Samir Amin, The algebraic model in, "The law of worldwide value"

SAMIR AMIN

An explanation of the algebraic model offered  in “ The law of Worldwide value”

Some readers had difficulty understanding what I meant with the letters “e” and “c” used in the model referred to. I offer here some explanations which I hope could help.

1.In order to understand my presentation,  go to the algebraic model.

1e  +  bh  =  qc   (equation for the production of q units of consumption good "c").

Imagine  now a factory producing in a year 1 000 000 meters of cotton fabrics .It employs to that effect 500 workers, 8 hours a day, 250 days a year. The quantity of  direct social abstract labor needed is therefore 1 000 000 h; h stands for one hour of social abstract labor. With respect to what is meant by social abstract labor, and how quantities of concrete labor can be re-measured in quantities of abstract social labor, refer to "Three essays on Marx’s theory of value" chapter III.

 
Imagine also that the capital (reduced to the equipment "e") needed for the factory has been produced by spending on it 10 000 000 hours of total (direct and indirect) abstract social labor. This equipment operates for a period of 10 years; i.e. the capital consumed in a year is estimated at 1 000 000 hours (h) of labor.

The equation becomes:
1 000 000 h + 1 000 000 h = 1 000 000  c (meters of fabrics)

If we assume the hour h being paid at one dollar; the production price of the meter of cotton fabrics is 2 dollars.

Now, in order to get an equation  which calculates the production price of one unit of that consumption good (i.e. one meter of cotton fabric)
we should divide each term of the equation by 1 000 000. We have:
1e + 1h = 1 c   ;  or (since 1e=1h)
1 h  + 1h = 1 m
if  h=one dollar; one meter m = 2 dollars
Indeed "e" is a composite of different tools and machines, quite small in size since it indicates the quantity of equipment needed to produce one unit of that consumption good, which is one meter of cotton fabric (of course there is no factory built to produce only one meter of cotton fabric!).

2.The total direct labor provided in the factory is 1 000 000 hours. The wages paid permit buying consumer goods whose value corresponds to 500 000 hours for their production; the profit (in that value system) corresponds to also 500 000 hours. The rate of profit coming out of this value system is:  500 000/10 000 000 , i.e.  5 % .

3. Phase two :
The technological progress permits the production of two units of that same consumption good (cotton fabrics) with:
 a) the same quantity of capital (i.e. an equipment whose annual amortizing value corresponds to 1 000 000 hours.

 b) less direct labour, say half; i.e. 500 000 hours.

The equation becomes:
1 000 000 h + 500 000 h = 1 000 000 meters

Therefore:
Either the price of the meter of cotton is maintained ( 2 dollars) and therefore the hour h has to increase from 1 to 1.33 dollars
or the wage is maintained (h=1) and the price of the meter is reduced from 2 to 1.33 dollar.

NB :

a)  I indicated clearly in my book that the unit of "e" used in phase 2 is qualitatively different from the unit "e" in the previous phase. Equipment is used to produce not more of the same equipment, but a new set of tools and machine, more efficient. For instance : steam engines are used to produce electric engines.
That appears in the equations for the production of production goods:

1e + ah = pe

Of course the equipment e produced is different from the equipment used for its production.

This is why I have identified the units of “e” by an index which relates them to the successive phases of accumulation.

e₁; e₂ means the value of e in phase one, in phase two.

b) The consumption good “c” can remain unchanged (one meter of the same cotton fabric but produced with a new type of equipment). But it could also have changed and become a new quality of cotton fabric. This is why also I have used the indices “i” to relate the good “c” to its phase of production.

c₁ ; c₂  means the value of a unit of consumption c in phase one, two etc

4. With respect to the phases:

a)     the shortest phase considered is “one year”. That is useful since “profits” and taxation are calculated on a yearly basis. Also a year takes into account for agricultural products the effects of meteorology which result into different quantities of commodities being obtained with the same labor effort. The year basis is useful to consider normal economic conjuncture. From one year to the next “e” remains unchanged as well as “c”.

b)    but  in order to understand the effects of technological change (the progress of productivity, the development of the productive forces ) we have to consider a longer phase, corresponding to the life time of the equipment, here 10 years, after which a new equipment, more efficient, replaces the previous. In that frame “e” for the second phase is surely different from “e” for the previous one :e₂ is different from e₁ .

5. My book offers here a kind of volume 2 bis of Capital.

It is exactly what Marx says in volume 3 of Capital with respect to the calculation of production prices.But instead of an approach by successive approximations I go directly to the equations needed to obtain the system of production prices. That exercise leads to 3 major conclusions:

 
a) that the reproduction needs real wages increasing at a rate which can be calculated.
b) that the rate of profit in that case does not tend to fall.
c) that the reproduction in a "pure capitalist system" is possible provided the credit system offers for each successive period a volume of credit that can also be calculated (my answer to Rosa Luxemburg).

6. My two books (The law of worldwide value ; Three Essays on Marx’s theory of value) provide together also a kind of volume 2 ter of Capital, introducing a third department for the absorption of the "surplus" (Baran/Sweezy meaning).

Why? Because the normal tendency of capitalism is not to let the real wages increasing as needed. The means by which this "fatal contradiction" has been overcome cannot be discovered in "theory", but through a study of history of apitalism. My very simple model (assuming an increase of productivity at the rate of 4,5 % per annum, and an increase of the wages at the rate of 3,5% ) produces a result (within 45 years) which is exactly what happened when comparing the distribution of production between the 3 departments for year 1900 and year 2000 for the major set of central countries (USA, UK, Germany, France). I am quite happy of this convergence between my model and reality.

The hypotheses that I carried in order to establish my simple model , as well as the measure of the growth of the relative volume of surplus (in accordance with  Baran/Sweezy concept of surplus) from around 1900 to our time call for some further explanations which I hope should help.

a)I carried a hypothesis of a growth of real wages in the major centers  (USA, UK, Germany, France) at a rate of 3,5 % per annum operating on  45 years . That growth of real wages was actually achieved during three periods: 1900-1913, 1920-1929, 1945-1975. But the century was also that of two world wars and the deep crisis of the 1930s. Therefore the reader should understand that it took in historical capitalism one century – and not half a century – to achieve that increase in real wages (even if menaced today by neoliberalism).

b)The rate of growth of the productivity of social labor (4,5% for 45 years, the results being also reached only along a whole century)  is not artificially imagined by me, albeit establishing the proof of it out of current available statistics remains terribly difficult, for the very reason mentioned in the following paragraphs.

The conventional concept of productivity of the various so called factors of production (labor, capital, nature, science), conceived as separated from one another is fallacious, unscientific. It separates what constitutes in reality a single integrated unity. In contrast,  for Marx there is only one productivity, that of social abstract labor. Labor operates with equipment, on the basis of given natural conditions, and in the frame of scientific/technological knowledge available in society.

The metrics of the growth of that productivity proceeds from comparing the total quantity of social abstract labor (direct and indirect) needed for producing one unchanged unit of use-value. That quantity declines from a first phase of production to the following. There is the additional difficulty of measurement related to the transformation of quantities of concrete labor into abstract labor (Ref. Three essays on Marx’s theory of value, chap.III). Available statistics have not been conceived to facilitate that metrics, but only to provide tools for the management of the economy by capital.

A rough approach to this measure might be obtained by dividing the relevant part of GDP , that associated to production – i.e. the conventional primary and secondary sectors - plus that part of the tertiary sector directly linked to them (Ref. Three Essays…, chap.II, p. 69-74) by the quantity of labor spent in those sectors. Such a rough calculation would indeed suggest a rate of growth of 4,5% per annum for the periods 1900-1913, 1920-1929, 1945-1975 (say around 45 to 50 years),  keeping in mind that these result were in fact diluted over a century.

It should be obvious for a Marxist that the rate of growth of productivity of social labor (in accordance with Marx’s concept of it) is necessarily higher than that of growth of real wages. Otherwise capitalism would not suffer from its fatal contradiction – resulting in over accumulation and need of outlet to absorb the surplus. Liberals would be right : capitalism produces continuous harmonious economic growth !

That being said metrics of the surplus is no less uneasy than that of the productivity of social labor, for the same reason, i.e. the irrelevancy of available statistics. The sector of GDP usually called « tertiary » amalgamates activities of absolutely different nature,  some directly associated with primary and secondary sectors  (transport and marketing of goods produced in those two sectors), other representing indeed the outlet for the growing surplus (these activities being for some of them socially desirable, other not). Refer here again to Three Essays…, chap II). Yet a rough look at the statistics relative to the components of the tertiary sector indicates easily that the surplus has grown from around 10% (maximal) at the beginning of the 20th century to no less than 50% today.

That growth corresponds almost exactly to what is derived from my simple model. I think it gives to the exercise its relevance.

7. I repeat as a conclusion of these comments : my « Capital books 2 bis and 2 ter » offer a theory of capitalism (just as Marx intended to do in Capital), not an empirical study of historical capitalism.

That theory of capitalism is Marx’s theory (in my humble opinion) enriched (« revised ») in order to include : (i) a theory of worldwide law of value, (ii) a theory of the absorption of the growing surplus in a Department III which has to be added to Departments I and II in order to overcome the fatal contradiction of capitalist accumulation in the frame of monopoly capitalism. Misunderstanding, uneasy and unnecessary questions related to the empirical « measurement » of indicators result from confusing the theory of capitalism and the reading of historical capitalisms, and reducing them to one single issue. Those thinkers suffering from deep anglo-saxon empirical philosophy tradition will always have difficulty to avoid that confusion since empirical evidences relate by nature to the deployment of historical capitalism. The formulation of the theory of capitalism proceeds through a process of abstraction in accordance with Hegel/Marx concepts.