THE UNIVERSITY OF CHICAGO
Booth School of Business
Business 33032
Spring 2009
Canice Prendergast
Topic 6
Team Production and Promotion
In the last lecture we considered the use of piece rates, where the idea was simply to trade
off the desire to provide incentives (and hence have sensitive incentive schemes) and the desire
to shelter the worker from risk. In this section of the course, we first extend the idea of piece
rates to consider two important extensions:
1. The use of team bonuses
2. Promotion
I.
Team Production
Placing individuals in teams has a number of effects. The first is what are known as
production complementarities, where the product of the individuals’ efforts is greater than the
sum of their parts. In effect, people being different skills to the table that increase each person’s
productivity. This is not the primary interest of this topic here. Instead, our interest is in what is
called a free-rider problem, which notes the harmful effect of team based compensation on
performance.
A Simple Model:
Suppose that a team is involved on a project (rather than a single worker as before). The
output of the team depends on the efforts of all members and is given by
f(e1, e2, ..., en),
where ei is the effort exerted by the ith worker. There are n workers on the team.
A typical compensation scheme would be to offer each member of the team an nth share
of output. So if there are two workers, each gets one half of output. The worker exerts effort
until his marginal benefit equals the marginal cost of effort, that is,
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(1/n)f’(e1, ..., en) = C(e),
where C(e) is the marginal cost of effort and f() is the marginal product of effort (for the ith
person). The optimal effort to exert is where
f() = C(e),
where total marginal product equals cost. But the worker will not exert the right amount of effort
because he has to share the extra output he produces with everyone else. This is known as the
free rider problem.
An example:
Suppose that three workers are involved on a project.
Output is y = e1 + e2 + e3.
The marginal cost of effort is e.
*What is the optimal amount of effort?
* Now suppose that everyone shares the benefits equally. (This is what is known as a partnership
contract, where everyone gets 1/3 of the pie.) Who hard will people work?
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Empirical Evidence:
The simplest place to identify the effects of teams on performance is by looking at partnerships,
such as law partnerships or medical partnerships. There is considerable variation on how partners
are paid: a general set-up is where
Pay = a* Own Performance + b* Partnership Performance
At one extreme, a = 1, b = 0,. and the partner keeps all his own output, while at the other
extreme, a = 0, and b = (1/N), which is complete profit sharing.
Empirical evidence: As a falls, partners bill fewer hours, and do not control costs as well.
Profit-Sharing in Large Companies
Q: Based on the model offered above, should large firms offer profit sharing plans?
By, if so, why do they?
Tests of the role of profit sharing plans on productivity:
1. Cross Sectional
2. Within firm
3. Is this sufficient?
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Solutions to the Free Rider Problem
There are two general classes of solutions:
Contractual solutions:
1. Pay more on individual output.
2. Where you offer contracts that are not simply equal shares of output. In other words,
make wages very sensitive to output.
In the previous example, if output rose by one dollar, wages went up by 1/n dollars. Instead, the
contract could make the worker’s wage go up by one dollar.
An example: Don’t give out B’s and C’s for the course. Only give out A’s and D’s, where
anything that does not deserve an A gets a D.
Problems:
(i) You may make workers face too much risk.
(ii) There is a precommitment problem. This is where one worker says, “I’m going to
shirk. You better work harder to make up for my lost output.” With compensation schedules
that are very sensitive to output, workers will make up for the slack of other workers by working
harder.
Peer Pressure:
A recent suggestion is that the main role of profit sharing is to cause workers to monitor one
another. In many cases, we would imagine that workers are better at monitoring one another than
managers are at monitoring workers. Profit sharing then gives workers an incentive to exert peer
pressure on one another. As a result, we would expect profit sharing to be more successful in
instances where (i) other workers can spot shirking and (ii) they can do something about it.
There is some recent evidence on the role of peer pressure. For more details on this
literature, see the readings. One example is a manufacturing setting, which initially offers
workers individual piece rates when they join the firm. However, after some period of time on
the job (usually 3-6 months) they place workers in teams, where the employees are rewarded on
the basis of team production. Though data on individual production are still available, two
effects were noted as seen in the figures below:
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The Selection Effects of Teams
Throughout the course, we have emphasized the importance of selection: who chooses to work
under a particular contract. To see this, consider the figure below, which maps the turnover of
workers under team production. Who do you think is most likely to quit when switched to a team
based compensation plan from an individual piece rate?
II.
Promotion
So far we have ignored the fact that incentives are designed over a worker’s entire career
rather than just on the basis of a single period of production. This is not lost on most companies,
who use promotions as the main opportunity for worker advancement. The purpose of this
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section is to determine how promotions should be structured, i.e., how big should the wage
increase be at promotion.
Promotions should be seen as contests or tournaments, rather like tennis tournaments, in
that to get promoted a worker needs to outperform all others looking for the job.
The key idea is that you pay on the basis of relative performance. The importance of this
is that the effort you exert depends on what you think other competitors are doing.
Let’s say there are two workers competing for a promotion, j and k. The firm needs to
determine two wages: the wage for the winner, W, and the wage for the loser, L. (The promoted
worker is the winner, of course.)
The firm’s problem is to maximize its profits subject to the worker’s incentives. Let
output for worker i be
qi = ei + li,
where ei is the effort exerted by worker i and li is his luck. (For example, his machine could
break down, his best client could leave, and so on.) With the previous model, how much you got
paid depended on how much effort you exerted. Here it depends on how much effort you exert
and how much your competitor exerts.
The firm observes qj and qk only. Worker j wins promotion if
qj > qk
or
ej + lj > ek + lk.
This can be rearranged to
ej - ek > lk - lj.
The interpretation of this is that if the amount harder that you work is greater than the extent to
which he is luckier than you, you get promoted. (In other words, if he is really lucky, then you
can lose even if you work harder.)
To get any further, we need to talk about distributions; in particular, we need to talk about
the distribution of luck. We can imagine that with some probability, one worker gets really
lucky. With another probability he gets really bad luck. In general, we can talk about the
probability distribution of luck for a worker. This is given by G(lj) for worker j. Similarly,
worker k will have a distribution G(lk). Let lk - lj have a distribution F.
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The way to interpret this is the following. Consider Figure 1. This means that with
probability p worker j will have output that is $3 higher due simply to luck. With probability p
he produces $2 less than worker k due to luck. The probability that worker j wins is if the
difference in luck [lk - lj] is less than the extra effort that worker j exerts [ej - ek]. This is given by
the shaded region in Figure 2. The area to the left of any point is known as the cumulative
distribution, F(ej - ek). What happens if each worker works equally hard? Then ej - ek = 0, so
there is a 50% chance of victory for each worker, F(0).
The key point to remember here is that the worker exerts effort to increase the probability
of victory. For example, if worker j increases his effort then the area to be shaded moves to the
right.
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The worker gets W if he wins the promotion and L if he does not. Therefore the prize
from promotion is W - L. By exerting more effort, the worker increases his chance of promotion
by f(ej - ek), the density of the distribution. (This is the same as the p and p above.) Then he
chooses effort until
(W - L)f = C(ej).
But worker k does the same, so that
(W - L)f = C(ek).
Thus they both choose the same level of effort.
The firm gets to choose W and L. It does so to maximize profits. The optimal level of effort is as
follows. Worker j produces ej + lj. The marginal product of effort is 1 (as a one-unit increase in
effort increases output by one unit). Optimal effort is then C(ej) = 1. All the firm then needs to
do is set the wages W and L such that effort is set optimally. (If the wage spread is too large, then
workers work too hard — and are unlikely to take the job — while if the wage spread is too low,
they shirk.)
Technical Derivation [Optional]
Worker j’s probability of victory is E(ej - ek). He then chooses effort to
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maxej F(ej - ek)W + [1 - F(ej - ek)L - C(ej).
The first-order condition characterizing the optimum is
f(ej - ek)[W - L] = C(ej).
The other worker has identical incentives so he chooses the same effort level. Hence this
equation simplifies to
f(0)[W - L] = C(e),
where e is now the common effort level.
The firm then chooses W and L to (i) get optimal effort, C(e) = 1, and (ii) guarantee that
the worker gets his outside income, U*. The spread is achieved by setting
[W - L] = 1/f(0).
[Check this.] L is then chosen so that [W + L]/2 = U*, since each worker has a 50% chance of
promotion.
What determines how hard you work?
(i)
The spread in prizes (W – L)
(ii) How the likelihood of winning the prize changes if you work hard.
Part (i) is obvious; part (ii) is concerned with how much luck there is in the tournament.
In other words, when there is a large element of chance you will work less hard than when luck
plays a small role.
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Empirical Evidence on tournaments:
This is described in detail in the readings. Most of the examples come from sports tournaments,
such as professional golfers, who shoot lower scores in tournaments where the prize money is
more sensitive to performance. Similar evidence is found for Nascar drivers, bowlers, etc.
What are the advantages of promotion as an incentive scheme?
(i) Informational Requirements: it is often difficult to determine how much a manager has
produced but easier to tell who is the best manager. Consequently, promotion cuts down on
measurement problems (i.e., it only needs rank-order information).
(ii)
It may make incentives more credible. This operates in two dimensions: (a) to pay
out, and (b) to allocate based on merit.
Why is this?
(iii)
It forces management to make decisions on employees.
(iv)
It gives incentives to monitor.
(v)
It aids sorting: “killing two birds with one stone”
Disadvantages
(i)
It can harm sorting: “Engineer problem”, where there is promotion of employees
to jobs for which they are unsuited as it is the only way of rewarding.
(ii)
Not all contests are equal – problems are (a) giving up, and (b) changing risks.
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(iii)
Maxing out.
(v)
May involve substantial risk.
(vi)
Pyramids become flat in many firms.
(vii)
Cooperation may be harmed.
Questions
1. Two companies employ two trainee managers each. The boss of company A is pretty
attentive and takes care to carefully monitor his two subordinates. The boss of company
B is lazy — he plays a lot of golf, does a lot of consulting outside the firm, and generally
is not very attentive to his workers. In which company will promotion incentives need to
be greater? Interpret this in terms of the analysis above.
2. Is promotion likely to work as a better incentive for R&D engineers or general
managers?
Prizes over a Worker’s Career
We finish off this topic by considering how the returns to promotion vary within an
organization. To begin, consider the tennis example; if you look at a tennis tournament, you
generally find that about 50% of the prize money is bunched among the top 8 finishers.
Similarly, if you look at organizations, there are often quite small returns to getting promoted
initially, but enormous increases when you get to the top of an organization. Why is this?
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III.
Up or Out Rules
Many organizations use compensation schemes where after some period of evaluation,
they either promote a worker or they fire her. The key thing that characterizes up-or-out rules is
that firms do not have the option to continue the relationship as is: either the worker is fired or is
kept on.
Examples are:
 Academia
 Law Firms
 The Military
 Some consulting companies
Note that this type of contract can involve considerable costs: in particular, if workers
collect significant specific skills, these are typically lost if the worker is not up to par.
Given these costs, why do firms use such schemes?
1. It is a way of freeing up important slots.
 but isn’t this true in many firms?
 what is so special about, say, a top law firm that makes it use it while the
typical company does not?
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2. It may give good incentives for workers: typically the worst that you can do to an
employee is to let them go. Therefore, this may be the way to provide most incentives.
3. It forces firms to make important decisions so that it really gives an incentive to
monitor very carefully: otherwise, big costs are incurred if you allow promotion of an
incompetent worker.
4. It stops firms from tagging workers along; either they have to reward them or let them
go.
Tenure
There is another component of up-or-out rules that the above discussion does not deal
with; namely, that if the individual gets the promotion, they typically have enormous security of
tenure.
Why should firms offer such guarantees?