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DEWEY
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ALFRED
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WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
FORMAL AUTHORITY VERSUS POWER
IN PROFIT
MAXIMIZING ORGANIZATIONS
Julio
J.
by
Rotemberg
Massachusetts Institute of Technology
WP#3652-94-EFA
February 1994
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
FORMAL AUTHORITY VERSUS POWER
IN PROFIT
MAXIMIZING ORGANIZATIONS
Julio J.
by
Rotemberg
Massachusetts Institute of Technology
WP#3652-94-EFA
February 1994
M.I.T.
FEB
LIBRARIES
2 51994
RECEIVED
Formal Authority versus Power
in Profit
Julio J.
Maximizing Organizations
Rotemberg
Sloan School of Management
Massachusetts Institute of Technology
January 31, 1994
Abstract
I
consider a setup in which the firm genercilly wishes to follow the wishes of individuals (or groups)
with large amounts of specific
human
capital even
if their willingness to pay for decisions is less than that
power over decisions. In a situation where costly communication
prevents the owner of the firm from knowing the valuations employees attach to all decisions, the owner
will give formal authority to one individual (or group). I show that, as long as individuals have the
of others. Thus, these individuals have
possibility of protesting against decisions they do not like, it may be profit maximizing to give this
formal authority to someone other than the powerful individual. The reason is that the threat of formal
protests by powerful individuals
is
more
effective as a check
on the discretion of the person endowed vnth
EI
Toulouse
comments
formal authority.
'I
wish to thank seminar participants at
in
for helpful
In
all
but the smallest of firms, authority
make
get to
delegated in the sense that employees other than the
is
decisions that have a lasting impact on the organization. This delegation
CEO
of costs associated with giving the
as a starting point, the
all
is
CEO
probably the result
the relevant information. Taking information transmission costs
team theory approach originated by Marschak and Hadner (1972) allows one
predict the allocation of authority in organizations.
In effect, decisions are
best informed about the consequences of the particular decision.
A
made by
the employee
similar conclusion
is
who
to
is
reached by Jensen
and Meckling (1992).
As
is
widely recognized (Radner 1992) the main shortcoming of the team theory approach
is
that
regards each employee as ma.ximizing the welfare of the firm without regard to personal objectives.
related defect
is
that, in practice, decision
individuals' preferences (as
opposed
to only
making
inside organization appears to
who
particular decision's outcomes. Rather, employees
their wishes tend to
this allocation of
be reflected
who
cope with
in decisions.
In
seem highly correlated with information about the
are important to the firm either because they control
difficulties
Rotemberg
it
single
provide a model which rationalizes
ability of
groups and individuals to get their
does not provide a satisfactory model of the delegation of authority.
owner
(or
CEO) who knows
theory approach, the
what
I
power.
I
CEO
A more
all
it
considers a
possible decisions and
satisfactory treatment would recognize that, as in the
team
has to rely on information provided by his subordinates to reach a decision. That
consider in this paper.
The gathering and transmitting
terprises,
In particulcir,
the private benefits that employees derive from
decides directly whose wishes to follow.
is
appear to have disproportionate influence:
(1993),
While that model matches the observations concerning the
way,
depend rather heavily on
has most influence in organizations (see PfefFer 1981).
Influence over particular decisions (or power) does not
it
A
on individuals' information). One can conclude that preferences
matter from the extensive literature that studies
important resources or because they help
it
of information
is
intimately related to issues of authority. In actual en-
middle managers gather and transmit information. In practice, this gives them authority because
they have a monopoly on the information they gathered so that their choice of what information to transmit
tends to dictate what their superiors choose.
selves with only
minimal reporting to
In other cases, the middle
their superiors.
But,
in
corporate
managers make the choice themlife,
authority
is
rarely absolute.
Subordinates
who
to those that
lie
that their superior's decisions slight their interests generally have the right to protest
feel
above their superiors. These are able, and often do, countermand those decisions that have
been protested against.
Thus
in this
paper, authority will be given a very particular meaning.
authority over a decision
upwards.
However,
I
if
in
will also
authority. However, as long as those
The aim
who
some power although
of this paper
regard individuals as having
incorporate explicitly the notion that the person
potential for protests reduces the effective power
authority will confer
will
they can de facto dictate the decision by manipulating the information they send
protests so that he, in effect, has to worry about the wishes of those
Thus the
I
the ability to get
power
will generally fail to
to consider a very stylized situation in
is
two possible organizational charts.
which a particular activity
whose protests
must incur some of the
protest
this
i.e.,
What
located.
is
in
authority
subject to
will potentially
be heard.
what one wants, of those
costs associated with protests,
be absolute.
which a firm must choose between
distinguishes the two organizational designs
Consider
is
is
the tutelage under
concreteness the logistics activity that concerns
for
itself
with warehousing finished products and shipping them to customers. This activity relates directly both to
the production and to the sales departments of a firm so that
either department.
Whether
it is
better to locate
it
issue
is
plausible to place
under a particular department
part on the technical complementarities involved. In practice,
two departments. The
it
it
will also
under the aegis of
it
obviously depend
will
depend on the
relative
in
power of the
then whether, ignoring the technical aspects, the most powerful department
is
should also be given direct control over this particular logistics activity.
While
this real
world issue motivates
my
analysis,
my model
ployees and one decisions that has the potential of affecting
human
capital so that, as in
about the nonpecuniary
valuable employee
to
i.e.,
utility that the
their
extremely stylized.
them both. The employees
power would
differ if the
for the decision.
CEO
employees draw from various decisions.
the one with the most specific capital, would get his
pay the same amount
to have full information
Rotemberg (1993)
is
The
issue
about the available options,
I
consider in this paper
this valuable
employee
I
consider two em-
differ in their specific
had
information
In particular, the
way when they
is
full
are both willing
whether, once the
will also receive
most
CEO
ceases
formal authority
over the decision.
I
show
that, while there are benefits
from giving authority to individuals that the firm wants to empower.
The
there are costs as well.
cost
even when he thereby gains much
result,
it is
that the powerful Individual will then choose his favorite
is
less
sometimes attractive to
than others would gain with alternate choices.
employees who are
let
less
that, as a
is
attractive because
it
has been shown by
(1955) and other subsequent researchers that people without a strong position in the hierarchical
structure often have a great deal of power.
shows that people with high rank are
that
show
important to the firm have formal authority.
This potential separation between formal authority and power
Thompson
I
outcome
many
That
'
is
not to say that rank confers no power. Ibarra (1993)
be viewed as powerful. But, the main point of her paper
likely to
is
other characteristics of employees are related to their power as well.
The paper proceeds
(1993). In this
portionately
In the first section,
as follows.
model one of the two employees
if it
following section,
had access
I
to information
is
I
set
powerful
up a model that
in
is
very similar to Rotemberg
that the firm would follow
about the employee's valuation
wishes dispro-
its
for the different projects. In the
cissume that the firm has to learn the valuations from the individuals themselves and
that this transmission of information
is
costly.
Moreover,
I
assume that there are economies of
scale in the
sense that an individual employee can credibly transmit the benefits of both employees from a particular
project for the
same
cost as
should be interpreted
is
it
would cost to transmit information on just
gets.
own
valuation.
particular option, the firm can
Because of these economies of
only from one employee.
As we
tell
scale, the firm benefits
shall see below, this
values he transmits largely determine the
employee
outcome of the
how much nonpecuniary
I
am
following Tirole (1986) and LafTont (1990).
assume that the person
The way
this
will in effect,
decision.
at the top
is
in
"'
benefits each
from requesting the details of a project
In
have authority because the
assuming that economies of scale
the gathering and transmission of information determine the existence of a person
hierarchy,
^
that there are economies of scale associated with describing any particular option.
Once an employee describes any
employee
his
who
While they do not derive
is
at the top of a
their hierarchy, they
charge of transmitting information. That such a hierarchy
'Thompson (1955) provides an example from the military where the
out in great detail. He shows that, nonetheless employees' de facto power
in
is
hard to
each employee are spelled
extend to areas for which they are not officially
official responsibilities of
cjvn
responsible.
whose vziluations are unknown and lets the transmission
However, in that literature this cost is not independent of the
individual's valuation. Instead, information is transmitted by having the individuals with different values sort themselves in
terms of the actions they take. Here, instead, I consider the possibility that the individuals can prepare documents that establish
their valuation for different outcomes.
They also consider optimal arrangements (or side-contracts) between the person in authority and his subordinates. 1
neglect these here and assume that no payment can take place between the person who transmits the information and the other
employee. While there is a clear incentive for such contracts, they are made difficult by their lack of enforceability in the courts.
The standard mechanism design
literature also considers individuals
of this valuation involves a cost (Baron
and Myerson
1982).
derive without
making
special assumptions about the costs of information flows
is
suggested by Baron and
Besanko (1992).
It
seems natural to view the person who
as having authority since
we
is
in
charge of transmitting the information about one project
are used to seeing individuals with authority transmit information upwards.
However, authority tends to involve more than just transmission of information.
right to collect information and,
more
also generally involves the
specifically, of asking questions of one's subordinates.
both of these features of formal authority play a pivotal
role. In particular,
with authority can costlessly discover the nonpecuniary benefits of
Thus
It
He
the employee with authority has several advantages.
is
my
model,
assume that only the employee
projects for the other employee.
gets to scan the private values of alternative
projects and transmit upwards the characteristics of a project he
described, the right to protest as long as he
all
I
In
likes.
The other employee
The main
willing to incur a cost.
has, as
I
already
conclusion of the paper
The
hinges on the fact that the incentive to protest will generally be larger for the more valuable employee.
result
is
The strong
that giving authority to the other employee can be attractive.
incentive to protest of
the valuable employee ensures that the employee with authority does not abuse his authority in the
way
as
A
would the more valuable employee.
secondary conclusion of the paper
attractive because
it
is
that protests will sometimes be observed in equilibrium. This
reproduces a fact of organizational
protest even though they are not always successful.
life.
who
are not always successful because the employee
modified to ensure that
it
also gives
nonpecuniary
third section deals with a related,
the transmission of information
is
for giving
protests
utility to the
the process that takes place following a protest so the
The
Moreover,
demonstrate that employees
I
Protests, like the influence activities of
Roberts (1988) take place here because they have the potential
They
same
outcome
though somewhat
is
more
much
in authority.
of the protest
Milgrom and
is
the project can be
This
is
discovered in
stochcistic.
different definition of authority. In this section,
so costly that the employee with authority simply
without communicating the employees' valuations
will
rents to individual employees.
not sure how
employee
is
for the decision.
makes
his decision
Since the firm does not learn these
valuations, employee wages are unaffected by the decisions that are taken.
The aim
of this section
is
to
show that the conclusions of section
2 are robust to the introduction of this
even larger impediment to information transmission. Putting the employee
who
is
less
valuable in charge can
be attractive because the other employee has a larger incentive to protest. The other substantive conclusion
of this section
any
is
that
loss in profits.
making wages independent of the decisions that are actually taken need not involve
The
optimality of wages that are literally constant requires arises only under special
circumstances. However, the fact that profit maximization
more
its
general.
wages
may
It
may
suggests that the barriers to information transmission that prevent the firm from adjusting
cause only second order losses.
"*
The Model
1
As
in
Rotemberg (1993)
needs to be
I
suppose that there are two
made on which
each period that employee
i
risk neutral
value of
simple,
its
I
also
so
it
The
it
I
i
with probability (1
—
z\ for
and that a decision
firm operates for two periods.
does not know the value of these outside
pays him
B
and
^
The
In
outside offers of
assume that the firm cannot precommit the
consider a very simple stochastic structure for these offers.
^2
A
remains at the firm, he generates a value equcJ to vV
future wages and that
the outside offer of employee
pays him
employees
their desires are potentially different.
the employees represent the other determinant of their wages.
I
involve constant wages suggests something
working elsewhere
P). Without loss of generality
in
I
I
offers.
assume
To keep
that, in the
the anaJysis
second period,
that period with probability
P
while
it
let
^i
<
4
(1)
v'
>
zi
(2)
assume that
is
socially efficient for the
employee
to
remain
In the first period, the outside offers of each
in
the second period.
employee guarantee a certain present value of payments
working elsewhere. This present value of payments equals
y\
with probability Pi,
j/j
for
with probability Pt and
(1985) and in Barro and Romer (1987). Mankiw (1985)
from the optimum price leads a monopolist to incur only
second order losses. Thus, the losses from keeping the price constant in response to a smeill perturbation cire of second order as
well. This is similar to my setting in that the firm generally incurs only second order costs when its wage differs slightly from
the optinuun. However, my result is stronger because a constant price can actually be optimal in my model. In that respect,
the model is more closely related to Barro and Romer (1987). They show that constant prices can be optimal in their model
of full-day tickets at ski resorts because the price of the thing people actually care about (namely ski-lift rides) is effectively
varying even though the posted price for full-day tickets is constant. Simil^lrly, the constant wage in my model is consistent
with variations in total compensation, although these variations are not due to a congestion effect like that in Barro and Romer
^The argument has some
similarities to the
arguments
in
Mankiw
starts from the observation that charging a price that difTers slightly
(1987).
This is the wage of any potential replacement plus the difference between the revenues generated by the employee and those
generated by the replacement.
j/^
with probability (1
-
-
Pi
P2).
Once
again,
I
let
<yi<y'3
y\
I
will also
assume that
Assuming that the firm does not discount the
the employee for two periods.
>
2v' so this requires that 2v'
of
1/3
and avert
From
in
for
all
smaller than the present value of the benefits the firm gathers by keeping
is
j/3
(3)
The
j/3.
result
is
that
would be
it
future, this present value equals
efficient for the firm to
pay a present value
departures.
the point of view of the owner of the firm, there are a great
terms of the revenues that they generate and
both employees. To simplify the analysis,
I
potential projects which differ
terms of the nonpecuniary
in
utility that
they generate
assume below that while the owner does not know the
will
know
characteristics of potential projects, he does
many
that there exist
some projects which have an acceptable
pecuniary return. In other words, he knows that there exist projects which raise revenues by
To reduce the need
investment of N.
for transmission of costly information,
projects which meet these specifications.
that they provide are ex ante random.
a particular project
_;'.
I
£
and
0.
In this section,
I
first
unknown. What
is
taken up
wages of both employees
effectively faces a choice
will
'One could
exist, the
nonpecuniary benefits
the nonpecuniary benefit that employee
by the projects that are feasible
known
is
that the
x'-'s
(i.e.,
i
attaches to
that satisfy the
can take three values, namely
h,
the values attached by employees to the various projects.
the next section.
between paying
:\
-
zi,
<
P{v^
-
and
The
z\)
z'2.
The former keeps
firm
now compute
the
the employee with probability
P
while
better off paying the lower wage as long as
is
or
[l
-
assume throughout.
justify this
I
both periods as well as the profits of the firm. In the second period the firm
in
v'
I
in
the owner entertains only
understanding the firm's choice of projects.
for
the latter keeps him with probability one.
which
know
is
for a fixed
that the project that has been implemented gives no nonpecuniary benefits to either em-
This provides a good baseline
ployee.
x'-
x's provided
the owner also
let
Costly information transmission
Suppose
denote by
I
assume that the
financial constraints) are initially
While projects that meet them
®
R
by assuming that no superior projects
exist.
P)(v'
-
z{)
<
zi,
-
z{
(4)
I
now turn
Here the firm essentially has a choice of whether the
to the analysis of the first period.
present value that employees can expect by staying
probability Pi, Pi
+
P2 and one respectively.
employee that remains
in the first period.
I
is
y[,
y!^
or
now compute
To do
this,
the expected present value of earnings of an
assume
I
These lead to employees remaining with
j/3.
for simplicity that neither the firm nor the
workers discount future payments. Since (4) implies that employees receive
remain with the firm
for
both periods, remaining
in the first
second period
z\ in the
period in exchange for a
first
they
if
period wage of
w
leads to an expected present value of earnings equal to
w+Pz\+il-P)z{
Paying the wage that leads to an expected present value of
P,[v\l
+
P)
-
(1
_
+ P) -
y{
+
y-
<
P).']
(5)
maximizes expected
y\
(Pi
+
P2)(y'
-
profits
if
(6)
y{)
and
-
(1
Pi)[v'{l
maximized by paying the
Profits are
first
+
(1
-
P)zi]
<
(yi
-
(7)
y\)
period wage that leads to a present value of
1/2
if
(6)
does not
hold while
-
(1
holds.
Finally, a
I
will
leads to a present value of y\.
1
now
-
+ P) -
P2)[i;'(l
assume that
The purpose
utility to individual
(6)
when
similar analysis applies
—
X.
The
latter
is
P)zi]
maximizes
in
().
As
in
{yi
is
if
i
-
profits
y')
if
(7)
his
To
wage
(8)
and
(8)
both
fail
equilibrium wage in the
to hold.
first
period
to ensure that decisions that give
for raising their total
a nonpecuniary
Rotemberg (1993), such
the second period.
his outside offer equals Zj
<
(7) hold so that the
consider the effect of decisions that give employee
the second period
z\
-
employees also have the potential
probability that the employee remains
or
j/3
(1
of this assumption
the firm (where x can take the value of h or
in
and
+
y^
wage that leads to a present value of
For purposes of illustration
nonpecuniary
Pi
utility
x
compensation.
if
he remains at
decisions can change the
see this, note that the employee
in the firm
when
his outside offer equals z\, the firm effectively
more
profitable
is
more
smaller than ;2
~
now
*•
leaves
Since a
has the choice of paying ^2
~
^
if
{l-P){v'+x-z{)<zi~z[
(9)
For large enough x, (9) can be violated even though (4) holds.
employee with probability one
if
z
sufficiently large.
is
will
I
assume that h
does indeed keep with probability one any employee whose x
I
will
occurs
be concerned with the case
in particular if
v^
similar but A's outside
in
v^
larger than
is
off'ers
will focus
,
on the case where the
;'s
is
is
sufficiently large that the firm
equal to h.
has more specific
human
capital than B.
This
though a similar analysis applies when the internal values are
are lower (which
valued outside the firm). In either case, (9)
I
A
which employee
This nieans that the firm retains the
is
(and the
also consistent with having capital that
is
more
likely to
be violated
same
y's) are the
for
A.
To keep
is
relatively less
the analysis simple,
both employees but where
for
v'^yv^
Given
it
(10),
it is
possible that,
is
equal to
(9)
£,
is
(9)
is
violated for both employees
now turn
I
when x =
when
when
the firm adopts a project
adds
One
to the analysis of the first period.
rents
i
little
new
whose nonpecuniary
is
holds for B. Alternatively,
The
wages that induce a present discounted value of earnings of
while the present value
C
it
When
is 2/3
when the nonpecuniary
the nonpecuniary payoff
that period. Accepting to stay
is
in
h,
employee
the
first
i
payoflT
utility of i
and gain even larger rents
the employees' taste for projects
some
must be the case that the firm pays
2/2
is
case
where both employees gain some
perfectly correlated with the nonpecuniary utility that they derive from them. This case thus has
offer
in
is
h. In this case,
obvious intuitive appeal. For this perfect correlation to obtain,
is
it
insights.
interesting case
utility
while
consider both cases below.
will
1
them nonpecuniary
the firm adopts a project that gives
A
violated for
possible that, in this case, (9) holds for both employees.
is
where
is
when x
(10)
when
first
the project's nonpecuniary payoff
h.
stays for sure in period 2 and gets Z2 of total compensation
period with a wage of
u;
thus leads to an expected present value
of
w+
To ensure
:i,
that the firm chooses a present value of
+
2/3
h
in this case,
we must have
{l-P,)[2{v'+h}-y{]>{y',-y\)
(11)
and
(1
-
P,
-
P,)[2{v'
+h)-
2/']
>
(y-
-
J/')
(12)
These
period
1
inequalities are consistent with (7)
leads to
and
because h
(8)
is
large
being earned by the firm with higher probability
i;'
and because paying a high wage
in the
subsequent period.
Since (11) and (12) hold for both employees, both earn a present value of
that gives
them h
in
nonpecuniary
utility.
gives
him a nonpecuniary
benefit of h
expected present value of income
is
off.
The employee
gain, however,
is
.4
and
different.
D
rises at that
An analogous
of h.
It
+
yi
implemented
offer in the first
also strictly better off
first
is
if
period
the decision that
period outside
offer.
+ P2iyi-yi)
same
His
A
The
firm's
a nonpecuniary utility of h gains the firm
+ P) - yf +
2h - P,[v^{l
(13)
to have such a project implemented.
Implementing a project that gives
-
a project
if
point by
are willing to pay the
2v^
is
taken before he knows the value of his
Pi{yi-y\)
Thus employee
y'-^
This makes any employee whose outside
short of this present value strictly better
falls
(1
- P)z^]
equation applies when the firm implements a project that gives
thus follows immediately that, assuming (10) holds, the firm gains
(14)
B
a nonpecuniary benefit
more from implementing the
project that helps A. In particular, the gain from implementing a project whose nonpecuniary utility for
IS
h versus that of implementing one which gives this
much nonpecuniary
utility to
B
is
positive
if v"^
employees have power
I
now turn
in
exceeds v^
.
in
the sense that the firm wants to
to considering the effect of projects
the second period.
Thus
his
is
is
Thus, the wage that gives a present value of
m
their wishes.
utility of
£.
I
start with the case
not sufficient for the firm to keep employee
is
z\
—
i.
For any given wage
i
with probability
in the first
period, the
thus
w+e+
+
accommodate
which give nonpecuniary
second period wage
present value of the employee's compensation
p-,[{v'
(15)
This the essence of Rotemberg's (1993) conclusion that valuable
where the implementation of such a project
one
^4
is
{v^-v'')i2-il + P)P,)
This
in
Pz\
j/2
's
+ (i-p)zii
optimal
+ p)-y\ + (i10
p)zi]
if
> (A +
PnM - y\)
(16)
and
{I
Because
2/2
—
y\
£
when
-Pi-
+ 0(1 +
P2)[{v'
yU
-
^)
the firm adopt the project that gives
him
value of y\. Thus, his ex ante gain from this adoption
£
-
and
<
P)-o]
Assuming
positive, (16) can be consistent with (6).
is
(1
-
{y'3
(17)
y'2)
and (17) hold, employee
(16)
equivalent to £
of both employees
is
which gives
period.
The
+
P)
once again, bigger
is,
it
( lo
The
the same.
A
\s
even higher
+
-
(1
for the
if
P)z',]
+
(18)
firm's gain
nonpecuniary compensation to employee
in
P2[v'{i
So that
is
(P,
+
i
is
from implementing a project that gives the
is
+ P) -
P2)(^(i
employee whose value
the result
gains
his outside offer turns out to involve a present
Piiy'2-y{)
Thus the gain
i
that the firm keeps
A
Piy{
The
higher.
is
t^'
+
y'2)
(19)
gain to choosing a project
with probability one
in
the second
firm then gains
(P,
which exceeds (19) because
+
Po)(2t;^
v'^
- yf +
2£)
-
Pi[u^(l
+ P) -
t/f
+
(1
- P)z^]
(20)
exceeds 2^.
Individual projects potentially provide nonpecuniary benefits to both employees. Let there be / feasible
projects indexed by
of income that
i.
Each
feasible project
A and B would
generated by the project.
i
can be described by a vector {xf,xf} which gives the amounts
have to receive to be indifferent with respect to the nonpecuniary
A's favorite project
among
all
the feasible ones
is
utility
denoted by a. This project
satisfies
2;^>^^Vz<;
The
first
inequality ensures that no project has a higher value for
inefficient choices
given level of
x^ > xf J B xf = x^
and
when agents
utility,
A
x^
.
To eliminate
(21)
results
due to
are indifferent the second inequality ensures that, conditional on receiving a
prefers projects that
make
B
better
off.
Similarly, P, the project that
B
prefers,
is
defined by
X0
> xf
,
Vi
<
/
and
.11
x^ > xf
,
;
9 if
= if
(22)
Table
1
Possible Characteristics of
a
/?
for each a
Table 2
Projects whose ranking
{h
is
ambiguous
If .4 is
A
given authority and
reports.
The
result
is
that
B
never reports the value of any projects, the firm implements whatever project
A would
always report the characteristics of q,
on the ambiguities surrounding the projects displayed
from what the firm would implement
Optimality of
2.1
There
if it
In particular, this occurs
full
A
g{h,0)
first
is
inequality implies that g{i,t)
larger than g(i,i) so that
a
is
in fact
optimal from the point of view of the firm.
and
all
g{h,0)
>
g{e,h)
also larger than g(0,h).
is
(25)
Moreover, the second implies that
the ambiguities in Table 2 are resolved in favor of A's preferences.
when A cannot
The second
project that the firm prefers to a.
get
more than
A
and
i
from any project, there
same
inequality ensures that the
a project. In this case, the firm ought to give authority to
is
projects.
all
if
Basically, the first inequality implies that,
there
reported project will sometimes differ
2, this
information on
choose
g{e,0)> g{0,h)
The
Table
Depending
authority
/I's
one case, however, where letting
is
had
in
his favorite project.
is
this authority
never any reason for the firm to favor an option that makes
B
when A
true
is
in
is
no
gets h from
some sense
absolute,
better off than the choice favored by
A.
However,
this
is
an e.xtreme case. Matters are
less favorable to giving
inequality in (25)
is
reversed. This would occur
the difTerence between
the second inequality in (25)
relative to the profits
second inequality
is
v'*
and v^
is
A when
the second
small. In that case,
reversed because the difference between g{h, 0) and g{0, h), (15), can be small
A
from having
in (25)
if
authority to
get nonpecuniary utility which
is
worth
£ to
him.
The
violation of the
captures a very plausible scenario. In this scenario, the firm prefers some projects
that the less valuable employee adores to projects that give only a tiny bit of e.xtra utility to A.
For purposes of illustration,
I
concentrate on the case where, in addition to the violation of the second
inequality of (25),
9iO,h)>giiJ)
It
follows immediately that g{Q,h)
from (26) that
.'/(/!,
0)
is
Suppose that A gets
is
also larger than g(C,0).
(26)
Since g{h,0)
is
larger than g{0,h),
it
follows
also larger than g{(,C).
to choose the project
and that he can e.xpect
14
B
never to protest.
He would then
,
choose a.
If
the resulting project gives h to B, Table
from giving authority to A. Similarly, nothing
exceeds g{Lh) which
and from the
itself
firm's ideal
exceeds g{0,h).
outcome. The
lost
is
namely when a
is
when a has nonpecuniary
is
first is
when a
The
is
which a
in
and there
entails {l,i}
better off with the latter.
payoffs given by {/i,0} while {i,h)
is
so that nothing
when a has nonpecuniciry payoffs of {h,£}
The same
is
since g(h,i)
both from p
inefficiency arises in
available. Finally, the third
The
available.
is
differs
violation of the second
better off with {C,h} in this event.
B's Protests
issue
is
then whether
D
would protest
move from a
project that gives
equivalent to
/?,
his gain
in
these tliree instances.
him non nonpecuniary
utility to
If
such a protest leads the firm to
one that gives him a nonpecuniary
given by (13). Thus, in the last two instances, his gain
is
In the first case, the protest only leads to a
gain from protesting
change
(27)
already positive nonpecuniary
in his
Even vvhen the expression
projects.
At
The reason
best, he
is
in
(27)
that
gets
when such a
does know
is
is
B
positive,
project
all
is
worthwhile
exist
his
is
B
(28)
B
will protest in
utility that
which give him nonpecuniary
him h
is
A
the third case, when a
draws from alternative
utility equivalent to h.
the best for A, he does not
A
would have preferred
the project from which he gets h gives £ or zero to A.
will prefer a. So,
and which appears best
for
A
I'll
suppose that there
gives ^ to ^.
if
Even
know how
he protests.
if
described by {h,h} (since
be to no avail since the firm
that the project that gives h io
not certain that
adopted. This, he discovers only
that no feasible project
latter, the protest will
it is
the projects that give
Thus B's uncertainty concerns whether
Q
Thus
'
does not know the nonpecuniary
knows that projects
assuming that he knows which of
much A
utility.
is
Pi{y3-yi) + P2{y'3-y2)-C2
features (/i,0).
utility
is
Piiy3-y\) + P^.iy3-y2)-C2
B
lost
is
also exists a project described
given by {^,0} while a project with {0,/»}
inequality in (25) implies that the firm
2.2
a and p coincide
indicates that
However, there are three cases
by {0,/i}. In this case, (26) implies that the firm
the second case,
1
B
will
is
this as well).
If it
does the
a probability
then find protesting
'
,
Q[Pi{yz-y\) + P2{y^-y^)]>C2
15
(29)
Suppose that the expressions
in all three
where
A
What
contested cases.
and the firm prefer
or
in (27)
B
whether
have to protest to get
many
succeed
To
words, there
way
outcome that
is
B
an equilibrium
proposes projects with {i,i}, {^,0} or
he observes that a project exists that gives him
h.
But, there are also equilibria where
equilibria exist
if
his way. In other
offer the
will get his
A
always proposes {0,h} when such a project
so
B
would immediately
B
when
always proposes a. In this equilibrium
{/i,0} as long as
A
whether
less clear is
is
will
and (28) are positive and that (29) holds. Then
is
that
A
is
is
protests
available
I
if
assume that a protest by
given either by {(,£} or {^,0}.
is
essentially indifferent as to
he protests and can be expected to protest
avoid this indifference,
and a
what he does
A
reports a.
B
has a cost for
A
in the cases
as well,
and
I
where
A
The reason
B
is
sure to
denote this cost by
C3. This can be thought of as the cost of delivering credible information on A's valuation of B's proposed
project.
feasible
In the presence of
and a
is
even a
trivial cost of this type,
Q with probability
A
because
is
one, then the fact that (29)
then loses C3, this
is
available but
is
a equals
{/i,0}.
positive implies that
B
If
A
is
then choose a with probability one.
The equilibrium must
A
proposes {h,0} with probability one
if
Thus, B's benefit from protesting
protests with probability one.
{i,h}
is
B
never protests
thus involve mixed strategies.
not available and with probability t^
In equilibrium, tt^
as to
is
such that this expression
He thus protests with probability
what he
reports. His gain
which must be zero
in
tt/j.
from reporting a
(1
is
zero so that
B
is
(30)
indifferent
This probability must
in
is
yi)]
equilibrium. Note that a high value for the
likely to
be
B
A
is
2ind not
indifferent
is
- TB)[P,(y* -y\) + P.ivi -
low while the probability that
between protesting
turn be such that
-
ttbCs
left
hand
from getting one's way, implies that the probability that the probability that
(t^a)
if it
is
^AQ[Pi{yi-y{) + P2(y'3-y'2)]-C2
protesting.
is
expected to propose
not an equilibrium. Nor can there be an equilibrium where
A would
In equilibrium
is.
propose {0,h} when such a project
will
given either by {i,C} or {^,0}.
Matters are more complicated when {£,h]
Since
A
protests a suspicious project
efficient.
16
is
side of (29),
A
high.
i.e.,
a large gain
proposes the wrong project
Thus
the
outcome
is
more
So
firm.
far
have treated the costs C2 and C3 as incurred by the individuals themselves as opposed to by the
I
However, the firm probably could pay
for
some of
these costs itself by, for instance, giving individuals
time and resources to mount their protests. Suppose that
project that gives
A
replacing
him
h.
D
If
has proposed {/j,0} and that
protests, the firm has a probability
at the cost of losing the e.xpression in (15).
i)
A
Thus
Q
its
B
knows about a
of gaining the expression in (19) (with
total gain
is
Q{r7(^,0)-b(/i,0)-g(0,/i)]}
While the violation of the second inequality of (25) implies that
D
than the private gains to
which are given by the
,
left
hand
(31)
this
Of
firm would not gain ex post by financing B's protest.
commit
itself in
advance to pay
A must
pay to defend himself remains bounded away from zero. The reason
the expression in (30) to zero,
and
set n,^ near zero. But,
the fact that (31)
2.3
I
it
is
such protests so that the cost faced by
that ^'s response to a low value of C2
seems
likely that in practice the firm
below Ct implies that individuals must pay
is
(29)
is
is
violated so that
sometimes pays to
let
a
B
To maintain symmetry,
B
violated so that
has identified a project that gives him
it
smaller than
course, the firms would love to
B
is
is
is
negligible while the cost that
that, as
one can see by setting
to grant B's wishes right
cannot commit
itself in this
away
way so that
the cost of their protests themselves.
Optimality of B's Authority
now suppose that
of (25)
for
could well be smaller
it
They could thus be
side of (29).
Ci so that the
for
positive,
is
is
h.
I
does not protest a project that implies {h,0} even when he
continue to suppose that (26) holds while the second inequality
not always optimal for the firm.
I
assume that
the violation of (29) also implies that
D
Proposition
and {£,h}
is
1:
if
A knows
respectively.
that,
under these circumstances,
A
that a project with {h,h}
Q
will fail to protest
be (he probability that
a and P
is
Thus
1.
are associated with
nonpecuniary payoffs of {h,0]
and {Q,(}. Then giving authority
17
B.
under some circumstances. Nonetheless, giving
Lei Ao be the probability thai they are associated with {h,i}
the probability that they are associated with {£,0}
unavailable but knows
to the event that this project gives ( to
profitable under the conditions of Proposition
Let Aj
show now
have authority.
of a project that gives him h, he assigns probability
authority to
I
and {i,h} while A3
to
B
is
more
is
profitable
- [g{h,0)-giO,h)]}
Ai (3(^,0)
Proof: To go systematically through
{x',x^} with {x^,x'].
when B reports
do better.
When
/?
because
would
lose his protest
.4
outcome
If
B
efficient
is
It
because
involves {C,h} and {h,C]
if
is
(0,/i}.
him h
picks
A
available,
is
to A,
it
p
will
The same argument
Lastly, there
in
A
available,
is
/?
in this
1.
a
(32)
for
in
Table
1
and replace
In the first three rows,
A
case and neither the firm nor
and the firm would prefer the
is
violated,
A
latter.
gets h
A
can
However,
does not protest so the
is
would protest because he would know that a
and that he would thus win
available
Neither would any inefficiency be present
case where
expression
B
only {h,0} were available and (29)
in
his protest for sure.
the case where
/?
Knowing
this,
B
would
gives {^,0}.
gives nonpecuniary utility equivalent to {0,/i} also fails to create inefficiencies.
On
alternatives {£,i} and {^,0} are inferior.
gives
X3{W,0)-g{QJ)]}>0
inefficient.
is
project that gives
The
-
the possible outcomes, exchange
all
were to propose {(,£] when {0,h}
propose
X2{[g{h,0)-g{0,h)] - [g(e,0) - g{0,i)]}
then proceed to consider the rows of Table
I
The outcome
l3.
-
the other hand,
be preferred by the firm so
implies that
the issue of
(18) exceeds C^,
B
will
what
A
A would
protest.
propose {/i,0} when P
will
occur when
protests and wins.
/? is
if
is
an alternative project were available that
Thus,
B
bows
to A's wishes in this case.
given by {0,£} while {h,Q}
given by {0,£) while {^,0}
But,
if
The
this expression
is
is
is
available.
also available. If the
smaller than C2,
A
does not
gain by protesting even though such a protest would lead to a more favorable project being implemented.
The
result
The
would then be that
outcome
B
is
outcome
benefit of giving authority to
outcome when a and
to
this
is
inefficient.
(relative to giving
it
to
A)
is
thus that the firm gets the efficient
have nonpecuniary payoffs of {h,0} and {i,h} respectively.
/?
potentially inefficient in the events whose probabilities equal Ao
more
The key
B
is
profitable,
when
to the proof
is
and
A3.
The
cost
is
that the
Thus, giving authority
(32) holds.
that an efficient
while a project whose payoffs equal {h,t]
is
outcome obtains when P
available. This
gives nonpecuniary payoffs of {0,/i}
was not the case when the
roles
were reversed
B
because
when he
protest
result
could not be sure to win
B
that
is
if
he protested. Because
sees a project that gives
makes the
right decision.
him h while
In other
fl's
A
is
more powerful, he can be sure
proposal gives him no nonpecuniary
words, ^'s power prevents
to win his
utility.
The
B
from imposing a very bad
is
consistent with the other
outcome on A.
There
still
is
conditions
the question of
have written down.
I
numerical values to
satisfied.
To
which Ai
is
get a
when
(32)
That
there
the parameters and
all
more general
intuition
likely to
is
is
hold and whether
no inconsistency
show
will
it
be demonstrated below, when
that, for these veJues, (32)
on what (32) requires,
it is
I
give
and the other conditions are
useful to consider the special case in
equal to Ao and A3. Then, (32) becomes
X:{g{C,0)-2[gih,0)-g{0,h)]}>Q
Thus,
favorite
A
it
is
and
derives
profitable to give authority to
project
Z?'s favorite
some
utility.
A
a
lot
A
in the
,4
authority
while giving
a lot of nonpecuniary benefits.
take advantage of
3
B
the difference in profits between implementing A's
not too large relative to the value of implementing a project from which
In this case, giving
pass over projects that benefit
that give
is
B when
Giving
is
relatively unattractive because
him an intermediate
B
of Decision
is
too tempted to
level of utility in favor of projects
authority solves this problem without leading
same way because A has a bigger
The Delegation
A
B
to
incentive to protest.
Making
<-
In the
previous section, the employee in authority communicated the valuations of both employees to top
management.
In the
absence of protests, top management used this information only to adjust employee
wages. Since employee wages do not appear to be adjusted every time a decision
realistic to
assume that
costs of information transmission prevent the firm
valuations. In this section,
unless there
is
a protest.
possible projects.
If
I
will
is
made
it
might be more
from knowing the employee's
suppose that, indeed, top management remains ignorant of these valuations
Protests, as before, do reveal the benefits that employees derive from various
a protesting employee incurs the cost Co and the employee in authority incurs the cost
C3, the firm does learn the valuations for both the project that has been originally proposed and for the one
favored by the protesting employee. Thus, after a protest, the situation
before.
19
is
identical to the
one considered
absence of any protests, however, there
In the
about projects between the employee
looks "as
if"
Rather than carry out
is
no communication
authority and top management. Thus, the employee in authority
It
appears that decision making
itself
has been
in authority.
this analysis in general,
that the firm loses nothing from
making wages
that the firm's preference regarding
I
focus on a special case in which the parameters are such
insensitive to decisions.
who should be put
the two employees are transmitted or not.
The reason
from the transmittal of valuations by the person
That such
a difference. In particular, there
he had discretion over the decision in question.
delegated to the employee
is
in
is
in authority
is
is
The advantage
of this special case
the same whether the valuations of
that, in this special case, the firm gains nothing
in authority.
a special case can be constructed at
all is
of course of independent interest.
The
reason
is
that
one does not see continuous adjustment of employee wages as decisions are made inside firms. This can of
by the sorts of costs of information transmission alluded to above. However, because
cour.se be rationalized
the cost of transmitting credibly the valuations associated with just one project are probably not
great, one
to gain
would be worried about the lack of wage adjustment
from
this information.
The
if
is
existence of a special case where the firm gains nothing from knowing
relatively low so that
is
relatively costless.
The reason keeping wages constant can be optimal
utility
that
one thought the firm had a great deal
the employee's valuations suggests that, in general, the gain from such knowledge
keeping wages constant
all
from a decision generally sees
ma.xiniizing to cut the employee's
his total
wage by
is
that, as
compensation
his full
we saw, an employee who gains nonpecuniary
rise as
a result. In other words,
nonpecuniary gain. Thus,
it
is
it is
not profit
not surprising that there
are parameter configurations that lead to an increase in employee compensation that
is
exactly equal to the
nonpecuniary gain.
I
conduct the analysis
in
two steps. In the
needed to ensure that a policy of constant wages
is
1/3
when the project
is
worth
/j,
y'o
when
it
is
first,
in
I
show the conditions on the
periods
1
and
worth £ and
2 implies that total
y\ otherwise.
ensure that, with this policy of constant wages the employee remains
/i.
In the
needed
second step,
for this
I
in
assume that these conditions on parameters are
;'s
and the
y's that are
employee compensation
Moreover, these conditions also
period 2 only
satisfied
and
I
when
his valuation
rewrite the conditions
pattern of compensation to be optimal as well as the condition that implies that
20
is
B
should
be given authority.
In effect, this
section are
all
these conditions can be satisfied at once.
numerical example also shows more generally that the conditions
all
Proposition
fails
then show with a numerical example that
I
wrote down
I
the previous
in
compatible with one another.
2:
(J,),
//
for both when x
is
(6), (7),
(1 1), (12), (16), (17) hold ivhile (9) holds for both
employees when x
is
£ but
h while
z'2
=
z\
+
h
(33)
yi
= y\+i{l + P)
(34)
yi
=
(35)
and
the firm loses nothing
Proof:
[y\
I
will
— P:\ —
(1
from
its
y\
+
h{l
+
P)
inability to observe the valuations of the project that
is
actually implemented.
prove that the firm cannot earn more than by paying
z[
—
implemented. Since these wages are
P):'2]
independent of the
ill
the
level of
first
period regardless of what project
nonpecuniary
is
in
the firm loses nothing from
utility,
the second period and paying
its
ignorance of the employees'
valuations.
Given that
(4) holds, the firm
wants to pay
the employee with any nonpecuniary utility.
z\ in the
Thus,
z\
is
second period when the project does not provide
optimal
in this case.
equals h implies the firm wishes the employee's compensation to equal Zo
implemented gives h
to the
employee when
his in
this
the firm would pay the employee z[
While
z\ is
wage equals
gives the
i
(6)
z\.
in this case.
—£
Thus, once again,
The
(rather than z\)
and
when
7)
his outside offer equals
imply that the wage of
employee no nonpecuniary
utility.
a present value of compensation equal to
[y\
z\
is
if it
knew that
it is
z'^
failure of (9)
compensation accrues
optimal and ensures that the
the project gave
i case implies that
him
i
of nonpecuniary
important to note that the wage of
because (33) implies that
— Pz\ —
(1
—
P)zn]
is
when x
project that has been
when x equals
fact that (9) holds
not the wage would pay in this case,
the employee to depart
Conditions
when the
to the employee. But, (33) implies that, in this case, this level of
employee stays with probability one
utility.
The
z\
+
£ is less
indeed optimal
z\ still leads
than
when
Z2-
the project
Conditions (11), (12) imply that the firm wishes to give employee
j/3
when he
21
gets h of nonpecuniary utility. Given a
wage of
z[ in
the second period, this requires a
rA
where the
first
- 2h -
first
=
z{
period wage of
+
y{
(1
+ P)h -
-
2/1
z\
=
- Pz\ -
y{
equality uses (35) while the second equality uses (33). Thus,
(1
- P)4
[y\
— Pz\ —
(1
—
P)z2]
is
optimal
once again.
Conditions (16) and (17) imply that the firm wishes to ensure that employee
of compensation equal to
probability
P
in
when
y],
where the equality
is
+ P)l-
employee
Thus, the firm loses nothing paying
equalities (33), (34)
and
is
z\ in
-
Pz\
implied by (34). Thus,
offsets the fact that the
The
nonpecuniary
utility
the second period and receives a wage of z\
y),-{\
wage
his
(1
[y\
-
period 2
(I
much"
paid "too
when
if
—
in
P)i2\
period 2
there are only 8 independent parameters, namely v'^
9 conditions hold. However, the fact that (9) holds
period wage of
when
in all cases.
his
Note that
nonpecuniary
utility
when x equals
i,
A
is
the condition (2). Since
some
thus show that there
e.xist
£ implies that (4)
holds as well. In addition,
I
for the 8
when x equals
failure
when x equals h
-
-
P)(v'
z\)
Using primes to denote the transformed conditions, the
+ P) +
>
0.
i
is
assumed
all
the relevant
in Proposition 2 in
terms
now
(9')
is
{\
^.[.(l
i
simultaneously.
e-z\)<h
(\-P){v' +
its
all
independent parameters such that
rewrite the 8 independent conditions
of the eight independent parameters. Condition (9)
whereas
>
of these conditions are highly nonlinear, there appears to be
numerical values
conditions hold. Before, doing so,
L
Pi and Po- Proposition 2 assumes that
no simple method to check whether parameters can be found that satisfy them
I
is
and leaving aside employee B,
there are the conditions (1) and (3), although these are implied by (33), (34) and (35) as long as h
Finally, there
this
the employee gets this level of nonpecuniary utility.
zf, yf, P, h,
,
first
P)zi^
optimal
is
imply that, focusing just on employee
(3.5)
that the employee stays with
he stays, this requires a
= y\-Pz\-{\-
P)z\
— Pz\ —
L Given
equals
gets a present value
:
z\{l
- P) -
yi]
<
(P,
22
> Ph
(9")
rest of these are
+
P2)(l
+ Py -
P2(l
- P)h
(6')
-
(1
(I- Pi-
P,)[v'{l
P2){2v'
P2[i;'(l
(1
assuming that
-
Pi
P, P]
y\, :\,
,
+
-
P)
+
P)
{I
-
y\)
+
conditions are satisfied as long as
v'
/i
is
-P)-
z\{l
P,){2v'
> (P -
z\{l
P2)[t''(l
Po and
+
1
-
y\)
> {P + P,)h
-
2Pi
- 2P2)h +
- P) -
+ P) +
y{]
To preserve the
increase in i
that, since
is
< 2Ph -
.1,
.5,
P2)(l
+
P)e
(12')
- P)h
(1
.3,
+
(16')
P)£
(17')
and
.3
£ is
11 respectively, these
between 5.7 and
The
9.
broad range of parameters implies that one can find
for
parameters that are not.
j/o
In general, g{i,0)
is
increasing
rnust be increased together with i so that any
employee a higher present value of earnings. The
£,
local
result
changes
is
in this
affect profits.
given a nonpecuniary utility of
violated so that
are kept constant then
it is
all
i.
If
P2
is
raised to
the conditions of Proposition 2 continue to be
B
is
employee actucdly stays when he
Using the above parameters with £ equal to 9 and letting Aj
better to give authority to A.
this case, giving authority to
.4
and
met but
all
(32)
=
At
=
is
A3,
the other parameters
is
satisfied as well. In
optimal.
Conclusions
4
The
-
Pi
P2(l
feasible to increase g{i, 0) by raising Pt, the probability that the
It is
is
-
for relatively large values of g(£,0).
to pay the
(T)
(11')
+ P)£y']
- P)]h
wages and the probability that the employee remains are independent of
parameter do not
(32)
Pj(l
between 11.2 and 13 and as long as
equalities of Proposition 2, however,
matched by the need
Pi(l
(1
are given respectively by 8,
parameters that are consistent with (32) as well as
in £.
>
- P) -
z{{l
fact that the conditions are satisfied for a relatively
Condition (32) tends to be satisfied
< [2P +
y\]
setting
I
have considered
is
obviously stylized.
However,
it
shows how one can deal formally with
organizational design issues in situations where the firm want to allocate power differentially to different employees.
One obvious
extension involves consideration of a setting where there are more than two employees.
This would allow one to deal with situations where people are divided into departments and where some
of the
power
is
departmental power as opposed to individual power. Because departments contain different
23
individuals at difTerent points in their life-cycles that
sort considered in
Rotemberg
may
require an overlapping generations
(1993).
For the model to provide a positive theory of organizational charts,
In particular,
direction.
model of the
it
also
must be extended
in
another
the model will have to include not only "strategic" decisions whose effects are
long lasting but also operational (or day-to-day) decisions. In practice, hierarchical control over day-to-day
linked to formal authority over
decisions
is
makes
easier to
it
know
more
lasting choices.
Perhaps
this is
because operational control
the benefits that accrue from different potential strategic choices.
between learning, operational control and strategic decisions needs further exploration
if
This interplay
the model
is
to be
used to understand organizational charts.
5
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P.
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Ibarra, Herminia, 1993,
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25
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