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Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design

By Bengt Holmstrom and Paul Milgrom (1991)

Modigliani group: Belen Chavez, Yan Huang, Tanya Mallavarapu, Quanhe Wang

April 12, 2012

1. Introduction

In the standard principal-agent model incentive systems are utilized to allocate risks and reward

productive work. However the credibility of this model reduces when the agent is risk averse and

would prefer a fixed wage system. This theory has also not been able to explain why

employment contracts usually specify fixed wages with very little importance given to

incentives. At the same time the model has not been effective in addressing issues such as asset

ownership, job design and allocation of authority.

What distinguishes this model from most others is that the principal can allocate different tasks

to one or many agents, or the agent’s single task can consist of several dimensions.

The model discussed in this paper overcomes some of the shortcomings in the basic principal

agent model. Holmstrom and Milgrom’s multitask principal-agent model:

Accounts for paying fixed wages even when outputs can be easily measured and agents

are highly responsive to incentive pay

Examines ownership patterns even when contracts can take account of all observable

variables

Explains why employment is sometimes chosen over contracting even when there are no

productive advantages

Determines how tasks get allocated to different jobs

One of the prime examples to illustrate the issue the model is trying to address is whether

teachers should be paid through incentives based on their students’ test scores. Supporters of this

system say that the incentives will motivate teachers to take a greater interest in their students’

success. However, opponents argue that the teachers would neglect the importance of deeper

critical thinking, creativity, and activities in arts and focus all their time on basic skills that are

tested in standardized exams. The opponents suggest that teachers get paid based on a fixed

wage.

Key Components of Model

Multidimensional Tasks

Most tasks tend to be multidimensional. For instance, production workers are responsible for

producing high volume and high quality goods and may also be required to clean the machines

they utilize. In this case, if the agents are paid based on the volume of output since it is easy to

measure, they are likely to sacrifice on the quality of the output and focus only on the quantity.

Or, if quality can also be measured, the incentive rate system might cause agents to neglect

taking care of the machinery they use. Therefore, when an agent is responsible for multiple tasks,

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incentive pay can allocate risks, motivate hard work and direct attention to their various duties

accordingly.

Going back to the example of teaching to illustrate the point of job design. If the task of teaching

basic skills can be separated from teaching higher-level thinking or arts, these tasks can be

assigned to different teachers at different periods. Looking at this is the context of production

workers, separating the maintenance of a productive asset and the use of the asset for production

the use of a piece rate system would be more efficient. Job design is an important aspect for an

efficient use of incentive based pay. This is similar to the concept of specialization.

The model proposes that an increase in an agent’s incentives for any one task will cause him to

reallocate some of his attention away from other tasks. The efficiency of providing incentive

based pay for an activity decreases with the difficulty of measuring performance in any other

activities that are competitive for the agents time and attention. This is because the principal

would not be aware of the performance of agent in the other activities that are equally important.

This point could help explain why the one-dimensional principal agent model has not been able

to explain why incentive based pay is not as common as expected.

Asset Ownership

The model also examines the case where the unmeasurable aspect of performance is how the

value of a productive asset changes over time. The difficulty of valuing assets is recognized. In

the case where the principal receives the returns from an asset the optimal compensation system

would be to provide a less incentive based on output contract to avoid any abuse of the asset or

any deviation of effort away from asset maintenance by the agent. However when the agent owns

the asset returns the optimal compensation system would involve an intensive incentive contract

to engage in production to avoid the situation where the agent uses the asset too cautiously or

pays too much attention to its improvement. The conditions where the agents owns the assets

would be successful if i) the agent is not too risk averse ii) the variance of asset returns are low,

and iii) the variance of measurement error in other aspects of the agent’s performance is low. In

recent times, firms have been giving their employees stock options in the company along with

their fixed wage. This is an effective way to ensure that the employees are performing well in

their allocated tasks but at the same time carrying out activities that improve the asset of the

company.

This helps explain why franchisees have steep performance incentives, while managers of

similar company-owned outlets receive no incentive pay. This also explains why a free-lance

writer gets paid for articles by the word, but a reporter for the same publication gets paid a fixed

wage.

Personal Activities

Holmstrom and Milgrom continue to extend the one principal-agent model by incorporating

personal tasks into the model. How does a firm optimally set policies limiting personal activities

during working hours? They suggest that “outside activities” should be more severely restricted

when the performance of the task for the firm is difficult to measure. Therefore, a salesperson

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who is paid on commission will optimally be permitted to engage in personal activities during

business hours than a bureaucrat who is paid a fixed wage. This is because the commissions

direct the salesperson to inside activities, which cannot be done for a bureaucrat. However, this

seems to be changing for many companies today. For instance, Google, which pays most of its

employees through fixed wages, gives them a lot of freedom with how they decide to engage in

personal activities. Google even goes to the extent of encouraging its employees to engage in

outside activities by providing them with a gym, game room and TV’s around their campus.

According to the analysis on outside activities, incentives for tasks can be provided in two ways:

the main task is rewarded or the marginal opportunity cost for the task can be lowered by

reducing the incentives on other competing tasks. Constraints are used instead of incentives

when it is difficult to measure the performance of an agent. This helps understand large-scale

organizations. The larger a firm gets the more difficult it becomes to constantly monitor their

employees and therefore imposing constraints on personal activities is the most efficient system.

Job Design

In this case, Holmstrom and Milgrom extend the model to where the employer can divide the

responsibility for many tasks between two agents that further allows the employer to decide how

performance for each task is compensated. Each task must be allocated to just one agent. The

tasks should then be grouped into jobs in a way that tasks that are easily measured are assigned

to one worker and the other tasks are assigned to the second agent. This relates back to the

argument of specialization, where the differences between measurability of quality and quantity

in production make the incentive problems difficult. But here by grouping all the tasks for

quality as one job and the tasks for quantity as one job the effectiveness of incentive pay

increases. Even if the agents are identical before they start their tasks, they still should be

separated to have measurement characteristics that are as different as possible in their jobs. The

principal should then provide the agent whose performance is easily measured with a more

intensive incentive pay and require more work from them.

2. The linear Principal-Agent Model

Notation:

t=effort contributed by agent

C(t)=cost of agent

B(t)=benefit of principal

x=information signals

w(x)=wage of agent

=parameter of incentive wage

β=minimum wage

r=measurement of agent’s risk aversion

=representative of effort

CE=certainty equivalence

∑=covariance matrix

V(t)=asset value

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Purpose of the model: Choosing the (t, ) to maximize the total benefits, meanwhile, maximizing

the agent’s profit.

Assumptions:

(1) The wage payment is a linear function of measured performance.

(2) Agent is required to make one-shot choice of how to allocate his efforts.

(3) The principal is risk neutral, which means, he only pays attention on the expected return.

In other words, the risk will only influence the agent’s choice rather than the principal’s.

(4) C is strictly convex, while B is strictly concave.

Description of the Model

In this model, the agent is asked to decide how to allocate his efforts between k tasks1:

t=(t1,t2,…, tk). The agent’s efforts will generate both cost C to himself and benefit B to principal.

Meanwhile, this effort will also produce a kind of signal

x=

which will help principal to decide how much wage this agent deserves to receive in an incentive

strategy:

w(x)= ,

where denotes the base pay the agent will receive even in an incentive strategy. Two important

things to note are, first is that only serves to allocate the total profits between agents and

principals--since it is a constant, it will disappear when taking the derviative That’s why we

don’t observe in the latter equations. Second, denotes the risk an agent has to bear in an

incentive wage. This parameter reflects the uncertainties, such as fortune, bias, etc. which will

influence the evaluation of an agent’s effort. Since there exists uncertainty, the authors here

adopt expected utility theory to get the agent’s certainty equivalent wage (CE)

,

where (we know from the Arrow-Pratt equation that this utility function has

CARA: constant absolute risk aversion with constant r), r measure the agent’s risk aversion and

denotes the variance of the agents income that the agent needs to bear.

From now, we can evaluate the expected profit of both agent and principal

, (1)

, (2)

1 Note: The paper has a typo, the n in this model donates the amount of agents

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So now the problem is to find the (t, ) to maximize (1) and (2) subject to: t maximizes

, which is the same as to maximizes

Features of the model:

a) Application:

(1) Different activities can be applied in this model, no matter how difficult it is to measure.

(2) We can study cases where performance measures can be influenced by activities, rather

than by principal’s desire. The agent has the freedom to allocate their effort, and

sometimes the effort allocation will not be what the principal desire.

(3) We can study cases where number of observables is smaller than that of activities. In

other words, the principals cannot fully gain the information of agents’ behavior.

b) The return to the principal is not necessarily to be observed.

(1) If B=C, then it is optimal for principal to set =0.

(2) If B is different than C, especially when B is difficult to measure, then the incentive

wage will not be adopted.

Simple Interactions Among Tasks:

Assuming (the effort is equal to the signal) then we can take the derivative of

equation , gaining following equation Further differentiating (3) and (4), we can get

and

,

, (5)

where B’=(B1,…,Bk) is the first derivatives of B.

Two things worthy of noting:

(1) When the error terms are stochastically independent ( ) and the

activities are technologically independent ( ), then the function (5) can

be further simplified as . The commissions are set

independently of each other since the cost of each task is independent, in other words, the

incentive of a particular task will not influence the opportunity cost of other tasks. As

expected, the incentive is decreasing with people’s attitude towards risk and risk itself but

increasing with marginal profit gained by principal. Moreover, the incentive is also

increasing with the

, which means the more responsive the agent is to incentives, the

more ambitious the incentive put forth by principal will be.

(2) However, most of time, we cannot neglect the cross-partials of C ( ).

When , situation of complementary between different tasks will occur. That is, if

agent increases his input in one task, he will also increase his input in other task. (When

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(

)

, if t2 increase, then (

) will decrease, which means, under the same amount

of cost C, the input t1 should increase. In a word, the incentive to task 2 increases the both

input in task 1 and task 2.) So at this situation, increase the incentive to a particular task

will benefit the whole profit gained by principal. When , situations of substitution

between different tasks will occur. At this time, increasing the incentive in a particular

task will drive agent to reallocate the time input from less incentive one to more incentive

one. So in general when inputs are substitutes, incentives for any given activity ti can be

provided either by rewarding that activity or by reducing its opportunity cost. That is,

when some tasks are hard to measure, the only way to “increase the incentives” for these

tasks is to reduce the incentive to other easy to measure tasks.

Above arguments are based on the assumption that t>>0 (attention to all tasks in the vector are

positive) (the necessary condition for the existence of equation (5)). Lastly, the author discusses

the situation that t is 0. In this situation, the cost of providing positive incentives for a small

amount of effort has a minimum cost, which is . This value will not be zero,

since (Marginal private cost to agent will be greater than zero.) This observation

plays a significant role on job design.

3. Allocation Incentives for Effort and Attention

In this section, the author tries to analyze realistic observations based on his model. One extra

assumption in this section is that an agent can take pleasure in working up to some limit

(C’(t) for t ). This means that there exists a range of effort allocation among which the

cost of agent is indifferent to whatever he chooses to allocate his effort. In other words the

agent’s effort is homogeneous and can be allocated among the tasks in whichever way the agent

likes.

Case 1: Missing Incentive Clauses in Contracts

Problem: In daily life, it is uncommon for the principal to set incentive clauses in actual contracts.

The author cites the example of a contract for home remodeling as an example, in which the

incentives for timely completion of construction is seldom seen, even though construction delays

will harm the profit of homeowner.

Explanation: If one task (quality of construction) is important but hard to measure, then adopting

the incentive wage in the other easy-to-measure task (speed of construction) will drive the agent

(construction workers) to pay all their effort on the easy-to-measured one and neglect the hardo-

measure one, which will eventually reduce the profit of the principal (homeowner). The

mathematical proof is in the previous section.

Proposition 1: For the home contractor model, the efficient linear compensation rule pays a fixed

wage and contains no incentive component ( ), even if the contractor is risk neutral.

This proposition argues that piece-rate may be infeasible in the job design, which includes tasks

with different degree of difficulty in measurement.

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Case 2: “Low-Powered Incentives” in Firms

Problem: Williamson argues that the incentives offered to employees in firms are generally “low-

powered” compared to the “high-powered” incentives offered to independent contractors.

Explanation: The ownership of asset is the key point to this problem. Here the author classifies

two modes: contracting and employment. The former one denotes the situation where the change

in asset value accrues to the agent, while the latter denotes the situation where change in asset

values accrues to the principal. The basic idea is that if the principal owns the asset, then he will

prefer a conservative strategy (fixed wage), which will protect his net asset value. On the

contrary, if the agent owns the asset, then the principal will adopt incentive wage to encourage

agents to increase the usage of their own asset, which eventually will bring net receipts to

principal. Good evidence are firms like McDonald’s and Burger King which are franchises that

provide strong incentives.

When the principal owns the asset or he prefers a fixed wage payment, an extra assumption is

necessary, which says it is highly desirable for principal to induce the agent to devote a positive

amount of effort to both tasks.

Proposition 2: Assume that . Then the optimal employment contract always

entails paying a fixed wage ( ). Whenever the independent contracting relation is optimal,

it involves “high-powered incentives” ( ). Furthermore, there exist values of the

parameters

for which employment contracts are optimal and others for which

independent contracting is optimal. If employment contracting is optimal for some fixed

parameters (

), then it is also optimal for higher values of these parameters. Similarly, if

independent contracting is optimal, then it is also optimal for lower values of these parameters.

This proposition argues two opinions. First, when the principal wants to achieve profit from

hard-to-measure tasks, it is better for him to hire employment with a fixed wage. This idea is

actually similar to that of proposition 1. Second, both risk and agent’s attitude towards to risk

will also influence the wage payment. When the risk is too high or agent is too risk-averse, the

agent will not be encouraged by an incentive wage. In other words, the incentive wage will be

infeasible.

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4. Limits on Outside Activities

With so many distractions in today’s world like iPads, cellphones and the internet, how does the

principal set constraints on the agent to avoid these distractions? If I were a worker in a call

center or a secretary with access to a phone, I could easily make personal phone calls. Thus, the

principal needs to set constraints so that the agent will not neglect the principal’s task. It is easier

for an employer to prohibit all outside activities than it is to monitor them and limit their extent.

For example, Holmstrom and Milgrom state, “a rule against personal telephone calls during

business hours is easier to be controlled than the rule limits the percentage of personal calls to

2%.” This makes sense since we should also keep in mind that “monitoring” these rule limits

would result in an additional cost for the principal.

Assumptions:

1. Constant returns to time for improving performance measurement and benefit to the

principal.

2. Assume the agent has an finite pool K={1,……,N} of potential activities. These activities

that the principal can control by exclusion could only benefit the agent and not the

principal. The agent’s personal business can be allowed in a subset of tasks (A⊂K) or

excluding them (kA) .

3. The principal can control the incentives (commission rate) and the set of allowable

personal tasks A⊂K

The personal benefits for the agent can be described as follows:

c(t,t1,…,tn)= C(t+∑ktk)- ∑Avk(tk) (8)

Let t denote the attention the agent devotes to the principal's task and tk the time he devotes to

personal activity k. The notation ∑k stands for summation over k in K. The agent’s personal

benefits are the same as the cost of his total efforts excluding the cost of his personal efforts. The

return from personal activity k is measured by the function vk(tk); these functions are assumed

strictly concave with vk(0)=0. Assuming constant returns to effort for profits and improving

performance can be described as:

B(t,t1,…,tn)= pt, x(t,t1,…,tn)=t+ε (9)

To simplify this problem, we will study the principal’s problem in two stages. First, we fix α and

consider the optimal choice of A, denoted A(α), and then we determine the best α.

Stage 1: we fix α, set A(α) based on that, and find the optimal α .

αt+∑Avk(tk)-C(t+∑Atk)

We can see the amount of time the agent spends on all tasks and personal tasks depends on α not

on A. Therefore, if the number of tasks increases, with a fixed α, the agent will spend more time

on personal tasks and less time on the principal’s tasks. As such, the agent stands to gain

vk(tk(α)), while the principal stands to lose ptk(α). This makes sense as your wage remains the

same (compensation), the agent will spend more time on personal tasks if the number of possible

tasks increases.

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The optimal set of allowable tasks, illustrated in figure 1, is:

A(α)={k∈K︱vk(tk(α))> ptk(α)}, (12)

Explanation of figure1:

This graph shows the relationship between the agent’s return and his efforts, v1 and v2 two

curves the returns from two private tasks. It is optimal to allow task 1 but to exclude task 2,

because if the agent is given t1(α) amount of time, he will yield more from doing his personal

tasks than doing the principal’s task. Since v1(t1(α))>pt1(α), but v2(t2(α))<pt2(α).

Intuitively, A(α) expands as α increases, because tk(α) is decreasing as vk is strictly concave. As

α is raised, the agent will spend less time on private business and more time on principal’s tasks.

Furthermore, we see that the critical value of α at which private task k will be excluded when vk

= pt. Since this follows tk(α)≤ tkhat iff vk′(tk hat) ≤ α.

Proposition 3: Assuming α allows for t(α)>0:

(i.) If the average product vk(tk(α))/tk(α) exceeds the marginal product p in the

principal’s task, it is optimal to let the agent pursue exactly their private activities

that belong to A(α) defined in equation (12).

(ii.) The higher the agent's marginal reward for performance for the principal’s task, the

greater is his freedom to pursue his personal activity. Formally, if α≦α’, then

A(α)⊂A(α′).

(iii.) If we exclude one task for not meeting the previously noted criteria, then we should

exclude all tasks where the average product does not exceed the marginal product.

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Important notes about the commission rate:

1. The incentives make the agent reallocate his efforts in a way he benefits the agent and

principal because the agent receive a better incentive by doing his personal tasks.

2. Responsibility and authority should go hand in hand. More specifically, if the agent is

more responsible for his performance, he will get more freedom to do his own

business. But this is not the same everywhere. Normally, in North America, chairman

owns both responsibility and authority, while CEO have more authority than

responsibility. In China, the state control a lot, even though you are a leader in this

company, you don’t have a lot of authority. In Scandinavian corporations, most

people may have shared responsibility and authority.

3. Increasing an agent’s commission rate will lead to more personal tasks allowed for

the agent.

Proposition 4: Assuming t(α)>0:

i. From equation (5), we got the best commission rate is given by

α=p/[1+rσ2/(dt/da)] where dt/da=1/C〞+∑A(α)(1/vk〞)

ii. If the error in performance measurement (σ2) decreases or the agent becomes less

risk averse, the principal can relax the set of allowable tasks and increase the

commission rate. Otherwise, if the employee’s performance cannot be precisely

measured, there will be more restrictions on his activities.

iii. Any tasks that are excluded from first best arrangement will also be excluded from

the second best.

Ending remarks

1. α and A(α) complementary instruments: increasing either leads to an increase in the

other.

2. Since performance of bureaucracy is hard to measure, the incentive strategy is not easily

applied in this situation, so the most effective way to constrain activities to reduce their

freedom.

3. If exclusivity is easier to enforce within firms across firms, then poor sales measurement

and employment are positively related.

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5. Allocating Tasks between Two Agents

Notation:

{ } is the vector of total attention to be devoted to the various tasks

is the total attention devoted by agent i

is the commission paid to agent i for task k.

C is the agent’s private cost

From what we have seen so far, we know that the commission rate, , serves to do the following

important items: allocate risk, motivate work, and direct the agent’s efforts across tasks.

When any of these three objectives are in conflict with each we have a trade-off. Holmstrom and

Milgrom point out that things such as job restructuring and relative performance evaluation can

help mitigate these problems.

Optimal groupings

In their model there are two identical agents, indexed: i=1,2 , who allocate their

attention across a continuum of tasks indexed by ∈ . Attention given to task k

by agent i is:

Assume agents can share a task and that their labor inputs are perfect substitutes

Profit is a function of total time vector: { ∈ } where

In other words, total attention is a sum of the agents’ efforts

devoted to task k.

Task k has a performance signal which is given by and only depends on

total attention devoted to it.

Error variance of task k is and the errors are assumed to be independent.

Agent i’s total labor input is given by the following function:

∫

The agent’s private cost is C which is assumed to be differentiable and strictly convex.

Holmstrom and Milgrom stress how we are interested in the optimal solution which is non-

symmetric so this means we have to be careful to deal correctly with inherent non-convexities of

the problem.

The problem is set up in the following manner

∫

Subject to:

(12) The optimal set of allowable personal tasks, (13) Total labor input, and the incentive

constraints:

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if

if ∈

These can be obtained through first order conditions. We can see that these mean that if the

attention to task k is positive then marginal private cost to the agent will be equal to the cost of

risk-bearing.

Proposition 5: In the model described above, it is never optimal for two agents to be jointly

responsible for any task k.

For the mathematical proof see page 45 of Holmstrom and Milgrom’s paper. Some intuition we

should take away from this is that the principal incurs some fixed cost as the agent assumes some

fraction of the risk associated with that task and/or that task’s measurement. Assigning joint

responsibility for any task would incur two fixed costs (one for each agent) for the principal.

This is simply unnecessary. Thus, for every one task there should only be one agent assigned to

it.

Having established this fact, we now turn to how the tasks will be grouped. Holmstrom and

Milgrom redefine some variables for ease of interpretation:

Now, is the hypothetical commission rate that the principal would need to pay the agent to

elicit some level of effort from agent i if he were assigned task k (see equation 17 which is a

constraint in the minimization function).

Task assignment variable: =1 if agent is assigned to task k, 0 otherwise.

Thus, actual commission rate paid to agent i for task k is:

if agent i is assigned to task k

=0 otherwise

Proposition 3 implies that at the optimum, . This means that the task

assignment to agent i times the time spent on that assignment will be equal to the attention agent

i devotes to k. Either the agent is assigned to that task or not, so this makes sense.

Now, the principal’s task assignment problem can be stated as it is in equation 16 of the text

(page 45) with respect to constraints (17)-(20). Holmstrom and Milgrom give a detailed

explanation of how these equations work together so that all feasible assignments yield the same

total CE wealth.

Since we are interested in the asymmetric case, Holmstrom and Milgrom let . This means

that agent 1 devotes less attention to her tasks than agent 2. Relaxing constraint (20), they allow

for the task assignment variable to simply be greater than 1 (recall it used to be either 0 or 1)—

this new equation is (21). Since we have two agents we will have two Lagrange multipliers

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(associated with constraint in equation (18)). After optimizing equation (16) subject to (17) –

(19) and equation (21), Holmstrom and Milgrom obtain equation (22).

if

and

if

We know that given their assumptions: . Equations in (22) characterize the solution to

the original problem (the relaxation of (20) to (21) is not very different) and identify the marginal

tasks. Marginal task is defined as a task where the advantage of assigning the task to agent 1, in

terms of lower risk premium required, is just offset by the higher marginal value of agent 1’s

time. There are costs here related to measurement error attached to the task and the amount of

time the task requires. For this reason, Holmstrom and Milgrom define the following

The noise-to-signal ratio of task k is defined as:

⁄

Information coefficient is defined as:

Let

-1

Note that a higher means that it will be harder to measure performance in task k.

The equations in (22) can be restated as the following proposition:

Proposition 6: Suppose that the two agents devote different amounts of total attention to their

tasks (i.e. ). Then, tasks are optimally assigned in this model so that all the hardest-to-

monitor tasks are undertaken by agent 1 and all the easiest-to-monitor tasks are undertaken by

agent 2. That is, agent 1 is assigned all the tasks k for which , and agent 2 is assigned

all those with .

This states that tasks which are harder to measure are grouped together, while tasks which are

easier to measure are grouped together. This idea is a little simplistic and doesn’t encompass the

idea of the piece-rate example where we might want the agent to produce quality and quantity

items.

Holmstrom and Milgrom then go onto giving normalized performance measure and they

determine that the normalized commissions must all be equal for an agent. This follows from the

fact that all attention to various tasks are perfect substitutes in the cost function (one of the

assumptions made earlier in the paper. Even though the two agents in the model are identical ex

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ante, an optimal solution necessarily treats them asymmetrically requiring them to specialize in

different tasks. More information is given in the following proposition:

Proposition 7: Suppose that the information coefficients are not all identical and consider

the variant of program (16)-(20) in which the variables. are added to the list of

choice variables. This program has no symmetric optimal solution. There is an optimum at which

agent 1 is assigned less strenuous work ( , takes responsibility for the hard-to-measure

tasks and receives lower “normalized commissions”

The mathematical proof of proposition 7 is found in page 48 of Holmstrom and Milgrom’s paper.

Since we know agents are not allowed to work on the same task then it makes sense that there is

no optimum where there is a symmetric solution. Since we know by proposition 6 that there

needs to be grouping involved, it will turn out that one agent will be assigned the harder to

measure tasks. By proposition 6, then the other agent will be given the remaining tasks which are

easier to measure.

Caveats:

1. The assumption that tasks are “small” and that the principal has perfect freedom to group

them together in any way to form a job are two assumptions which are particularly

attractive.

a. There could be a finite number of tasks (this reverses some of the conclusions that

Holmstrom and Milgrom make).

b. Tasks cannot always be separated (such as maintaining quality and producing a

product). This “caricatures” the problem of how jobs are constructed.

2. The assumption that the errors of measurement are independent is not valid.

a. According to a previous paper by Milgrom he had found that the errors were

positively correlated to each other and that separating the tasks allows use of

comparative performance evaluation. Also, grouping tasks in which performance

is negatively correlated reduces the agent’s risk premium. Present model,

according to Holmstrom and Milgrom, is incomplete.

3. The attention allocation model is a simplication which forces all activities to be equal

subsitutes in the agents cost function. This excludes the possibility that some activities

may be complementary.

a. There were varying findings regarding complementaries. These distinctions with

resepct to attention allocation are things that the theory cannot address.

4. Model does not allow for issues of job rotations (like in real world). The models they

have studied assume that the agents focus their attention on the same tasks for all time.

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Conclusion

With an incomplete set of performance measures and a complex set of potential responses from

the agent, how does one incentivize the agent in a way to attain maximum utility from them?

The problem of providing incentives to agents is far more complex than what the standard

principal-agent model examines. The performance measure that is used to reward agents could

aggregate highly disparate aspects of performance into a one and cause agents to ignore the other

aspects of performance that are also essential to the firm. Holmstrom and Milgrom approach the

principal-agent model with a more holistic view.

They address the fact that to control an agent’s performance in one task requires more than just

deciding how to pay for their performance. Their analysis extends to change of asset ownership,

restrictions on ways a job is conducted, and changing the limits and incentives of other activities.

Along with these extensions, the principal-agent can also be related to other papers we have

studied. Mortensen and Vishwanath’s model on personal contacts proposes that the wage offered

by an employer will be higher if the employee applies for the position through a contact.

Incorporating this idea into the model would suggest that if an agent were to apply for a job

through a contact the principal would offer them a higher wage. In this case the wage will be

determined by information signals and contact probability, w(x,p). At the same time the amount

of effort that an agent puts into his task changes with the contact probability. If the agent is hired

through a contact, the amount of effort he puts into his task will more higher. Another paper we

could relate this model to is Akerlof’s “Market for Lemons” which deals with cases of

asymmetric information. For a task where performance cannot be measured effectively a

situation of asymmetric information arises. Here only the agent is aware of the actual effort he is

putting into the task since the principal has no direct way of measuring the performance of the

agent. This affects the way incentives are structured for the agent.

The concept of outsourcing can also be drawn from this model. In the section on job design,

tasks that are easy to measure are assigned to one agent while the difficult to measure tasks are

assigned to another agent. In the case of a firm, they separate operations according to how easy it

is to measure them and they are then assigned to different departments. The reason sales calls for

companies have been outsourced to call centers in countries like India is because the task is to

answer a certain number of calls or make a certain amount of calls per day and can be easy

measured.

Although Holmstrom and Milgrom have extended the standard principal-agent model, there are

many more variables that could affect the way incentives are structured for agents by the

principal.

16

Appendix

Derivation of function (5):

Differentiate

subject to t and set it equal to 0, then

=0

Q.E.D

Derivation of function (7):

Function (5) is the set of , so you can easily derivate function (7) just by open the matrix and

with the assumption: is infinite

Derivation of (10) and (11)

Derive wrt t: α- C′(t+∑Atk)=0, α= C′(t+∑Atk) (10)

Derive wrt tk: ∑Avk′(tk)- C′(t+∑Atk)=0, ∑Avk′(tk)= C′(t+∑Atk),

Using (10) we can simply the equation to get:

∑Avk′(tk)= ∑Aα, α=vk′(tk) (11)