Status and Incentives
ABSTRACT Parker and Van Praag (2009) showed, based on theory, that the group status of the profession ‘entrepreneurship’ shapes people’s occupational preferences and thus their choice behavior. The current study focuses on the determinants and consequences of the group status of a profession, entrepreneurship in particular. If the group status of entrepreneurship is related to individual choice behavior, it is policy relevant to better understand this relationship and the determinants of the status of the entrepreneur. For reasons outlined in the introduction, this study focuses on (800) students in the Netherlands. We find that the status of occupations is mostly determined by the required level of education, the income level to be expected and respect. Furthermore, our results imply that entrepreneurship is associated with hard work, high incomes, but little power and education. Moreover, we find evidence that individual characteristics, such as entrepreneurship experience, vary systematically with the perceived status of occupations, thereby contributing ammunition to a fundamental discussion in the literature. Finally, we find a strong association between the perceived status of the entrepreneur and the estimated likelihood and willingness to become an entrepreneur.
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Article: The Trophy Effect[Show abstract] [Hide abstract]
ABSTRACT: By extending a typical endowment effect experiment with the possibility to win the endow-ment in a real effort contest, we found two enforcing effects that led to a complete market failure. Subjects who won the item in the competition had an extremely high willingness to accept (trophy effect). By contrast, subjects who were not successful had an extremely low willingness to pay for the same item (reverse trophy effect). We disentangle the different components of the trophy effect, compare it to similar experiments, and discuss its important economic implications.Journal of Behavioral Decision Making 12/2013; · 2.84 Impact Factor
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ABSTRACT: This paper offers a comprehensive econometric investigation of the impact of income inequality on the values endorsed by people. Using survey data from all thirty-four OECD countries over a period of almost thirty years, the following dimensions of value systems are investigated: work ethic, civism, obedience, honesty, altruism, and tolerance. In most cases, no robust effects from inequality on values are detected. However, there is evidence that a more unequal income distribution strengthens the work ethic of the population. Thus, income inequality seems to generate work incentives not only via the pecuniary reward of work but also through the symbolic reward it receives.The Journal of Economic Inequality 01/2012; · 0.81 Impact Factor
Status and Incentives
The paper introduces status as re?ecting an agent's claim to recognition in her work. It is a
scarce resource: increasing an agent's status requires that another agent's status is decreased.
Higher status agents are more willing to exert e?ort in exchange for money; better-paid agents
would exert a higher e?ort in exchange for an improved status. Results are coherent with actual
management practices: (i) egalitarianism is desirable in a static context; (ii) in a long-term
work relationship, juniors' compensations are delayed; past performances are recompensed by pay
increases along with an improved status within the organization's hierarchy.
Keywords: repeated moral hazard, internal labor markets, social status.
JEL classi?cation: D82, L23, M12, J33.
(*) ARQADE and IDEI, Université des Sciences Sociales de Toulouse, and Institut Universitaire de France.
(**) Université de Cergy-Pontoise, ThEMA and Institut Universitaire de France.
We should like to thank the editor and an anonymous referee for their fruitful comments and suggestions. We
are also indebted to seminar participants at Fourgeot seminar (Paris), Institut d'Analisi Economica (Barcelona),
Université d'Aix-Marseille 2, Université Catholique de Louvain, Université de Caen, Université des Sciences So-
ciales de Toulouse, University of Virginia, Stockholm School of Economics, Erasmus University and the partici-
pants in the workshop Social Interaction and Economic Behavior in Paris December 1999 for stimulating criticism
and comments on an early version of the paper, participants at the conference Organizational Behaviour, structure
and Change; The Economics of Personnel and Organizations in Toulouse May 2003, and especially Lucy White,
for their comments and fruitful discussions. We are thankful to Thomas Mariotti and Marie-Christine Henninger
for their help and suggestions. All remaining errors are ours.
Although economists have put out a substantial amount of research on work incentives, their
approach remains at odds with much of the management and organization literature on the
subject. The logic of using money to induce e?ort, which is the main focus of economic analysis,
is de?nitely a key feature of actual incentive packages. Yet, a mere description of monetary
incentive schemes falls short of providing a full account of management practices. Even in cases
where direct monetary incentives are used extensively they are associated with other types of
bene?ts ranging from travel or merchandize to symbolic rewards. It is for instance a common
practice to grant top sales people medals, rings, sculptures, plaques and so on, handed out
during lavish ceremonies (see Nelson 1994). It is often argued that merchandize, although a poor
substitute for money according to standard economic theory, is an e?ective means of providing
incentives because of its trophy value: it reminds the winner and others of her/his high past
performance. Wood (1998) quotes Will Ha?er vice-president of sales with Bowne-publishing,
reminiscing about winning a large screen TV: ?Actually the main reason I wanted it was that it
was the top prize. I could a?ord to buy a big screen but it was not the same as winning it.?
Whereas the above examples suggest that there are some bene?ts in stressing di?erences
among employees, the opposite point is often made that it is appropriate to adopt an egalitarian
approach by expunging symbolic di?erences (see Pfe?er, 1994). There has been a substantial
body of research, in the wake of Adams (1965), on the impact of ?unequal? or ?unfair? treatment
on work motivation. According to Adams' ?equity? theory, people react to inequity by making
up for it. For instance, they lower their input if they feel that what they obtain in return is
insu?cient relative to others around them.1While status di?erences are enjoyed by those with
a high status, they are disliked by those with a low status who, as a result, lose motivation.
Hence, recognition should not be viewed as a cheap substitute for money. It has a cost because
it is valued in relative terms: what matters is earning more recognition than others. In the
present paper we propose a simple framework in which the desirability of using status to stress
1For economic arguments against large pay di?erences see Milgrom (1988) and Lazear (1989).
di?erences among organization members can be assessed.
Typically, sociologists use social status to capture the need for social recognition. As de?ned
by Weber (1922), social status is ?an e?ective claim to social esteem in terms of negative or
positive privileges?. He insists that a status ranking is not directly related to wealth or income
though it may be a?ected by them. Thus, Veblen's theory (1899), in which status stems mostly
from relative income or wealth, is somewhat restrictive.2An opposite argument could actually
be made for the reverse causality: a higher status is the basis for earning a higher income.
There is some experimental evidence, both from psychologists (Jemmott and Gonzalez, 1989)
and economists (Ball and Eckel, 1996, Ball and Eckel, 1998, and Ball, Eckel, Grossman and Zame,
2001) that an exogenous and random distribution of status among individuals has a signi?cant
impact on their relative performance.3Belliveau et ali. (1996) study how CEO compensations
are a?ected by the CEO's status relative to that of the compensation committee chair. They
?nd that high status CEOs matched with low status compensation chairs are signi?cantly better
paid than low status CEOs matched with high status compensation chairs.
We consider a multi-agents moral hazard problem and allow for an agent's preferences to
depend directly on her status as well as income and e?ort. There is not much debate among
economists over the fact that individuals care about status. There is however some discussion
over the proper modeling strategy. Letting social status be an argument of the utility function is
what Postlewaite (1998) calls the "direct" approach. It may be traced back to Frank (1984)4and
has found its most compelling support in an evolutionary argument developed in Fershtman and
Weiss (1998). The proponents of an alternative ?instrumental? approach, where status indirectly
2Empirically, there is obviously a strong correlation between social status and material well-being. There is for
instance a clear positive correlation between the ranking of occupations in term of social status by respondents in
surveys and the average income in these occupations. However, the status ranking of occupations may be much
better explained if education is added along with income as an explanatory variable (see Perrot, 1999). See the
survey by Weiss and Fershtman (1998) for references on the implications of Veblen's theory in economic models.
3Ball et al. (2001) created status by arbitrarily awarding a ?gold star? (a pin) to half of the subjects. All the
subjects then played a standard buyer/seller game (oral double auction). Status was found to be a signi?cantly
positive (and unconscious ?the gold star was never mentioned in the strategy the players reported to follow)
determinant of a subject's earnings. The result held whether it was clear or not to the participants that the gold
star was awarded on an arbitrary basis.
4In the pioneering work of Frank (1984), status is derived from the ranking of relative income. This assumption,
which is natural when dealing with macro-economic problems such as growth, consumption and saving, is not
appropriate when focusing on internal labor markets. Firms di?erentiate employees' status through other means
than relative income (e.g., the hierarchical structure). In fact wages are rarely public information in ?rms.
a?ects an individual's consumption level, criticize the direct approach for lacking robustness:
results are sensitive to the speci?cation of preferences (see Postlewaite, 1998). In Section 2 we
argue in favor of preferences characterized by a complementarity between status and income:
high status agents are willing to exert more e?ort in exchange for additional income while better
paid agents are willing to exert more e?ort in exchange for an improved status. As sociologists
would put it, agents exhibit a taste for status congruence.
Organizations may grant recognition to their members through various formal sources of
status: wage distribution, distribution of scarce non monetary resources (such as o?ces, furniture,
computers, locker rooms, dining facilities...), conspicuous awards or, most commonly, positions in
the organization's hierarchy. Although some of these attributes clearly provide material bene?ts
(more independence, more in?uence, better work conditions) many others are symbolic and their
value to employees stems mostly from the social or psychological bene?ts they entail (self esteem
or social recognition). Here we ignore material bene?ts and consider a pure status ranking that
could ensue, for instance, from the ranking of positions in a formal hierarchy. The choice of a
status allocation in a hierarchy is constrained by the production process (i.e., the technology). Yet
there are many instances of ?rms in the same industry resorting to di?erent hierarchies despite
similar production technologies. For instance in the auto industry Toyota has seven layers of
management between its CEO and employees on the factory ?oor, whereas Ford has seventeen
and GM has as many as twenty-two (see Milgrom and Roberts, 1992). Using a panel of 300
US ?rms over the years 1986-1999, Rajan and Wulf (2003) ?nd a signi?cant trend of reduction
in the number of layers in management over the period, while controlling for various variables
pertaining to the ?rm's structure, in particular its size. This evidence suggests that ?rms are
somewhat able to adjust hierarchies and this ability may be used to provide work incentives. In
order to emphasize the relationship between status and work incentives we abstract from the
technical role played by the hierarchy and leave much latitude to the principal to act as a social
Leaving technology aside, the principal still faces two categories of constraints. First, status
bestowed upon agents should be deemed legitimate in order to signi?cantly impact their behavior.
Our results show that, for incentive purposes, the principal only chooses to award di?erent status
levels to agents who have had di?erent past performances: thus legitimacy may reasonably be
rooted in such di?erences in performance. Our focus is rather on the second constraint that
arises because status is enjoyed through interpersonal comparisons. Regardless of the method
used to grant social recognition, its value is perceived in relative terms. For instance, if status
is derived from a person's position in a formal hierarchy, in order to increase one agent's status,
it is necessary to improve her position in the hierarchy relative to others who, inevitably, su?er
some loss. In other words, status in organizations is a scarce resource.
Our results show that career pro?les greatly di?er depending on whether or not the employer
may commit to long term incentive schemes. In a short term interaction with no commitment,
the employer chooses to introduce limited status di?erentiation, which usually translates into a
relatively ?at hierarchy. Monetary compensations are performance based so that wages should
re?ect productivity di?erences. Indeed, in a one-shot work relations, status may not be handed
out as a reward for good past performances. Then the relevant question is whether an employer
would ex ante choose to di?erentiate status among a-priori identical workers. The answer is no.
Although agents with a high status are more responsive to monetary incentives, the resulting
bene?ts are outweighed by the impact of a lower work motivation for those with lower status.
This short term result emphasizes the cost of status di?erentiation stigmatized in the human
resource management literature.
In order to bring in the bene?ts of di?erentiation, we adopt a long term perspective and
consider an organization comprised of overlapping generations of agents. We ?nd that it is
optimal to give young agents a status as low as possible along with no monetary incentives. Their
motivation to work stems solely from the prospect of being promoted. For incentive purposes
promotions are more substantial for those who have been successful in the past; they end up
with prestigious positions paid above their marginal productivity. Because individual preferences
exhibit complementarities between status and money, symbolic and material rewards reinforce
each other. By concentrating both types of compensations in the same time period and in the
same state of nature, the organization exploits their complementarity so as to reduce the total
wage bill. Although this di?erential treatment of older employees reduces instantaneous pro?t,
the loss is more than compensated by the bene?t resulting from the added incentives for junior
employees. In other words an employer that is able to commit organizes an internal labor market
where pay is attached to jobs, rewards are delayed in time and a larger income is associated with
more recognition (e.g. a higher rank in the hierarchy). Whereas wage di?erences are small
early in the career they become very substantial in excess of productivity di?erences as tenure
increases. We show that these results are robust to the introduction of income risk aversion,
a case where a standard repeated moral hazard model would prescribe to smooth consumption
over time (see for instance Rogerson, 1985, Chiappori et al., 1994).
More complicated issues would arise if we were to take into account an equilibrium status
allocation with multiple organizations. For instance Fershtman, Hvide and Weiss (2005) consider
a model with competitive ?rms, each comprising one principal and two agents, where workers
have the same productivity but di?erent status concerns. They analyze the impact of cultural
diversity in the work place on the labor market equilibrium.5Performing a similar equilibrium
analysis for large corporations is challenging because large ?rms use their market power to shield
their employees from market pressures.6As a ?rst step the present paper focuses on internal
We present the static setting in Section 2 where we describe the organization, the agents'
preferences and the allocation of status among agents; we also establish that optimal short
term incentives involve no di?erentiation in status among agents. The overlapping generations
framework is introduced in Section 3 where we show that promotions are optimal if long-term
commitment is feasible. Section 4 illustrates the empirical relevance of our theoretical ?ndings
5They show that when status, which is based on wage comparisons, is derived locally (i.e., within the ?rm)
?rms choose to mix workers to enhance 'cultural trade'. This policy increases total output and wage dispersion.
In contrast, when some workers care about global status (i.e., they compare wages with a reference group outside
the ?rm) while others care about local status, segregation may arise.
6This is true to some extent only. For instance Lazear and Oyer (2004) exploiting Swedish data show that in
the long term, wages are determined externally, presumably re?ecting centralized bargaining.
through a comparison of work relations in the US and in Japan and Section 5 compares our
approach to some related literature on work incentives. We ?nally provide concluding remarks
in Section 6.
2 The cost of status manipulation
We consider the provision of work incentives to agents whose e?ort level is unobservable. If, as is
usually assumed, an agent's preferences are fully characterized by a taste for money and a distaste
for e?ort, incentives may be provided through monetary rewards and penalties. As we argued
in the introduction, actual incentive procedures typically involve many non-monetary attributes
that are valued mostly as signs of a greater workplace recognition. We use the concept of status
to summarize the overall access to the psychological or social bene?ts that an employee may
secure through her position in the organization. In this section we describe the static framework
and show that it is costly to di?erentiate status among organization members when the work
relationship is short term.
The organization (bureau, subdivision, ?rm,...) supervised by a risk-neutral principal. There are
n ≥ 2 workers indexed by i = 1,...,n. They are ex-ante identical individuals, hired to do the
same type of work, so that there is no a priori legitimate motive for treating them di?erently.
The principal aims at maximizing expected pro?t, with pro?t π de?ned by
π(Q,w1,...wn) = Q −
where Q =?n
Each worker contributes to the collective outcome by exerting an e?ort ei≥ 0. The harder
agent i works (the higher eiis), the larger is the probability of a high output. Formally, individual
i=1qiis total output (its price is normalized to 1) and wiis agent i's wage.
i's output qimay be either high qi= q, with probability µ(ei) or low qi= q, with probability
1 − µ(ei) (q > q > 0). Individual output, and thus absolute performance, is veri?able. This is a
case where direct individual monetary incentives are particularly appropriate. The probability
of a high performance for agent i increases with eiat a decreasing rate. The function µ(.) is also
assumed to be three times continuously di?erentiable with a strictly negative third derivative.7
Assumption 1 µ?(e) > 0,µ??(e) < 0,µ???(e) < 0
e ≥ 0,
lime→+∞µ?(e) = 0.
We next discuss in some detail the two novel ingredients of our framework: the employee's
preferences and the allocation of status in the organization.
A key feature of our approach is the speci?cation of the agents' preferences that assumes some
complementarities between status and income. We postulate the following utility function:
u(w,s,e) = sw − ψ(e),
s ≥ 0, w ≥ 0, e ≥ 0.
where s is status, w is wage income and e is e?ort. The disutility of work, ψ, is taken to be
a strictly increasing, strictly convex and twice continuously di?erentiable function and has a
strictly positive third derivative.8
Assumption 2 ψ?(e) > 0
ψ??(e) > 0
ψ???(e) > 0
e ≥ 0.
This speci?cation re?ects in a simple manner the agents' taste for money and status and
their distaste for e?ort. Setting status equal to 1 yields as a special case the standard quasi-
linear utility, so that our results may be readily compared with predictions of a standard moral
hazard framework. Linearity with respect to wage indicates that agents are risk neutral regarding
income. In subsequent sections, we discuss how our results may be a?ected if this assumption is
relaxed.9The requirement that status and wages should be positive is a normalization. Utility
could easily be rewritten to allow for non zero lower bounds. The important point is that there
are such lower bounds.
7This condition, along with some similar condition on preferences in Assumption 2, ensures the convexity of
an agent's optimal e?ort with respect to work incentives.
8See footnote 7.
9The interpretation of linearity with respect to status is provided in section 3.
Since income and status are both positively valued, indi?erence curves relating these two
variables for a given e?ort level are strictly decreasing. This re?ects the substitution between
status and income. However preferences over status and income are strictly convex so that there
is not a perfect substitution between these two variables: a prestigious title does not compensate
for the absence of wages, nor does a good wage make up for the contempt of others. Utility
also has important implications for the income-e?ort and status-e?ort tradeo?s. Formally, the
marginal rate of substitution between e?ort and income is decreasing in status while the marginal
rate of substitution between e?ort and status is decreasing in income. These cross e?ects may
be best interpreted by relating them to the psychological analysis of work motivation and the
conventional wisdom prevailing among management practitioners.
We ?rst consider the impact of a change in status on the income/e?ort tradeo?. Our speci-
?cation of preferences implies that, for a given level of monetary incentives, an agent should be
all the more willing to exert e?ort that she has a higher status. The literature on job satisfaction
suggests that a higher status enhances work commitment. On the one hand, status is closely
related to the need for recognition which has been found to be a key factor in job satisfaction
(e.g. Dunette, Campbell and Hakel, 1967). On the other hand, many studies have shown that a
low job satisfaction results in high turnover and absenteeism rates.10Tahlin (1999) found in a
study on job mobility in Sweden that everything else being equal people with low status (i.e., a
low prestige score according to Treiman, 1977) are more likely to make a voluntary job shift than
people with high status. It should be expected that a low satisfaction also results in shirking
which, contrary to absence and resignation, is not easily observable.11
We now examine how the trade-o? between e?ort and status is a?ected by a person's income.
According to our speci?cation of preferences, richer agents care more about their status in the
sense that they are willing to exert more e?ort in order to improve it. The hierarchy of needs
proposed by Maslow (1954) provides a nice interpretation of this phenomenon. Maslow argues
10See for instance Day and Hamblin (1964), Baum and Youngblood (1975).
11Many studies have shown that there is a positive correlation between job satisfaction and quality of services
(see Varma et al., 1999). A positive e?ect of status on productivity has been found by Greenberg (1988) in a
study on o?ce reallocation.
that there is a ?ve levels hierarchy of human needs ranking from bottom to top: physiological
needs, safety needs, social needs, esteem needs and self-actualization needs. Higher level needs
correspond to less material (more psychological) preoccupations. A person develops a taste for
higher level needs only after ful?lling those at lower levels. In the present context, income is
the means of ful?lling material satisfaction while status is the means of ful?lling psychological
satisfaction. Then, individuals with low income are mostly preoccupied with material needs and
care little about status while those with higher income having satis?ed their material needs are
mostly concerned about increasing their status. Various observations, either in the work place or
in broader social contexts, illustrate the relevance of Maslow's construction. Certers and Bugertal
(1966) ?nd evidence that factors at the top of Maslow's hierarchy play a more important role
for employees earning higher wages. This is consistent with the logic applied by practitioners
when they use non monetary compensations. A human resource management guide indicates
that using merchandize to reward employees is inappropriate for those earning low wages while
such prizes are highly valued by those who are paid su?ciently well (see Nelson, 1994). Similarly,
rich people seeking social recognition through the funding of charity or ?ne arts re?ects such a
shift in tastes caused by a higher income.12
The next section describes how the organization may allocate status among agents.
2.1.2Status in the organization
Social status is a scarce resource because it is valued in relative terms. In order to model its
scarcity let us de?ne s = (s1,...,sn) as a status allocation in a feasibility set S ⊂ IRn
component measuring the status of agent i. Scarcity of status is re?ected by the property that
+, the ith
it is not possible to improve an agent's status without worsening some other agent's status.
The feasibility set S is therefore analogous to a Pareto frontier. Secondly, individuals being ex
ante identical, the feasibility set should satisfy an anonymity condition: if a status allocation
12For instance children with high income parents typically select high status positions (see Treiman and Ganze-
boom, 1990 and Lillard and Reville, 1997). On a more anecdotal note, Cornellius Vanderbilt Whitney earning a
Ph.D. for the sheer pleasure of being referred to as Doctor Whitney illustrates this appetite for status among rich
people (see Fussell, 1983).
is feasible, then any permutation of this allocation is also feasible. Finally, we assume that
the status feasibility set is convex. Scarcity and anonymity together with convexity, imply that
feasible status allocations must satisfy the following linear constraint:13
si− n = 0, s ∈ I IRn
Overall status summing up to n is a normalization. Any other strictly positive constant
would lead to the same results. However, n has the convenient property that, when no status
disparity is introduced, all agents have a status of 1 so that our results may easily be contrasted
with those of the classical moral hazard literature with quasi-linear agent preferences.14
Finally we assume that, contrary to wages, status is awarded before the agent exerts e?ort.
The status of an agent is based on her situation within the organization, typically her position
in the hierarchy, within a given period. This is consistent with our interpretation of preferences
where recognition induces work satisfaction which in turn induces a higher responsiveness to
monetary incentives. Any attempt by the principal to reallocate status once work has been com-
pleted, for instance by awarding a medal to employees who have performed well, will only impact
the agents' status in future periods, all the more so that they remain in the same organization.
Before characterizing the optimal short term incentive scheme, we brie?y describe a bench-
mark ?rst-best solution.
2.2First best allocation
We now discuss what would be the optimal incentive scheme in the ?rst-best situation where each
agent may fully commit to a contractible e?ort level as well as to an unconditional participation in
the organization. This ?rst-best analysis is meant to provide intuition about the solution that the
principal would ideally favor, rather than to make a statement about the welfare implications of
our setup. Since the only binding constraint is the ex-ante participation constraint of the agents,
13The linear functional form is a consequence of the convexity assumption. It is somewhat restrictive and is
meant to ease the exposition of the results (especially in the optimization problem). Some discussion of the
robustness of our results to more general functional forms is provided in Section 3.
14Here status may be adjusted continuously (preferences are de?ned for a continuous variable). In contrast
Dubey and Geanakoplos (2004) study the relative merits of absolute versus relative rewards in providing incentives
when preferences are only de?ned over status rankings.
it is optimal for the principal to o?er each agent to participate in a lottery where a unique winner
receives all of the status and is the only employee being paid whereas all agents commit to exert
the same ?rst-best level of e?ort. The main argument in the proof is that, instead of having
two agents with positive status, the joint status could be given to only one, where each of them
would receive this total status with some probability. The added status for each agent when she
is paid exactly compensates her for a lower probability of being paid. This allows for paying
each agent less often, thus lowering the expected wage bill.15Because of the complementarities
between status and income, it is optimal to concentrate status and monetary compensations on
one individual so as to lower the wage bill. One might think that the optimality of a lottery
depends on income risk neutrality or on the linearity of the status feasibility constraint. It turns
out that the result is quite robust.16
Actual work relations allow for much less commitment on the part of the agent than what
was postulated here. Henceforth we investigate the implications of our model in more realistic
settings. We ?rst reconsider the static problem.
2.3Optimal short term incentives
Real world work relations typically involve a moral hazard problem since e?ort levels are not
perfectly veri?able. Furthermore, the ability of an agent to commit is limited by work legislation
which usually forbids clauses that would prevent her from quitting at any time. The moral hazard
problem and the agent's lack of commitment translate into incentive compatibility constraints and
interim participation constraints respectively. The information structure of a static relationship
is as follows:
stage 1: the principal o?ers contracts stipulating each agent's status and wages;
stage 2: agents choose whether or not to participate;
15The lottery divides the total wage bill by n relative to what it would be when agents have identical status with
probability 1. The individual probability to win the lottery is
where e∗is the ?rst best e?ort level (i.e., it solves ψ?(e) = µ?(e)∆q). With such a lottery individual expected utility
is U, each agent commits to e?ort level e∗and the total wage bill is U + ψ(e∗), to be compared to n?U + ψ(e∗)?
when agents have identical status and all receive a wage with probability 1.
16A lottery is still optimal if, utility is linear in one argument and either the agent is risk averse regarding
income, or utility is strictly concave in status. See section 3 for related arguments.
n. The prize is swin= n and wwin= U + ψ(e∗)
stage 3: interim information (the draw of a lottery, if any) is revealed and agents choose whether
to quit or not;
stage 4: agents chose their e?ort levels;
stage 5: outputs are observed and payments are made.
The new constraints are a consequence of stages 3 and 4. The interim stage 3 may seem unnatural
in this context and is solely introduced for the sake of comparability with the ?rst-best solution by
allowing for lotteries before the task is carried out. The lottery in the ?rst-best contract violates
both the interim participation constraint of stage 3 and the incentive compatibility constraint of
At stage 5, status is already determined from stage 3. As in the classical principal/agent
setup there is no point to running lotteries on monetary rewards alone. Payments may however
depend on output. Let wibe agent i's ?xed salary and ∆wibe agent i's bonus in case of a high
performance (i.e., wi+∆wiand wiare agent i's wages associated to outputs q and q respectively).
Worker i chooses her e?ort so as to maximize:
Under assumptions 1 and 2, the agent's utility is strictly concave in e?ort and therefore has
a unique maximum point. Agent i's optimal e?ort, e∗(si∆wi), solves the following ?rst order
Standard comparative statics shows that, from the concavity of µ and the convexity of ψ, e∗is
increasing in si∆wi. It is independent of widue to income risk neutrality. Moreover, as can be
seen from Equation (A1) in Appendix A, sign restrictions on third derivatives of µ and ψ ensure
that e∗is concave.
Taking into account additional constraints, the principal's program may be written as
µ(ei)(∆q − ∆wi) − wi+ q
17It is a-priori less apparent whether the added constraints rule out lotteries all together. Proposition 2 shows
that they do.
with probability 1,(6)
si[µ(ei)∆wi+ wi] − ψ(ei) ≥ U
∀ i = 1,...,n, with probability 1, (7)
∀ i = 1,...,n with probability 1. (8)
We omit ex-ante participation constraints since they are implied by interim participation con-
straints. The following proposition states three conditions that should hold in an optimal allo-
cation and which, in short, say that a higher status goes hand-in-hand with a higher income.
Proposition 1 Under Assumptions 1 and 2, an optimal solution has the following properties with
(i) ∆wi≤ ∆q
∀i = 1,...,n.
(ii) ∆wi= ∆q or wi= 0
∀i = 1,...,n.
(iii) si< sjif and only if wi= wj= 0 and ∆wi< ∆wj, or wi< wj.
Proof : See Appendix A.
Part (i) is the standard result that there is no point for the principal in giving more than
full incentives. Part (ii) is also quite standard: given that the agent is risk neutral regarding
income, the principal abstains from giving full incentives only when she is restricted in the
choice of the low performance wage. The novel insight is in part (iii). It states that agents
with di?ering status, either receive di?erent low performance wages (the higher status agent
being better paid) or receive di?erent incentives (the larger high performance reward going to
the higher status agent). That is, di?erent status levels imply an unequal treatment in monetary
as well as symbolic rewards. This logic is exploited fully in the ?rst best solution, where the
whole status and money is concentrated on one agent. It enables the principal to save on the
wage bill by taking advantage of the complementarity between status and income in the agent's
preferences. However, as the next proposition shows, the lack of commitment on the agents'
part, makes unequal treatment among agents suboptimal.
Proposition 2 (symbolic egalitarianism) Under Assumptions 1, 2 and 3, in order to maximize
instantaneous pro?t, it is optimal to give identical agents identical contracts (same status, same
Proof : See Appendix A.
Assumption 3 is a technical condition that is provided in the Appendix and is used to es-
tablish the result when limited liability constraints may be binding. As we now show, it is quite
straightforward to establish the result when limited liability does not bind. Consider the case
where at least one agent, i, receives a strictly positive low performance wage. Then it is easy to
show that if some other agent's status di?ers from that of agent i, pro?t may be increased. To
see this, note that (iii) in Proposition 1 implies that the agent with the larger status necessarily
has a strictly larger expected utility (which is therefore strictly above U). Moreover her low
performance wage must be strictly positive since it is at least as large as that of agent i (see
(iii) in Proposition 1). Hence the low performance wage of the agent with a larger status may
be decreased without violating her incentive constraint nor her individual rationality constraint
so that pro?t would increase. The situation where the principal chooses to give strictly positive
low performance wages arises when U is large enough, namely when18
U > µ(e∗(∆q))∆q − ψ(e∗(∆q)).
Appendix A analyzes the case where U is low so that limited liability may be binding.
The argument above uses the property that status and wages are substitutes in the agent's
utility so that, if status di?ers across agents, the principal may save on wages by paying less those
agents whose status is higher. This however con?icts with the result established in Proposition
1 that, if status and wages may be adjusted jointly, they should be used as complements. It is
therefore never optimal to di?erentiate status across agents.
Proposition 2 is a ?rst formulation with the tools of economics of the equity theory in social
18This lower bound is obtained as follows. The status of the agent getting the worst treatment may not exceed
1. Since, from (i) in Proposition 1, monetary incentives may not exceed ∆q, if (9) holds, her individual rationality
constraint requires that she receives a strictly positive low performance wage. From our previous argument all
agents must therefore have an equal status of 1. Then (ii) in Proposition 1 prescribes that all agents be rewarded
∆q for a high performance.