Status and incentives.

(iii) [s.sub.i] < [s.sub.j] if and only if [[w.bar].sub.j] = 0 and [DELTA][w.sub.i] < [DELTA][w.sub.j], or [[w.bar].sub.i] < [w.bar].sub.j.]

Proof. See the Appendix.

Part (i) is the standard result that there is no point in the principal providing more than full incentives. Part (ii) is also quite standard: given that the agent is risk neutral over income, the principal abstains from giving full incentives only when she is restricted in the choice of the low performance wage. The novel insight appears in part (iii). This states that agents with different status either receive different low performance wages (the higher-status agent being better paid) or receive different incentives (the larger high performance reward going to the higher-status agent). That is, different status levels imply unequal treatment in monetary as well as symbolic rewards. This logic is exploited fully in the first-best solution, where all of the status and money is concentrated in one agent. This enables the principal to reduce the wage bill by taking advantage of the complementarity between status and income in the agent's preferences. However, as the following 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 profit, it is optimal to give identical agents identical contracts (same status, same compensation scheme).

Proof. See the Appendix.

Assumption 3 is a technical condition that is provided in the Appendix and which is used to establish the result when limited liability constraints might 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 differs from that of agent i, profit 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.bar]). Moreover, her low performance wage must be strictly positive because 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 higher status can be decreased without violating her incentive constraint nor her individual rationality constraint so that profit would increase. The situation where the principal chooses to give strictly positive low performance wages arises when [U.bar] is large enough, namely when (18)

[U.bar] > [mu]([e.sup.*]([DELTA]q))[DELTA]q - [psi]([e.sup.*]([DELTA]q)). (9)

Appendix analyzes the case where [U.bar] 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 differs across agents, the principal can save on wages by paying those agents with higher status less. This, however, conflicts with the result established in Proposition 1 that, if status and wages can be adjusted jointly, they should be used as complements. It is therefore never optimal to differentiate status across agents.

Proposition 2 is a first formulation using economic tools of the equity theory in social psychology, according to which it is harmful to introduce differences between workers performing identical tasks (see Adams, 1965). Indeed, hierarchical differences among workers are an obstacle to communication, cooperation, and commitment for those who are in lower positions. Pfeffer (1994) argues that "symbolic egalitarianism" is a key feature of human resource management in successful companies. He describes examples such as the car manufacturer NUMMI, where the executive dining room has been eliminated, or the manager of the contract manufacturer Selectron giving up his/her private office. The well-documented story of Nucor Corporation is another striking illustration (see Ghemawat, 1995). The success of the company, which is known for profitability far above that of the rest of the steel industry, cannot be explained by technological advantage (its technology is similar to that of most of its competitors). It is in fact a result of its innovative human resource management. In line with the results of Proposition 2, external signs of hierarchical differences are systematically eliminated (no personal secretary, common parking lot, everybody flying economy class, and so on). Moreover, the number of layers in the executive hierarchy has been restricted to four, as against a dozen on average for the rest of the industry. Nucor relies on direct monetary rewards to provide work incentives. The average Nucor salary is comparable to the average salary of its competitors, but its structure is more incentive based.

In a short-term relationship, only technological constraints motivate the introduction of hierarchies. We now turn to the study of incentive schemes in long-term work relationships.

3. Status and promotions

* Overlapping generations in the organization. Work relationships between individuals and organizations are in general medium to long term. (19) As workers stay longer than one period within the organization, the principal has more instruments than in the previous section to provide work incentives. She can indeed replicate the static contract, but she can also propose an intertemporal incentive scheme that links future rewards to past performance. We study this problem within an overlapping generations setup with an infinite horizon. At each date, the organization comprises two "generations": the "young" (juniors) who enter the organization in the current period and the "old" (seniors) who joined the organization in the previous period and who will not be around in the next one. Hence each cohort stays for only two periods. Lotteries are ruled out and we assume that the principal is able to commit. Finally, we restrict the analysis to equitable contracts: all young agents at period t are offered the same two-period contract. Thus identical agents (i.e., with identical resumes) receive identical treatment. Proposition 2 suggests that this restriction is reasonable. (20) The timing for a cohort joining the organization at date t is as follows.

Date t:

Stage 1: the new cohort is offered contracts stipulating a starting status, a monetary incentive scheme, and a promotion system (future status and wages depending on past performance);

Stage 2: agents choose whether or not to participate;

Stage 3: agents choose effort based on current monetary incentives and status, as well as promotion prospects;

Stage 4: outputs are observed, transfers and promotions occur;

Date t + 1:

Stage 5: agents choose whether to stay or to leave;

Stage 6: workers choose an effort level according to their current monetary incentive and status (which might depend on how successful they were in the first period);

Stage 7: outputs are observed, transfers occur, workers retire.

Stage 5 implies that, as is the case in actual work contracts, an agent may not commit for two periods. Hence an individual rationality constraint for old agents must be imposed.

Each agent's intertemporal utility is additively separable with a discount factor of [delta] < 1.21 The expected utility of an old agent exerting effort [e.sub.pt] whose past performance has been p [member of] < l. (21) h} (l stands for "low" and h for "high") is as in equation 3:

[EU.sub.pt] = [[mu]([e.sub.pt])[DELTA][w.sub.pt] + [[w.bar].sub.pt] [s.sub.pt] - [psi]([e.sub.pt]). (10)

A young agent's expected intertemporal utility for effort [e.sub.lt] is

[EU.sub.lt] = [s.sub.lt][[mu]([e.sub.lt])[DELTA][w.sub.lt] + [[w.bar].sub.lt] - [psi]([e.sub.lt]) + [delta][[mu]([e.sub.lt])[DELTA] [U.sub.t+l] + [EU.sub.l(t+1], (11)

where [DELTA][U.sub.t] = [EU.sub.ht] - [EU.sub.lt]. Individual rationality constraints are

(IR') [EU.sub.pt] [greater than or equal to] [U.bar], p [member of] {h, l} and [EU.sub.lt] [greater than or equal to] (1 + [delta])[U.bar].

Let [e.sup.*] be implicitly defined by equation (4). It is easy to check that the incentive-compatibility constraints for young and old agents can be written as

(IC') [e.sub.lt] = [e.sup.*]([s.sub.lt][DELTA][w.sub.lt] + [delta] [DELTA][U.sub.t+1]) and [e.sub.pt] = [e.sup.*]([s.sub.pt][DELTA][w.sub.pt]) p [member of] {h, l}.

The population is large and so can be represented by a continuum with a measure normalized to 2. Then, at each period, the proportion of old who were successful when young, denoted [[gamma].sub.t], is equal to the probability [mu]([e.sub.l,t-1]) that, in the previous period, a young agent had a high level of performance. The feasibility constraint on status allocation is

(F') [s.sub.lt] + [[gamma].sub.t][s.sub.ht] + (1 - [[gamma].sub.t]) [s.sub.lt] = 2 with [[gamma].sub.t] = [mu]([e.sub.l,t-1]).

Let [c.sub.lt] = ([s.sub.lt],[[w.bar].sub.lt], [DELTA][w.sub.lt]) denote the contract of a young agent at date t, and [c.sub.pt] = ([s.sub.pt], [[w.bar].sub.pt], [DELTA][w.sub.pt]) denote the date t contract for an old agent with performance p [member of] {h, l} at date t - 1. As in the static model, the principal faces three ( factor as workers, [delta] < 1, so that there is no exogenous bias against, or in favor of, delayed monetary rewards. Her intertemporal profit is written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (12)