The capital-output ration :its stability and usefulness in development planning

' •

(

.. 1it..:;.u. .. .:.ttio .:.>,

.2\.~..riC:..lJ. .il .:3tirut.. .::or •coaa~ic L..".!Vèlop:r.-~...:..1t ru1r "'lë>nfÜiir ₁

- .a.r,

>J.::.~h;;; .Jül

.1.~Jis Ja,:_:x:r is L "' artial !:uliil , 'üt :).::: t 1t.. course.. of ^t.1.L l.-~j :lctiv_ an

:;tratD;y Co1..1.Ts~ at I. J. • _,.

.,

....

CAPITAL-OOTPUT RATIO

Different O::mœpts and Definition of capital-output Ratio

It is important to distinguish between average and marginal capital- output ratio. T'œ average capital-output ra·tio is the value of the total stock of capital diviàed by the total annual inoorœ; while the marginal or increrœntal capital-output ratio is the total value of stock of capital divided by total annual inoorœ ( et-i:-Jational Inc:x:xre). Net-invest::rrent is estirra.ted over the plan-period, the .increase .in net output is also est:i.mated

~~g:--

the beginning of ~ plan-period and the last :year of tl~ lan. All :rœasure- rœnts are made at the saJ.re priœ level. f.'Jany African countries use the

rna.;-

ginal or incre:œntal capital-output ratio .in their plans, I have, therefore, selected igeria, Sudan, Ghana and Ethiopia to shmv how th.ese countries use

the capital-output ratio approach.

In framing a develo-prœnt plan, i t is carnon practiœ to calculate the arrount of additianal capital

required

to produœ a cne unit increa.se in annual output at the margin. It is .in tlli.s sense that the

marginal

capital- output ratio is used, wlli.ch the nmv fam:>us . ~Ja.rroc1-D:Jmar theory of growth relating to rate of growth of inccme to d.ts sav.ings anÇl output ~s now used. It sh:>uld be noted .here, ll.O'IIIBver, tl1at the plarll.~ers in developing com1tries are making a great rnistaJœ by us.ing tlte Ha.rrod-IX:mar rrodel since i t was neant, and is still neant, for advai1ced econanies. 'IDe Harrod-La:nar theory also

• •

^-

^2-

p:resupp:::>se5 tha oonstant flow of invest:rœnt which is not the case in developing eoonanies. We n.c:M can examine the oonœpts of capital-output ratio in a

hypothetical case:

Year I · Year II

y= lOO

y

1 = llO ••• ^{(1) y = GDP at M.P •}

c= 80 c =

1 85 ••• (2) c = ccnsurrption

s= 20 s =

1 25 •••

{3)

s

=

^savings

Sinœ

s

^{= I} _{sl = Il} ^{I =} investrœnt

I = 20 I ₁

=

²⁵ •••

{4)

'l11US

, the Average capital-output ratio is

K = 20 (see Year I) Average capital-output

Ratio

(5)

ïOO

^•••

y

Net Gross ⁿ

"

ⁿ

.llK 25

{see Year II) Iv'Jarginal

" " "

⁽⁶⁾

fly =

ra

^•••

Net Gross

" " "

or

I K' 25

2.5 capi tal-Qutput Ratio

(7)

-;;y

^{= =}

ro

^{= •••}

'!bus I = ^!:lyK'

But Èi. _y = lOO¹⁰ x T ^lOO = _10% = Rate of Growth in r ational Inrorœ

•••

(8)

Fran

the

above data {5) and (6) , we note tl.1a.t

the

Average and ~1arginal

Capital-output Ratio is further divided into net and gross oonœpts. 'lt.le

. • ^{- 3 -}

only difference in

the

net and

gross

concepts li es in

the deduction of

deprec- iatian of capital stock frcrn gross capital and output levels.

As v..e

already kr1ow,

pl

arming

in

i ts broadest sense i s a description

of

¹¹

a desirable state of affairs

projected to

a

giv

en point in the future, supported

b-".f

an ouU.ine of the ste9s t hought requ.isi te to a chi eve that state." (l) One of t hese requisites i s

the

ca

pital-output ratio approach.

'Il1e main

task of plaru1ing is to

e.xarn:L.J.e the

feasibility of

the p

lan

by

·carpar.ing its objectives an.d s trategi es with tl.1.e exist.ing resources, as well as scientific and teclmological

kn01'trhow,

in temtS of finance, physical output, and

b-y

analysing

the n

-eans availabl e for increasing

"t:h= present productive resources in

tl.1e n ust efficient way. I f , as is usually

the

case, a ga p still remains between .requirernents and the resources , a scale of

priori-

ties, for gradual achieVE'X!alt of tl1.e objectives envisaged , has to be established.

'llle

rrost i

mportant task

of p léù

'1I1in

g

is the

àetenninat.ion of that pattem of resource allocation that IDuld maJr...e

b'le

g.reatest c::ontributicn

to the

increase

in N

ational output ( G. D . P.).

'Ihe

simplest method for this

purpose

i s

the

use of the investlœnt

coefficient and of

the

capital-output ratio.

In

this

pa:per, I

w ill

deal

w ith

the

capital-output ratios of t he Developrre:nt

Plans

of

Ghat."1a, Et

hiop ia, N igeria

(1)

Burke, F . G .,

N

ational Plaruting Series, Tanganyika Preplanni.ng,

Syracuse

Ul.iversity Press,

1965.

- 4 -

and Sudan,

and~ show

t:h;ir

aJ.

:>

plicability, stability

and

usefulness in develos::m=nt planning, as well as ;tzt:{ dem:mstrate

the

liJ:nitations of such p ara- reters in Africa.

The invesurent coefficients,

the national prcxluct withdrawn :t::ror

a

oonsurrption and allocated for investrrent.

DEFll'ITTIO\l: "'Ihe

Capital-output ratio, or rate of productivity of capital, measures the a:n:ount of capital requi.:L"Bd

to

i.ncrease output

by

one extra u.lit". { 2

)

L1 principle, a

distinction is

rnade

bet~en. average capital- output ratio of a

œrtai.n

activit

y,

or even of the econarrry as a

~:,..1].10le, and

tt~

marginal capital-output ratio.

'Ihe

forrœr is the ratio of total capital invested to total

proouct

~~)

,

and t

he

latter is the relation of a new ca

p

ital investrnent to the i

.ncreJ.rent in production resulti..-"lg- f

r

om

such

production

(~).

y

(N.

B.) Cbnsidered

ov

a

r

a

l0i.

1.c peri.od, Ï.10v~ever, t."le n

"Brginal capital-output ratio is equivalent

to

th

e

average capital-output ratio for

the

.i.ndustr.f cxlnœnl.ed.

iYbreover, O'Hing to

the .i.nevi. table lagS between

the

tirre

the

invest-

~(.,[.l..Ll..

ment was

irlélde _c..----

and t11.e

t:i.Iœ

oonstruction is startecl and

equi.prrent is purchased f\...c., .

and the

time

i.nvesbr ent becarres

productive, sf:lo:lws--thi:olt

c

apital-output ratio

is rreaningful only over relatively long

period.s of

t i

ne.

If reli.able statistical info:rmation i.s available, both on

the

cap ital- output ratio

and

on

the

annunt of cq_

:

üta.l

which

c

an

oo

^made

available for

(2) r-r

.eier, Issues in Developnent Econo:n lics,

p.lO

l-4.

•

^{- 5 -}

investiœnt out of darestic savings and (if available) foreign aid, i t is :possible to calculate the rate of growth/tha ecan~ should

re

^{able to}

achieve. I sha.ll show this la ter in stati.stical and diagramatic rrodels of Ghana, iUgeria, Sudan a.'1d Ethiopia. 'l11e achi.evable rate of grcrvlth is obtained by dividing the investrœnt coefficient by the capital-output ratio.

'lhus, if the arrount of claœstic savi.ngs is equivalent to 10% of the

National product, and additional resources provided by foreign ~ants and loans are equal to 2%, the invesb.nent ooefficient will arrount to 12%. With:·a given

capital~utput ratio of 3, national -" roduct oould grov1 at a rate of 4%. If

tl~ populatioo i.ncreases at say 2% per

a:nnum,

per capita i.ncare would rise by c:nly 2%. It can already be noticed that, capital-output cannot serve as the exclusive criterion for the induœnent and establishrrent of a àevel0f11Slt p:rogram, for i t ignores the influenœs of various pararreters and factors such as the existing level of scientific and technological kno-vv-how, natural

resources, and

the hunan factor v1hich can, to a great extent, detennine the efficiency of roth capital and production.

Harrod-I:Xnlâr 'Ita:>ry of GrcM-th

I, ncM, tur.n to examine in statistical an.d graphical exarrples, ~

capital-output ratio nooel aamronly referred to as the Harrod-D::m:rr tœocy of g~, GC

= s .

• ,

• •

..

•• •

y

=

c

+ I

y = c+s c

=

a y

I

= elly y = ay

+

c6y y

-

ay

=

cl!. y y(l

-

a)

=

cl!. y

Ys

⁼

cl!. y s

=

cl!.

y

y s

= cG

-

6-

J?arameters

{1) G =

rate of

GrrMth

{2) c = capital-output ratio {3) s

=

rate of investm:ant {4) y =national

incx:me

{5)

1-a = average

propensity to

save

{6)

a

= average propensity to

(7)

oonsùrre

(8)

~=G

y (9)

(10)

T'.nis

fomn.ü.a of

Harrod-IXrnar was

meant for capitalist countries,

so

that

~y do

not have to fluctuate into depressions

and

accessions

as

eJG?er- ien.ced

by

u.s.

during tl:e 1930's. '!his Irodel also sl10NS

that when

I > s, there is

inflation

I <

s there is deflation

(e..~œss

of liquidity).

Sinœ

Ge

= ^s

Èi..l s y

·6y

=

_y

1 s

y =

y 1 =

s

.

'Jlùs is the

rrodel

being used b-.t

rrost

Cieveloping natian.s.

AssUTptions

are

that

there

is:-

• ^{- 7 -}

(a) Full enployrrent

(b ) Foreign trade is not taki.ng p laœ.

'Ihus,

when

·we consider that y

=

c+s+G + (E 11) is not fully represented

in

t1e GC

=

S fornrula,

then \~ begin

to see t."Je limitations, and

pitfalls

,

in i

ts applicabili ty.

Its Stabilit;Y and Usefulness

'Ihe

stability and usefulness of ca

pital-output

ratio approach in

developrrent plarming

is

subject to wany interpretations. Cbe of these

.inter-

pretations

is

that in the absenœ of another fonrula of develop.rent which shows clearly the role of ca pital in relatianship to

total p

roduction,

the H.arrod-Domar

:rrodel

is still seoond

to none. Another view

is that

the Harrod-

r:anar rrodel could :te inproved upon and :made workable

in

the existin

g

candi- tians

in

underdeveloped countries.

'Ihus,

the

alternative

to

the

H

arrod-D:>rn ar m:rlel lies

.in

re-adjusting the rrodel

to

suit the oonditions prevalent in TIDSt develo

ping

eoona:n:i.es such as abund.ant labour forœ, relatively laN saving capacity, wastage etc.

'n1e

present nodel being

:œa:mœnded by

E.C.A. of ficial nanely

N

r.Abang-wa ,

Dr.carney and R.Garàner, in the fomula that inclues betten:ent and wastage

paraxœters,

wllich

when exarni.ned have been found to

be

respon.si.ble for

twJ

major types of Gross D.:Jn:estic Product, narrely (a)

the Potential

G .D.P.

₁ and

(b)

the Actual G

.D.P .

'lbe

fo:rmula runs as follows:-

•

•

•

6y

= ^r+by-wy 1

0

1

~

1 . l!i

= ^{- • .1:.. + - !!:i.}

y y k y y

0 1

r

_y

= ^- i ^+b

^-w

ko ¹

1

- 8 -

(1)

{2) (3)

G1ossary of Pararreters

b =

betterrœnt pararreter

e .g. Science and

'Ieclmo1ogy

w = \•TaSteful

parê!Iœter e

.g.

L-:1efficient use

of

:œsourèes

~

⁼

capital~utput ^ratio.

i ¹

Graphically ry =

k + b - w can

be shown tin the

fo.:r:mulation or

the ch::>iœ

0

of

develor;.mant

strategy.

0 ---~---~---~---

~,~~~?a

< ...

^J.~%

b-W

• _•

• •

- 9 -

'Ibe

setting up of the rate of

growth

fran r

⁰

y =

^4%

to r' y =

^8%,

i

i1

1J?lies also the

detenni.n:i.ng

of rate of invest:n.lel1t and o::ll1Sl.l!ïpticn at a given peria:l in

~

plan. It also neans setting up a new scientific and technological

behaviour as y increases. If, hcMever,

the

rate of

grCMth

is set or

changed

ârastically, say fran

5%

to

^9%

or

4%

œ

^7%

^it

^m

^{ay cause} political upheaval as well as a

social

dyspmria, since

i

t

means cutting down

an oonsurpticn drastically.

'lb do

so

to

an

already

undemourished people is tantan ount

to

giving a persan a rope to

bang

Wmself.

In

the above diagram,

the

sianese-relatianship

betv-.een

invesi:mel."'lt rate and population rate

and

its effects en capital invest:Irent

and

final

growth

rate of the eoonomy can

be

assessed by including or' drawing curves showing

~

rate of growth of populaticn, which nostly affects the per capita inc:are distributicn.

'lhe

above

rroëiel ·is the

one being advocated for African countries.

Plan I

•

:bdels of Ethiopia, Sudan,

.c

igeria. and Ghana

We

can, now, examine the usefulness or stability of capital-output

1n:xlel

as presently constituted

and hov1

i t

is being

used by

m

:m

y

African pla.Jners

in their

develqmmt planning

rrodels.

In

b'lls regard, I extracted

the

statistical data from Dr.Camey's

article entitled "Replac:anent capital",

to

use

f

or this

particular

analysis.

'!he

article of Dr.Carney's ar)peared in the

,Jow:nal of

Indian Ecxlna:nics of

1966.

•

" • ^{- 10-}

'Ibe data also he1ps us

to

examine Rostow

¹

s

1

Arthur

lavis ¹

s, Baldwin

¹

s

and the

rest of those develq:mant tla:>rists

~ propose

the investirent of a

oertain

percentage of àorœstic capital in oréler

to realise growth

or

àeve1oprœnt

;iJ.1 underdeveloped cxrur~.tries.

Certain

invclstm::mt

.

fêatures of

the above~renti.a1ed

four countries are going

to

render

the

theory a

œrtain degree

of ci.rcumspect

b-,t the

fact that

they ali

invest far

nore al::ove the

"talœ-off" .i.nvestrœnt requi..remants of 10

to

12%. 'Ihis does not rrean, however, that they have deve1oped even if

'they

have invest.ed over 12% of their national savings.

The

stark effect or

truth is that they

have

not even satisfied

·th; pre-ccnditicns (if

there are any) neoessary

to

reach a "take-off" stage

such

as indegenous scientific

and œchnological

knovrlVH.

I

shall first of al1, examine

the seoorld

Five

Year Plan

1955/59 of

Ethiopia,

its rate of

~lth,

its marginal capital-output ratio

and t:ln

sl"K:lrtcxxaings of their invest:Iœnt criteria.

P1aa:Tari~:

1. GDP

(a~ .t9Ss:-~adét

^{prkel) (Y)}

.-m.

•Diion · ••• .

~ l~taJ Ou.tpat

(A.YJ

$&dao

· dion

s.

Tatal Ioftltakn& (l) $Ella• mmion

Or

^{which :} Private Sec:lor~·

Pabllc

Srctoi

lacftaM

^{la Stoc-ka}

~ Incrementai lnftltment (Al) $Eth.

aûllioÎl . ••• •

5~ lnc•..atal C.plla&oOutpat buo

(IIAY) . ••· ...

6. Recurrent CoMa (...._ted oa avera•

· ratie Of Total llK1trNDt to. ,Tocal

~r:oc:· .

apencllt11rè•

-~-) ·~

4.3 12,119.0 2.224.2 407.8

ll.S •1.657.3 261.6 9.8 11.037.5 . 170.6 13.5 544.3

17.8 55.5

11.5

a,tœ.s

85.2 7.B

1~.5

2,519.8 •; .2.419.5 95.6 99.7

~90.9 ^> 325-6 187.5 205.7

94.4 9.2 29.5

s.o

214.1

107.1 10.8

32.7 3·2

238.2

360.1·.

22$.0

121.6 12.7 56.6 3.5

165.1

...

^{~.~D iD} lM Plan la . . bùt in th &blence of tiM annual br•lltia• ' ffi · ... dM cllo . . toce Il aal ..-,ace.~~ .... for .

·"

a..-

^{k • 3.4} Replacèment ·^{i p -} .01~. ^. w -CapitAl ^·.

.cm,

(R. • G

-

~ç;•Y

^....

c

12.8 13.3 13.9 14.5 15.1 .

• 006Y) .. ' ·••• • •• 4.3 69.6

To maintaia income

1J11

•pila ('r c:

153.J kpY

=

.061Y) · .~. • •• 4.5 708.2 130.1 135.7 141.5 147.6 .

To raite income ^{kwY • .OB.JY)}

/JII •li'o

^{. .} (T' ^.

-

^{4.3 987.8}

_---

^{181.3 189.1 197.2 205.7 214.5}

1765.6 324.2 ~38.1 352.6 S67.8 383.5 Net Investment (k (p+w) Y •

· kG\' • .146Y) (1696.0)

A.

Ft~r 11•0.5, • =.157

(311.4) (324.8) (338.7) (353.3) (368.4) Groa '•ving (S= • Y=.l56Y) .•• 4.3 1812.7 332.7 347.0 361,9 377.4 393.7 lt v~atmrnt in Tecbnology (kG' (1-11)

\'.• .003Y) 4.3 34.9 6.4 6.7 7.0 7.2 7.6

Planned l•ss Computed lnveatment

· (Savinr)

... . ..

^{175.4 -71.1 -56.1 -38.3 ~17.2 7.5}

B. For l'=li.75, • •.154

'Gro~a Sa~ing (S= • \'

=

^{.154Y) ...} 4.3 1789.3 328.4 342.5 S57.2 372.6 • . 6

lnveotmcnt 1n fccbnology (kG• (1-JI)

Y=.00a57Y) ••• 4.3 17.5 3.2 3.4 3.S 3.6 3.8

Planned l•ss Computed lnvcatment

(~ving)

... . ..

^{-152.0 . -66.8 -51.6 -33.6 -12.4 12.4}

c.

F• •=0.90. • • .153 .

Grosi S.vi11g (S:.. •Y= .ISSY) ••• 4.3 1777.8 326.3 340.3 354.9 370.2 386.1'

· Jnvcatmcnt in fecbnology (kG• (1•1')

. y= .0006\') 4.3 7.0 1.3 1.3 1.4 1.4 ^{.. 1.5}

Planned liss Computcd lnveatment

(Saving) -140.5 -64.7 -49.4 ~31.3 -IQ.O

No1e: Components may not cxacdy add up _{. .}

to

totàla becauao of ro11ndmg ot ligures.

J

1

1 _{r , ,}

•

~

!1 c l

• •

.

^{t' ,}

1

ⁱ

G-.:

s,.,.r,.

O.v•loJI•nl Pt-. 1961/64,-1969/70

%Rate Total,

1963/64 of gn,wtb plan

in plan period period ·

Plan Targe11:

1. Planr•ed OutJ ut (Y) (;G million (at

196u-62 average valuel) ••• 5.9 4,675 564 591 623 . 659 698 744 796 2. lncrrmer.tal Ou• put (A Y)

LG

million 232 27 32 56 39 . 46 5!

s.

Planntd lnvettlllent (1) {.G million 9.2 1,016.5' 110 119 131 14! 156 17~ 166.5 Of wh'ich : L>eprccJauon 5.9 140.2 lfi.9 17.7 18.7 Hl.8 20.9 22.5 239

Nrt 1 nvestment 9.6 876.3 93.1 101.3 11~.3 ll2.2 135.1 149.7 J6l.6

e

4. Incrementai Invcament (A 1) LG

million ^{. .}

-

^.

-

9 12 11 If 16 ¹⁴⁵

a

5. Incrementai CapicaJ.CÀtput llatio

(1/~ Y) Av.=3.93 4.4 4.1 3.9 4.0 3.7' ^{... 6}

o. J:

Given: _k•:i.9 pc.026, ^'W ~:.033, Gc:.059,

Q

Replacmtent Capital (R-= kG¹Y-=

.5.9 60.0 7.2 7.7 8.0 8.5 9.0 9.5 10.1

.OIJoY)

To w;euuain inc· mel"

"'IÏM

(T'

5.9 446.0 53.4 57.2 59.9 63.2 66.8 70.8 75.f

•kpY=;t0•4Y)

To ra11e inccme /JI'

MJiil•

^.(T'•

5.9 56?.0 67.9 72.6 76.1 80.2 84.8 89.8 i5.8

kwYa.1.4:87Y) ·

... _---

107~.0 128.5 137.5 144.0 151.9 160.6 170.1 181.3

~et lnftllment (k(p+w) Y•

(121.3) ^(129.8) (136.0) (14!.4) (151.6) (160.6) ( 171.2)

kGY•.2SY) (1015.0)

A. F•11 _Oro~~ •0.5. • •0.25 · Saving (S• •Ya.25Y)

u

^{1101.7 151.8 141 147.8 155.8 164.8 174.5 186}

lnvenment in TechnolOI}' (ka-

5.9 29.0 3.5 3.8 4.0 4.2 4.5 4.7 5.0

( 1-I&)Y •• 0068Y) ...

Planned luc Computed lnvestment

-85.2 ^-21.8 -22 -16.8 -13.3 -8.8 -2.5 0.5 (Saviog)

J!.

^F• ~&c:0.75, • =.247

5.9 1088.6 150.3 139.3 146.0 153.9 162.8 17'1.5 ^183.8

~·

Gross Saviog (S

=- •

^{Y~ .247Y)}

Joveatment in Techno1ogy (kG¹

.5.9 14.9 1.8 1.9 2.0 2.1 2.2 2.4 2.5

ti·

\!.;"")

nned lus Complted lnvestment ^{Y•.OOMY) ...}

i

-72.1 -20.5 -20.3 -15.0 -11.9 ^{-6.8 u0,5 2.7}

(Saving)

s: ·

c.

^F•

".o.90 .•

= .245

5.9 1079.6 129.2 1S8.2 144.8 152.6 161.5 171/l 182.3

!

GroP S.viog (.:a • Y • .245Y) IoveRment in TechnoJogy (kG¹

.5.9 ·6.1 0.7 0.8 0.8 0.9 0.9 1.0 1.0

~

(1-•)Y=·.0014Y) •••

Plaooed lus Computcd Investmeot

-63.1 ^{-19.2 -19.2 -13.8 -10:6 -5.5 1.0 4.2 ~}

(Sa ring)

::t·

~

---~~~~==~~---i

• ••

,_("'....,--.n~au

ma v not exactlv add OD to

tota~

bcca".IC Of rounding of figures.

Îlan Ta,..U.(•preaed or Jmplicit in Plan) 1. GDP (at 19" market pricct, projectrd at

4%

p.

a. on 1960 value of

lN

1,11!!.5

• mühon) (Y)

lN

miUion •••

2. lncrementll Output (.6. Y) J;N million ••.

!. ·Tocal ln•ettment (at 15% ot GDP) (1)

lN

million

l-Of wllich : Government sector (67 .1 %) Private Sector (residua1) •..

JI-Of w•kh: Government ~ector (63.!>%) Private Sector (reaidual) .••

4. lncremeatallnveatment {,6.1)

l · "

mHiion 5. IDCII'UDCDtal CapitaW>utput Ratio (1/.6. Y) 6. Rocurreat E•penditure on Government Inveau•ent (eatimaced on averaae ratio ol To&al Rtcummt co Total Capital eçendi&we)

(a) At 1.2 ~ million (b) At 1.27

lN

million .

%Rate of iTotal, growth in ·plan plan period period

4.0 4.0 4.0 4.0 4.0 4.0

4.0 4.0

7829.4 255.7 1183.3

79,.8 389.5 751.3 432.0 (Av.=3.93

954.0 954.0

1180.4 1227.6 47.2 178.2 185.4 119.6 124.4

.56,.6 6J)

113.2 117.7 65.0 67.7 7.2 3.g3

143.5 149.3 143.8 149.5

1276.7 1327.7 49.1 51.0 192.8 ~00.5 12~M IS4.5

63.4 66J) 122.4 127.3 70.4 73.2 7.4 7.7 333 3.93

155.3 161.4

15~4 161.7

1380.9 1436.1 53.1 55.2 208.5 216.9 139.9 145.5 68.6 71.4 132.4 137.7

i6.1 79.2

8~0 8A 3.92 3.93

167.9 174.6 168.1 . 174.9 Note a- UN S&adltic.l Yau~...,_. 1963 givea 1.9~ p.a. for the mie or poP'IIation growth in the period 1958-62 whüe

· lM.,.. . . . of 1953 (30.4 million) and 1963 (56 million) give an intercenaa1 rate of about 6.3%. The latter ra ... ifftlid, would make the deve1opmena plan~ ridaculoua. Talr.int into account the atron1 evidence of ...-.n11meratJGn ia the 1952·53 cenaua a rough weighted me•n of tbe cwo rates woulci be about 3.2, whlch ia nOl un11aual in Alrica. A race '>f 3% ia uaed in the calculationa which follow :