first-period spot contract in the second period.
At node A1, if un2(n) < un1(n) for all n  R+, the agent does not prefer the first-period spot
contract to the second-period contract (whether she expects the principal to accommodate or
not). Therefore, the agent’s resistance is not a problem. At node P1, the principal can offer
the first-best spot contract for period two (derived in Section 4.1) and it will be accepted.
When un2(n) > un1(n) for all n  R+, but x 2  x1  R is small so that condition (4.1) is not
true, the agent anticipates that the principal will fight. As a result, she will not fight even
though she prefers the period-one contract. Again, resistance is not a problem. The first-best
period-two spot contract will be accepted by the agent.
When un2(n) > un1(n) for all n  R+ and x 2  x1  R is large9, the agent prefers the periodone contract and the principal is better off accommodating. Anticipating the principal will
accommodate, the agent will ask for the first-period contract. If the principal chooses to offer
the first-best period-one spot contract in the first-period, he will also use it in the second
period because of the agent’s resistance. Alternatively, he may want to offer other spot
contracts in both periods to minimize the damage from the agent’s resistance. Either way, his
payoff will be less than the payoff when the agent cannot resist.
If the principal and the agent can commit to a long-term relationship and the principal can
commit to a long-term contract he offers, the principal can solve this problem by decreasing
the amount of cash payment in the first-period and increasing the amount of cash payment in
the second-period, as shown in Appendix 2. Another way to solve this problem is to use
informal compensation, as discussed below.
9
When un2(n) > un1(n) for all n  R+ and 1P > 2P, we have uˆ n 2 (n $ )  uˆ n1 (n $ ) for all n$  R+, which
implies that fn2$* > fn1$* and that the right-hand-side of (4.1) is positive. Condition (4.1) is true when
x 2  x1  R is large.
32
4.3 Informal Cash Compensation
In practice, formal pay is more rigid and more difficult to change. For example, unions exist
in many organizations so that a large number of employees can join forces to resist
unfavorable changes in cash or non-cash compensation. Informal compensation is less rigid
for many reasons. For example, informal compensation is often paid to a small number of
employees.
Mars (1982), for instance, reports that the hidden economy (informal and
illegal) rewards “are usually allocated on an individual basis through an individual contract
with a specific contract-maker – usually a first-line supervisor.” (p. 8). Thus, employees paid
informally do not have much collective bargaining power to negotiate informal
compensation. Also, consider illegal or immoral informal pay. By negotiating the illegal or
immoral informal pay with her employer, an employee overtly admits she has done
something “wrong”. Her confession can be used against herself in the future. This, in
practice, could prevent many employees from bargaining for informal compensation. In
addition, practically, we can negotiate our salaries but generally cannot negotiate the
reimbursement policy, or the control over other organizational resources, which determines
the amount of informal pay. Therefore, I assume that there are two ways to pay: formal and
informal. Formal compensation is more rigid and subject to resistance from the agent. On the
contrary, I assume that the agent cannot resist the change in informal pay.10
Let fct = fctf + fcti where fctf and fcti are the fixed cash wages paid formally and informally,
respectively. The resistance-proof spot contract pays the agent informally in the first period.
fnt$RP
such that uˆ nt ( f nt$RP ) = uct(fctRP) = 1, i.e., fnt$RP = fnt$ *
nt$RP =
nt$*
fctRP
=
U + v(a=0) - uˆ nt ( f nt$ RP ) with
fc1RP
=
fc1 f RP + fc1i RP

[u n 2 ( f n$1 RP /  1P )  u n1 ( f n$1 RP /  1P ), U  v(a  0)  uˆ n1 ( f n$1RP )]

if u n 2 ( f n$1RP /  1P )  u n1 ( f n$1RP /  1P )  0,

0
otherwise,

fc2*
=
f ci1RP
fc2RP
10
=
=
0,
U + v(a=0) - uˆ n 2 ( f n$2RP ) ,
Admittedly, the analysis will be more rigorous if we can create a model that explains why the agent does
not find it optimal to resist changes in informal pay or why it is optimal for the principal not to accommodate
the agent’s bargaining over informal compensation. I am currently working on this issue.
33
ctRP
=
ct*
=
v/p.
The fixed non-cash wages and bonuses, the cash bonuses, and the second-period fixed cash
wage are similar to those characterized in Section 4.1 above. The difference is that now the
principal pays the period-one fixed cash wage both formally and informally. The formal
compensation is such that the agent is weakly better off in the second period with the periodtwo contract than with the period-one contract.
Lemma 1: In a two-period setting, the principal is better off with an option to pay informally
if
(i)
the principal and the agent cannot commit to a long-term relationship, i.e., the
principal can only offer a spot contract in each period;
(ii)
the agent has bargaining power to resist the change from period-one spot contract
to period-two spot contract; and
(iii) the concave utility with respect to the quantity of non-cash compensation shifts up
in the second period, while the linear utility with respect to cash remains the same.
4.4 Informal Non-cash Compensation
Previously we considered the case where the utility from cash is linear while the utility from
the dollars spent on non-cash is concave. In this section, I consider another polar case,
where the utility from the dollars spent on non-cash is linear, i.e. uˆ nt (n $ ) = btan$, while the
utility from cash uct is concave. For simplicity, let uˆ n1  uˆ n 2 and un1 = un2. I repeat the
analysis done in Sections 4.1 to 4.3. I find that the principal can solve the resistance problem
by paying part of the period-one fixed non-cash wage informally.
In the setting where both uct and û nt are concave, the analysis is much more complicated. In
addition to the resistance problem, we have to consider consumption-smoothing issues and
renegotiation to increase the total welfare ex post by eliminating the incentive risk after the
action is taken. In such a setting, given the results shown above, I anticipate the use of both
cash and non-cash informal compensation to solve the resistance problem.
Lemma 1 and Section 4.3 give examples of the settings in which the principal may want to
use informal compensation to solve resistance problems. This leads to Proposition 7 below.
34
Proposition 7: In multi-period settings, if the principal and the agent cannot commit to a
long-term relationship, i.e., the principal can only offer a spot contract in each period; and
the agent has bargaining power to resist the changes in spot contracts from period to period,
the principal is weakly better off with an option to pay informally.
V. The Use of a Subjective Bonus When the Performance Measure Is Not Verifiable
In addition to flexibility, the principal pays informally because he wants to gain some power
over the agent to promote cooperation, to deter undesirable actions, etc. In particular, this
section considers the case where the principal wants to prevent employee litigation. In the
US, employee litigation has become a real problem for employers. According to Doyle and
Kleiner (2002), the punitive damages awarded to plaintiffs are on average $2,875,000, and
the incidence frequency is increasing. The most frequent lawsuits are those related to
discrimination. Webster (1988) argues that the firm’s employee-evaluation practice is
commonly used to prove discrimination. The more subjective and ambiguous the evaluation,
the more likely the firm will lose the case.
To study discrimination litigation, I consider a setting where the performance measure (i.e.,
the outcome from production) is observable to both the principal and the agent but is not
verifiable to the courts11. Also, I assume that there is no other informative signal about the
agent’s effort. Because the performance measure is not verifiable to the third party, the
contract based on such a measure cannot be enforced by the courts. After the agent has
chosen the desired level of effort a = 1 and the high outcome is realized, the dishonest
principal has an incentive to renege by not paying the promised bonus. Thus, we have a
commitment problem on the principal’s side. On the other hand, the agent may have an
incentive to shirk (and receive the low outcome and thus no bonus for sure) and then sue the
principal for discrimination in performance evaluation. The principal cannot prove to the
courts that the bonus is not paid because the outcome realized is low, not because of
discrimination.
11
Examples of this kind of performance measure include the satisfaction obtained from the job performed
by an employee, the quality of the article written by a journalist, etc.
35
Since the issue of interest here is the use of informal pay to deter employment litigation, I
assume that the principal can only pay in cash. For simplicity, I also assume that the agent’s
utility is linear in cash.
5.1 The Optimal Subjective Bonus Plan with No Employment Litigation
In this section, I assume that there are two types of principal: honest and dishonest. The type
is not known to the agent, but she knows that the principal is honest with probability  and is
dishonest with probability 1- . If the honest principal reneges by not paying the bonus
when the outcome is high, he suffers from guilt so that his payoff becomes -. The dishonest
type, on the contrary, incurs no guilt at all. Note that the dishonest type has no incentive to
offer a different contract to signal that he is dishonest. By imitating the honest principal, the
dishonest one obtains the gain from reneging later on.
Anticipating the honest type will honour the contract and the dishonest type will renege, the
agent will choose a = 1 if the following is satisfied:
(ICa)
f + p - v(a=1)

f – v(a = 0).
The minimal  that satisfies (ICa) is   = v/p. To induce the agent to accept the contract,
the fixed wage f is chosen to satisfy the agent’s participation constraint (PCa):
f + p - v(a=1)

U.
The lowest f satisfying (PCa) is the first-best fixed wage f  = U + v(a=0). The honest type’s
expected payoff is x  U  v(a  1)  v(
1

 1) , which is lower than the first-best payoff
with contractible performance measure, x  U  v(a  1) . The dishonest type’s expected
payoff is x  U  v(a  0) , which is higher than the first-best payoff. The existence of the
dishonest type renders the honest type worse off.
5.2 The Optimal Subjective Bonus Plan with Employment Litigation
5.2.1 The Agent Has Unlimited Liability
Here I assume that the agent has unlimited liability and there is no lower bound on the
compensation. The agent can sue the principal if she is not paid a bonus, whether she has
chosen a = 0 or a = 1. Let D denote the expected gain from the discrimination lawsuit to the
36
agent, whether the agent has chosen a = 0 or a =1.12 Assume that there are no deadweight
litigation costs to the agent (e.g. the agent and her lawyer can agree to a contract in which
they will share the gain from litigation if they win but in which the lawyer is responsible for
costs if they lose.) Assume for simplicity that D is also equal to the loss to the principal. If
the expected gain from the lawsuit is positive, the agent will always sue if she is not paid the
bonus. The principal cannot prevent the lawsuit. It also becomes more difficult to induce a =
1, since the agent’s other option is to choose a = 0 and then sue the principal at the end of
the period. The contract (f ,  ) in Section 5.1 can no longer induce a = 1. Anticipating the
agent will sue if she is not paid the bonus, the principal then increases the bonus to induce a
= 1 and reduces the fixed wage accordingly. Below are the agent’s participation constraint
(PCa)D and incentive compatibility constraint (ICa)D. The incentive compatibility constraint
ensures that the agent’s expected payoff if she chooses a = 1 (and receives the bonus if the
outcome realized is high and the principal is honest, but receives no bonus otherwise), and
then sues the principal if the bonus is not paid, is greater than her payoff if she chooses a = 0
and then sues the principal to get the expected gain D.
(PCa)D
(ICa)D
f + p + p(1-)D + (1-p)D - v(a=1)
f + p + p(1-)D + (1-p)D - v(a=1)
p



U.
f + D – v(a = 0), or
v + pD.
The optimal fixed wage and bonus are thus f D = U + v(a=0) – D, and  D = v/p + D.
With this compensation scheme, the agent chooses a = 1 and sues if the bonus is not paid.
She receives only her reservation utility. The honest (dishonest) principal’s payoff is similar
to that when the agent cannot sue the principal. The principal is not worse off with employee
litigation.
Importantly, the above result - that the principal is not worse off with employee litigation - is
based on the assumption that the agent’s utility with respect to cash is linear and that she has
unlimited liability. If there is some lower bound on the fixed compensation and the gain
12
Note that the agent’s action is not verifiable and I previously assume that there is no other signal that is
informative about the agent’s action. Therefore the agent cannot prove to the courts that she has worked
diligently. As a result, I assume that the expected gain from the suit is similar whether the agent has chosen a =
0 or a =1.
37
from the discrimination lawsuit is large such that f
D
= U + v(a=0) – D is less than the
lower bound, the principal is worse off with litigation.
5.2.2 The Agent Has Limited Liability
When the agent has very limited liability or the lower bound on the compensation is rather
large, one way to solve the litigation problem is to pay part of the fixed wage informally.
The nature of the informal pay is necessarily “dark”, i.e., it should be illegal or immoral so
that the agent does not want the public to know about it. If the agent sues the principal, the
principal can prosecute the agent. He can argue that the bonus is not paid not because of
discrimination but because of the agent’s misbehaviour. This strategy will potentially reduce
the agent’s chance of winning the discrimination suit and hence reduce her expected gain
from the suit. If the loss (monetary, or non-monetary, e.g. reputation loss) from being
prosecuted is sufficiently large, the principal’s option to prosecute can deter the agent from
suing the principal. In fact, the principal may not have to go so far as prosecuting the agent.
He may simply threaten to fire the agent and notify the media and other potential employers
that the agent has misappropriated the principal’s assets, all of which may be sufficient to
deter the lawsuit.
To illustrate, the Sue/Prosecute subgame between the principal and the agent, after the agent
has realized that the bonus is not paid, is as shown below.
Prosecute
Sue
P
Not
Prosecute
A
Prosecute
Not Sue
[D - d(i) - GP(t) - h(t),
GP(t) - P - (D - d(i)) ]
[D, -D]
[-GP(t) - h(t),
GP(t) - P]
P
[0, 0]
Not
Prosecute
Figure 3: The Sue/Prosecute Subgame
38
Concerning the discrimination lawsuit, D denotes the gain from the discrimination lawsuit to
the agent and the loss to the principal when that principal does not prosecute the agent. If the
principal prosecutes the agent for misappropriation after the agent sues the principal, I
assume that the potential gain the agent receives decreases by the amount d(i), where i is the
degree to which the control system can produce evidence to convict the agent. When the
control is more rigorous, it is more likely to be able to produce the evidence to convince the
courts that the firm has taken proper actions to deter theft and that the agent has
misappropriated. Regarding the misappropriation lawsuit, let t denote the amount
appropriated (or “theft”) and GP(t) denote the expected gain the principal receives from
prosecuting the agent (increasing in t)13, while P denotes the prosecution cost to the
principal. If prosecuted, in addition to paying the expected loss GP(t) to the principal, the
agent also incurs the cost of reputation loss h(t). Examples of h(t) include difficulties in
finding a new job due to the litigation, the disutility from shame, etc.
In order to sustain the subjective bonus scheme and also to deter the agent from initiating the
discrimination lawsuit, we would like (Not Sue, Not Prosecute) to be the only equilibrium of
the game. Therefore, the principal must choose (i, t) such that
(i)
If the agent does not sue, the principal will not prosecute, i.e.,
GP(t) – P
(ii)
< 0;
If the agent sues, the principal will prosecute, i.e.,
GP(t) – P – (D - d(i))
(iii)
> -D;
Given that the principal will not prosecute if the agent does not sue but will
prosecute if the agent sues, the agent chooses not to sue, i.e.,
D – d(i) – GP(t) – h(t)
<
0.
In general, if h(t) is sufficiently large, the agent will not sue the principal ex post. After
choosing the appropriate (i, t), the principal’s optimization problem becomes that as if the
gain from the lawsuit to the agent was exogenously assumed to be zero, as shown in Section
5.1. Note that it is important to choose t and i such that without a trigger event (a
discrimination lawsuit), prosecuting the agent is not optimal. If it is optimal ex post to
prosecute the agent, the agent will not appropriate the asset, and she will still have an
13
In fact, the principal can control GP(t) by choosing the degree of illegality or immorality. The amount
GP(t) will be higher for the outright illegal or immoral pay than for the perhaps-illegitimate pay.
39
incentive to sue the principal. However, if the agent ex post does sue the principal, the
principal must be at least weakly better off prosecuting the agent. Therefore, the amount of
informal compensation and the control must be such that if the agent does not sue, the gain
from prosecution is non-positive. There is an upper bound for the informal compensation.
This explains why we generally do not observe an organization that pays only informally,
despite the fact that the informal compensation is tax-free to the agent but mostly taxdeductible to the principal.
As for the control, to pay the “dark” informal compensation, the control implemented must
be adequately weak to facilitate the “theft” of certain organizational resources, yet
sufficiently strong to limit the “theft” to a particular resource, to a certain employee, and to a
certain amount (i.e. sufficiently strong to prevent and detect unwanted thefts.).
In addition to the prevention and detection aspects of the control, the principal also needs to
consider the conviction aspect. The control must be sufficiently weak not to give hard
evidence of the “misappropriation” very easily and inexpensively, but adequately strong to
give evidence in the investigation with some cost. If the control can produce conviction
evidence easily and with minimal additional cost (e.g. if the principal installs surveillance
cameras everywhere), ex post the expected gain from prosecution to the principal will be
positive. Anticipating the principal will prosecute, the agent will not accept the informal pay
and hence will still have an incentive to sue. On the other hand, with further investigation,
the control must be able to produce convincing evidence. Therefore, the agent knows if she
sues the principal, the principal can show the evidence to the courts and argue that the bonus
was not paid not because of discrimination, but because of the agent’s misconduct.
Note that wage bargaining and employee litigation are simply the agent’s attempt to extract
some wealth from the principal. They do not have any productive value but are costly to
those involved. The costs of bargaining (which may involve strikes) or lawsuits reduce the
total welfare of the two contracting parties. The total welfare will be higher if either the
agent can commit not to initiate wage bargaining or not to sue the principal - or the principal
can commit to pay the agent the amount called for without a fight. Hence, the use of
informal payments to deter opportunism can improve total welfare. The results in this
section are summarized in Proposition 8 below.
40
Proposition 8: Assume that the performance measure is not verifiable and the principal may
be liable for discrimination lawsuits. When the agent has limited liability and her expected
gain from suing the principal is positive,
(i)
the principal is better off with an option to pay informally,
(ii)
ceteris paribus, the greater the expected gain from a discrimination lawsuit, the
greater the amount of optimal informal compensation and the higher the degree to
which the control can produce evidence to convict the agent, and
(iii)
the amount of the informal compensation and the characteristics of the control
must be such that the gain from prosecution is non-positive when the agent does
not sue, and vice versa.
Caveats
In the analysis above, I assume that any level of control is available to the principal at no
cost. In reality, control is imperfect and is costly. The difficulty and cost of control are
different for various organizational resources. I anticipate that, for informal compensation,
the principal will choose an organizational resource of which the potential damage from
unwanted theft is small.
Additionally, I assume that there is no cost for using “dark” informal compensation. In
practice, public companies may incur some cost for using “dark” informal compensation.
Investors and other outside stakeholders may not fully understand the optimality of the use
of informal pay and hence may interpret the informal pay as agency costs. This can lead to
reputation losses (and possibly litigation) if the use of informal compensation becomes
publicly known. The cost of using informal compensation may be larger in certain industries
where a reputation for being honest and transparent is important in attracting the customers.
Examples include the banking and auditing industries. When this cost exists, the principal
pays “dark” informal compensation when the gain outweighs the expected cost.
VI. Concluding Remarks
The main idea in this paper is that the compensation decision is multi-dimensional. I address
two important aspects of compensation: cash vs non-cash and formal vs informal. In part
one, I show that the composition of compensation is determined by the agent’s utility, her
reservation utility, the economy of scale in providing the non-cash compensation, and the
production technology. In part two, I examine a setting where, as time passes, the agent
41
gains some bargaining power, whether it comes from the skills or knowledge that she
acquires or from her ability to misuse the employee protection the state provides. When an
employer needs flexibility to change the compensation according to the changing business
environment, the prior formal agreement with an employee individually or with the union
can be cumbersome. I show that the employer can avoid the labor conflicts ensuing from the
change in compensation by paying informally. Also, I demonstrate that the principal can use
informal compensation to deter the misuse of legal employee protection.
In this paper, I focus my analysis on a setting in which the agent’s preference is additively
separable in cash and non-cash compensation. Future research that considers a more general
preference and relaxes the assumption that the agent’s preferences are known to the principal
will help us better explain the use of non-cash compensation in the real world. Also, very
little is known about how a business selects which organizational resources to pay informally
and how it restrains “theft” or “abuse of control” to a desired level. A further formal analysis
and field research will contribute much to our knowledge of informal compensation.
42
Appendix 1: A Case Study on Non-cash and Informal Compensation
This case studies the use of non-cash and informal compensation in a private pharmaceutical
manufacturer in Bangkok, Thailand. The data were collected in July and August, 2004,
through an interview with the production manager and in Dec, 2004 through a questionnaire.
Background Information
The family-owned partnership produces pharmaceutical products for local consumption and
also for export to neighboring countries. It employs 289 employees with the total assets of
about US$ 3 million. The workforce consists of skilled lobour paid monthly and unskilled
labour paid daily.
Formal Compensation
The formal cash compensation includes a monthly salary or a daily wage, a cash bonus paid
every Chinese New Year to all employees, and a cash bonus for good performance. For
certain jobs (i.e. medicine coating), accurate monitoring is not possible. In particular, there is
naturally an idle time during the production process (waiting for a certain task to be done by
the machine), and there are random factors other than carelessness and unskillfulness that
lead to defective outcomes. Mistakes are also costly. In addition to salary, these employees
will be paid an additional bonus called “assurance money” for satisfactory production
outcomes finished in time.
The formal non-cash compensation includes fringe benefits required by law like health
insurance, a yearly medical check-up, and paid leaves. It also includes the productivityenhancing compensation such as training programmes, and food and lodging. An executive
is also paid in terms of a better office, a better paid vacation, and secretarial service. The
social activities which are believed to help increase the productivity are a birthday party
arranged monthly for all the employees born in that particular month, and a monthly Tuk
Bart ceremony where employees and executives respectfully give food to Buddhist monks.
In providing the non-cash compensation, the business does not seem to benefit much from an
economy of scale.
The business does not pay its employees in terms of defective or overstocked products,
because in Thailand drugs are legally banned from distribution without pharmacists’
approval. One exception is in the case of employees’ minor illnesses. The pharmacists at the
43
plant can issue some medicine for immediate use. The medicine given away is the flawed or
excess product that cannot be sold.
The use of non-cash compensation in this business seems to be consistent with the
theoretical prediction, i.e., the business includes in compensation portfolios the non-cash
items which are necessary for survival and/or are productive. Also, an executive receives
more various non-cash items as compensation.
Informal Compensation
The informal reward includes the cash paid to important employees in various departments
(e.g. the department head or some other significant employee) and to employees in the
mixing department, for satisfactory work and ability to solve problems. The founder-owner
simply adds the amount of this informal pay to be distributed into the production manager’s
monthly salary. The production manager then distributes this amount himself.
This idea was originally initiated by the production manager to solve the turnover problem in
the mixing department. Today, the majority of employees paid informally are in the mixing
department. The mixing job is extremely tiring (but this fact is not necessarily known to
others). Absenteeism is high, because the workers need to rest. The turnover rate is high
because of the hard work. This had been very problematic in the past. The production
manager solved this problem by paying cash informally to compensate the workers for their
hard labor. This system works well; absenteeism and turnover have decreased.
The informal cash compensation is paid not only to the mixing workers, but also to the heads
and key employees in various departments. The production manager chooses not to ask the
department heads or supervisors to distribute the money, but does it himself, for fear of
embezzlement and because he wishes to maintain some power over those key employees.
The informal pay makes the payees more cooperative and more responsive to the production
manager’s orders, especially those related to the job beyond their job descriptions or the job
for which a formal order is not issued yet. Furthermore, he chooses to pay informally
because this method is more flexible.
44
Flexibility seems to be an important motive. In fact, the business even changes the employee
evaluation and compensation practices yearly to prevent the employees from resisting the
changes by arguing that the current practices are the organizational norms or tradition.
The employees are told that the informal compensation is not to be expected monthly – it is
paid only at the discretion of the employer and it can be cancelled at any time. Also, it is
paid to a rather small number of employees so that it is less likely that they can join force to
resist the change in informal compensation. The amount of informal pay is not large (around
3% – 6% of the monthly salary) - i.e., there is no real tax benefits from paying informally,
but it is effective in motivating good performance and cooperation.
The theoretical prediction is that the amount and the “darkness” of informal pay should be
increasing in the power the payer requires. In this setting, the production manager simply
wants to elicit better cooperation. The informal compensation is legal and moral, and the
amount is not very large. Also, the production manager can very well control the payee, and
the amount and frequency of pay, because he pays this informal compensation himself. The
founder-owner can perfectly control the total amount of pay since it is he who adds that
amount of money into the production manager’s salary.
Appendix 2: The Optimal Two-period Contract with Full Commitment
Here, I assume that the principal can commit to a long-term contract offered. As before, I
assume that the agent has a time-additive utility function, and her preference with respect to
cash is linear, but her preference with respect to the dollars spent on non-cash compensation
is concave. Also, the non-cash is not productive and is not available from the external
market. The unit cost of non-cash compensation to the principal is constant and is denoted
by Pt, t = 1, 2. The agent cannot save the non-cash from one period to consume in another.
Note that since the periods are independent and the agent’s utility is linear with respect to
cash, the bonuses are paid in cash and no risk premium is paid. Without loss of generality, I
consider a simple contract where the second-period compensation is based only on the
second-period outcome, rather than one where the second-period compensation is based on
both the first-period and second-period outcomes.
45
A2.1 The Agent Cannot Resist the Change in Compensation Plan
When the agent cannot resist the change in compensation schemes, the principal’s
optimization problem is as follows:
Max U P ( f ,  , a  (1,1))
f ,

x1  x 2  [ f c1  p c1  f n$1  p n$1 ]  [ f c 2  p c 2  f n$2  p n$2 ]
subject to
( PC a )
U a (a  (1,1))

2U
( IC1a )
U a (a  (1,1))

U a (a  (0,0))
( IC 2a )
U a (a  (1,1))

U a (a  (0,1))
( IC 3a )
U a (a  (1,1))

U a (a  (1,0))
( IC 4a )
where
f c 2  p c 2  (1  p ) uˆ n 2 ( f n$2 )  p uˆ n 2 ( f n$2   n$2 )  v(a  1)  f c 2  uˆ n 2 ( f n$2 )  v(a  0)
Ua(a =(1,1)) ≡ fc1 + fc2 + p(c1 + c2) + [(1 - p) uˆ n1 ( f n$1 ) + p uˆ n1 ( f n$1   n$1 ) ]
+ [(1 - p) uˆ n 2 ( f n$2 ) + p uˆ n 2 ( f n$2   n$2 ) ] – 2 v(a=1)
Ua(a=(0,1)) ≡ fc1 + fc2 + pc2+ uˆ n1 ( f n$1 )
+ (1 - p) uˆ n 2 ( f n$2 ) + p uˆ n 2 ( f n$2   n$2 ) – v(a=0) – v(a = 1)
Ua(a=(1,0)) ≡ fc1 + pc1 + fc2 + (1 - p) uˆ n1 ( f n$1 ) + p uˆ n1 ( f n$1   n$1 )
+ uˆ n 2 ( f n$2 ) – v(a=1) – v(a=0)
Ua(a=(0,0)) ≡ fc1 + fc2 + uˆ n1 ( f n$1 ) + uˆ n 2 ( f n$2 ) – 2 v(a=0)
The participation constraint (PCa) is to make sure that the agent will accept the contract,
while the incentive compatibility constraints (ICa)s are to ensure that the agent is weakly
better off choosing a = 1 in both periods.
The results from Section 3.1 indicate that when there is no wealth effect associated with the
cash wealth but û nt is concave, the principal will not pay a non-cash bonus. Therefore, to
simplify the analysis, let n1 = n2 = 0. With (PCa) and (ICa)’s binding, we have
c1 = c2 = v/p, and
fc1 + fc2 = 2(U + v(a=0)) – uˆ n1 ( f n$1 ) - uˆ n 2 ( f n$2 ) .
46
Substitute the above into the objective function and solve for the optimal non-cash fixed
wages. The interior solution is as shown below. For t = 1, 2,
fnt$*
such that uˆ nt ( f nt$* ) = uct(fct*) = 1,
nt$*
=
0,
any (fc1*, fc2*) such that
fc1* + fc2* = 2[U + v(a=0)] - uˆ n1 ( f n$1* ) - uˆ n 2 ( f n$2* ) , and
ct*
=
v/p.
Because we assume that the agent’s utility with respect to cash is linear, given the contract
derived above, the agent has no incentive to borrow or lend. Also, since no risk premium is
paid here, there is no room for ex post beneficial renegotiation to increase the total welfare
of the two parties by removing the incentive risk after the action is taken. Below, I assume
that the agent can resist the change in compensation plans at the beginning of the second
period.
A2.2 The Agent Can Resist the Change in Compensation Plan
Now assume that, due to the firm-specific skills and knowledge she acquires in the first
period, the agent has bargaining power to resist the change the compensation plan. If the
agent is better off with the period-one compensation scheme, the agent can pressure the
principal to continue to use the period-one scheme.
With the agent’s bargaining power, we need to add one more constraint to the principal’s
problem above to ensure that the long-term contract characterized is resistance-proof. The
resistance-proof constraint (RP) below is to ensure that in the second period, the agent is
weakly better off with the period-two scheme than with the period-one scheme. In the
second period, if the first-period scheme [proposed second-period scheme] is used, the agent
receives fc1 and c1 [fc2 and c2] as cash compensation and fn1 = fn1$/1P and n1 = n1$/1P [fn2
= fn2$/2P and n2 = n2$/2P] as non-cash compensation. The resistance-proof contract is
such that the agent weakly prefers the proposed second-period scheme.
( RP )
f c 2  p c 2  (1  p) u n 2 ( f n$2 /  2P )  p u n 2 (( f n$2   n$2 ) /  2P )  v(a  1)
 f c1  p c1  (1  p) u n 2 ( f n$1 /  1P )  pu n 2 (( f n$1   n$1 ) /  1P )  v(a  1)
47
Substituting the interior solution from Section A2.1 into (RP), the interior solution that is
resistance-proof is as follows:
fnt$RP
such that uˆ nt ( f nt$RP ) = uct(fctRP) = 1,
nt$RP =
0,
any (fc1RP, fc2RP)
such that
fc1RP + fc2RP = 2[U + v(a=0)] - uˆ n1 ( f n$1RP ) - uˆ n 2 ( f n$2RP ) , and
ctRP
fc2RP

U + v(a=0) - uˆ n 2 ( f n$2RP ) + ½[ uˆ n 2 ( f n$1RP ) - uˆ n1 ( f n$1RP ) ], or
fc1RP

U + v(a=0) - uˆ n1 ( f n$1RP ) - ½[ uˆ n 2 ( f n$1RP ) - uˆ n1 ( f n$1RP ) ],
=
v/p.
Notice that the fixed non-cash wages and the cash bonuses are similar to the solution in
Section A2.1, i.e. fnt$* = fnt$RP and ct* = ctRP. Only the fixed cash wages are different.
The resistance-proof solution is such that the agent receives less than her reservation in the
first period, but more than her reservation utility in the second period when
[ uˆ n 2 ( f n$1RP ) - uˆ n1 ( f n$1RP ) ]

0.
This condition is always true if the non-cash utility functions are such that
uˆ n 2 (n $ )  uˆ n1 (n $ )  n$  R+. The function uˆ n 2 is dependent on the agent’s valuation of the
non-cash and on the cost of the non-cash to the principal. The increase in the agent’s
valuation of the non-cash and the decrease in the cost of the non-cash to the principal shift
the utility û nt up.
Appendix 3: Proofs of Propositions 4 and 6
Proof of Proposition 4
The settings in which either utility function with respect to cash or the dollars spent on noncash is linear are discussed in Section 3.1.2.1. Here, consider the setting where both the
agent’s utility with respect to cash uc and her utility with respect to non-cash û n are concave
(and ĝ is weakly concave). Consider the first-order conditions with respect to fn$ and n$
below.

$*

gˆ ( f n$ ) x  (1  p ) [ wc (U  v(a  0)  uˆ n ( f n )) uˆ n ( f n$* ) ]
fn$:
v

$*
$*

 p [ wc (U  v(a  0) 
 uˆ n ( f n   n )) uˆ n ( f n$*   n$* )]  1.
p
48
n$*:
v


p [ wc (U  v(a  0) 
 uˆ n ( f n$*   n$* )) uˆ n ( f n$*   n$* ) ]  p .
p
Let (fn$**, n$**) denote the solution where the non-cash compensation is not productive.
Consider the first-order conditions with respect to fn$. With an additional marginal product
term, we need higher values of fn$ or n$ than (fn$**, n$**) for the condition to satisfied.
Consider the first-order condition with respect to n$; with (fn$**, n$**),
v


p [ wc (U  v(a  0) 
 uˆ n ( f n$**   n$** )) uˆ n ( f n$**   n$** ) ]
p

p.
With both fn$ > fn$** and n$ > n$**,
v


p [ wc (U  v(a  0) 
 uˆ n ( f n$   n$ )) uˆ n ( f n$   n$ ) ]
p

p.
So we need either fn$ > fn$** but n$ < n$** or vice versa. But if the non-cash bonus is not
productive and û n is concave, the principal is better off increasing fn$ but decreasing n$.
Proof of Proposition 6
The optimal non-cash pay when the agent does not have access to the non-cash market is fn**
 **
**
**
such that x g ( f n )  u n ( f n )  K P ( f n ) , and n** = 0.
Let the marginal utility with respect to non-cash compensation represent the incremental
utility the agent receives from one more unit of non-cash. If the agent purchases one more
unit of non-cash, the incremental benefit is approximately un(fn**) = KP(fn**) - x g ( f n ) .
**
The incremental cost is approximately (1+)KP(1). If the principal can benefit from an
economy of scale, i.e.,  > 0, and KP is linear or mildly convex, the incremental cost
(1+)KP(1) > KP(fn**) > un(fn**). Thus, the agent will not purchase the non-cash. If  < 0,
(1+)KP(1) < KP(fn**) = un(fn**)+ x g ( f n ) . The incremental cost to the agent is less than
**
the incremental benefit when x g ( f n ) is small and when | | is large.
**
 **
**
**
With q > 0, x g ( f n )  u n ( f n  q)  K P ( f n ) . The optimal contract should be such that
 *
*
*
x g ( f n )  u n ( f n  q)  K P ( f n ) . Therefore, the principal optimally reduces the fixed noncash wage from fn** to fn*. Accordingly, the principal increases the fixed cash wage to satisfy
the participation constraint.
49
References
Doyle, Tanya and Brian H. Kleiner. 2002. Issues in Employment Litigation. Managerial
Law 44(1-2): 151-155.
Greenberg, Jerald and Kimberly S. Scott. 1996. Why Do Workers Bite the Hands that Feed
Them? Employee Theft as a Social Exchange Process. Research in Organizational
Behavior: An Annual Series of Analytical Essays and Critical Reviews, 18: 111-156.
Hashimoto, Masanori. 2000. Fringe Benefits and Employment. In William T. Alpert and
Stephen A. Woodbury (Eds.), Employee Benefits and Labor Markets in Canada and
the United States, Kalamazoo, Michigan: W.E. Upjohn Institute for Employment
Research.
Keeney, Ralph L. and Howard Raiffa. 1993. Decisions with Multiple Objectives:
Preferences and Value Tradeoffs. Cambridge, UK: Cambridge University Press.
Lee, Gerald, Zoltan Matolcsy, and Peter Wells. 2004. The Compensation-Performance
Relation in China for State Dominated Enterprises and Non-State Dominated
Enterprises. Working Paper, University of Technology, Sydney, Australia.
Long, James E. and Frank A. Scott. 1982. The Income Tax and Nonwage Compensation.
Review of Economics and Statistics, 64(2): 211-219.
Marino, Anthony M. and Ján Zábojník. 2003. In-kind Payments as a Compensation Strategy.
Working Paper, University of Southern California.
Mars, Gerald. 1982. Cheats at Work: An Anthropology of Workplace Crime. London:
George Allen & Unwin Ltd.
Murray, Carla Tighe. 2004. Military Compensation: Balancing Cash and Non-cash Benefits.
Economic and Budget Issue Brief: A series of issue summaries from
the Congressional Budget Office. January 16, 2004. (Available at
http://www.cbo.gov/showdoc.cfm?index=4978&sequence=0).
Rosen, Sherwin. 2000. Does the Composition of Pay Matter? In William T. Alpert and
Stephen A. Woodbury (Eds.), Employee Benefits and Labor Markets in Canada and
the United States, Kalamazoo, Michigan: W.E. Upjohn Institute for Employment
Research.
Webster, George D. 1988. The Law of Employee Evaluations. Association of Management
40(5): 118-119.
Wells, Joseph T. 1997. Occupational Fraud and Abuse. Texas: Obsidian Publishing
Company, Inc.
Zeitlin, Lawrence R. 1971. A Little Larceny Can Do a Lot For Employee Morale.
Psychology Today, June: 22-26, 64.