Labour Values and the Theory of the Firm

8/12/2019 Labour Values and the Theory of the Firm

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Labour Values and the Theory of the Firm

Part I: The Competitive Firm

Klaus Hagendorf

eurodos@gmail!om

"niversit# Paris $uest % &anterre La '#fense( 'e!ember )**+

,bstra!t: This paper is the first part of a Marxian critique of the theory of the firm, focusing on

the analysis of labour values. Starting from Adam Smith's example of the deer hunter marginal

analysis is introduced, culminating in the derivation of the Labour alue !unction as the supply

curve of the competitive firm in terms of labour values. The analysis is based on a ne" definition of

labour value, "hich is Marxian in spirit and respects explicitly production conditions and by this

becomes an integral part of modern mathematical optimi#ation methods not found in Marx. The

analysis offers a further development and coherent interpretation of Marx's value theory. The

analysis is limited to the case of the competitive firm.

Key-ords: Marxian economics; labour theory of value; value theory; marginal analysis;

microeconomics; theory of the firm; marginal cost; the labour value function; supply function;

Adam Smith;

./L !lassifi!ation: ,012 3042 3)42 3502 ')02 '402 '46

I Introdu!tion

Marxists have been particularly week in providing a critique of orthodox microeconomic theory.

This is mainly due to the failure of not having developed a consistent approach to the labour theory
mailto:[email protected]:[email protected]


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of value. This paper is part of an effort to put forward a Marxian theory of production based on a

definition of labour value! which is Marxian in spirit and modern in that it takes properly account of

production conditions and by this becomes an integral part of modern mathematical optimi"ation

methods! which have been absent in Marx#s work.

This article begins with examining Adam Smith#s example of the deer and beaver hunters! $ustifying

labour as being the natural determinant of price. Surely one would have wished Adam Smith to be

more elaborate on his example! but %&hm'%awerk#s claim! Smith had only asserted the labour

theory of value without having provided a proof! is simply un$ustified! as is the claim that the labour

theory of value applies only to the #early and rude state of society#. This is shown in generali"ing

Adam Smith#s example by introducing diminishing marginal productivity of labour. (e show that

this is sufficient to explain surplus labour. )n a further step! we introduce capital and provide an

analysis of labour values within the theory of the firm for the case of perfect competition. The core

of the paper is the derivation of the Labour alue !unctionas the minimum labour value! required

to produce a commodity! depending on the quantity of output and the factor price ratio. (e show

that marginal cost is labour value expressed in monetary terms. *inally! implications of the analysis

for the theory of capital are briefly addressed.

II The 7orishima % Pasinetti 'efinition of Labour Value is False8

The elimination of Marxism and Marxists from economic theory proper must end. (estern +old

(ar Marxism! including Sraffians and neo',icardians certainly had the effect of creating great

confusion in the labour movement and within the ever growing strata of the population acquiring

higher education ' and this not only in the (est ' but it did not have any serious impact on orthodox

-


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economics! neither did it contribute in any way to practical ameliorations of the conditions of the

labouring classes.

n the other hand! bourgeois economics was challenged by scientific socialist developments! but

here again #+ambridge Marxists# were very effective in denouncing /antorovich and other

progressists! as #anti'Marxist#. At the core of this #+ambridge Marxism# is a definition of labour

value which has a strong appeal to Marx# original concept! but which is simply false in that it whips

out the absolutely important distinction between labour valueand labour po"er! the difference of

which issurplus labour.

(hat the +ambridge Marxists declare as labour value ' 9 an;I % ,


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concept stemming from feudal times. The modern Morishima'2asinetti definition 0the vertical

integrated labour coefficients1 is simply a summing'up of labour time used directly or indirectly to

produce a commodity. )ts ma$or shortcoming is the neglect of the production conditions. A certain

progress has been made by Sraffa with his concept of quantities of dated labourwhich is based on

Sraffa#s cost of productionor in conventional terms on average cost. More generally production

conditions are properly taken account of only! if one uses marginal cost. (e propose the following

definition of labour value$

The labour value of a commodity is the increment of labour, necessary to increase output by one

more unit, leaving all other factors of production constant. The minimum labour value for a given

socially determined quantity of a commodity is its socially necessary labour.

)n mathematical terms! the increment of labour is >Land the increment of output is >?. The labour

value of that increment of output is =% L

%& or for infinitesimal changes =L

& . (e use

partial derivatives to indicate that other factors of production remain constant. otice that labour

valueis $ust the inverse of the marginal productivity of labour =

& /L.The usefulness of

the definition will become apparent in the following! establishing the validity of the labour theory

of value for perfectly competitive markets by applying this definition of labour values to the

analysis of the theory of the firm and the determination of equilibrium prices.

@ years before the publication of apital08941!


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economic principle to the use of labour. As labour ' apart from ature-' is the onlysource of value,

its use in any working process has to be optimi"ed and marginal analysis as one of the most

important methods of mathematical optimi"ation is the method naturally to be employed.

The problem is that 2olitical 7conomy is a social as well as a political science; it is the science

which is at the bottom of the analysis of the class struggle and therefore bourgeois economists have

banned labour values in their efficient marginal definition! systematically from economics.

Cnfortunately there are no socialist or Marxist economists! who had understood the concept

properly. There is no account in the economic literature on Devons# remark that commodities

exchange according to labour values6 0Devons! 84! p. 841! a remark which is based on the

marginal concept of labour value.

ow we shall develop some of the straight forward properties of the marginal concept of labour

values! using Adam Smith#s example of the hunters chasing deer and beaver.

III The Classi!al Vision of Produ!tion1

Adam Smith consideredE

F)n that early and rude state of society which precedes both theaccumulation of stock and the appropriation of land! the proportion betweenthe quantities of labour necessary for acquiring different ob$ects seems to be

the only circumstance which can afford any rule for exchanging them forone another. )f among a nation of hunters! for example! it usually costs twicethe labour to kill a beaver which it does to kill a deer! one beaver shouldnaturally exchange for or be worth two deer. )t is natural that what is usuallythe produce of two days or two hours labour! should be worth double ofwhat is usually the produce of one day#s or one hour#s labour.G

0Smith!449! %ook. )! +hapter H)1

- )n this discussion we ignore atures contribution to the creation of value! assuming its services to be costless. Thisis of course absolutely inadmissible for our times and the reader is invited to advance the discussion on this point in

particular.

@ f course this section is a caricature of the +lassics to unveil the anti'thesis Marxism I Marginalism as bourgeoisideology. ne only has to think of Turgot#s S'shaped production function in agriculture.

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Applying to this example the modern tool of the production function! we recogni"e at once that

Adam Smith makes a very special assumption of fixed coefficients of production. This appeared to

him to be sufficient as he considered a primitive form of production under usual circumstances.

This view has been taken over also by Marx. %ut even under primitive circumstances! there are no

usual production conditions which is why the hunter'gatherers were nomads.


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&*=A*L* )

&*amount of beaver,A*average productivity of labour,

L*amount of labour power used to hunt beaver

0aA

)t is very important to reali"e that the input of the production process is labour po"er! or the amount

of labour force! which has to be distinguished carefully from labour value0Marx! 894! +hapter 8!

5er Arbeitstag! p. -8; *isher! 3J9! p. 4:! footnote1.

Figure )shows the average labour productivities of producing deer and beaver. *or the case of

fixed coefficients these are equal to the marginal labour productivities. They are constant and

independent of the quantity of output and of labour power employed.

4

0 1 2 3 4 5 6 7 8 9 10

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

Figure 2: Average and Marginal Productivities of Labourfor Deer and Beaver Hunting

Labour

Average,

MarginalProductivity

A(=&(

L(=&(L(

A*=&*

L*=&*

L*


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To obtain expressions for labour values! we have to take the reciprocals of the average and marginal

productivities of labour. These are presented in Figure 1(showing labour values as understood by

+lassical economists and Marx. The labour values are independent of output; but this is a very

special case indeed.

Figure 4shows the production possibility function for deer and beaver for this special case of a

constant average productivity of labour. The function shows the feasible combinations of amounts

of deer and beaver which can be obtained using a given amount of labour power efficiently.

Therefore the negative of the slope of this function!=B! shows the price which has to be paid in

terms of one good if the other good is increased by one unit. The price is to be understood as the

opportunity cost of producing a particular good. The price ratio is equal to the ratio of average or

marginal labour values and equal to the inverse of the ratio of average productivities of labour.

This very special case of production conditions ' labour power being the only factor of production and its outputelasticity! a K ! with a hori"ontal supply curve of constant labour value! which represents therefore the sociallynecessary labourwhatever the demand conditions ' offers the standard unit of measurement of labour value . hourof labour power employed under these production conditions is equal to unit of labour value. This standard unit of

value is also independent of distribution! i.e. remains constant whatever the values of the wage rate or the rate ofinterest.

8

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

Figure 3: Average and Marginal Labour Valuesfor Deer and Beaver Hunting

Output

Average,

MarginalLabou

rValues

(=L(

&(=L(

&(

*=L*

&*=L*

&*


9/36

The derivation of the equation for the production possibility frontier is straight forward. *rom 0A

and 0aAwe derive the inverses

L(=&(

A()A

and

L*=&*

A*)aA

A given amount of labour power! L(can be employed either in deer or in beaver hunting.

L=L(L* 1A

)A and)aA substituted in1A isE

L=&(

A(

&*

A*4A

,esolved for QD

3


10/36

&(=A(L +A(

A*&* 5A

The slope of the production possibility frontier 5A is the ratio of the average productivities of

labour and this is equal to the inverse of the price ratio as shown in equation 6A.

*

(=

A(

A*=

&(/L(&*/L*

=L*/&*L(/&(

=L*/&*L(/&(

6A

Csing vto designate labour power 0per unit of output1 and 9 forlabour values 0per unit of output1

respectively and defining vandas

v=L/& )=L /& A

we can express 6Aas

*

(=

A(

A*=

&(/L(&*/L*

=v*

v(=*(

6aA

An important consequence of the constancy of average labour productivities and labour values is

that the production possibility frontier is a straight line. (hatever efficient combination of output is

chosen! the ratio of prices 0labour values1 remains constant. This is a condition where #demand# has

no impact on labour values and therefore also no impact on prices6 ne can interpret the hori"ontal

lines of average and marginal labour values in Figure 1as supply curves in terms of labour values.

The supply curves in terms of money are obtained by multiplying the labour values with the wage

rate. (herever these curves are cut by a demand curve the price remains constant. The commodities

exchange according to their labour values. )f we multiply the ratio of prices as shown in the

equation 6Awith the ratio of outputs we obtain the ratio of total values! L3DL'.

* &*

( &(=

L*

L(=

L*&*

&*

L(&(

&(

EA

J


11/36


12/36

Figure 5shows production functions for deer and beaver with diminishing marginal productivities

of labour.

The average and marginal productivities of labour for deer and beaver hunting! which are now

changing with the level of employment! are shown in Figure 6aand Figure 6b respectively.

-

0 2 4 6 8 10 12

0

2

4

6

8

10

12

14

16

18

Figure 5: Production Functionsfor Deer and Beaver Hunting

Labour Power

De

er,Beaver

&(=A(L(a(

&*=A*L*a*

5eer

%eaver

0 1 2 3 4 5 6 7 8 9 10

0

0,5

1

1,5

2

2,5

3

3,5

4

Figure 6a: Average and Marginal Productivities of Labourfor Deer Hunting

Labour Power

Average,


&(

L(

&(L(


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To obtain the functions of average and marginal labour values! the production functions have to be

inverted and average and marginal labour values have to be constructed on the basis of these

functions as demonstrated in Figure aand Figure b. ne should notice that the marginal labour

values are necessarily greater than the average labour values.

@

0 1 2 3 4 5 6 7 8 9 10

0

2

4

6

8

10

12

14

16

Figure 6b: Average and Marginal Productivities of Labourfor Beaver Hunting

Labour Power

Ave

rage,


&*L*

&*

L*

0 2 4 6 8 10 12 14 16 18

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

Figure a: Average and Marginal Labour Valuesfor Deer Hunting

Output

Average,

MarginalLabourValues

(=L(&(

L(

&(


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)n fact! the marginal labour value as a function of output is nothing else but the supply function in

terms of labour values.

0 2 4 6 8 10 12 14 16 18

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

Figure !a: "#e Labour Value Functionfor Deer Hunting

Output


(=L(&(

=f&(

9'

?'

0 1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

Figure b: Average and Marginal Labour Valuesfor Beaver Hunting

Output

Average,


*=L*

&*

L*

&*


15/36

This function shall be named the Labour alue !unction.

fQ 00A

All points on the Labour alue !unction represent the minimum labour value required for the

production of the corresponding level of output. The point where the demand function- intersects

this function defines thesocially necessary labourfor the production of the commodity.

ow we leave Adam Smith#s example for a moment and consider a market situation for which we

have derived the ?abour Halue *unction. The multiplication of the labour values of the ?abour

Halue *unction with the wage rate! -! gives the marginal cost curve! showing marginal cost as a

function of output.d'

d&="=" f & 0)A

wheredC

dQI marginal cost! -I wage rate!

: A demand function in terms of labour values attributes to each quantity of a commodity an amount of labour the

consumer is willing to sacrifice in order to obtain an additional unit of the commodity =L

&

=f& .

These labour values are #labour commanded#! 0 pD-1 in the sense of the +lassics.

:

0 1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

Figure !b: "#e Labour Value Functionfor Beaver Hunting

Output


*=L*

&*=f&*

93

?3


16/36

Figure +shows an ordinary diagram with thesupplyand demand functionsof an industry for the

case of perfect competition. The equilibrium price is well determined by the labour values. )n

equilibrium! labour commanded! pe/w! is equal to labour embodied!e. The equilibrium price!

pe(is the socially necessary labour,e,multiplied by the wage rate! w.

Cnder perfect competition the price is proportional to the labour value. The supply function of the

industry is the sum of the quantities supplied by the firms of the industry.

ow we derive the roduction ossibility !rontier for the general case of diminishing marginal

productivities of labour. The procedure is the same as beforeE

*rom the production functions

&(=A(L(a(

01aA

9

0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

25

30

35

40

45

50

Figure $: %u&&l' and De(and Functionsof an )ndustr'

Output (in Thousands

Price

=d

d&=S&="=" f&

P

?

=( &

e="e


17/36

and &*=A*L*a* 01bA

we derive the demand functions for labour po"er.

L(=&(

A(

/a(

04aA

and L*=&*

A*/a*

04bA

A given quantity of labour po"ercan be employed alternatively in deer or beaver huntingE

L=L(L* 05A

04aA and04bA substituted in05A gives

L=&(

A( /a(

&*

A* /a*

06A

and this resolved for?'is

&(=[A( /a(LA(/a

(

A*/a

*

&* /a*]

a(

0A

0 2 4 6 8 10

0

5

10

15

20

25

30

35

Figure *+: Production Possibilit' Frontier forDeer and Beaver Hunting

Beaver

Deer

=*

(=*

(=L*/&*L(/&(

L

2

4


18/36

The negative of the slope of the roduction ossibility !rontier! known as the marginal rate of

transformation! 0M,T1! represents the ratio of prices in the sense of opportunity cost as discussed

above.

MT=d&(

d&*=a([A(

/a(LA( /a

(

A* /a

*

&*/a*

]a(

[a*

A(/a(

A*/a

*

&* /a*

] 0EA%ut this slope is also equal to the ratio of marginal costand also equal to the ratio of labour values.

This holds for all points of the roduction ossibility !rontier. The point selected by the demand

conditions represents the equilibrium price ratio and also the ratio of labour values which are the

expressions of the socially necessary labourfor the production of the corresponding commodities.

All these conditions are valid only under perfect competition. This state of affairs is #areto

efficient#. )n aareto efficient equilibrium prices are proportional to labour values as we have

stated in equation 0*A above.

MT=*

(=*(

=

L*&*L(&(

0*A

(hat distinguishes the general case of variable marginal labour values from the special case of

Adam Smith#s example of constant marginal labour values is the occurrence ofsurplus labour. As is

shown very clearly in Figures aand b! there is a difference between marginal and average labour

values. This difference between the marginal labour value! ! and average labour value! v! is

surplus labour0per unit of output1! s=Ls

&:

s=v 0+A

or more explicitly

8


19/36


20/36

conditions and the monopolistic firm. The competitive firm faces an environment where the price of

the product! p! as well as the prices of the inputs9! -and r! are taken as given and the firm has no

power to influence these prices. )ts output is negligible in relation to overall output of the industry

and its demand for the factors of production is also not sufficient to influence the prices of these

factors.

)n order to maximi"e profits the firm equali"es its marginal costto the price. This results from the

maximi"ation of the profit function.

=.&'& )4A

where I profits! I revenue! CI cost

,evenue is p?! and under perfect competition pis constant. ThereforeE

d .

d &=p )5A

+ost consists of the cost of the inputs. )n general! some cost are fixed and some cost depend on the

level of output. The following expression distinguishes the variable inputs labour power!L! in terms

of working hours! and capital! K! in terms of money! and an amount of fixed cost! CFin terms of

money. The cost equationisE

="Lr1! )6A

where -' the wage rate! r' the price of the services of capital 0the interest rate1

The first order condition for maximi"ing profits isE

dd &

=d

d &

d

d &=J )A

and therefore

d

d &=

d

d &)EA

9 (hen we consider ras a price of the input capitalthis does not mean the price of the capital good as a commoditybut the price for using the value of the capital good for the length of the production period. Csually one speaks of

theprice of the services of capital. (e do not discuss the determination of r; this will be the sub$ect of another paperdealing with /antorovich#s norm of effectiveness.

-J


21/36

As from )5Aat the point of maximum profits! price! p! is equal to dDd?and substituted in )EA

p=d

d &)+A

*or the competitive firm! generally! marginal cost is an increasing function of output. The firm

expands its output until marginal cost equals the price.

)n order to calculate marginal cost! dCDd?! we have to transform the cost equation )6A into a

function of output only! the resulting function is called the classical cost function, C f?A.

The firm faces its production conditions represented by its production function! ? gK( LA! and

tries to minimi"e cost. The cost minimi#ation problemcan be expressed in form of the ?agrangianE

2="Lr1[&Jg1 , L] 1*A

The first order conditions for cost minimi#ationareE

2

L="

g1 , L

L =J

2

1=r

g1 , L

1 =J

2

=&Jg1 , L=J

10A

*rom this we obtain the following expression for the optimal factor input combinationas a function

of the prices of the inputsE

"

r=g1 , L/L

g1 , L/11)A

otice! that the marginal productivitiesare functions of thefactor input combination. This can be

expressed as an implicit function which is called the expansion path

"

rg1 , L/L

g1 , L/1=J 11A

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22/36

The expansion pathis the locus of the optimal factor combinationsfor different levels of output on

the capital labour plane. The total differentialof a given level of output isE

d&=&

LdL

&

1d1=J 14A

which givesE

d1

dL=

&

L

&

1

15A

Braphically this can be shown as followsE

Figure 00 shows a production function of type +obb'5ouglas in three'dimensional space. The

border lines between different colours represent isoquants! points with the same level of output.

Figure 0)shows the same production function on the capital labour plane. )n addition! an iso'cost

line and the expansion pathare presented.

n the capital labour plane an isoquant! 14A! represents a level of output produced by different

factor combinations. The factor costs are represented by an iso3cost line, the slope of which is the

--


23/36

factor price ratio, w/(1+r). The iso3cost lineisE

1= '

r

"

rL 16A

The optimal factor combinationis there where the iso3cost curveis tangent to the isoquant. Along

the iso3cost lineit is here! where output is highest. All the points of tangency for different levels of

cost! 0different iso'cost lines which are parallel1 represent the expansion path.

The expansion path allows us to express the optimal amount of one factor input! Lor K(as a

function of the other. )n our case we have - functions! L fKAand K fLA. Substituting capital

for labour we can express cost as a function of capital only! C fK1! and substituting labour for

capital we can express cost as a function of labour only! C fLA. Then we derive the inverses of

these functions and obtain another - functions expressing the optimal amounts of factor inputs as

functions of cost! L fCA and K fCA. These expressions can now be substituted into the

production function which gives us output in terms of cost only. The inverse of this function is the

classical cost function, C f?Aand the marginal cost function can be derived from this. The

-@


24/36

marginal cost function

d

d&=f '& 1A

is thesupply function of the firmunder conditions of perfect competition. *or a presentation of the

derivation of the marginal cost function see 0 uandt! 38J! p. 8@ ff1.

)n this type of derivation of the marginal cost curvethere does not seem to be any labour values

involved. utput is the result of the combined effects of the factor inputs. To attribute the result of

the production process to the labourer only seems to contradict the facts of economic analysis. %ut

surely! the only one who produces is the labourer. The other factors of production only increase his

productivity. To reveal this! we shall derive the Labour alue !unction.

VI The 'erivation of the Labour Value Fun!tion

The cost minimi#ation conditionsreveal also that theLagrange multiplier! N(is marginal cost. This

can be shown as follows. The total differential of cost is

d=L

dL1

d1 1EA

and the total differential of output is

d&=&

LdL

&

1d1 1+A

*rom the cost equation )6Awe can derive the derivatives of cost with respect to labour and capitalrespectively asE

'

L="

'

1=r

4*A

and substituted into 1EAwe get

-


25/36

d'=" dLrd1 40A

*rom the first order conditions 10Awe get

"=&

L

r=&1

4)A

and these expressions substituted into 40AisE

d=&

LdL

&

1d1 41A

which is equal to

d'=[&

LdL&

1d1]44A

%ut the term in brackets is d?from 1+A. Therefore

=d

d&45A

?ooking again at 4)A we see that

"=&L

46A


26/36

certain output! ?! can be produced with minimum cost. The labour valueof a unit of that output is

the marginal labour value, MLDM?( calculated on the basis of the optimal factor combination!

0/O! ?O1.

(e shall use an example presenting the derivation of the Labour alue !unctionE

?et the production function be

&=A 1aL

b) and a ,b ) ab 4+A

and the cost function

="Lr1 5*A

*rom the first order conditions for cost minimi"ation we have as in10A

"=&

L; r=

&

150A

and as the marginal productivities of labour and capital for the production function 4+Aare

&

L=b

&

L

&1

=a&

1

5)A

we can derive the optimal factor combination for a given factor price ratio as in 1)A

"

r=

&

L

&

1

=b

a

1

L51A

This gives us the optimal quantity of labour power! L! as a function of Kand Kas a function of

L.

L O=r

"

b

a1

1O="

ra

bL

54A

7xpressing Kin the production function 4+Aas a function of Lwe get

-9


27/36

&=A[ "ra

b L]

a

Lb

55A

The inverse of this function is the demand for labour po"eras a function of output

LO=

[

A [ "r ab ]

a

&

]/ ab

56A

ow we express marginal labour valueas the reciprocal of the marginal productivity of labour

from 5)A for an optimal amount of labour power! L! that is for a point on the expansion path.

L

&=

b

LO

&5A

and substitute labour by the expression of labour demand from 56Awhich gives us labour value as

a function of output only! which is the Labour alue !unction.

=L

&=

b

A

ab [ "r

a

b ]aab &

ab

5EA

7xpressing the complicated constant term as AO the function becomes

=L

&

=AO&

ab

5+A

AO=

b

A

ab [ "ra

b ]a

ab


28/36

These labour values multiplied with the wage rate give the marginal cost function. The labour value

which corresponds to the equilibrium point where the!unction of Labour ommanded0the demand

function in terms of labour values1 cuts theLabour alue !unctionis the socially necessary labour

to produce the commodity! PO. )n fact! it is the reciprocal of the real wage.

O=p

"60A

TheLabour alue !unctionresolves a long'lasting dispute about labour valuesand changes in the

factor price ratio. )n fact! the function reveals that labour values are not only dependent on the level

of output but also on thefactor price ratio. )n the analysis above this ratio is treated as a constant.

%ut changes in thefactor price ratioresult in changes of the labour values. This is rather natural

because prices are proportional to labour values! they reflect labour values. A change in thefactor

price ratioindicates changing cost of the use of inputs in terms of labour values and this must lead

to a different optimal factor input combination. Therefore a requirement that labour valuesmust be

independent of thefactor price ratiois simply unreasonable.

-8


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n the other hand! the standard unit of measurement of labour value should not and does not

depend neither on the factor price ratiowhich reflect the dynamics of an economic system nor on

demand conditions. )t is the time of labour employed in the very special production process which

uses labour po"eronly and which has constant returns to scale! that is! where the productivity of

labour does not depend on the level of output but is constant. uantities of labour values are

always expressed in terms of thisstandard labour value.

VII The Gtandard "nit of 7easurement of Labour Value

The production process which offers a definition of thestandard unit of measurement of labour

valueis a process which has the following production functionE

&i=AiL 6)A

where ?iI amount of output of commodity i! ,iI average labour productivity which is a constant

and therefore equal to the marginal labour productivity. There is no surplus labour in this

production process. )n this production process the value of a unit of labour po"eris equal to a unit

of labour value! for example hour of work in this process is unit of labour power as well as

unit of labour value. This is the standard unit of measurement of labour value.

The total amount of labour value0hours worked1 in the standard production process is equal to the

labour value 0per unit of output1! 9itimes output. This is equal to average labour value! 0D,i(times

output.

L=i& i=

Ai& i 61A

-3


30/36

)n a perfectly organi"ed economy where all factors of production are fully used and optimally

allocated to the production processes of the economy! which is usually termed perfect competition!

prices are the monetary expressions of labour values.

i& i="iO&i=" L& i&i 64A

The total labour valuerepresented by some quantity ?of commodity iisE

iO

& i=,i & i

" =

L

&i&i 65A

(hen we say that the production of a quantity of commodity i! ?i! has cost*iQi, in terms of

labour, this refers to the standard unit of labour valuewhich is labour time producing commodity

according to production function of type 6)A This does not mean that there have been*iQihours

of work involved! but usually less. The difference is surplus labour! LG! as shown already above in

equations 0+A and )*A. This also means that the hours worked are being weighted according to

their capital intensity.

LS=[v ]&=

[L

&

L

&

]& )*A


31/36

(e have established that the price of a commodity divided by the wage rate equals its labour value

60A. The labour value can be divided into the value of labour po"erused up in the production! this

value is represented as v! the vector of vertically integrated labour coefficientsandsurplus labour! s.

=sv 66A

)ts relation to price is

p="="s" v 6A

ow we regard the production process as the consumption of labour po"er! Li! and some constant

capital, ci,which is a sum of commodities! the capital goods! to create a new commodity.

&i Lici ) ci=x i4 6EA

)n monetary terms this is the cost of production equation

p i& i="Li p4x i4 6+A

The value of output is the sum of profits! the wages for the direct labour power employed! as well as

the value of the commodities which constitute constant capital. 7xpressing profits as surplus labour

in monetary terms 0 = ws1

p i & i="si"Li p4x i4 *A

This holds not only for the commodity i! but also for all the other commodities constituting

constant capital! the iN (e know that their labour value depends on the factor price ratioas it is

expressed in their Labour alue !unctions. (hen the factor price ratio changes so changes the

optimal factor input combinationas well as thesurplus labour. So the value of constant capital

changes.


32/36

There has been a big debate! if it is possible to relate factor price ratiosunequivocally to optimal

factor combinations. )t has been proven that for the case of ?eontief production functions using also

constant capitalwhere there are no possibilities of substitution! re'switching of factor combinations

can occur so that a certain factor combination is optimal at two different levels of the factor price

ratio. This has been considered as a great defect of neoclassical economic theory. %ut although this

has been shown to be a valid criticism for the special case offixed coefficient production functions

there has not been presented an example for a production system which allows for substitution

amongst the factors of production.

n the other hand! it has been proven that for the case of the static ?eontief model the #pure# labour

theory of value holds! which means that there is nosurplus labourand therefore the rate of interest!

r( is "ero. This reflects precisely Schumpeter#s position that in a stationary economy the interest rate

must be "ero. And this implies that in a stationary economy there is no factor price ratio. So the re'

switching debate is based on the Sraffian system which is basically flawed as one cannot assume a

static! stationary economy without marginal changes and at the same time introduce a positive rate

of profit which occurs only under dynamic conditions.

VIII Gome $bservations on 'emand

*inally! we want to make some observations on labour values and demand in a perfect economy. )n

Figure +we have already introduced a demand function in terms of labour values4

= f & ; =L

&0A

4 See the comments and the footnote to Figure + above. There will be another paper F?abour Halues and the Theoryof +onsumer %ehaviourG

@-


33/36

)n such a demand function represents labour commanded ! =p

"! which means that amount

of labour power which can be bought by a sum of money. This has to be distinguished from the

labour values! 9! in the supply function =f& ! which represent labour embodied. Cnder

perfect competition prices are nothing else but monetary expressions of embodied labour value; all

revenue is also nothing but labour value and so is demand as expressed on the markets; labour

commanded is equal to labour embodied! 0 91. %ut this does not mean that all revenue has been

gained through labour. The owners of capital may not have worked at all! receiving nevertheless

profits.

These profits are representing labour values only in a perfect economy; if there are mark'ups due to

monopoly power this is no longer the case. So! considering demand! we have to distinguish between

at least @ different situations.

)f the economy is not perfect! there is monopoly power and there are mark'ups increasing the prices

above their embodied labour values! 0 O 9 orp - O -91! and consequently the revenue derived

exceeds the monetary value of embodied labour values! and the demand based upon this revenue in

terms of labour commanded! ! is greater than the 0embodied1 labour values created in production

0 O 91.8

Cnder conditions of perfect competition! 0 9A( one needs to distinguish between - cases. *irst!

there is no relation between the property of capital and work effort or the amount of labour power

provided for production. This means! there is no relation between earnings from labour and income

from profits for the individuals. Cnder these conditions demand does not express purely the wants

of the labourers although all demand represents embodied labour values.

8 This shall be dealt with in another article on imperfect competition.

@@


34/36


35/36

edge approach to the social sciences.

)n the follow'up part )) of this paper we shall be leaving the perfect world. )n the real world we live

in! there exist indeed serious problems of reaching an efficient organi"ation of production processes.

+onsidering monopoly capitalism! the failures of the markets are becoming more and more apparent

and this on a global scale! in particular concerning the proper management of the eco'systems and

natural resources. The solutions of these problems seem to be well above the scope of capitalistic

organi"ation! its costs are increasing permanently! the real limitation being wage labour.

Cniversit= 2aris uest! 3.-.-JJ3

/laus


36/36

2AS)7TT)! ?. ?. 03441.Lectures on the Theory of roduction.

?ondon and %asingstokeE The Macmillan 2ress ?td.

SM)T

?ondonE Strahan and +adell. 7dited by +ampbell and Skinner.

xfordE +larendon 2ress; 349.

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Labour Values and the Theory of the Firm

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