Technical Choice Under Full Employment in a Socialistic Economy Author(s): Nobuo Okishio

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Technical Choice Under Full Employment in a Socialistic EconomyAuthor(s): Nobuo OkishioSource: The Economic Journal, Vol. 76, No. 303 (Sep., 1966), pp. 585-592Published by: on behalf of theWiley Royal Economic SocietyStable URL: http://www.jstor.org/stable/2229523Accessed: 12-02-2016 23:29 UTC

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TECHNICAL CHOICE

UNDER FULL EMPLOYMENT

IN

A SOCIALISTIC ECONOMY'

PROFESSORJOAN OBINSON,

n her remarkableExercises

nEconomic nalysis,

1960, considered the problem of technical

choice under full employment

of

labour in a socialistic economy.2

The aims

of

this paper

are:

(1) to correct some

errors in her argument;

(2)

to show the criterion for the choice

of

technique

under full

employment

of

labour.

This will help our understanding of the nature of obsolescence in a

socialistic

economy.

I.

AsSUMPTONS

For

simplicity we

adopt the following assumptions

made

by

Mrs.

Robinson:

(a) there is only one kind of consumption-goods;

(b) some

kind

of

equipment is necessary

to

produce

the consumption-

goods;

(c) we ignore circulating capital and assume constant returns to

scale

and an

infinitely elastic supply of land;

(d) equipment

is

produced by unequipped labour;

(e) equipment

is highly durable

and

retains

its full physical effi-

ciency for

an

indefinitely long working life;

(f)

technical knowledge

remains

unchanged;

(g)

labour is

homogeneous

and

the labour

supply

remains

constant;

(h)

when

our

story begins,

all

labour

in

the

consumption-good

sector

is

equipped

with

Gamma

machines;

(i) all labour supply is input either in the production of consump-

tion-goods

or

equipment

(full employment);

(j)

the investment

policy

is

designed

so

that the amount of

labour

in both sectorsremains constant.

I.

PROBLEM

The total

supply

of labour

N

is

divided

as

N= Nc

+

Ni

.(1)

where Nc and Ni are the amount of labour in the consumption-goodssector

and

the

equipment

sector

respectively.

The

planning

authority

must

make

a

decision as

to the

kind

of

equipment

to

be

produced by

Ni.

1

I greatly appreciate the assistance of Mr. R. W. Peters (University of Western Australia)

in

making this paper readable.

2

Joan Robinson, Exercises n EconomicAnalysis, 1960, pp. 38-56.

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586

THE ECONOMIC

JOURNAL

[SEPT.

As can be

seen,

it

is

of

no

use to

produce Gamma-type

machines

by

Ni.

By assumption (h)

the labour

in

the

consumption-goods

sector Nc is

equipped

with

Gamma equipment,

and

by assumption (j)

the

authority designs

investment

policy

to

keep

Nc

constant.

So

if

Ni

is

the

input

to

produce

Gamma equipment this newly produced Gamma equipment cannot find

labour to man it. By assumption (e) Gamma equipment with

which

Nc

is equipped keeps its full efficiency until scrapped.

Therefore the

authority

must

choose a

type

of

equipment

other than

Gamma. What

kind of

equipment

is

best to

replace

Gamma?

Let us suppose that the authority

has

knowledge

of

only

three

techniques:

Gamma,

Beta and

Alpha:

(bV,kv), (be,

kp),

(ba,

k)

.(2)

where b denotes the amount of the consumption-goods produced by a unit

of

equipped labour and k denotes the

amount of

labour

necessary

to

produce

the

respective equipment

to

equip

a unit

of labour

in the

consumption-

goods

sector.

If

we assume

O

<

bv <bp

<ba

O

<k <k<ka.(3)

should Beta or

Alpha type equipment

be

produced?

III. MRS.

ROBINSON'S

CRITERION

Mrs. Robinson's criterion governing

the choice is

bp-kb

bk

-kbv

(4)

kp

-

k

'

ka

-

y

Beta

will be chosen if the left side is greater

and

Alpha

if

the

right

side

is

greater.

b

k

Fig.

1







1966] TECHNICAL

CHOICE

UNDER FULL EMPLOYMENT 587

If the three techniques

are plotted as

in the

above figure,

Mrs. Robinson's

criterion would mean

the introduction

of

Beta-type

equipment- Let us

suppose that, for the time being, Beta

shows the

highest marginal efficiency.

(This

is

represented

n

the

diagram by

the

slope

of

y,B

which

is greater

than

that of yoc.) Beta equipment graduallyreplaces Gammain the consumption

sector. '1 Is this criterion a reasonable

one?2

IV.

CORRECTION

Mrs. Robinson's criterion (4)

can be shown to be wrong.

The compari-

son of the gain

obtained

from

replacing

Gamma equipment by Beta

and

Alpha cannot be

expressed by (4).

If

Ni is the input to produce

a

Beta machine, then the amount of con-

sumption-goodsproduced

in

the

next period is

(Nc-+Ni)by+

k-b

.(5)

The

Beta machine

produced by

Ni can

equip

Ni/k,

labour. This

labour

is

taken from a Gamma machine, which

must be scrapped irrespective of

its

physical condition.

If Ni is the input to produce an

Alpha machine the

amount

of

consumption-goods

n the

next period is

(NC

k by +

Ni

ba.

(6)

Therefore the comparisonbetween Alpha and Beta must be expressed by

bX

-

. . . .

(7)

If the alternative techniques are shown

as in Fig. 1, then

Ni must be the in-

put

to

produce

an

Alpha machine

not Beta. Alpha is

superior to Beta as

a

substitute

for

Gamma.

It must be

noted the

criterion

(7)

does

not

depend

on

k,.

It

does

not

matter

how

much labour

was required

to produce a Gamma machine in

the

past. The only

factor which concerns

the choice of newly introduced equip-

ment is the amount of consumption-goodsforgone by scrapping a Gamma

machine.

In

a

capitalistic economy private capitalists

may consider the

historical cost

of

the machine to be

scrapped.3 But it

has no meaning from

a

social point

of

view.

V. OBSOLESCENCE

Let us assume

that

by

the

criterion

(7) Beta is superior

to Alpha:

b?-by

ba-by

bC

-

bv

>

b*

** *

(8)

Ts

am

This relation does not change while Gamma machines remain. Because if

1

J. Robinson, op. cit., pp. 52-3.

2

Mrs. Robinson's criterion

is reasonable if

the production process of a

Gamma machine

is

reversible.

In

other

words, if we

could release the same amount

of labour which

was the input to

produce a

Gamma machine by scrapping a

Gamma machine. The writer is

indebted to Mr. D. G.

Champernowne

for this

point.

3

C. P.

Kindlberger, Obsolescence and

Technical

Change, Oxford University Institute of

Statistics

Bulletin, August

1961.







588 THE

ECONOMIC JOURNAL

[SEPT.

Gamma machines

remain, the

amount of

consumption-goods forgone

by

scrapping them continues to

be

b,.

So it

seems to

be reasonable

for

the

authority to

continue to input Ni to

produce

Beta machines

until

all

Gamma

machines are

scrapped.

But the following question arises: even if the relation (8) holds, is it

reasonable to

continue to produce Beta

machines

knowing that

in

the

near

future Beta

machines will also

have to be replaced

by Alpha?

In

other

words,

is

not it

necessary to bring

into

consideration

the

inevitable

obsolescence of Beta

machines

?

Mrs. Robinson

considered this question

and said:

The prospective life

of Beta machines grows

shorter

as

the

date

at

which

Alpha equipment will begin

to be

installed comes nearer,

and

after a

certainpoint has

been reached, Beta becomes

inferior

to

Alpha,

so

that it becomes preferableto replace the remaining Gamma machines

with

Alpha ones.

1

On

what

reasonable criterion

is the certain point

after

which Beta

becomes

inferior to Alpha

based? In

order to get an answer

to this

problem

we

must consider

not only

the immediate gain but

also

the

future

gain.

The

criterion (7) is deduced

only from consideration

of the immediate

gain.

If

we

consider the future

gain the

criterion should be

modified. What

modification is

necessary?

VI.

TIME PATH

Let us

investigate the time path of the

amount

of

consumption-goods.

If

we

continue to

replace Gamma machines

with Beta

until

all Gamma

machines

are

scrapped, and after that

time we

replace Beta machines

with

Alpha,

then

we

can get

the time path of the

amount

of

consumption-goods

as

shown

in

the curve

PQR in

Fig. 2.

R'

R R

I

~~~~~~~~11-

0

t,'

t,

t,'

ti

t2'

t2

Fig.

2

1

J.

Robinson,

op.cit.,

p.

53.







1966]

TECHNICAL

CHOICE

UNDER

FULL

EMPLOYMENT

589

The point t1

on

the t

axis

shows the

time

point

at

which

all

Gamma

machines are

replaced

with Beta and

t2

shows

the time

point

at

which

all

Beta

machines are replaced

with Alpha. By

assumption (j)

t= kgNc/Ni

t, t,

+

ka

Nc/Ni

.(9)

The

heights

OP, t1 Q,

t2

R

are

b,

Nc,

bp

Nc and

ba.

Nc

respectively.

So the

slopes

of

PQ

and

QR are

(bp

-

b,)

Ni/k8

and

(ba,

bp)

Nilk,

Next,

if

we replace Gamma with

Alpha

from

the

beginning,

then we

get

the time

path

as

shown

by

PR'.

The point

t2'

shows

the time

point

at

which

all

Gamma

machines

are

replaced

with

Alpha:

t2t-

ka

Nc/Ni.

(10)

The slope of PR' is

(b.

-

b,)

Ni/k,,.

Finally,

if

we

begin to replace

Gamma

with Beta

and

after

a

certain

time we replace the

remaining

Gamma

machines

with

Alpha,

then

we

get

the time

path

as

shown

by

PQ'Q R .

The

point

t1'

shows

the time

point

at

which the

remaining

Gamma

machines

begin

to be

replaced

with

Alpha:

t1'=

kp

A

NcINi.(11)

where

ANc(

<Nc)

denotes the amount

of labour

re-equipped

with Beta

until

t1'.

The

height

of

t1'Q'

is

b8Nc+

(bp

by)

A

Nc. The

slope

of

PQ'

is

the same

as that

of PQ.

The

point t1 shows

the

time

point

at which

all Gamma machines are

scrapped

and

now

Alpha

machines

begin

to

replace

Beta:

t =

t11

+

k(l

-

A)

Nc

(12)

Ni.(2

The

height

t1

Q1

s

bpANc

b,(l

-

A)Nc.

The

slope

of

Q'Q

s

the same

as that of PR'.

The

point

t2

shows

the time

point

at which

all

labour in

the

consump-

tion-goods

sector is

equipped

with

Alpha

machines:

t2=

1

?+

.

A

N.

(13)

The

slope

of

Q R

is the same as

that of

QR.

Now which time

path

should

we

choose, PQR?

PR'?

or

PQ'Q R ;?

VII. TIME HORIZONAND TIME PREFERENCE

It

is

easily

seen

from

Fig. 2 that,

if the

time

horizon of

the

planning

authority

is shorter

than

t1,

of

course

PQR

is best.

So it

is recommended

that

Gamma machines be

replaced

with

Beta,

as the criterion

(7) shows,

until

all

Gamma machines are

scrapped.

In

fact,

if

we consider

only

the







590

THE ECONOMIC

JOURNAL

[SEPT.

time interval from

0

to t1

the

amount

of

consumption-goods produced

is

always

greatest on

PQ.

But

the

longer

the

time

horizon of

planning

becomes,

the

more difficult

it

becomes to

choose the best

time

path.

For

example,

let us

assume

the

time horizon to be t2' and let us

compare

PQR

and PR'.

We

can see that

in

the former

part of the time

interval

[0

t21] PQR

is

better than

PR'.

However, there

is no

a

priori

reason

to choose one as

superior

to

another.

In

order to

make

a

definite

choice,

we

must

introduce

some measure

with

which to

compare

consumption-goods

at

different

dates.

This measure

is

concerned

with

so-called

time

preference

.1

Here we

simply

assume

that

the authority

puts

the same

weight

on

consumption-goods

at

different

dates

and has the

time

horizon

t21.2

Under these assumptionswhat criterion can be deduced?

VIII.

A

CRITERION

The time

path

PQ'Q R

is the

most

general

one.

If

we

put

A

=

1,

it

changes

to PQR.

If

we

put

A

0

it

changes

to

PR'.

So

we can concen-

trate our

attention

on

PQ'Q R ,

where

0

<

A

<

1. The

total sum of

consumption

goods

from

0

to

t2'

which

corresponds

to

PQ'Q

R

is

3

S(A)-AA2 + BA + C . (14)

where

A

-

b

bx

-

b

ko

kx

ko

Nc2

Nl

k,q

kx

km kp

Ni

B

{

b

-

bv

bcby

}

k

k

NC2

.

.

(15)

C=

i(b + bx)

kx

Ni

As we assumed that by the criterion (7) Beta is superior to Alpha,

B

>

0.

And A

< 0,

because

by

(3)

and

(8)

by

b a b

by-b?

____?

b

+

b

L

-

b

<

ko

b-b

+

bx

-b

by

-

big(

+

kg

b)

+ ba-

kcx

.

(16)

<

b

k

(

1 +

kg

k-k )

kpkcx ,x

:

1

M.

Dobb,

An Essay on

EconomicGrowth nd

Planning,

1960, chap. 2.

2

If

we choose

the time

horizon longer than

t2', we must

know, for

example,

the time

path

of

PR'

after

t4'.

But in

order to know

it

we

must

drop

our

assumption

(j).

I

am indebted

to

the

referee on

this

point.

See

the section

X.

8

In Fig. 2,

Rtb2'

=ba

Nc

-

(ba

-

bo)

k

A

Nc.

k0x







1966]

TECHNICAL

CHOICE UNDER

FULL

EMPLOYMENT

591

Of course

C

> 0.

The maximum

is obtained

at A

=

A*

< 1:

S'(A*) =2AA*

+

B =0

(17)

Thus,

we can

get the following

criterion:

at first

we investigate

the

criterion (7). If by (7) Alpha is superior to Beta (B

<

0), then from the

beginning

we must

replace

Gamma

machines

with Alpha.

If

by

(7)

Beta

is superior

to Alpha

(B > 0), then

we must replace

Gamma machines

with

Beta until

the proportion

of labour

equipped

with

Beta machines

in the

consumptionsector

becomes A*.

After

that point we

must

begin to replace

the remaining

Gamma machines

with

Alpha.

The proportion

A*

determines

Mrs. Robinson's

certain point

after

which

Beta becomes

inferior to

Alpha.

The time

point

corresponding

to A*

is

=

ko

A*

Nc/Ni .(18)

IX.

A

SEQUENTIAL

CRITERION

When

our

story begins,

all

labour

in the

consumption-goods

sector

is

equipped

with Gamma machines.

The

planning

authority

makes some

decision as

to

the

kind

of equipment

to

be produced

to replace

Gamma.

Let

us

suppose

the

authority

chooses Beta.

Then

in

the next

period

a

part

of labour in the consumptionsector is equipped with Beta machines and the

other is still equipped

with

Gamma.

The

authority

must

make a

decision

again

as

to the

kind

of

equipment

to be

produced

considering

the new

situation

in

the

consumption

sector.

And so

on.

In

this sense

the planning

authority must

make

a

sequential

decision

in

successiveperiods.

So it is desirable

to

get

the criterion

for this

sequential

decision.

Under

our

assumptions

it is

easy

to

get

such

a

criterion.

Our

choice

is Beta

or

Alpha.

From

the above

argument

we can

say

that if

S'

(A)

> 0,

then we

are recommended

to

produce

Beta,

and if S'

(A)

<

0,

then

we must begin to produce Alpha. And S' (A) is a monotonic decreasing

function

of

A.

So as

time

goes on,

even

if at

first

S'

(0)

> 0,

S' must become

zero

after

a

certain

time.

Thus our

sequential

criterion

can

be

written

as

S'(A)

2AA+B

-.

(19)

This

is

rewritten

as

bkg

{ 1ka2

-

kkA

ka

.

If the left side is greater than the right side, then Beta machines

must be

produced,

otherwise

Alpha

machines

must be

produced.

It is

interesting

to

compare (20)

with the

old criterion

(7).

At the start

A

=

0,

so

(20)

coincides with

(7).

And if the left side is

not

greater

than

the

right side,

Alpha

machines

are chosen.

But

if

at the start

the left side is

greater

than

the

right side,

then

Beta machines

are chosen.

At

the next







592 THE

ECONOMIC

JOURNAL

[SEPT.

1966

period A

becomes

positive. Then even

if

by

(7)

Beta

is

superior to Alpha it

does

not guarantee

the superiority of

Beta, because

something must be

deducted from the

left side.

The greater A becomes,

the greater

deduction

must be made.

This deduction

can be interpreted as the

accounting

equiva-

lent to Obsolescence.

X. SUCCESSIVEOBSOLESCENCE

In

this

paper

we

neglect technical

progress

in

the sense that

technical

knowledge remains

unchanged.

Furthermore,we

assume that the planning

authority

knows

only

three

techniques: Gamma,

Beta

and

Alpha.

This

assumption

facilitated our

argument very much.

But this assumption

prevented us from

considering

the effect of obsolesence

upon Alpha

machines.

Alpha

machines

are assumed to not be

replaced

and

scrapped

by more

productive

machines.

This

assumption,

in

the

long run, contradicts

the

assumption (j)

about

investment

policy. After

all,

labour

in

the

consumption-goods sector

is

equipped with Alpha

machines,

the

additional

Alpha

machines

produced

in

the equipment

sector cannot be manned

without

a

change

in

investment

policy

(j).

In

order to

man

these additional

Alpha

machines

it

is

necessary

to

increase labour

in

the

consumption-goods sector

and

decrease labour in

the equipment sector.'

If

we

retain the

assumed

investment

policy we must introduce

ceaseless

technical

progress

or

assume

the

existence of

additional

alternative tech-

niques

which are more

productive. Then all

kinds of machines are

exposed

to obsolescence and

the criterion

(19) must

be

modified. The

longer is

the

time

horizon of

planning, the

more necessary the

modification becomes.

XI. LIMITATIONS

The criterion to be adopted by the authority, as known from the above

argument, depends

mainly on

four

factors:

(1)

the investment

policy; (2)

the

knowledge of alternative

techniques; (3)

time horizon

of

planning;

(4)

time

preference.

Very simple

assumptions

were

made about these four factors

in

dealing

withl

the problem.

Hence, the

next

stage

is

to investigate

the

effect on

the

criterion of

different

assumptions

about the four factors.

NOBUO OKISHIO

Kobe

University, apan.

1

J.

Robinson, op. cit., pp. 54-5.


Documents

Technical Choice Under Full Employment in a Socialistic Economy Author(s): Nobuo Okishio