Dewey
HD2C
.
MA 1
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
A THEORY OF lOTER- INDUSTRY WAGE
DIFFERENTIALS
by
Julio J. Roten±)er^
Garth Saloner
WP# 1822-86
September 1986
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
A THEORY OF INTER- INDUSTRY WAGE
DIFFEREOTIALS
by
Julio J. Roten±)erg
Garth Saloner
WP# 1822-86
September 1986
Sloan School of Management and Department o£ Economics,
respectively.
We wish to thank William Dickens,
Lawrence Katz and LaiNrrence Summers for helpful discussions
and the NSF for research support.
M. I.T.
ABSTRACT
of this paper is to present a modeJ which broadly fits
features of Inter-industry wage differentials.
of
salient
some
the
The purpose
Several recent empirical papers have found wage differences accross
They also show high
industries to be large and persistent.
countries.
High wages appear to
accross
occupations
and
concordance
ratios and are
industries
that
have
high
capital/labor
be paid in
explains
these
facts
on the basis of
Our model
highly profitable.
individual
workers. We
firm-specific human capital accumulation by
workers
and the firm
focus on the bargaining between experienced
experienced
worker
over the division of the surplus output an
workers
We show that
produces over that produced by inexperienced
trained
workers,
this surplus, and therefore equilibrium wages of
depends on the the capital/labor ratio when the technology has
putty-clay features. We also show that when there is multilateral
bargaining between all firms and experienced workers, wages also
.
depend on the
profitability of the firm.
oo">t
61987
\
I
Introduction
The purpose
fits
of this
paper
some of the salient features
differentials.
is
to
present a model which broadly
of inter-industry
These features are discussed
in a
wage
number
of recent
papers including those of Krueger and Summers (1986a. b) and
Dickens and Katz (1986a, b).
of
These papers find that inter-industry
wage differences are large and persistent.
They are
also highly
correlated across countries with substantial concordance across
Western industrial countries and Eastern Block countries.
and Katz (1986a)
also
show that the concordance
fairly narrowly defined occupational groups.
is
Dickens
high across
One very striking
feature reported both in Krueger and Summers (1986) and Dickens and
Katz (1986b)
is
that industries in which, broadly speaking there are
more variable profits,
and variable costs
particular,
is
i.e.
where the difference between revenues
greater, tend to have higher wages.
In
industries with high profits tend to have high wages
even controlling for a host
of other variables while the
same
is
true, although to a lesser extent, for industries with a high
capital/labor ratio.
Our model explains these
differences on the basis of on-the-job
accumulation of specific human capital by individuals
.
After an
employee has accumulated specific knowledge about the important
characteristics of his job, like the specific mechanical motions
required of production workers, the idiosyncracies of particular
filing
systems for administrative assistants or the tastes of
Important clients for sales personel he
than are new trainees (see Becker 1964)
automatically
mean that
more valuable
is
.
This does not
a trained individual will receive
Suppose
compensation than his untrained counterpart.
that
all
workers have the same marginal
workers would be willing
to the firm
more
in particular
disutility of time.
Then
long-term contracts that
to sign binding
involve wages equal to this marginal disutility of time whether they
Our model assumes
are trained or not.
infeasible.
There
is
that such contracts are
thus ex-post bargaining between the firm and
the worker over the division of the excess output produced by the
trained worker-"^.
Without more knowledge about the institutional framework for
this bargaining
it
is
impossible to predict
(or surplus) will be divided.
take-it-or-leave
first at the
which
it
is
it
how
this excess output
Suppose the firm can make credible
offers to workers;
in
other words,
it
moves
beginning of each bargaining period, quotes a wage
wUling to employ the worker and
is
at
committed to ignore
any counteroffers.
The worker can only accept or
This gives the firm
all
the "bargaining power" so
it
reject the offer.
receives
all
lln the voluminous literature on specific human capital accumulation
this bargaining, which Is often not discussed expUcItely, plays an
important role nonetheless.
In particular, whether in the presence
of specific human capital there will be too many quits, too many
layoffs or both depends critically on the division of the surplus
between workers and firms (see Stiglitz (1974), Salop (1979),
Mortensen (1978), Jovanovic (1979), HaU and Lazear (1984), Parsons
Stiglitz (1974) and Salop (1979) let the firm unllateraUy
(1984).
pick wages, Mortensen (1978) studies arrangements which lead to
efficient separations whUe Jovanovic (1979) assumes the worker pays
for aU his training and receives the value of his ex-post marginal
-5-
the surplus^.
If
instead the workers can make credible take-it-or-
leave-lt offers to firms they receive
we present require only
The models
that workers receive at least some positive
This
fraction of the surplus.
the surplus.
all
Is
intuitively reasonable for two
reasons even granting the ability of firms to acquire reputations of
being unbending in their negotiations with workers.
First,
in the
model we present below, firms are ex -ante indifferent between having
and having one
a reputation for hard-nosed bargaining
the present value of their paynments to workers
Second,
either event.
in a richer
model
is
for softness,
the same in
which workers are
in
heterogeneous, a flexible attitute in bargaining can
elicit
information about workers true alternative opportunities and thus
avoid inefficient separations.
Once one accepts that workers receive some
their abUity to outperform trainees
difference
is
we
still
of the surplus from
must explain why
this
related to industry variables such as profits and the
The
capital/labor ratio.
latter turns out to be a
consequence of
assuming both that trainees are less productive than incumbent
workers and that the technology has some putty-clay features so that
the capital labor ratio
assumption
is
is
higher value
product.
fixed ex-post.
The
to restrict the firm to replace
worker with a single
output lost
is
less productive trainee.
the surplus to be divided.
if
it
is
produced with more
role of this latter
any given incumbent
The difference
in
This output naturally has
capital.
To make the
role
Parsons (1984) surveys some of this literature
2When the firm is uncertain about the alternative wages available
Individual workers (as in Stiglitz (1974) and Salop (1979)) it will
1o
Output
of capital clear consider the following example.
by combining people and
is
buy tractors
number
Ex-
of different sizes.
post only one worker works with a given tractor.
the same
produced
Ex-ante the capital/labor ratio
tractors.
variable since the firm can
is
If
make
trainees
of mistakes independently of the size of the
tractor, the cost of their mistakes will be bigger the larger are
the tractors.
on the
Thus
the surplus that incumbents can extract depends
size of the tractors
The
role of profits in a model of this type is less clear
because, for any profit maximizing firm, the marginal revenue
generated by the last unit sold equals
might be seen
to imply that the
fraction of marginal cost which
firm.
its
most a worker can receive
is
be shared by workers nonetheless.
a
is
a
independent of the profits of the
We present two reasons why some
workers have
This
marginal cost.
The
of the rents of the firm can
first is that
ex-post, some
very substantial effect on firm output (or profits)
This would be the case, for instance, for individual computer
software developpers working on a large project
any one
the
of them,
fall in
output
slows
is
down the whole
this large,
approximated by the units
.
project substantially.
the lost revenues
lost times
The departure
may
of
When
not be well
marginal revenue.
For
instance, in an oligopolistic industry, one would also have to take
into account that marginal
revenue rises as output contracts.
The
faster marginal revenue rises the more surplus the worker produces.
Insofar industries with steeper marginal revenue curves also have
offer some of this surplus as
wages
to
prevent quitting.
-7-
higher profits this induces a correlation between profits and wages.
It
must be noted that there
an important shortcoming of
is
viewing each worker as bargaining Individually with the firm after
he has acquired specific human capital.
This
that the
is
sum
of the
marginal contributions of trained workers can easily exceed the
Then,
total value of output.
bilateral
firm-worker bargaining can
A more
yield negative profits for the firm.
appealing formulation
would take into account the mutual interdependence
would recognize that
more, less
is
if
of
workers
available for the rest of the workers.
Unfortunately,
solutions to this n- player noncooperative
bargaining problem.
Suppose for instance that
simultaneously make take-lt-or-leave
the
sum
all
workers
offers to the firm subject
it
to the constraint that the firm closes unless
If
It
other workers have bargained and obtained
WG do not have good
profits.
.
it
makes nonnegative
workers
of the marginal contributions of
exceeds the value of the output this game has a multiplicity of
This occurs because
equilibria.
if
1
believe that
many other
workers are demanding their marginal contributions
to
demand
less
and keep the firm
my
Many such
marginal contribution.
Conversely,
alive.
others to be modest in their demands,
will
1
I
will
if
I
be content
expect
ask up to the value of
beliefs about others,
together
with each individual workers resulting offer, constitute equilibria.
Given the absence
this problem,
The
solution
of a satisfactory noncooperative solution to
we consider
we consider
also a cooperative bargaining solution.
is
has a variety of advantages.
due
to
Shapley (1953).
First,
it
is
This solution
unique and explicitely
-8-
takes into account the mutual interdependence of workers.
players are treated symmetrically by this solution,
it
Since
can be
thought of as the expected value of what they would obtain
variety of noncooperative settings.
Finally
it
is
all
in a
a natural
generalization of the Nash bargaining solution for two-person games,
for which a noncooperative rationalization does exist.
solution,
we show
that workers,
because they cannot
Using this
be always
all
regarded as "marginal" workers, receive some of the inframartginal
by the
profits generated
There
is
firm.
an additional advantage of our model using the Shapley
This advantage
value over that of bilateral bargaining.
is
that our
current model of bilateral bargaining considers only one homogeneous
class of
capital.
workers which obtains more when
This
a
is
that
all
.
One
workers share
employees Involved
asssociated with
is
coupled with more
drawback because the perplexing feature
inter-industry wage differences
different workers
it
in
much
of
that they apply to a variety of
is
attractive feature of the Shapley value
in the rents that
they help generate.
is
So
marketing (who perhaps are not directly
capital)
still
increasing in the capital/labor ratio
collect
if
some surplus that
they are needed to
is
sell
goods produced by surplus-generating production workers.
Both the bilateral bargaining model as well as the one based on
the Shapley value must be regarded as models in which individual
workers bargain individualistically
with models based on unions
in
.
They thus stand
which workers engage
in
in
contrast
collective
bargaining (for examples see Aoki (1980, 1982), McDonald and Solow
As WG discuss further
(1981)).
in
our concluding section, this
is
an advantage because the pattern of Inter-industry wage differences
cannot be explained by unionization alone.
The models we consider predict
that trained workers will obtain
higher wages than untrained workers and that this difference depends
on profits and the capital/labor
Yet, industries with high
ratio.
wages wUl naturally attract workers.
Thus,
if
the labor market
functions well, the present value of payments must be equalized
across industries.
This naturally requires that
in
industries in
which incumbents extract high rents, trainees must receive very low
(or even negative) payment.
at least
It is
easy to show that
in this case,
under some circumstances the input and output decisions
the firm are efficient.
of
This results from the fact that the present
value of the payments to the different factors equals their
opportunity cost.
Even
will also
in this
case firms with higher wages for trained workers
have higher average wages because, as the future
discounted, the reduction in the payment of trainees
is
the undiscounted increase in the wages of incumbents.
is
lower than
Yet,
in
computing average wages the wages of trained workers are not
Nonetheless, this version
discounted relative to those of trainees.
of the model has the prediction that differences in average
can be explained entirely by differences
time.
There
is
at least
in the slope of
wages
wages over
some evidence, discussed below, that
appears Inconsistent with this implication.
If,
for some reason the
wages
of trainees cannot be lower than
-10-
some value, be
wages
of
It
the minimum wage or some "fair" fraction of the
incumbent workers one obtains the type of unemployment that
has been discussed
(1979), Lindbeck
by Shapiro and
in similar
models by Stiglitz (1974), Salop
and Snower (1984) and
Stiglitz
in
"efficiency wage" models
(1984) and Bulow and
Summers
These
(198G).
barriers to low initial wages prevent the equalization of the
present discounted value of worker compensation across jobs making
some jobs more attractive and generating queus for these jobs.
show that these barriers raise not only the wages
also those of incumbents since these can
more expensive outside workers.
We
of trainees but
now only be replaced with
This mean that these barriers only
exacerbate the differences in average wages we obtain
in
our model
with market clearing wages.
The
and profits on average wages
effect of capital-labor ratios
naturally has the consequence that estimates of profitability or of
price-cost margins will be biased across industries.
Heavily
monopolized industries with high prices wUl tend to have high wages
as well so that the usual measures of price-cost margins wUl
understate the difference between price and social marginal cost.
The paper proceeds as
the labor market clears.
follows.
In section
We
II
start with models in
we present
a simple
which each worker bargains unUaterallly with the firm.
III
we analyze mutually Interdependent bargains.
which
model in
In section
In section IV
we
consider barriers that prevent the wages of trainees from being low.
Section
V presents some conclusions and argues
that the model
also capable of explaining the positive effect of establishment
is
and
11-
flrm size on wages that
is
discussed in Brown and Medoff (1986).
Bilateral Bargaining
II
We consider
capital.
Its
a firm which produces output with labor
production function has constant returns while
decisions are taken
amount
and
in
two stages,
of capital per worl<er
is
initially capital as well as the
chosen.
In the
second stage
employment can be varied but the maxiimjm number of employees that
can usefully be employed
is
given by the amount of capital times
divided by the predetermined amount of capital per employee
means that
capital can be thought of as tractors or
workstations whose size
used by
at
is
k/n the amount
level of
employment such
=
This
computer
ex ante variable but which can only be
most one worker ex post. Letting k denote the level of
capital,
q
.
worker and
of capital per
e the
ex post
a production function can be written as:
ef(k/n).
Note that this production function
e < n
is
a
returns to scale production function when e
(1)
standard constant
is
equal to n
.
In
our
model, we also distinguish between skUled, experienced "insider"
labor and inexperienced "outside" labor.
(1984)
when
As
in
Lindbeck and Snower
"outside" workers are first hired they are trainees for
one period and during this period their productivity
fraction a of that of the existing "inside" workers''.
is
It
only a
is
useful!
-12-
number
to define the
[(n-r)
+
where n
or]
of "effective" employees z
employment and
total
is
which
r is the
is
given by
number
of
trainees employed.^
Analogously to
(1)
we consider the ex ante production function
given by:
q
=
(n
-
r)f(k/n)
+
af(k/n)
< r < n
zf(k/n)
=
(2)
e.Once again, the firm musi choose ex
so that z corresponds to
ante both the level of capital and that of the capital/labor ratio.
Since both k and k/n are
point.
Our interpretation
capital stock to be
workers.
now
and n are determined
it
(if
at this
expects the
of (2) is that the firm
used mostly
This means that
fixed, k
not exclusively)
by trained
expects output to essentially equal
nf(k/n) unless an incumbent worker
is
replaced by a trainee.^
3This is superficially similar to the assumption of Shaked and
Sutton (1984), that new workers can join the firm only at
predetermined intervals of time. In both cases a certain amount of
output is lost if the incumbent worker and the firm cannot reach
agreement. The difference is that if the wage is subject to
periodic renegotiation in Shaked and Sutton's (1984) model, the wage
falls to the reservation wage every time the firm is actually
capable of hiring outsiders.
41n this formulation it is implicitely assumed that firms never let
the total number of employees fall below n.
This is not an
Important restriction since our model has perfect foresight so that
the firm knows how many employees it wUl hire when it chooses k and
k/n.
It would thus never purchase capital which would be unused ex
post.
SThere Is a somewhat more general formulation for this ex ante
problem that yields essentially identical conclusions. In this
alternative formulation the potential use of trainees is
Suppose the firm
contemplated more directly when capital is chosen
is allowed ex ante to pick k, n and r the anticipated number of
trainees that wUl work with the capital stock.
Let z be [n-(lThen supposing
a)r], the anticipated number of effective workers.
.
-13-
Ex post
it
Is
only possible to change r taking k and n as
Instead of using (2) directly as our ex post production
given.
function we sometimes use a slightly more general formulation which
assumes that ex post output
q
=
given by:
is
g(z)
where g
(3)
is
a
nondecreasing function.
considered above the function g
Workers have access
reservation wage of
forever.
w''
is
zf(k/n).
to a perfect capital
per period.
Thus they are
For the particular case
First,
market and have a
we assume that they
live
willing to join the firm as long as the
present value of their compensation equals at least w''V(]-p) where
is
a market determined discount factor.
worker would be
willing to accept to
Obviously, the least a
work
in
any given period
is
We thus focus on the most the
firm would be willing to pay,
the compensation of workers
they are able to make take-it-or-
leave-it offers.
This
is
if
p
done with the undestanding
on
for most
that,
reasonable bargaining games, the worker wUl receive only
i.e.
w'\
a
fraction
that the number of trainees wiU equal r, output is zf (k/z)
Ex
Then output
post, however the number of trainees r might exceed r.
equals [z-(l-a) (r-r) ]f (k/z)
With r set equal to zero, this
Its advantage lies in
formulation is Identical to that in the text.
that It allows the firm ex ante to hire relatively less capital for
The idea of the two
trainees (who use capital less productively).
production functions is the same. Ex ante workers are substitutable
for capital but ex post capital per worker is fixed so that
substituting trained workers by trainees reduces output by morte the
higher is the capital/labor ratio. The reason for choosing the
formulation with r equal to zero is that, if capital is long lived
it will mostly be used by trained workers and the firm will lose if
it taylors its capital to the abilities of trainees.
.
.
14-
between what the firm
y of the diffGrencG
With this proviso,
make take-it-or-leave
pay and
wiliing to
w''\
both potential trainees and insiders
offers to the firm at the beginning of each
These offers specify
period.
to
it
let
is
a
wage
at
which each worker
is
willing
Each of these offers can be either accepted or rejected.
work.
accepted the worker receives the required wage and becomes
If it is
(or remains) an insider at the
end of the period.
the individual worker
rejected,
is
If it
is
not employed and maintains (or
regains) the status of outsider.
Let the wage of trainees be denoted by wj
W2, W3, W4
.
.
Then
that of insiders
where the subscript denotes the period
.
and R(q) be the revenues
output.
,
of the firm
when
it
sells
of
by
employment
q units of
the following proposition summarizes the equilibrium
values of these wages:
Proposition
1
The unique perfect Nash equilibrium
of the
game has wages given
by:
wi
wj
-
-
w*
w*
=
=
-pp
(1
-
(4)
P)B
i
> 2
(5)
where
P
=
R[g(n)]
-
R[g(n-(l-(x))j
(6)
-15-
=
(l-a){R'g'
-
(l-a)[R"g'2
.
R'g"]/2i
(7)
and primes denote derivatives evaluated
at r equal to zero
Proof:
Outsiders
will
always lower the wages they demand during the
traineeship until the present discounted payments of lifetime
employment
profile of
w''/(l-p).
is
So suppose that insiders ^yj demand a
wages whose present value
at time
is
x
St-
Paying this
present value to an insider forever instead of turning to an
outsider
S^
is
-
that
acceptable to the firm only
w*/(l
is
if
wages equals
-
p)
<
=
R[g(n)]
-
if
RIg(n-(l-a))l
(8)
the difference in the present discounted value of
at
most the current difference
in
revenues obtained
(since in future periods the revenues are the same)
make take-it-or-leave-it offers they demand
hold with equality.
a
wage
This equation implies that S^
is
.
Since insiders
that
makes
(8)
constant over
time which implies that wages of insiders are constant over time.
Thus without
loss of generality
equation (5) follows.
we can write S^ as W2/(1-p) and
Equation (4) follows immediately from the
requirement that the present discounted value of wages equal w'V(1-
•17-
that the typical production worker reduces output so
replaced by a trainee that marginal revenue
much when he
is
On
itself is affected.
the other hand, there are clearly some production and some clerical
workers who are pivotal
significantly
members
in
any organization and who reduce output
when they depart.
For them, as well as for the
of a smoothly functioning string quartet,
important and
its
end up reflected
average wage.
to a discussion of the efect of R'
To do
differential.
ex-post production function
.
ratio remains the same.
+
in
is
which
constant
(2)
gives the
Thus the
The present value
capital/labor
of the cost of these
is
vk/n)/(l-p)
where v
is
(10)
the rental rate of capital.
ratio remains the same, output increases
and by f(k/n) thereafter.
these inputs generate
Since the capital/labor
by af(k/n) the
first
period
So, the present value of the revenues
is:
6Thus we are neglecting
for instance the dynamics associated with
all the workers are trainees, output is
marginal revenue is correspondingly higher than in later
the first period in which
low and
which R'
of firms.
Let the firm add one additional worker
as well as k/n units of capital forever.
(w*
in
Also we concentrate on the case
additional inputs
on the wage
we consider the ex ante decision
so
For simplicity we focus on steady states
over time."
may be
relevance even for only a minority of workers may
in the
We now turn
the R" term
-16-
p)
.
Equation (7) results from a second order Taylor expansion with
respect to r.QED
Note that more generally, when W2
-
equals approximately (1-
w''
p)y(l-o){R'g'-(l-a)[R"g'2+R'g"]/2}, the difference between W2 and wj
is
given by:
W2
(l-a)y{R'g'
=
wi
-
-
(l-a)[R"g'2
R'g"]/2l
+
Several comments deserve to be made about (5)
(6)
,
and
(9)
.
the premium earned by incumbent workers over the reservation
First,
wage
(9)
proportional to the premium they earn over the trainee wage
Is
the latter
is
larger because trainees must "pay" for their jobs by
earning less than
larger
Is
the
Second, the larger are (1-a) and
w''.
fall in
g',
i.e.
the
output from replacing an incumbent worker with
a trainee, the larger
is
the wage premium earned by incumbent
workers
Now
consider the second order term and ignore g"
perfect competition R'
zero.
is
Under
.
equal to the competitive price and R"
For a firm with market power R"
is
negative and gives the
rate at which marginal revenue decreases as output increases
the firm perceives a linear demand curve for
the absolute value of
R"
is
will
be larger
and that R"
the firm.
order term
It
is
its
slope.
in absolute
will
It
is
is
its
product
,
.
If
R" gives
thus natural to expect that
value the more monopolistic the firm
therefre be correlated with the profitability of
must be pointed out that the relevance
unclear.
On
the one hand
it
is
of this
difficult
to
second
imagine
-18-
[a
If
*
p/(l-p)]f(k/n)R'
the firm
is
(11)
maximizing profits, (10) must equal (11)
in a
steady state so that
R' = (w*
whicli
+
vk/n)/{f(k/n)[p
means
that,
if
+
(l-p)tx]i
we can neglect the second order terms, the
premium received by incumbent workers
in particular (6)
W2
-
and
w*
is
=
(1
-
p)(l-a)(w" +vk/n)/[p
proportional to (w"'+vk/n)
prove that
+
(l-p)a]
in the capital/labor ratio
Independent of the form of the function
ratio
is
;
becomes:
thus increasing
(13) does not
(12)
a single firm,
f.
It
is
(13)
and
worth noting that
by raising the capital/labor
would raise wages of incumbent workers although this foUows
Immediately from (6) and (7) as
k/n goes up.
f
(and therefore
g')
goes up when
Instead (13) proves that different firms with
different production functions will pay higher wages the higher
the optimized value of their capital/labor ratio.
is
We show below
that under certain circumstances this optimized value
is
actually
efficient
The reason
for this result
is
that one can always define the
unit of output as the amount produced
periods.
by one worker and the amount
19-
by the capital/labor
of capital given
of the unit so defined
only on
w
+vk/n.
must equal
The marginal revenue
ratio.
its
marginal cost which depends
Replacing one incumbent worker by one trainee
leads to the loss of (1-a) units so defined hence the surplus
proportional to (l-o) (w' +vk/n)
From
.
(13)
is
one can conclude that
unless the second order effects are important
,
only the
capital/labor ratio and not the level of profits affects wages.
Efficiency of the capital labor ratio
It
might be thought
at this point that since insiders
some of the compensation due
to capital they
capture
would bias downward the
This does not follow necessarily from
capital labor ratio of firms.
a model of this type as can be seen by considering the ex ante
decision problem of firms
capital labor ratio they
At the moment firms pick capital and the
.
know
expenditures per employee
of
k/n
that the present value of its
will
be w'V(l-p).
optimal choice
satisfies:
w'^f7[v(p
which
is
+
(l-p)o)(f
-
f'k/n)] =
the same as would obtain
receiving w* per period.
The
1
if
workers could precommit
possibility that the capital/labor
ratio is efficient should not be overstressed
relies
Thus the
heavUy on
realistically
a single
however since
ex-ante capital/labor choice.
some of the capital
is
it
More
purchased after some trained
to
-20-
workers are on the premises
capital will be
.
This may have the implication that
chosen taking the dependence of wages on capital
Intensity Into account and that capital choice wiU be distorted.
'
Putty-clay vs. Putty-putty
At this point
it
is
worth commenting on the importance of the
assumption of putty-clay technology.
If
the technology were putty-
putty, both the ex-ante and the ex-post production functions would
be given by:
q
=
zf(k/z)
which corresponds
In
(1)
to allowing ej
and e2
post subject to the constraint that they be equal to each other.
this case,
even with
a fixed capital stock,
ex
to be picked
In
the loss of ovitput from
replacing an incumbent worker with a trainee would only be (l-a)(ff'k/n) instead of the (l-a)f which occurs in our putty-clay model.
The
loss is smaller because capital can be put to
uses by combining
it
more productive
with the more productive incumbent workers.
Moreover, we now argue that
if
the same substitution
post as ex ante the capital labor ratio plays no role
collected
by experienced worker.
This
is
in
so because,
is
possible ex
the premia
by an argument
analogous to the one used above, the marginal revenue produced by
similar ex-post inefficiency may arise with respect to labor
turnover.
This turnover may be inefficiently low due to the
presence of high wages after the worker is trained.
7A
-21-
[a+p/(l-p)
]
produced by
(f-f'k/n) units of output, the extra output
one extra worker that
is
kept forever, must equal their marginal
This means that the loss
cost which equals w''V(l-p).
replacing one incumbent worker by a trainee,
(1 -a)
output from
in
(f-f'k/n) leads to
a loss in revenue proportional to w'' and independent of k/n.
Average wages and
finite
horizons
So far we have concentrated only on wage premia for experienced
workers rather than on average wages.
the average
lived workers,
experienced workers.
for such
wage
is
essentially equal to the
We now show
Suppose that, once an employee
(1)
in
T
which
periods.
first
joins the firm,
for
wages
we
if
T
assume that workers remain with the firm only
the firm only
wage
that industries with high
workers also have high average workers even
arbitrarily
in
Of course with infinitely
periods.
he remains with
For simplicity we revert to the technology
order approximations to the loss
from switching workers are sufficient.
Again,
let
in
revenue
workers make
credible take-it-or-leave-it offers.
Proposition
If
workers
2
join the firm only for
T
periods, the unique Nash
equilibrium has constant wages for trained workers equal to W2
These as well as the wages
of trainees satisfy
-22-
wi
-
w'''
=
-(p
W2
-
w*
=
(1
pT)3/(l
-
-
p)B/(l
-
pT)
(14)
pT)
-
(15)
Proof
Outsiders
will
now bid down the entering wage wi
present discounted value of compensation
value of the foregone reservation wage
Insiders
who expect
employed can,
value
at
to
work
most expect
equals the the present
w '(1 -p^)/(l -p)
for another
to bid a
until the
periods
j
.
remain
will
path of wages whose present
leaves the firm indifferent between keeping them and
Sj
replacing them with a sequence of
new workers.
For the firm to be
indifferent:
Sj
-
w^'d
-
pJ)/(l
where the LHS
the
RHS represents
(15).
-
p)
of (13)
< B(l
-
pJ)/(l
pT)
(16)
represents the extra disbursements while
the gain in revenue.
To demonstrate
-
that this
backwards induction. To obtain
is
true for
(14)
it
is
For
j
equal to
all
j
one proceeds by
enough
to
1
w'''(l
-
gives
remember that
the present discounted value of payments to a worker [wl
pT)w2/(l-p)] must equal
(16)
+
(p-
pT)/(l-p) and apply this to (15).
Note that the premium paid to experienced workers rises as
QED
T
becomes shorter because the strategy of replacing current
experienced workers with trainees means that the replacement for the
-23-
trainees themselves will have to occurr sooner.
This makes this
strategy more expensive and increases the value of existing workers.
To compute average wages we assume
leaving the firm
is
constant over time.
number
that the
of
workers
Then average wages w are
given by:
w
=
w
-
[wi
w*
That
+
(T-1)W2]/T
=
P[(T-l)(l-p)
this expression
is
For
can be seen as follows.
-
(p-pT)]/[T(l-pT)j.
increasing in
T
equal to
p)/2(l + p) and thus increasing in
is
increasing in
multiplying
3
T and
3.
all
2,
it
is
T
greater than one
equal to 3(1-
Moreover the numerator
the denominator
remains positive for
for
3
(17)
is
of
(14)
positive so the expression
T.
Comparison with efficiency -wage models
The reason why workers obtain more than
in this
model
is
outside workers.
their reservation
wage
that they are more valuable to the firm than
Instead, in efficiency-wage models
homogeneous productivity wages are high
behavior by existing workers^.
"efficiency" of workers.
effort (Solow(1979)),
It
to elicit a
This change
in
witli
workers of
change
in
behavior changes the
does this either by directly increasing
reduce shirking (Shapiro and
Stiglitz.
(1984),
SEfficiency wage models also include adverse selection models (Weiss
-24-
or reduce turnover (Stlglltz (1974,
first of these
elasticity of
Salop (1979)).
In the
models the wage premium depends only on the
supply of effort with respect to the wage and the
capital/labor ratio has no role.
Stiglltz also
1985),
The shirking model
has the property that
all
of Shapiro
and
firms for which efficiency
wages are an Issue pay a wage that prevents shirking independent
firm characteristics.
This conclusion probably depends
in
of
part on
the fact that the susbstitutabUity of effort (or lack of shirking)
for
number
of employees is modelled as
independent of the capital
stock".
On
the other hand the turnover-based efficiency wage models are
closely related to the model of this Section.
1985) there
is
a training cost
T.^^
In Stiglitz (1974,
In contrast to the model
presented so far, these models assume that quitting by workers
nondegenerate decreasing function of the wage they are paid
.
is
a
These
models also assume that trainees and experienced workers must be
paid the same wage and conclude that wages can exceed the marketclearing level.
wage
it
The reason
for this
is
that each firm raises the
pays untU the higher payroll costs are balanced by
reductions in quits which translate into reductions in training
costs.
Moreover,
if
the second order conditions are satisfied an
(1980) in which workers differ in their true (unobservable) ability.
a model in which this substitutabUity depends on
the capital stock is reaUy not very different from a model in which
workers are of differing qualities and high quality workers have a
comparative advantage in the production of goods with high
capital/labor ratios
lOSalop (1979) assumes that the training costs are an increasing
convex function of the number of trainees which makes it difficult
to analyze the cross-industry effects of different training costs.
90n the other hand
25-
Increase in T, which increases the value of keeping incumbent
workers raises wages.
With the putty-clay technology assumed here, T, the training
cost equals (l-o)f(k/n) which, as
k/n.
for
Thus
we have shown
if
increasing
in
their turnover model can be adapted to yield higher
more capital Intensive industries.
even
is
wages
This result would emerge
workers were allowed to pay for their training because, as
above, keeping the present value of wages constant, average wages
rise
when incumbent's wages
Thus
rise.
the putty-clay technology implies high wages
intensive industries even
long as quits
fall
when
capital
firms unilaterally set the wage, as
smoothly with increases
assumes instead that workers aU quit
while they remain otherwise.
in
if
in
wages.
Our model
they are paid less than w'
In this case, workers must have some
bargaining power for wages to increase with capital intensity.
Ill
Mutually Interdependent Bargains
The model
of bilateral bargaining presented above
assumes that
while each individual worker bargains with the firm (and threatens
to quit)
he expects
all
While this
may appear
suspect.
A more
the other workers to remain with the firm.
empirically reasonable
its
logic
is
somewhat
symmetric treatment of the threats of each
Individual worker would recognize that other individuals are also
threatening the firm and that, were they to leave, the individual's
26-
To put
bargaining position would be altered.
suppose that some of the other workers
this differently,
in the firm in fact quit,
then the additional departure of an individual worker
to the firm as long as
R"
is
individual can, in principle,
is
more costly
negative.
This means that the
demand
be paid taking into account
to
this eventuality.
Consider for instance an Economics Department.
experienced econometrician
is
Having one
clearly essential to guarantee the
quality and continuity of the Department's activities.
department has three econometricians each one ought
capture some of the surplus he would provide
if
Even
to
if
the
be able to
the other two were
to leave.
To model
this ability to capture
some inframarginal rents we
model a firm with n incumbent workers as an (n + 1) person game
which the firm (associated with
capital)
is
in
one of the players.
Since no convincing extensive forms for games of this kind have been
worked out we use an axiomatic
particular,
since the game
solution to this game.
well described
is
by
its
In
characteristic
function (see Shubik (1982)), the Shapley value (Shapley (1953))
is
a natural solution concept.
A second problem with
section
when
g'
is
is
also solved
the bilateral approach of the previous
by the Shapley value.
very large, so that the departure
very costly.
Then the sum
bilateral bargaininng
of all the
This problem arises
of
payments
any one worker
to
is
workers using our
approach may exceed the revenues of the firm.
In some sense this problem
is
due
to the fact that
workers are only
•27-
bargalning with the firm instead of bargaining with other workers as
This
well.
naturally taken care of
is
when
the n workers and the
firm are being viewed as bargaining at once.
We
by considering only
simplify the analysis somewhat
a single
period and considering the ex-post technology (1) with the function
g given by the product of f(k/n) times
its
output
a
=
is
The firm
argument.
an imperfectly competitive markets and
in
demand curve
q
its
its
perceived
given by:
bp
-
where p
sells
(18)
the price for the good.
is
Total revenues from employing r trainees and (n-r) experienced
workers
is:
R(r)
The
=
[a
-
f(n-(l-a)r)][f(n-(l-o)r)/b
characteristic function,
denoted v,
(19)
is
a function
from
subsets S of players to real numbers which gives the maximum revenue
by cooperating.
that the subset of players can obtain
incumbent workers are symmetric
coalitions with
j
workers with
characteristic function
is
without capital for which
The most
in
is
capital,
v(0,j).
this coalition can obtain
is
all
the
our example we consider only
for
whom
the value of the
v(k,j) and coalitions of
it
Since
Consider
jw''
j
workers
first
the latter.
since their special skills
can only be exercised together with the capital they arp familiar
28-
with.
Now
consider the coalition of capital with (n-r) experienced
This coalition
workers.
trainees and pay
will find
to each.
w'''
It
it
in its interest to hire r
thus obtains the revenue given by
The marginal revenue from
the expression in (16) minus rw''.
replacing an additional incumbent worker with a trainee can be
(to first order)
approximated
-m
A =
m
=
5 =
-
Cr
(l-a)f(a
-
2n)/b
r
is
the current
a) times the marginal
it
is
number
By
of capital.
Note that
m
is
(1-
the argument of the previous
equal to (1-a) times the marginal cost of these
Thus
for r equal to zero, this approximation neglects the
second order terms considered
in (17)
of trainees.
revenue associated with one additional trained
worker and (k/n) units
inputs.
(20)
2{f(l-o)}2/b
where
Section
by:
The approximation used
in Section 11.
can also be used to approximate (16) for any value of
r.
It
gives
n-1
R(r)
=
v(k,n-r)
=
R(n)
+
I
(
m
+
U)
-
rw"'
i=r
where
(21)
is
used
to define the value of the characteristic
(21)
29-
function associated with any coalition of capital together with (nr)
incumbent workers.
Now
we have expressed the characteristic function we can
that
calculate the Shapley value for each player
written, for example, as
i
.
This value can be
^j:
n+1
*1 =
I
(l/c(j))
I
[v(S)
v(S-{i|)J/(n + l)
-
(22)
j=l
where v(S)
is
the value of the characteristic function
associated with the coalition S.
Thus each player receives the
average of his marginal contributions
To compute
he contributes.
by Shapley
to all the coalitions to
this value
we use the procedure proposed
This procedure considers
(1953).
ordering the players.
which
For each ordering
it
all
(n
+
l)!
ways
of
attributes to any given
player (l/(n+l)!) of the contribution he makes to the coalition of
the players that come before him.
We obtain
<^y,
=
w*
+
^y^ for
m/2
+
workers and
^j^
for capital:
Un-l)/6
(23)
^k
=
R(n)
-
nw'''
+
nm/2
+
n(n-l)^/3
30-
When workers come "before"
capital they receive w"
come "after" they contribute w'+m even when
thus always includes
half the time
and after half the time
It
The term
is
C
m
split
is
50/50 with capital.
capital earns R(n)-nw'''
by using
thus guaranteed at least this amount.
captures the Increased marginal revenue of
Inframarginal units.
In particular
it
higher for steeper demand
is
curves and zero for horizontal demand curves.
Workers as a whole
receive only 1/6 of the total revenues that depend on
capital receives 1/3.
whenever
The average
zero.
is
Since each worker comes before capital
w''.
Even without any incumbent workers,
n trainees,
5
when they
;
The reason
for this
uneven
capital comes after at least some
^
while
splitting
workers
it
is
that
receives the
revenues of the early, most valuable, units.
One interesting feature
of
(23)
is
that as n rises the
compensation of each worker rises proportionally to n^
seem paradoxical since
it
leads to higher wages.
says that a larger level of employment
must be kept
It
in
mind however that n
represents the optimized value of employment.
that the
it
demand curve
to hire
into
A higher n thus means
of the firm has a higher intercept
more workers.
which leads
This larger demand naturally translates
more equilibrium surplus some of which goes
Since firms with a higher
of
This may
.
^,
to the
workers.
which can be interpreted as degree
monopoly power, have both higher profits (compensation
capital)
and higher wages, our model predicts
between profits and wages.
to
a positive correlation
This means that the level of accounting
-31-
profitabllity
may considerably understate
the level of actual
profits.
At this point the reader may wonder what
Aren't we simply asserting that the payment to one factor
capital.
depends on the worth
?
If so,
special about
is
why should
of the other factors with
worth vary across goods
this
this question is that
it
which he
is
capital
is
combined
The answer
?
which becomes less productive
to
if
combined with trainees while each individual worker has the same
option as any trainee, namely to leave and earn his reservation
wage.
This does not mean that incumbent workers need to be interact
with capital directly in order to receive premia for their
experience.
enough
It is
that they
enhance the productivity
other workers who do interact with capital.
To
see
we turn
of
to a
simple three agent example.
The three agents or
denoted
m
denoted
s
for
factors
we consider are
manager whose reservation wage
for secretary
whose reservation wage
each are available at the same wages.
function of the game
v(k,m,s)
=
v(k,m)
=
pp
-
v(k)
=
ap
v(m)
=
Wm
is
Wj
Wjn
-
is
Wj^,
Wg.
We assume the
a
worker
and a worker
Trainees for
characteristic
given by
p
-
is
capital,
Wj
where p can be thought
v(m,J)
=
w^
v(k,j)
=
ap
+
-
Wj
Wp,
v(j) = Wj
of as the value of the output
In this
-32-
example the replacement of incumbent
output by (l-p).
output of
m
by
a trainee
does reduce
This however can be interpreted as a loss
m
is
is
an incumbent or a trainee.
because when
whether
a regardless of
s
s
replaced by a trainee output
(2-a-3) can easUy exceed
Section
II
1
falls to
Note that
example the sums of the marginal contributions of
In this
in the
m and
which makes the solution proposed
s,
in
problematic.
The values
of the
game
to k,
m and
s
are given by
<^]^
,
and
^j^
respectively:
*k
=
v(k)
*m
=
v(m)
*s = v(s)
+
+
+
p[(l-a)/2
p[(l-a)/2
in last
s
m
team.
equally as
(l-P)/6]
earns more than his reservation wage
(which happens
players) he receives (l-3)p.
and
-
(l-P)/6]
p(l-B)/3
The reason why
when he comes
-
is
in
is
that
1/3 of the orderings of
This compensation to
s is
shared by k
the surplus (l-a)p from having an incumbent
Note however, that the dollar surplus of
s
depends on p
which, once again, depends in equilibrium on the amount of the
factor without alternative uses k.
IV Constraints on Trainee Wages
So far we have assumed that the labor market
clear.s
in
the
sense that trainees upon joining the firm can expect to earn no more
0g
-33-
than the present value of their reservation wages.
requires that trainees earn very
pattern that
is
in
high wage industries, a
not borne out by any available evidence. ^^
a particularly severe problem
our model.
little
This however
This
under one natural reinterpretation
is
of
In this reinterpretation trainees are no less productive
than incumbents but (1-a) units are lost in the transition, perhaps
because
all
it
takes time to recruit trainees.
This would imply that
wages are the same but that new hires would have
sum payment
to the firm,
The extent
to
much
to
make
as in efficiency- wage models
which trainees pay for high paying jobs
some extent an open question.
a
lump
"^^
is
to
Yet, the empirical evidence on
tenure, while not narrowly focused on this question, does not
support the notion that trainees earn particularly
wage industries.
of tenure
First,
Abraham and Farber
little
in
high
(1986) find the effect
on wages to be relatively small once one controls for the
ultimate length of the job^^.
Second, Katz
(1.986)
reports that
An alternative which may be more realistic in some environments
for trainees to work hard at a host of more menial activities in
addition to perfoming the tasks in which they are replacing a (more
11
is
productive) incumbent.
The value of these more menial activities
would then have to be subtracted from the trainee wage to obtain our
measure of wj
12In efficiency-wage models it is often argued (Akerlof and Katz
(1986)) that capital market imperfections prevent such lump-sum
payments. In the presence of these imperfections efficiency-wage
models tend to Imply that firms can gain by paying entering workers
low salaries and making them perform tasks for which efficiency
Thus insofar new hires do not receive
wages are not important.
low wages in high wage industries, some doubt is cast on efficiency
wage models as well.
ISAdmlttedly, for a large fraction of the sample, the ultimate lenth
measured to be an increasing function of actual
tenure.
Their paper is closely related to Altonjl and Shakotko
(1985) who show that there if one concentrates only on the effect of
the growth of tenure on wages (and ignores the effect of the level
of the job is
-34-
Inter-lndustry wage differences for workers with less than one year
of tenure
and those with more than ten years are highly correlated.
In this SGction
we consider
industry wages in our model
if
briefly the behavior of inter-
for some reason
pay entering workers low wages.
As
is
it
impossible to
is
apparent from the analysis of
Salop (1979) and Lindbeck and Snower (1984) such constraints also
Induce unemployment.
Another obvious consequence
is
as these
that,
constraints make labor more expensive they distort the capital/labor
ratio.
We consider two such constrainst on entering wages.
is
that entering
least
wages must equal, perhaps for
some minimum level w.
sociological reasons,
fraction
X
of the
The second
is
The
legal reasons,
first
at
perhaps for
that,
the entering wage must equal at least a
wage paid
to
incumbent workers.
In both cases
we
conclude that the imposition of this constraint raises wage.s for
experienced workers.
Moreover, average wages continue
to
be higher
the higher would have been wages for experienced workers in the
These increases
absence of the constraint.
to the question of the
wages naturally lead
what other constraints prevent wages from
growing without bounds.
end
in
Two such
constraints are discussed at the
of this section.
For purposes of this discussion we adopt again the analysis of
the beginning of Section
11,
though
little
would be altered
considered the multilateral batgaining of Section
III.
wages) one finds only small effects.
we
Before
computing equilibrium wages under the two constraints we
of tenure on
if
it
is
-35-
useful to prove the following lemma that relates wages of
experienced workers
to the
present value of payments
new workers
to
W.
Lemma
1
Suppose new workers earn
make take-it-or-leave-it offers
Then,
a present value of W.
to the firm,
wages
of
if
they
experienced
workers, W2, are at most given by:
W2
=
(l-p)(3
where
P,
+
W)
given in (7).
is
Proof
The firm can
earns
W
in
either keep the insider or hire an outsider
present value.
W2/(l-p)
-
W
<
It
will
keep the insider only
who
if:
(24)
P.
So that an Insider who makes take-it-or-leave-it-offers he
demands
a
wage given
at
most by (24).
Suppose that, starting
workers earn W2.
period, wj,
W
is
in the
QED
second period of employment
Then, whatever the value
given by [wi + pW2/(l-p)
]
of the
so that,
wage
at
in
most:
the first
36-
W2
<
(3
+
wi)/(l-p).
(25)
Three conclusions emerge from
The
equality.
(25),
first is that increases in
assuming
it
holds as an
wj, due for instance to
The second
Increases in w, raise W2 and thus raise average wages.
is
that increases in
wages.
continue to be reflected
3
in
higher average
we see that even constraints on wj, do not
Finally,
eliminate the prediction of the model that there must be a
difference between W2 and wj and that the difference between (l-p)w2
and wi must be increasing
Now suppose
in
3.
that the entering
wage
is
given by
X
times W2. This
gives a wage for experienced workers of at most:
W2
=
which
3/(l-p-X)
is
finite
(26)
only
X
if
is
less than (1-p); otherwise
incumbent workers are always cheaper than trainees and can thus
demand up
to
higher are
X
an infinite wage.
and
Again (23) implies higher wages the
3.
Since (22) and (23) can give rise to very large wages indeed we
now discuss two
limits
on wages.
First,
wages
of
workers can never
exceed their ex-post value marginal product R'f(k/n) which
course increasing
in
(k/n)
with this analysis
is
that
X
So one possibility that
.
is
is
is
of
consistent
one and that both trainees and
incumbent workers receive some fraction of R'f with the other
-37-
fraction going to the firm.
no slope
In the
In this case there
would, of course, be
wages received by workers over
time.
Second, the firm might hire some workers as "supernumeraries"
whose main function
is
to
be already trained (or semitrained) and
The presence
thus reduce the bargaining power of existing workers.
workers has the effect
of these
and thus lowering
of raising o
the wage firms must pay to existing workers.
3
and
Yet the analysis of
the equilibrium with such supernumerary workers
is
a far from
trivial task.
For instance, suppose that the firm has two workers for each
What should each worker demand
the n tasks.
or-leave
it
offers?
Suppose there
firm will cease to exist.
if
that each worker will
demand, taking the other worker's offer as given
effectively competing in Bertrand fashion
to equal at
w
Even
the other can demand more than
knows that
more
to the
willing to
if
if
w''\
To
in
pay a premium above
He can do
will
it
the last period
w'' to
they are
;
.
consider
see this,
one worker
the firm fires him at this point
remaining worker
w"
worker are constrained
most twice the reservation wage.
.
is
This should not be
.
to a single
the period before the last period
he can make take-it
a last period after which the
is
Then the most
viewed as predicting that wages
demanding
is
because he
this
have
The
to
firm
pay
is
the supernumerary worker in
order to maintain the threat against the other worker.
Nonetheless we expect that
some supernumerary workers
will
in
of
a realistic
be hired
able to contribute to production somewhat.
,
model of this kind,
particularly
if
these are
A richer model might
-38-
have firms with
liigh capital/labor ratios
and high rents spending
more on labor both through high wages and through excessive
employment
V
Conclusions
The basic message
of this
paper
is
that the pattern of inter-
industry wages appears consistent with a model
in
which three
trainees are not as productive as
conditions are met.
First,
Incumbent workers.
Second, technology has some putty-clay features.
Third workers have some bargaining power so that the wage
somewhere between the wage
It-or-leave-it offers
could make take-
would quote
if
it
and the worker would quote
if
he could.
a firm
is
WhUe
replacing this third assumption with the requirement that quits are
a smooth function of the
wage
also implies that capital/labor ratios
are correlated with the wage, our form of bargaining
is
probably
required to obtain corrrelation between wages and profits.
This naturally leads to the question of the relationship
between our model and models based on collective bargaining.
One
natural advantage of considering only individualistic bargaining as
we do
is
a union
that the public goods problem inherent
is avoided-'^'*.
On
is
the formation of
the other hand some workers are clearly
14In Aoki (1980, 1982) this problem appears to be circumvented by
letting the "representative (incumbent) worker" bargain in a two-
person game with management. Yet, unlike what is true when each
worker bargains individually, he does not take into account that the
demands of other employees alter the opportunities of any given
employee.
Aoki requires instead that the representative worker
that other workers wUl act exactly as he
assume, when bargaining,
39-
capable of overcoming these problems.
In models in which unions
maximize some measure of member welfare
it
of course not
is
surprising that workers can extract some monopoly rents or even some
of the quasi-rents
produced by
The
capital.
difficulty with
ascribing wage differences to collective action on the part of
workers
is
that
it is
difficult to imagine collective
the absence of institutions such as unions.
including
bargaining
Yet, most U.S. workers,
many high wage workers are not unionized.
This has led Dickens (1986) to postulate a model
The
threat of unionization can lead to high wages.
workers
in
in
in
idea
which the
is
that
some sense prefer to avoid the coordination costs of
forming a union as long as they do not earn wages much below those
they could obtain
will
if
they did organize a union.
take actions that prevent union formation
either raising wages or making
raising employment or both.
explaining
it
more
Thus
empirical difficulty with this model
is
This includes
difficult to
this
why high wherever unions
.
Firms, in response,
form a union by
model has the potential of
could obtain high wages.
that,
as
shown
in
Dickens
and Katz (198G) high wage industries also pay high wages
and professionals who,
Similar difficulties arise
in the
US, are very unlikely
when attempting
The
to
managers
to unionize.
to explain the relatively
high correlation of inter-industry wage differences accross
countries In which unionization
countries in which
It
Is
is
easy and the Eastern Block
essentially impossible (see
Krueger and
does.
This ensures that workers obtain what is in their collective
bring about
self Interest much as conjectural variations equal to
the monopoly outcome In oligopolistic markets.
1
-40-
Summers (1976b) who report
between log wages of .78
a correlation
between Germany and the USRR)
It
.
would seem that our model which
requires only bargaining with the individual worker, plus a modicum
of self interest
on the part
of the firm,
is
better suited to
Eastern Block countries.
Our paper has focused exclusively on inter-industry wage
differences yet ther
appears just as
is
is
one other source of wage differences which
difficult to reconcile with
standard models.
This
the widely documented effect of employer size on wages which
discussed in Brown and Medoff (1986).
of the establishment
They show
and the employer for which
positively correlated with wages.
They argue
a
is
that both the size
worker works are
that these effects
actually occurr within certain industries are are thus not directly
due
to inter -industry
To explain
wage differences.
this fact
one would naturally need to know
establishments and companies within industries differ
all
in
first
size.
why
If
firms are competitive and have access to a contant returns to
scale technology such as (2),
firm and establishment size are
Indeterminate and nothing ought to depend on these sizes.
suppose that there
firms
is
market power
in the
industry.
Clearly large
now have larger surplus but not necessarily larger surplus per
employee.
Suppose however that the products
actually differentiated.
of the firms are
Then our model based on the Shapley value
has the potential for explaining these size effects.
that
Now
if
the slopes of the
demand
We have shown
for various goods prodviced with the
same technology are the same, larger product lines generate more
-41-
Brown and Medoff
surplus for each worker.
(1986) argue that larger
firms actually have a smaller elasticity of demand.
Yet, their
estimates suggest a steeper slope for larger firms which
is
consistent with more surplus in these firms.
A second
explanation for differences in company and
establishment size
is
the presence of some entrepreneurial ability
which has diminishing returns.
This means that there are
Inframarginal rents which are bigger in larger firms
(establishments)
will
.
In a model based
on the Shapiey value workers
extract some of these rents so they
firms (establishments).
It
will
be paid more
in
those
must be noted that both these
explanations are consistent with the collection of facts Brown and
Medoff (198G) present
to reject
other theories of the size effect.
In particular, workers in these high paying jobs will quit less and
they
will lose their
high wages
if
they go to smaller firms or
establishments
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