Income Distribution: Line of Reasoning (Fassung 2)
Josef
Steindl
AC14446213
Aug 15
Inc no ^1:tributi n; Line of -ecsoniag
Elinina c 11 reference to le&iun>i and supply
The basic ichot -siy i : that f .a ho ( a at c ) and payment po- grade
w
r c is
X* oalth X* ank ir. p T-] e cr.VCh'j of offi oi lc( >®ni
> roe of skill r 3 7) ecialisati Oil i Pi CO i 1 O'
oe tiaos pi ace i. a hi o, archy of i ts and tal
The :g;o r ey better he 30 n as a 33 jy.Vf. to din onoi
inn c on the yr '•'do •
The z’-ade should he me nasurable :i tin *3c#eh riel
directly inftree tl y ( ocone of < oper ‘&1J i ns % -i
vo:l' *\ he 3 5gr 0 of c TVp* ny or or : ar:i sati on a d r
1 dor rchy,
or
managers it
the or anisaticn )
It night he connectoi ith historical elor.oat - years of training
ibr o ', cation, seniority); the whole domicoc -at r ay ’rave a
historical el out - technological and or orient' nal vol oaont.
Between various fiel is,however,ore ic . > direct
cotioarison ( although the c at of oducati » etp could o for
uch a r soii ity, this is not luoyo fully relevant n practice
and i. the case of gifts it does a t apply ). The c a orison
• 3 i. effect b so ; on considerate v s ofpresti :c ■■ f the. calling
tea iti n 1 standards, etc, factors irrati ual fr t. the cc n aists
0 i: t >f vie It is acts ■<£ economic • licy or t! side- ■£ employers
nhic? d cide inally these s anclnrfis It foil no that the
grading remains undefined as between profess! no callings, fields,
aad the c Qr'er:> son :s af.f'oo eh onl tax h> ■ plane of payments.
c ca: her’I' ro et distributions x ith respect to grade c ly ir
the vnri uc separate ields - mans era, fa- trailers, -*-Ins or
fi 3 etc. from this are erived ist ibuti s with rosp ct ot
■cynont; they have then to be mixed ith 'ietributi no of the
paranoterr btained - i p acltice the I roto coefficient - i the
le ~ jv Sat n of income earners in order tc obtain the
icteibuti n of income or this pop- hation.
Recor ciliation of the pa' tem of ; otribdtion for the oholo
and for the constituent pa trs The .r.ising has to explain .that
( that prosu poses lar n nbors of pr fo-si ns :c )
orhe. s the result obtained for the wealth distribution - tha
IMViti# 6M for tT e raM'^-is in epoa ont f td gtt.afc±te
distribution w.r.t.payment
agnont per g ado (return -n v/e ’Ith''cm ’ o 'jBBcrali o<2, ut that
oc ’ not see to contribute t the uesti n f tanda clo f vari us
r fesari n'.
Me accept o3 the general pattern of explanati a the interplay of
the two systems* s grades, and payment for grade differentials*
the potto a which wns outlined at the start in connection with
Chaiiioe nownoa theory. 'J'Lis duality of ,rades cad differentials
is preferable to that f demand and supply which is toe static
and is bound t> lead us astray7.
An the case of earned income the grad© would bo we 1th,
mid the different! 1 payments would be the return rates on different
amounts of wealth.
The Trade here defends indirectly on tinej in other cases -
burocaetiw pattern - the grade depends directly on tine (promotion);
in still other cases, the grade depends on the acquisition of knowledge
or skill, and therefore ^again on tine. In many cases, however,
the grades are provided by nautural gifts , as with the filn star,
the sportsman, and probably also the manager;in all these cases
learning! does play a very important role,too, but we could hardly
expect a close correlation between the time of learning and.the grade here
Rather, it would seem thet there is a natural distributi n of gifts
( not merely genetically , but also *ha duo to th influence of the
milieu and childhood influences). This distribution would, most plausibly,
bo rather skew, and that of the grades would therefore bo al3*> skew.
Jo might asume that it would be exponential or geometrical ( theoretical
reasons might be found in ConngePalm^.t^xkdxG theory ).
uhilo i the c- se ,f wealth he whole weight of the
oxplan^ti n was put on the distribution of wealth, which moreover
had alreddy all the required qualities which needed only to be shown
t re or-> due e th tiselves in the income distribut: n, the weight of
the yplan tory procedure in these other cases is shiftc entirely to
the distributi n of the payment. This is very largely dependent ,
indicrectly, on orocosses of economic development evolving in time.
The informa?ion space accessible to the owners of hi h grades gets
larger ad larger, and with it grows the payment received y that grade.
iTo must now argue from the distribution of payments condistional
on grade, via the distribution of grades, to the distribution of
payments among persons.
A/^
a he new men aloe ±icz tend to have wealth - simply because their
largo in come enable then to save a lot. However, to r wealth is
not e s urce of their income and ist will in genral bo
snail as comparedwith the wealth they would have to have in
or or to get fron it alsone the income they actually avo.
In order to take account of the e relations we should have
o wcrS out a process in wealth and incone, with allthe
feed-backs between the two.
One night- purely formally- calculate a fictici us capital
resulting fron the application of the return rate real wealth
to the incone f ho mana or. Then formally all income would
bo shown as return fwealth. lie proporti n of real w alth in
ho total would be the lower the newer the men would he.
II.Simon gives an exolanaii n f the earnings of managers
w ich i s based on the hi erarchy measured by scale f
o er tions, and on the relati n between tho grade and the
payment? there are again two exponential on tho face .f it
geonetr cal)listribu;i ns involved. Tho theory night bo
g noral.se to aoply to stars, specialists. :ro is one
fa it in tIt is not a no el of a Pr cess, rosooabligi this
the the ri.os of Roy etc. To he satisfactory, the hiora chy
f oyncats would have to be shown to evolve fron a historical
recess which c m i ues.
See .bimon, Hie c>®.' ensati n ox Executives. Socio ©try 1)57*
based on v ircal i veotigations by fioboz*to,-
A general theory ol executive con sensation based m
statistically tented propositions. Qu.J.E.1956
Bases of a historic a explana in would that tho
scale f cr-o.r ti ns i creases in time, or rather that there s
a diffusi n of the schale of operations in the course f ti e.
hi f:.oi n vo* tho space f income :.yno ts.
Reason for the iiff uoion is si:.ply the pro imp cor lexity of
the noon ’ ic system.
1q£ ro tho • orn ovrl aments we have already he* iclal ly tho
sane pattern i ' t o classic ! di isi n o ' l.aour which
i creased the mars et f the producer (craftsmen) ar .l ere- ed
i: one rifferentials.
The payments h:erarchy is full f irra i nal factors
and bo explained by soci logical factors, as <in rightly argues.
(Tni of the engineers in Austria !
Simon n executives
First asoumpt ons A constant span of control at all levels or
the hierarchy. n fHis ought oally to be a random v riablo.
This leads to: S else ( number of executives according to
Simon, but a reasonable mo .'..sure would b&
capital or sales) L level of the hierarchy
lrx S = L In n + con tant
Second assue tion: A constant rati ; bet .eon a eon's . :alary and that
of his subordinate, b (also that ought lobe a random variable )
C
That is used to determine the alary f the top executive in
terns >f these at other levels:
In C *■* L In b + constant
By elimination of the level L we obtain
1 U ^ In 1) 1u
——— In S + constant - constant
In n Ir. n
the ovlory of the top(official »)&ano£cr is a fancti n of oise >f
company
that is the rsmtxx relation empirically bservo by Leberta.
It mi I t be hoped that Robert" relati n also holds more
enerolly for all organisations Ire Los itala, city a minis rati ns
etc. alth ugh the measure of sise becomes again more r belomatic
(a-.-'loyaent? which would however not fit automatic d cor -ora ions).
Simon new passes to another empirical observation, a e by Davis,
The froquo.-oy distributi n or density of executive’s sal ...ieo
at General oiors in 193^ >!as a 1 arete distribution:
C* <=» n IT C’ sal ry , IT number of executives receiving 6’
The number of mangers 1 level L’ from the top is
II ( L’ ) . nL’’1
Simon new w ites from assumption P.
/ . 1-L’
C’(L’) = I£ b
but his II must be logically equal to the topsal ry C, although he
doon not say so.
The equation obtained by el :i.minuting L* i therefore
In b
In n
In C’
In H + In C
Bo to that the two empiric 1 rel ti no ere of an entirely
different kind. One hot rrainer the top salary in
various c.nspanies. The other determines the salary
'jQZ’rirGroouV.ng to the frequency with whi'oh'it i3 paid in
a certain c n. any ( the r ore nat r 1 ray of putting it
would be IT - m* C"5
•imongs point b-cafor in that with ..is expIon-.ti n the
oranoior is the same in thetwo very different e uati ns
.hich .squares with the empirical be?: resu' t.
Simons th ory follows the pattern of the usual Pareto
cxt>lan tion • the two exponential distributions -
but it is unsatisfactory because, like Roys omplanaii n of
1 .normal distributi n , it does not contain the tire ole nnt.
e auot got history iito it.'
A way y which it can enter* the sise ,f orqanioati no prows
with time.
Incidentally the oiyo distributi. n of oonpanlos in already
pareto distributed, therefore the top sal -:ry would bo do
•istribute- , sindo it is a linear functi n of t c tide.
Elaboration of the algebra* Sub3titutiaG froQ 3 in 7*
1 r In b . „ , lnb
in 0 *> r 1 ' :— In I« +
In n
In b
In n
( In - constant] ) + constant 2
In C1 «* ( In If + In S -constant.) + onsiant,,
In n * «•
The results of -imon imply that th e same parameter In b/ In n
occurs in both relations and the fact that the parameter is
err irlcdlly the same servos him as confirr ation.
Ho has inplioitly assumed tha the -ammeter is the same for
all companies, that is implied in his argument.
'0 stuck to this assumption in e.crivin the gneral distribution 9
which can c more conventionally put as follows*
In 35 » Tn‘"§ In C' - In 3 +constant1 - ^ cknstan 12
In n
IT
C»
s"
exp(oonstant1 -c nctenth )
If wo n w mix the above distribution of V. with the fro uoncy function
of S, the sise distributi n wo ov hi to get the frequency ;f
sal rior: for the ?h- le industry. The distribution f S is Pareto.