A critique of the capital output ratio and its application to development planning

.,,__. '

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•

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UNITED NA TI ONS

AFRICAN INSTITUTE FOR ECONOMIC

DEVELDPMENT AND PLANNING REPROOUCTION/09-81

D A K A R

• NI'fE.JKJNTH PROGRAAfv'E -IN DEVaOPMENT AND F;LANNING (October 1981 - June 1982)

A CRITIQUE OF THE 'CAPITAL/OUTPUT RATIO• AND ITS APPLICATION .TO DEVELDPMENT PLANNING

in

STREETEN, Paul

"The Frontiers of Development Studies"

Fawzy

MANSOUR

DECEMBEA, 1981 '

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•

CS.AP

6

REPRODU'ÇTIOI-J/09/81 Page 1

A CRITIQUE OF THE ¹ CAPITAL/OUTPU:T ·Rlt.TIO ¹ .AND ITS

' ' ' ', .. , ' ' 1

APPLICATION TO PEVELOPJ1'1ENT.· PLANNING .... :·

. .:~. ^·'·· .~-¹

.·_1 ^{·••• t..'} ',,

' -~-.

'THERE>:is one t:yp-e of mod'ef· thaf domin'ates the 1ite:ratuT·e

tÙ.1d' tli'è· :

plÈins;. This is t .e· Ea~rod-Doma.r' r:10del. 'imd :ïts 'nunerous Variation~s:. -

Iri

thii~' the

stra t e g i~ç -'X'~..r.~ab lcs

that are selected are aggre'gàtes

s~; c h

as

e'mp l oYfu ent~

., investment' a:nd output. ' B,iJ,t _in.s'tead\

o- f

the

~e o-cl a ssical

·assumptiob.'

;~t'· "

:pe·r_:fect subs:!fî_t-q.~à.b.ility of capital ·for labour, the' st a.rting p~iht.-:..is the assUI!lption .of· fixed t echnical or behavi oural· coefficie-nts, so· tb.àt a'ggre- gate output i s.'l·elatèd t o the ~tock of capital

b y

the capital/ ot.ti)Ut·: ~a-ho,

otherwise known as the capital coefficient. This ·is the ~aiient .· fea'ture : ______ _ added by the Harrod~Dcn!lar mcdel

t o

the K~yD.esian short-_,eriod theory of

employment. The crucial role, in economie iheory and planning, of the

'capital/ out put' rstio·.i.s -w-e.ll :~rrau:.j1t.--ou-t in·~nn...xrt·i;cle· by au-- I.nd.:i:mr~iter:

r r

there is- one concept that has dc~inated recent discuseiQns on. grovrth --t,he'bry erid 'devel'.. . opï:nent ,. . . planni~_g, i. t, ^~ ;,~s that_ 9f. .. the.. ·-~~~:P..:.~:i?.al- -output rat-io, ~r the ~api tal...;;coefficient

fis

i t i s sometimes cal led.

rt has be en . extensively used in vari~us . gr owth nodel s ,. 'e .g~' tho se of Harrod · !}611.1ar, Kaldor, and Mahalanobi s 9,_ and i t has àls·o· 'helped t,he forl'lt'll&tion of· our First and Second Five

Y e . ar

^{Plans.2 ··}

..... ^{:·~. ..~} ..,._ .... --^·-:

:..·

l 0 • . B .. raun, Il ^,~. '1:<'1 """" t ' ^~s,. :rr n.. ,~ ur1I ^• nf. ln.:, G • · ^{P t::~} th ur, ^Q û•.^-rt^, . M err e t t· , J · ·• M M t 1;. on :tas, .- G. Ohl in,. L •. Pasinetti .and A. K. , Sen_ contr:ibuted very· helpful commenta to

earlier drafts of thi s paper •.

r,

· 2

Pankaj Kumar Sen, ''Use· of the Bnpi tal-Output

~-.~~~-o

^{i n}

·~ ~ ~ nom\Ù

Pianning', The Indian Economie Review, ·v 1 (Feb. '1960) 23. See- also 't':he r~port of. a group of ex~erts: ¹~ft~r estirnating the current rat e of savings, the crucial question will be what anount of net rtationai output can be expected from the investment t~ be nade on t he b~sis of the estinated savings. A number of studies have been made on the a[1ount of capital required to increase output by one uni t per ennum in each sector of econony and for a national economy as a \ihole. This m~ount is cal led the "cepi tai-output ratio", or

' ' ..... ' . . · -'; . '1 ·:·:

REPRODUCTI ON/09/81 .

Page 2

.Another appr:oach-;··1 es s · per<Oi. .. n:ent:-t-o .. ·-pf'o1,l·ef!'l·s-~·of. ·.eC•OD:OF..l.:ηO···P lanning in South Asie, uses a G0-b~f>:ë~~l&e .. ·-pl'éd:'tloti-efl·,fu,n:c"t;i:·e-n- aî. tb.e form

Y= ei5B1d-.whe:re K and Lare the quantities of capital and labour, respec.:.. ..

.tively, and a,

d...

,_8are assuned constants, where (d...+!) !:'1SY ·e·q\2-aÎ-; ··exeeed, o,r b:e le.ss than I, .a:cc.ording t o J,v:hether co~stant, increasing or .decreasing returns t o sc.a.le are assumed? In t his kind of a.ppr oa.ch t'he re are al so certain difficulties, such· as 1J.ow' to treat chanGes ·in. the quality of

-.1

capi tel and· labour',, hov; · t o incorporate changes in. knm'lledge and the passage of .t.ime,- end how to determine the oagni tud-e· of the con·sta.nts. The capital/

·· output . .ratio in this formula:tion ··i s~ not a determining variable, but a resultant of .the changes in· K en.d Las weil as in ~and/1•·' icJhile one can therefore. easily de duce. average and ·mar.ginal capital/ output rati.os from the production funct ion, these are endogenous veriab.les, not determinants

"capital coefficient".' United Nations, Prograw.ming Techniques for Economie bevelc~bent: With s ecia.l reference to Asie and the Far East, Report by a group ·of experts Bangkok, 19

·o ,

^{pp-. 10-11:· • . "}

. fl.nà,: .'The rate of econo~ic growth mey be· analytice.lly considered as being a function of two factors, (a) the rate of capital formation and (b) the capital/output ratio, accordingl3r developoent policies may be described as a eimi:n.e to increese the former₉ red.uce the letter, ~p;r do beth. ¹ UN, ECAFE, 'Economie Developsent and Planning in ksia and the Far East' ,

Econonic Bulletin for A.sia and the Fer East , VI 3 (Nov. 1955) Bangkok, 1955)

25-6.

\

Lewis' s book The Theory of Econonic Grotvth, especially the chapter on capital, illustrates the --een-t~-1-·-posil;io-froo~ -this -conce·pt' -to-gethe-r··w±th · that of :tP.e sevings ratio: 'The c;entral p:roblen in the theory of econonic growth (s to und'eistand the proc'ess

b y

l-'lhich a· c'i:ml!i1Uni ty· .i's converted ·from 'being a

5 per cent to a 1?.: per cent saver ..: wi th all the changes in ·att'i tudes, in insti tutiono and in techniques which accomp·eny this conver"sion. ¹ W. Arthur Levi~, The Theory of Econonic Growth (London: All~n & Unwin, 1955) pp. 225-

: · .6. This ·ta b!lsed on a-· required grow:th rate· for nat~iopal income of approxi- mately j per cent end· a c.~pital/out.put rat io . .of. apuroxïmately_ l.!.

. . .• ,,....,_ .... ..c.:;,.:~~~-·· · • . . · ^{, , , 7 • •• •••·• ••• •} .~ ,_

.. ^~· ·. .

.:!-r~~r ·"!'····,.-~-·-

0 .·.:.. • • •

.

^..

/1. •

..

. . . ..

REPRODUCTION/09/81 Page 3

as they are in the

Harrod~Doner

^{analysis.1 Gince the plans are concerned} primarily with the capital/output ratio as à strategie relationship in

· deter:mining..:.the ~a.te of growt;h, w.e c.an i!?-__ ,~ur discnssion largely ignore

the Cobb-Douglas production function. Seme of the cri.ticisos would, however,

' "'

apply t o any of the traditional notio:J.s of a 'production fu.v.ction' • .:.

(a) it s meqning and ~easureoent~

(b) its use in planning or in. providing explanations9 prognoses, or predictions of development9

(c)_the meaning ~nd validitr of its use as~ criierion· for th~ alloca- tion of capital, as exanplified by the phrases: 'minimize the capital/output ratio', ¹naxiôise the reciprocal o1 the sociél marginal capital/output ratio, ¹ or ¹œllow for the fact tbat the capital/output and the savings ratios are interdependent'.

Our discussion is concerned with (a) and (b),. but has implicattons for (c). Criticism of ·.the ratio r:1ey he transcendental or il!l!!lanent;_. th~t is, the assunptions on which it rests mny be examine~ in terms of the logic of their adequa.-'Cy· to reali ty~ or vie mey eccept the essur.1ptions, and consider

1 In an article entitled 'The P~oductio~ Function in Allocat ion and Growth:

A Synthesis' 9 America:n Eccnomic Revie1r,", LII 5 (Dec. ~962) 99J:- l022₉ Harvin Frenkel shotl's how, matheP.J.atically 9 a nicro-e·a-onoo.ic Cobb-Douglas functicn for eaeh individuel firm can be combined with a macro-economie Harrod-Do:nar .function, Production in the enterprise is soverned by a function of the form

P · = affK~ iL~- where :H i s cal led the ¹ deve~opment modifier ¹; a parameter for tfie

~nterprige

^{but a dependent variable} if all enterprises expand together.

If Fi = (K/L)Ythe · aggregate productio:..1 functio:1 is P = a{E/L)Y:I L ;... and if y

=

end (J-+/1)

=

^{1, it reduces to P = aE:, the Har.rod-Dooar relation~ . In terms}

of our Fig. 6.2 (below. Section 5)9 each individuel enterprise believes it movee along a .. à,:i,p:linishing :rreturns curve, but i1"' all grow together they nove up the straiaht line.

2 After e brief discussion of the use of this type of production function in forecesting (not planning) growth in advanced countries (not in underdeveloped countries, where statistics are vastly i:1ferio.r), Ot.to .Eckstein concludes:

Since aggreEate production funct ions sc ~[;_:;_:· h·ave

not

^{yielcfed reliable'-·ëstimates}

of the relationship between investnent an~ growth₉ one:nust try other methods.' ('Capital Theory and Sone Theoratical Problems in Development Planning'.

Aroerican Econonic Revie''~• Papers and :Proceedings, LI ?. (lJlay 1961) p. 98),

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REPRODUCTIOIJ/ 09/ 81

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Page ·4

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^'·~

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particular ambiguities, inconsistencies and èifficulties within this freme.Hork. A. transcendental cJ>it ique sho1,;s that the ratio displ~ys four systematic 'biasesg adapted ceteris ·paribus or automat ic mutatis mutandis, one factor anelysis,: tiÎsplaced aggrègil.tion and illegitil'late isolation. 1

. , Mi spleced agg:r;egat icn and illegi t imate: i soiation go hend in hand when diff~rentiated ^{it ens are ageregated and the conpcnents are se}pareted from

model ali forms of capital are aggregeted and e~ch piace of construction and equiprient :is:isolated fron {a) it s specifie relation to other pieces of construction and equipment9 (b) ether influence$₇^· s~c1 as levGls of living (i~cluding:fecilities for acquiring ~kill~), hnman attitudes, and social iri~titutions~ and (c) ~olicies direGted. Qt.ot~er conditions. Yet

~1~1 ~-2:ree factors crucially affect thé contributioD. t o. gp.tpu:t of the parti- culer piece of invèstnent;

Iller;itiD.ate isolation·is ·a specifie manifestation of the assumption .that.,all other condit ions renain constant and adapteù to developnent. For if conditions are assumed to be constant whose ebange i·s either necess~ry

t9 the rëquired results or mt.kes en importent difference in their direction, speed and size ~ there . has be en illcgi t imate abstraction. If autorie>.tic

mutatis autanclis is relied on, sc that it is essu:D.ed that these other condi- tions will change but in such a way that they will always be autonatically adapted, there ·~is no isolation. But, as '!;>le h_. ave seen,- thi,s. essuopt.ion

-·~· -·· .. ^···~ ···-~. . .. ·-~-.... ^;-. . ....

oust be questioned on both eopirical end logical g:rou.nds. Enpirically we know that in ur..derdeveloped count!j:es :çonàiti.:~J.3.S .a~~ ~?~- eutonatically

· . ..

adapted in the required fashion. Logicelly~ the ~pecific contrï~ution of the vari~bles,under consideratio~ remains indeterrninate if we.al~ays keep

"'

in the pack a joker that can t ake all tri~ks. If we ~ave ~n u~~peci1ied comb'. ination of the two assunption::;' beth illee:i ti~ate., isolat ion and indeter-

ninacy are·preserit. It. is the purpose of- bot~ tbe ceteris pa~fbus an~ the mutatis nutandi.s assumptions to i soÙ.te th.e study bf the causaL relationship

' 1

• Ge:e Cl::tanter

5 .

.: ^:

···:..

..

... ^{. . "}

REPRODUCTivH/09/81

Page 5

between capital input and. aggr.egate output . This approaëh introduces the bias thet capi tal is

the · onl y ~ 0~ - thé

^{main9 soùrce of development in under-}

dev~loped countries: The separai ion of capital from c~rtain componen~~

in t he le.vel of' l iving that affect lab~ur input~ ^arre'!. labo~r efficie~cy. ^and

-' . ~ ' '. ... .

. from attitudes and ins-titutions crucial for effective capital use~ is one

. 1 •

of the main fermi of illegitiflate isolat ion.

'::'he effcct s of plant.· and equiprJe:nt on ont~'):lt. de~e~:.d I::.'Jt only nn where and how t he irrvestueJŒt occurs ut also on what otLer poliçies that affect levels cf living, at titudes and insti~utions are .purs.ued. In the under- developed. countries the two last-nal:!l.ed conditions cannot be regarded either as alrendy.· odapted to dev;elo:;:men:t or as a<:1.tomatically adaptable throu,gh investment. The effe.ets of a· deyelopment plan wi th .a given amount of investment will (tiffer (S!'eatl,y eccording to what polici~s- with regard to attitudes and inst itutipns are pursu~d in conjun~tion with the investment.

Moreover, illegit imate ,isplaticn is implicit in .ageregation if the cooplement arities between the compopents of the aggregate are. ~gnored.

The· output effects of one ir-vestment pro,iect depe.nd on ot he_r.. investment p;roj ect·s that are emharke:4.₁ on ei ther sü:ml tane,cusly or in sequence as phases of a· co-o;rdinated programne • In an economy 1-;rhere eac~ proj ect· is infini te- sim.ally. sl!lall and cam profit from adapted at titudes ·and inst itutions,

• 1° • 1 •

aggregetion irre·spect ive of conposition r.1ay ,be legitimate • . But in und-er- d·eveloped countries-investment proj ects are large 9• in. relation to bath the exi st ing stock o~. that type of capital end ann:ul ~ddi, t i.ons to ,i~.. The

! . ·'· 1 • • • ~ ' . 1 ! . ' i'·' . -_.

re.sul t:i,ng output· .. varies sharply. ·accordine; to the availabili ty of complemen- tery supplies, such l7,S appropriate C<?n.struction elsewb.ere e.nd other pieces of equipment , and the existence of appropriate demando It is then entirely misleadine to treat 'c~pital' as a homogeneous quantityo It is a hetero-

. )/

geneous collection of specifie bits and piec~s tbat have to be fitted

to~ether.

h . .. .

-

^.

'• ^;."•

Much investuent~ particulerly pù':..lic investment in highways, power

· st'ations ,- ·ports, ·rail ways·, v-'orkers ¹ ho1_ ses ;.. provides· opror'tunities and possibly incentives for

c on s equ~~tial ou tr,mt - rien~ret _i ng

investment.' This, indeed, is one of the reasons for carrying out p~blic investment, which

REPRODUCT I OI<t/ 09/81 Page

6

often seerns U?likely to reco-v'er its êosts

b y

^{profits. many :forms of}

private inve~tment are ~Iso of ·t!::is nature.· 'f~.e ,. ~nd~t.:..térm .àuCi·:· sec tora!

c 'apità.l/m~t put ~àtio

of a given. project. mày be hiGh.;· 'oùt

-~he

long-term

ràii.o

ni"ay

be m· ch l ovrer, if it can be ~alc1Üated

at . ·

^{al L It will depend}

on fuller utilisat ion of the proj~ct~s o~n capatity and th~ ca9aciti~s of ether a.lready exist incr entero;Jrises and also cn'the sei eure cf 'consequential

..

{ , . - c- . • 1

:r ~- 1~~ ~tooe g1ve r1se.

:vision costa ar.e unexpectedly high or· that · th:e e::::pect·ed corJ.plementary "invest-

~ent is .. not forthcoming₉ the long-term·r~tio9 which includes externe! effects on other projects, will be high or may rise. Certain projects·₉

.:'su' ch·

^as

improvements in cul t ivation nethoG.s ₉ may them selves req_uire l i"ttle (:~èpitel, b.ut may require conplementary investnent in transport, povrer9 storage end other facilities. Im ~ither case9 i t is certainly misleading' to· pay att ention only to the L.i t ial investnent anc.,. i t s direct e!fect s.

If a series ·of investment projects are intarrelated9 èither sectorally or tempcrally9·eech dependin_g on the ethers for it s success₉ the very notion of a -capital/ output ratio for any otie of them iti isolation b~comei·as

mean.ine;less as t he question. ldhat is the contribntio;;. of thê first violin to t he Nineth Symphony?2

Jt is the composition and t he

r e lat fon s h ipo~ · the

_parts thet matter in eppraising the resul t .· Hispl.~ced age;regat ion and illegitimate ieolation canceal this~ T .• e problém is like that of but t ing the pieces of a ji gsaw puzzle togethe~. It is the placement of the pieces in relation to eaçh other that mat t ers ₉ l'lot the di splay of any single piece

. (illegi"t.ima.te isolation) 9 n6r the countirig of" the total humber of pieces

t hrovrn. . tw~et-her

a.t

:ran:lor::1· (ni splaceù. n.r,p;retation) o

1' Changes

i n ~uti li sation

^{are discussed in Sect ion 9 below. The creation}

of investment opport uniti es falls outside the sccp~ of the normal assumptions end embraces variabl es no .. melly asst~::led const ant and adapted r adaptable, 2 Except in a situation of general equilibrium., in uhich a. capit al/output ratio can be at tributed to ~?ach industry 0::::1 the assuo.ct ion that the required edjustment s are made ïn all other inè.us-t:r:::.cs.

REPRODUCTION/09/81

Page

7

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If c~anges in atti.tudes and institutions are taken into account in

. . .

. ,. ap:prais~ng capital proj e·c.ts, some projects are sûen to be <more productive

than oth~x:s- not only, and often not p:dmarily, because of the ir physic.al

• • • 1 • •

effectiveness but also because of the-ir imp,act on ,decisi~n-taking in_cen'tives

. . .. · . .

to entrepreneurial or p.olitical act ioJ:l, at ti tudes towards vrork and venture, and the formati on, reforBs or destruciion of habi t i, traditiobs, customs and ' !l.Sj,:.irà·tions of wo:ike::rs aild ent::ro:_?reneurs. :~::,-~ .2,]'Jplicat i cn of ü iproved

tec.hniqu.es is in ;:uany 11rays :rcelate·d to investmant. lmpro-ving levels of l ivirig, particularly level

s

^{of nutrit i on-, h:eal th and} ed.u.cation, \vill rai se output. The conclnsion .. {s that unless supplenientary and consequential • actions are taken on>-à .wiê:e front; a.n investment pr oject ne.y misfire; and in spite of a positive direct fl ow of product ion

from

^it7 the ratio - . includ:hig. e:ffects oc other project s ànd-ent èrprises arid, often, priv4te énd publ ic 'actions - ciày rise to i~finity or become ne3ative f~r capjtal

. 1 .

1ncreaseil • The success and effect iveness of investment ·in contributing

~ to the growth of output depend not only on its beinG an addition to an

aggregate 'stock of capital' but on its direct ion (ne~lected by eggregation), its composition, and the pr esent and future complementary policies with

..

which i t is raclcaged (negle cted by isolation).

An appendix at t:he end of this chapter compares briefly the different ways in which the concept is used in the plans of the countries of South Asie and its estimated values. The usel essneas of t~is cioncept is conf{rmed by the large differenc~s between anticipated and actuel coefficients and betv1een th~. c oeff ic ie:2ts in different· 'countr~ ies. ·-. ^~. and -... ,, . . . a...;, t d. . . .. i^~ -:Her,:,. . ènt -times • .

Be cause of the wide spread use o{ the capital/ output ratio and 'i t s . strong grip on habits of thinking jn the f ield of dey~lopment planning~_~e ~onaider

1 oIt shou.ld be noted that not

~ ii - ~ ~ i~t- i.;~

^{ex poet in}creÏnental 'cë.p{tel/

.. out'pu:t_-retios' indicate \taste. It may be sensible 't o modernise and re- equip an indus-tr-y,- th.e. de.mandtfo:r J.lb9_§.e ·product is 'falling. Capital expen- ditu:re may reduce costs per unit of · output, \<J.hile eutplï;t is, rèduced. Sir!!ple- minded stu~ents of the câpit al/output ratio mi~ht conclude that output

could be raised by reducing the stock of capit al o See Sect i on ~ below.·

REPRODUCTION/09/81

Page 8

.a detailed immenent cri ticism justified-9 in spi te o:? the tre.nscendental

·cr.iticisms ~e have advanced •. Ex.peri.ence .. shows that exppsure. of ~he

inadequacy of the assumptio:::1_s on 1ihich a nodel is based is rarely convinc-

. ;ing. : Fac-ts rarely .refute t:heories. The tr~m .. ~cendentnl criticism. therefore

has to be complement:ed hy cri.ticisms that ecc1 e:ot••• s the assu~· mï"Jtions ..l. • and expostls loe;ical ùifficulties and 111ealmesses vithin t'2.e nodelo.

procedures bas t:iven rise₉ let US llO'.;' assume₉ :::or t~'}e sa~e of the argument in this p.a:rt₉ that they are legit imate. :le therefore assume that attitudes, institutinns₉ and ~olicies ore constant ₉ that changes in levels of living have no effect on· output~ and that secondary dypamic effects on· ôther · imre stments can be ignored. As ide from the se assumptions ~ both the ·theore- ticalmaster model and :the assumption o:f a constant ratio. have certain faults that make them particularly misleadi:..;g when applied to the problerns of development in underdeveloped countries.

1. The master model-¹

Let Y be income (or output)₉ S savings and

I investment.

De fine

S (the éavings ratio) s

= ^y

k

=&f

I ^{(the ceteris paribus i}nvestnient/incremental output or -the incrementa! capital/output ratio)

g

= ID_

^y (the rate of growth of income or output)

1 A clear statement of

th~

^{assumption of a constant} capitat/output ratio can be found 'in Gustav Cassel ¹ s Theoretieche So:dalôkonomie ₉ published in 1922.. The· quotation following is from· the English translation by Joseph McCabe:

(Footr.ote continued on next page)

•

l,

REPRODUCTION/09/81 Page 9

Then, if the incrementai capital/output ratio₉ kp is assume to be constant1 and i f savings equal investment (either as an ex post identity or a!;l an equilibrium

co~dition), it follows that:

or

Al t erne.ti ely ₁ we may assume tha.t O' tr.ilt p2r worker is ,ergwi_n.g __ at _Mt ann~al· percentage rate, p₉ and that the labour force will then require that aggregate demand grow at an annuel rate of p + r.

If both _ a.ssump_.t.i.an.s à..re· ·.made s inu;ü.:t.~r:u~.o-ç:s.lJC.:{nnO.

. J f

the. -~ b.ec orne infini te- simally small), fuli employm_e.nt Qr .. b.otP.. the labour force and the capital stock will require that these growth rates be identical, i.e~

s (3)

••••••'The meaning of the continuous formation of capital is .seen most çlearly

in the. evenly progressive economy. This may now be de:fined in more general terms.

In ·the monetary economy economie progress, assuming unaltered priees; can be

measured by the increase of the abstract total capital, ·and may.be r~garded as uniform when this capital increases annually by a definite 'and invariable percen- tage.- Let us call this capital C, ·and suppose that·C-:lncreases annu~lly by p per cent, p being constant . This increase of capital is, as we have ieen, ~nly

possible on ~onditlon that there is a certain a~ou.."lt of saving. Let us call the amiual in~ome 'I, ·and suppose that annuslly the proportion i/s_ ·- in absoltl.té

amount I/s - is saved. tie will cali this quotient which arithmetically expresses the community¹s thrift, the "degree of saving". Clearly I/s

=

^{(p/100)C, and}

consequently I

=

^{(sp/100) C. If we further suppose thet the degree of saving}

1/s, or the relative saving of the community~ is constant, which ·clearly · ··.r ~"'

..harmonis-es best w.i-th. .. our assumption oL an ... even. devel.opment~ we_ . .firid that · th.è- total income is in an invariable ratio t o the total capital • . From this we get the ~mportant principle that in the eveniy progressive economy the income

incr~as~s in the same percen~age as the capital. This principle is approximately correc·t ;or every economy if we take long periods into consideration. It .. is only during period~ of transi ti on that there will be ~my màterial difference in ;the rate of increase of capital and income. This result is important because ·i t a:(fords v.s·standing ground for a critical examinai;ion.of stat i"B11ical data asto the increase of income and capital. \Je ind also that it is possible to estima.te the inçome of an evenly progressive exchane;e economy by multiplying the capital by the.product of the percentage of increase and the reciprocal ·value of the degree of saving. This should be borne in mind in st at ist ical calculations and estimat-es.

1• One could, alternatively₉ assume t.bet the marginal capital/labour ratio (c = I/Âl) is fixed and k the dependent variable. If w =bY/'b.L is defi.ned as the marginal productivity of labour, I/ 6 Y

=

^{c/w and g}

=

^s.w/c.

REPRODUCT~ON/09/81 . Page 10

Should' this condition: not be ful:Ülled~ the full employment of labour · or .: th~ full utilisation · of the. stock of cepi tal ₉. or both, ·will be impossiblé.

On certain assumptions about the investment function, ~uch'models :can

illustrate a state in which chronïc inflation is accompanied by growing uncemployment.

2. Definitions

The following definitions will help cla:::-ify the suboec1:12nt discussion.

lo Marginal. incrementai, and averagé capital/output ~atio. The · marginal. capital/output .ratio is the infinitesimal, the. incrementai the .non-infinitesimal, .ad4ition to. capital div~ded by t~e add~tion to income

over a given period. The average capital/output ratio ~s the total stock .•

of capital divided by total income per unit of timeo

2. Ceteris paribus, historical, and projected capital/output ratio • .The ... ceteris par.ibus.. r..ati.o ... i.fl .t.P..e .:r.t;l.,tio .,of. cJ.l,p:i,:t.~l ,t.~ .. og.i;pu,_t .~a~t~4-. .QA .. l·ll,e .-'""·' '"

assumptiori tbat other productive factors and all other conditions, suèh,as .. knowledge, tastes, attitudes, and institutior1s,

~emai n t;.~ chan ged

and. that changès"in levèls of livi~g havé no effèct on output. : .. Histbrical ratids are derived from .observed past changes in c~pital and in income. Proj.ecteq

. . . . . ^(, .. . ^{. ~}

-1

ratios are·derived from projected changes in the labour force ·and in other

~esources ^{and;. possibly, .. improvements in knowlede;eo}

'If we assume, for

i n stanc e ~

that the percentage of progress

is . eqü~i

to 3, and that, therefore, the Capital

(c)

increaf)es annuall.y by 0 .03

c, :

and furthe~ suppose ihat one-fifth of the annuel incociè is saved, the i~come is~

accordinK t o what we have said, equal to 15 per cent of the capital. The~:~e .

figures must be about right :ln the c·a~re· o·f . Sw·eü~ti?" \•rhere .. 'th-e ··national- we'8lth and inccime in 1908 wer~ est lmated

at

about t~;noo,000,00b and 2,100,000,000

kronor~ . An of.f:.icial cq,mmissiori of nat ional ,defence, • in fact, estimated the . annuel pere ~·~-~age of increase

of

tb.e i'!.atio~.,al weal th during, the period 1885..;

1908 at 3.18 per cent~ Such figures càn, of course, never bé preciset but the figure given must be a fa~rly correct ·es:Pmate. ·

'For the ~ountries of Western Eur6pe·we may assume for modern times (before the (First Wo:dd)War) tbat the normal advance was about 3 per cent • . Although the figure is only ap~ roximate, it i s as well to have sorne standing ground for comparisons, and to be reminded thet on the whole, and for long peri'ods, the increase of both capital .: and income .must ;.be indicai;.ed by the

stme f isure. ¹· · Gue.tnv Co.ssel, 'f'he Tbeory of Soc-i . .o.l :Sconooy, tr~n:s. Jo·s~ph .HcCQbe 1 (London: '!'. Ftsher U:nwfn,. 19.?-3) 6-2-3;.

REPRODUCTION/ 09/81 Page 11.

). Net v • . gross capital/output .ratio. The net rat:l'o·-ëxcludeiiï depreciation from output. Depreciation can be calculated either es the

• ~. '• - <' :· . :'.,·· • • • •

lo~s of productivè·capaC"ity- dùè" io~ the·,iel:iring· out :of existing capital, or as the ·'cost in~u.rred in repla.c'ing it. Wi th technical progress ·the two

. . 1

measures will diverge,

l1:. Pro.i ect 2 sectoral, and global capital/ out;)ut ratio. The diffe- renee in ~heoe rati os depend on the extent t o ~hic~ the vroject under

' • • . 1,, • •

consideratiori(·f) infli'cts··c-ôsts· on~or--.. {ii) yiülds :t)eL~.é-i'i"ts 1_t,o other eri.terprises not included in the project. The ratio for a given·type of proJect .. :le._.likely. t.o j~rY .. 'Jro~.:Pl§.c ~. · to. pl.a.ce.J: . . ~!..?.~ .t.~111.E!

..

,to t~me, end· according to 'vhat other projects are executed and wha.t other products .

. 2

are produced. -

5.

Short-term v. long-term capital/output ratio. The distinction here is ba.sed on the length of:·time ·ov~r vrhie-h:·eost s érid yieldè are

considered9 &nd the weights attached to net·ouiput at ditferent times.3

.. -=-·:.:-- : ... : · ·6-i ·

^{·-·e-e-t·eri·s· pariliius :v•-mutati·l!l· mutand·i·s· ·eapi}

t · a-1/

éutpu-t ratio. The ceteris pari bus ratio assumes ali other plant and_ .... equipment~ . technicei knowledge, tastes, attitudes towards savings, l'lOrk, and venture, end in.l3.t.tt.Y,t i.oJ:ls. to be constant and adapted to output increases. The

·-· ....• ;;;:~.: .. 7. . •.. :'\, :... • .•.. .

1 With t echnical progress in the

mach i n e ~m ak i ng

^{sector, the. same cost}

~ow­

ever measu:>red) as that incurred ·for the· origüial machine will provide cepacity for greater output . Mea.suring capital in terms of its output

ca~acity would normally give a different ~esult from measuring it in terme

··of ·the ·i-nput·s requir-ed t·o -reproduee

+ t-· . - · · -· ·· · - · · · ·· · · · ... · ···

2 . . ... .

This distincti~n, if applied to the cetèris p~ribus ràtio₉ would~corres­

pond to Pigou' s distinction between social and privàt e marginal net product were it not for the fact that not all costs anii. benefits can be 'bro"Ucbt in relation to the measuring rod of money' .", It shoul·d be· noted thet :"the global ratio, as here defined~ is not the couritry-wide or aggreg~te ratio, but the ratio relat ing tc the sector or the project, vith allowance for

-~~ternal effects.

3 Since the capital/ output ratio is the ratï'o of a stock to a

[ Ïow;·

^{ft hes}

a time dimension. Hence the oddity of calling a 'ratio' short .... or long-term.

REPRODUCTION/09/81 Page 12

. .

mutat is mutandis ratio, if it could be caltulated₉ would take into account changes, in these conditions induced by the investment.¹

7.

C 1.rrent v • .technological o:api tel/ outp-ut ratio-;· Th-~ · teehnological ratio is dictated by the capâcity of completed project s to yield output

(a·ssuming _~ a normal _{. .} degree _. of utilisation). It di:ffers from the ratio of work c"Grr:::n·Üy · :~-l~teï.' _éonë-trv.ctior" te<· :JJ"J. ,rut·-w':--,e::l .. s:t~'>r~s ... ë.i:::"oT -~~,"om complâ- tio::::.s.

8. I:ncr.emental v. decrementai co ni tal/output ratio. The ratie will normally differ according to whether capital is increased or reduced.

' . ^'

9. Aggregate (or countty-wide) v. sèctoral capital/output ratio. The eggregate ratio is an average of ell sectoral capital/ output ratios, with sector outputs as weights. It can be an average of the average ratios or of the marginal rëtios'. · ....

10. Ex ante v. post capital/output ratio. The former is the planned, intended or expected ratio ₉ the latter simply an observed ste ti stical-~ residuel:

11. Investment/marginaÏ

outp~t

^"ra

ti~--- v ~- ' i"n'v~~'tiiïe.nt

^{'për t} ime-untiJ unit/

marginal output ratio. The former disregards the length"'"of 'time· ove·r which capital is added to the existing stoc~~ and the latter takes it into account.

Gome relations to familier concepts areg Keynes¹s marginal efficiency

,_,.---of -ea-pital-; li_ke Fisher-' s rate. o.f r~t~rJG,_ ove.r C?_st₉ is ~he ~eciprocal of the

ex ante ceteris paribus marginal gross project ratio, if a constant flow of output per unit of time is assumed.2

T.e Pigovian social marginal effi-

cie~cy of capital is the reciprocal of the ceteris paribus marginal global net rat io, excépt that sorne costs and benef~ts may resist being ¹biought into relation with the measuring rod 0f money'.

1 There itJould exist "n-ot

one·

·oüt a very large numbe;rr of mutatis mutandis

; - 1

-.l, ratios, depending on the: his tory of the economy,

tl

e impact of the investment

: '·' and its repercussions, and the type of çlisturï ·ance created. It is not a

usuable concept, but its function is to point up what we wouldhave t o know in order to use it. 'The ratio tha:t-·'W'e can kno',v is useless₉ the. one .that would be useful we cannot know.

· 2 Note also 1;;/icksell ' s natural rate. of interest9 see Gunnar Nyrdal H.onetary Eguilibrium (London: William. Hodge & Co.,₉ 1939) Chapter iv.

. ^'··

3.

Problems of measurement

REPRODUCTION/09/81 Page

13

The question of the measurement of 'capital ¹ and· ¹ Ol:i.tput 1 reis as a large munber of very difficul t problfollS, touched on o:nly ·brféfly here.

The question concerns us a.t tw~ l~vels~ at the statistical and

empiric~1 level and at the lev~l of logic and definition~ As for the first

. 'b1 ; ' t .

pro ~em, 1~ ~Gs~ co~n r1es 'develcpment expenditure', not

an~ csti~a_·. te~ _. Drivate investment

. . -

··are lumped together to arrive at capital input., In addit i,on, there is the ·'. que stiori o·f the correct valuat ion of ca pi ta.l a~d output in economies

; ..

·:Wh.er.e restrictions and direct ocJ;Ltllol s are ubiqui tous. Currency and

• . . 1

trade re~trictions

a nd.

li'censi:ng and all?cat ion preyent priees from equa.li-

·sirig demand and supply. To essert that actuel priees are largely arbitra.ry

. . .. ~ ~

is not to indicate that ¹equilibrium¹ priees, could they be ascertained, would·necessarily be adequ:etely measures for evaluatipq capital and output.

In some instances the discrepancy is obvious. lt!ith èurrency and excha.nge restrictions, the contribution of exports to·· development may exceed their market· priees and the capital/ output ratü) in export industries · is thus

smaller than weighting by market priees ~ould indicate. On the other ha.nd, if import ed capital 8quipment is used in

ihe

export industriesg the higher valuation appropriatè for export-oùtput enters into the.:numera.tor as well as _·. the denomina_·.... tor of the cap_- ital/output ratio and to that ex,ent cancels

'

.

^{-'/.. ..}

out. S~milar considerat ions ~pply to al.l inputs and-outputs whose: ma.rkét priees are kept l ow by government policies.

Ls for the second problem - that of logic and definitiori - we have

. . .

.

alreadi -pointed out tbat -the specifi-city, ;hete::rogeneiiy, complementar1ty and indivisH)ility of capital in South 'Asie mal;:e aggregation impossible.

Here we shall only 'enumerate some .of the general problems thai'· a~ises in the ~easu~em~nt of capital.

If there ar~ s_everal it ems on each side of the papi tai/output ratio, and if these ·9-o not change in tpe seme roportion₉ we are face-d not only with the prob}en of_J ndex numbers9 including the indeterminacy. introduced by: priee changes in the planning period and by different income distributions, but with all the difficultie~ peculiar to the measurement of capital that arise from the fact that:

REPRODUCTION/09/81

Page il±

{a) capital last s, but does not last fôif-- eveq

. .

(b) it takes t ime to construct?

(c) its quality changes asimprovêmènts are incorporated;

(d)·r~~lacement and improve~ent ar~_not .distinct ac~s; (e) it is u~iii~ed t o varying degrees at different times?.

(~) anything that changes the relative priees of ca~ital goods and consumer gooàs ₉ or Gf dU'f erent c;oods e;enera::..ly 9 vr! ether from tb.e demand si de or the supply side, v ill al ter tr1e capi tal/ output ratio, even without any change in physical capital, physical output, or technology. In part icular, changes in real wages, in the rate of interest, and in the priees of imports xill change the capital/output ratio, even thoue.;~ nei.ther the C(JID.20sition of investment nor techniques have changed ..

~lhen the producti vi ty of newly constrùcted cepi tel goods changes, the question arises whether the capital goods shoulù be measured in terms of output or of input. Heasurement in terms

of

output is useless for our purpose, for it would make the capital/output ratio a tautological constant.

The difficulty with the input measure, on the other herid? is that despite the increase in the producti vi ty of the se capital goods, ·the value of the resources used in tb.eir production may not have changed•

. " . ^.

Furthermore₉ there is the_ problem of rents end qù.asi-rents, whfch

. . .

arises in connect ion with the.use of scarce inputs in conjun~tion 'with

capital. _Consider two projects with identical initial capital costs • One uses an ... input thnt is scarce '(from n planning point of view), such as e scarce forc~gn exchange componen~ or a scarce type of ~kill9 while the other uses labour and :rm1 mnterinls in ~ore plentiful supply.. Shoul.d rents end quasi-rents be included. in valuing ·Jutput , a procedure that would give a lower capital/output ratio for the first than for the second project?

O:r should rents and quasi-rents, and thus the op~1ortunity costs of using complementnry factors, be excluded in valuin~ output? The problem is not on).y the accurate. evaluation of rents and quasi-rents, but whether to

in~ lude them at all. For many .large public sector proj ects, mcreover,

REPEODUCTIOH/ 09/81 Pc.ge

15

' ·'-

opportuni ty costs wur':~no·.ic;··''b~ ···reflected in any pricés ⁹ for thère are no

· otber 1

b idd ~~~ '.

· Should. ëapi,al/ou.tput ratio1;1 roflect not only the

· opportuni tl:es forgone now bu't olso tho se forgone la ter? ·

l ..

4:. Confusion between the avere.ge and the incrementel capita1/output ratio

S<nne w.:ri tc_r s falc:.llate the pr~vai lin.c nve:coge co~;i

tc.i /

c~..:tp-:.::t ratio in

-- .~dya~~~d .-~ ~·;.mt,r i es

^and e:r.:tTapolate it to proclict the margiJ.1al pt'oductivity

of capital (whatever this may meen) in u.nderdeveloped countries. Quite epart from other problems, the fallacy in thi~ arguiDent · is the con.fusion of the average capital/output ratio OA/f.~ (= BD/CD) with the ·incrementai

·---:~::.:...ra-tio !JD/BD (-Eig; .6.~1), .. as.s.umin.g ytth_·:tr.a.ditional theory ··-that -OBE is-.the

.. . .. ^". . -·-··-· . ... ' . ~ . . . . -

· f'*ction relaiing capital to tota,l product, all. other· things remaining

e'~ueÎ,

^{and BD the (non-oinf}i_nl. tesü:fal )·

i.nve s tme~t .

^{1 The marginal ratio}

BD/FD l~e~ between the other two.

5.

Confusion betwe~n theoretical; ¹ceter{s paribus' and historicel statistical ratios

Here, the average 'capital/output ratio is calculai{ed for certain years

·in the past . Since the ratio is found to be fairly constant ovèr long periods, it is concluded that tha maiginal and the incremerital ratios, being i dentical, _.,.~'~th the average, œn be extrapolated for increases in capital.

But this statist ical time series cau give n~ clue to the relevant incrementai· cepi tel/ output r:atio. Fir~t, even assuming. tl::)..at, we. 'were conce:rned with a single'furictional relationsh' ip, ~sin Fig.

6 . 3,

the fact

that ^.f} r~ti'o ii'.l .. constant for ;th~ee ob,seryed pdint s does n,ot necesserily mean that it will remain constant for smaller or larg:er ùl.crease~ in

1 .. ~ ,J

1 . .

, See, for exemple, b.. Shonfield;' Br it ish Economie Polie . since the War

(Harmondsworth: Penguin Books 1958 P• 109, and ,The Ecoriomist, 2 Merch 1960, quoted in . Col in Clark,. ·G-:r:?:wthmanship (London~ Insti tu te 9f -Eco'nomic Affeirs, 1961) p. 18.

REPRODUCTION/09/81 Page

16

capital. But, more importent ₉ both labour and capital have in the past impro~e~ end indreased₉ so that thé ceteris naribus pr6ductiviiy cu~ve has shifted upward (Fig.

6. 2).

Secondiy, the~~at~ collected in~orpoiate the effects of economie progress and of improvements in technicel knowledge, l>Thich a:;:-e at least partly au.tonomous ancl would have occurred even wi thout

. . 4

···-· add-itional· iaboùio ·end cap-i tel ^{o!L ...} H@UC@. productivi ty \:l'cmld. rÜJe in any case,

r)

..L • t .' l t t . . + " ,,

ori ~o ra1se a~a ou pu ~raport1onaua~y.

curve might decline steeply. Yet i t is the avowed purpose of the plans t o·raise the savings and inyestment ratios.

1• .If the curves in Fig.

6. 2

represent upward shifts resulting from improved equipment ₉ they assume ·perfect adaptation of the .. ,.;hole stock of capital to the new kno'l'iledge. In fact , there l'lill always -~e ¹ old' pieces coexisting with improved ones and the productivity of capital will thus depend on its age composition. The curve relat ing output t o an increase in investment will~

therefore be . steeper than the total_ adaptation cu.rve for the old equipment, but iess st"e.ep. t,'hi:m

the

straight .. l"ine?" J:f "th-e "ïnargiriiù'

prodüc iivi fy

of. the new equipment is the same as it would be if the whole.-stock consisted of new equipment, it will have the. same slope as the curve showing full adaptation to the ne\<! equipment , which lies vertically ebove it. Thus, st'arting at the point of intersection of curve 2 with the straight line9 it would show the

same slope as curve 3 vertically_above it a!ld wauld lie between the .line going through

2 and

^{the straight line.}

2 . . . . '

• Severa! studies have attempted to shov1 that 'tech:rdee.l progress ¹ ,has been responsible for 80 to 90 per cent of the grovth of output per' unit of labour, and capital for only 10 to 20 per cento But since .'t echnical

prcigress' is a catchall for economies of scale, external economies₉ improved health, education and skill of _the·labqur force, better management, changes in the composition of output, and oth~r improvements, as well as for technical progress in the strict sense, Moses A.bramovitz's term ¹measure of .oùr ·

ignorance' or Evsey Domar¹s residuel' would oe more appropriate, Cf E, Domar, 'On the Measurement of Technological Chan~e¹ 9 ^{Economie Journal (Dec.}

1961 ).

Others₉ including Kaldbr and Solow, have abandoned the notion of a 'real' stock of capital, measured in physical terms, and have combined tech- nical progress and changes in the 'stock' of capi~al, thus abandoning the distinct ion ·between-·· movem-ents along, ·and· shifts . of-₉ -the -p-roduction func·tion.

MarxJn Frank.~l h_~_s s_h(H-ln ~o-~ a micro-~conomtc Cobb~Dou,glas type of pr.oduc- . tiori function can be combiried wi th e macro-economie Harro.d-Domar. model, so

that ,

i ll"

our.Fig~ 6."2, ea~hfirm believes it is moving along a curve of:

diminishing returns, ~,•hereas alf .èrë ~:;jJÏov.ing together up the straight line.

See n. 19 p. 72 above.

. .

^,

J^'i, ,J

6

'1_,

i .

·:.·,;.

-.: ' Capital

~ ;;.. ·")

Jl'.J..g a o.j

Fig.

6 .s c

'? F

tl

')_ +.>

:;J (."l,

0

t

.. -~­

;.:1

B'

:::s

0

-. :

P..EJPRODUCTION/09/81 Poe;e 17

., · ----7

···---·-· ..

: . . ~

_p · ..

{ 1 é

'· C?..uital

Fiee :

6e4e

Capital/ output ratios t'!Ilcler :Z-à.iff~.r~nt. é\-S~'!.mlP t.im1~ • , ... :. ~-; ..

. ,

.. •·

... ··

. .... ^-.-~,,

..

^~·-;-·-····

. .