Status and incentives.

We now examine how the tradeoff between effort and status is affected by individual income. According to our specification of preferences, richer agents care more about their status in the sense that they are willing to exert more effort in order to improve it. The hierarchy of needs proposed by Maslow (1954) provides a nice interpretation of this phenomenon. Maslow argues that there is a five-level hierarchy of human needs, with the following 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 fulfilling those at lower levels. In the present context, income is the means of fulfilling material satisfaction, whereas status is the means of fulfilling psychological satisfaction. Then, individuals with low income are mostly preoccupied with material needs and care little about status, wheras those with higher income, having satisfied their material needs, are mostly concerned about increasing their status. Various observations, either in the workplace or in broader social contexts, illustrate the relevance of Maslow's construction. Centers and Bugental (1966) find 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 nonmonetary compensation. A human resource management guide indicates that using goods to reward employees is inappropriate for those earning low wages, whereas such prizes are highly valued by those who are paid sufficiently well (see Nelson, 1994). Similarly, rich people seeking social recognition through the funding of a charity or fine arts reflects such a shift in tastes caused by higher income. (12)

We next describe how the organization might decide to allocate status among agents.

Status in the organization. Social status is a scarce resource because it is valued in relative terms. In order to model its scarcity, let us define s = ([s.sub.1], ... , [s.sub.n],) as a status allocation in a feasibility set S [subset] [IR.sup.n.sub.+], where the ith component measures the status of agent i. First, the scarcity of status is reflected by the property that it is not possible to improve one agent's status without reducing some other agent's status. The feasibility set S is therefore analogous to a Pareto frontier. Then, individuals being ex ante identical, the feasibility set should satisfy an anonymity condition: if a status allocation 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):

(F) [n.summation over (i=1)][S.sub.i] - n = 0, s [member of] [IR.sup.n.sub.+].

That overall status sums up to n is a normalization: any other strictly positive constant would produce the same results. However, n has the convenient property that, when no status disparity is introduced, all agents have status 1, so that our results can easily be compared to those from the classical moral hazard literature with quasilinear individual preferences. (14) Finally we assume that, contrary to wages, status is awarded before the agent exerts effort. The status of an agent is based on her situation within the organization, typically her position in the hierarchy, in a given period. This is consistent with our interpretation of preferences, where recognition induces work satisfaction which in turn induces greater responsiveness to monetary incentives. Any attempt by the principal to reallocate status once work has been completed, for instance by awarding a medal to employees who have performed well, will only affect agents' status in future periods, all the more so if they remain in the same organization.

Before characterizing the optimal short-term incentive scheme, we briefly describe a benchmark first-best solution.

First-best allocation. We now discuss the optimal incentive scheme in the first-best situation where each agent can fully commit to a contractible effort level as well as to unconditional participation in the organization. This first-best analysis is meant to provide intuition about the solution that the principal would ideally prefer, rather than to make a statement about the welfare implications of our setup. Because the only binding constraint is the agents' ex ante participation constraint, it is optimal for the principal to offer each agent participation in a lottery where one sole winner receives all of the status and is the only employee paid, whereas all agents commit to exert the same first-best level of effort. 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 of them, with each receiving this total status with some probability. The added status for each agent when she is paid exactly compensates her for the lower probability of being paid. This allows the firm to pay each agent less often, thus lowering the expected wage bill. (15) Because of the complementarities between status and income, it is optimal to concentrate status and monetary compensations on one individual so as to lower the total wage bill. We 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 this result is quite robust. (16)

Actual work relations allow for much less commitment on the part of the agent than that which was postulated here. We therefore investigate the implications of our model in more realistic settings. We first reconsider the static problem.

Optimal short-term incentives. Real-world work relations typically involve a moral hazard problem because effort levels are not perfectly verifiable. Furthermore, the ability of an agent to commit is limited by work legislation which usually outlaws 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 offers contracts stipulating each agent's status and wages; Stage 2: agents choose whether or not to participate; Stage 3: interim information (the draw of a lottery, if any) is revealed and agents choose whether to quit or not; Stage 4: agents choose their effort 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 might seem unnatural in this context and is solely introduced for the sake of comparability with the first-best solution by allowing for lotteries before the task is carried out. The lottery in the first-best contract violates both the interim-participation constraint of Stage 3 and the incentive-compatibility constraint of Stage 4. (17)

At Stage 5, status is already determined from Stage 3. As in the classical principal/agent setup, there is no point in running lotteries over monetary rewards alone. Payments might, however, depend on output. Let [[w.bar].sub.i] be agent i's fixed salary and [DELTA][w.sub.i] be agent i's bonus in case of high performance (i.e., [[w.bar].sub.i] + [DELTA][w.sub.i] and [[w.bar].sub.i] are agent i's wages associated with outputs [bar.q] and [q.bar], respectively). Worker i chooses her effort so as to maximize:

[EU.sub.i] = ([mu]([e.sub.i])[DELTA][w.sub.i] + [[w.bar].sub.i]) [s.sub.i] - [psi]([e.sub.i]). (3)

Under Assumptions 1 and 2, the agent's utility is strictly concave in effort and therefore has a unique maximum point. Agent i's optimal effort, [e.sup.*] ([s.sub.i][DELTA][w.sub.i]), solves the following first-order condition:

[psi]'([e.sup.*]([s.sub.i][DELTA][w.sub.i]))/[mu]'([e.sup.*]([s.sub.i] [DELTA][w.sub.i])) = [s.sub.i][DELTA][w.sub.i]. (4)

Standard comparative statics shows that, from the concavity of [mu] and the convexity of [psi], [e.sup.*] is increasing in [s.sub.i][DELTA][w.sub.i]. Effort is independent of [[w.bar].sub.i] because of income risk neutrality. Moreover, as can be seen from equation (A1) in the Appendix, the sign restrictions on the third derivatives of [mu] and [psi] ensure that [e.sup.*] is concave.

Taking into account additional constraints, the principal's program can be written as

max E [n.summation over (i=1){mu}{[mu]([e.sub.i])([DELTA]q - [DELTA] [w.sub.i]) - [[w.bar].sub.i] + [q.bar]} (5)

subject to

[n.summation over (i=1)][s.sub.i] = n, with probability 1, (6)

[s.sub.i][[mu]([e.sub.i])[DELTA][w.sub.i] + [[w.bar].sub.i]] - [psi] ([e.sub.i]) [greater than or equal to][U.bar] [for all]i = 1, ..., n, with probability 1, (7)

[e.sub.i] = [e.sup.*]([s.sub.i] [DELTA][w.sub.i]) [for all]i = 1, ..., n with probability 1, (8)

We omit ex ante participation constraints because they are implied by interim-participation constraints. The following proposition states three conditions that should hold in an optimal allocation and which, in short, say that higher status goes hand in hand with higher income.

Proposition 1. Under Assumptions 1 and 2, an optimal solution has the following properties with probability 1.

(i) [DELTA][w.sub.i] [less than or equal to] [DELTA]q [for all] i = l, ..., n.

(ii) [DELTA][w.sub.i] = [DELTA]q or [[w.bar].sub.i] = 0 [for all]i = 1, ..., n.