## Thursday, 4 January 2018

### Theories of Surplus Value, Part II, Chapter 12 - Part 6

Marx then presents tables A-E in a different format. In the process, he introduces a new term called “Differential Value”. Marx defines Differential Value later as being the difference between the market value and the individual value of a commodity. It is calculated per unit. So, for example, if the market value of coal in the examples is £2 per ton, and the individual values for each mine are £1, £1.20, £1.50, £200, £2.50, the differential values would be £1.00, £0.80, £0.50, £0, and - £0.50.

Table A
 Class C Capital £'s T Output Tons TV Total Value £'s MV Market-Value £'s Per Ton IV Individual Value £'s per Ton DV Differential Value £'s per Ton CP Cost-Price (price of production) £'s per ton AR Absolute Rent £'s DR Differential Rent £'s AR in T Absolute Rent in Tons DR in T Differential Rent in Tons TR Total Rent £'s TR in T Total Rent in Tons I 100 60 120 2.00 2.00 0 1.833 10 0 5 0 10 5 II 100 65 130 2.00 1.846 0.153 1.692 10 10 5 5 20 10 III 100 75 150 2.00 1.600 0.400 1.466 10 30 5 15 40 20 Total 300 200 400 30 40 15 20 70 35
Table B
 Class C Capital £'s T Output Tons TV Total Value £'s MV Market-Value £'s Per Ton IV Individual Value £'s per Ton DV Differential Value £'s per Ton CP Cost-Price (price of production) £'s per ton AR Absolute Rent £'s DR Differential Rent £'s AR in T Absolute Rent in Tons DR in T Differential Rent in Tons TR Total Rent £'s TR in T Total Rent in Tons II 50 32.5 60 1.846 1.846 0 1.692 5 0 2.708 0 5 2.708 III 100 75 138.461 1.846 1.600 0.246 1.466 10 18.461 5.250 10 28.461 15.416 IV 100 92.5 170.769 1.846 1.297 0.548 1.189 10 50.769 5.416 27.50 60.769 32.916 Total 250 200 369.230 25 69.230 13.541 37.50 94.230 51.041
Table C
 Class C Capital £'s T Output Tons TV Total Value £'s MV Market-Value £'s Per Ton IV Individual Value £'s per Ton DV Differential Value £'s per Ton CP Cost-Price (price of production) £'s per ton AR Absolute Rent £'s DR Differential Rent £'s AR in T Absolute Rent in Tons DR in T Differential Rent in Tons TR Total Rent £'s TR in T Total Rent in Tons I 100 60 110.769 1.846 2.000 - 0.153 1.833 0.769 0 0.416 0 0.769 0.416 II 100 65 120.000 1.846 1.846 0 1.692 10 0 5.416 0 10 5.416 III 100 75 138.461 1.846 1.600 0.246 1.466 10 18.461 5.416 10 28.461 15.416 IV 100 92.5 170.769 1.846 1.297 0.548 1.189 10 50.769 5.416 27.50 60.769 32.916 Total 400 292.5 540.000 30.769 69.230 16.666 37.50 100 54.166
Table D
 Class C Capital £'s T Output Tons TV Total Value £'s MV Market-Value £'s Per Ton IV Individual Value £'s per Ton DV Differential Value £'s per Ton CP Cost-Price (price of production) £'s per ton AR Absolute Rent £'s DR Differential Rent £'s AR in T Absolute Rent in Tons DR in T Differential Rent in Tons TR Total Rent £'s TR in T Total Rent in Tons I 100 60 110 1.833 2.000 - 0.166 1.833 0. 0 0 0 0 0. II 100 65 119.166 1.833 1.846 - 0.012 1.692 9.166 0 5.000 0 9.166 5 III 100 75 137.500 1.833 1.600 0.219 1.466 10 17.500 5.454 9.545 27.500 15 IV 100 92.5 169.583 1.833 1.297 0.540 1.189 10 49.583 5.454 27.045 59.583 32.50 Total 400 292.5 536.250 29.166 67.083 15.909 36.590 96.25 52.50
Table E
 Class C Capital £'s T Output Tons TV Total Value £'s MV Market-Value £'s Per Ton IV Individual Value £'s per Ton DV Differential Value £'s per Ton CP Cost-Price (price of production) £'s per ton AR Absolute Rent £'s DR Differential Rent £'s AR in T Absolute Rent in Tons DR in T Differential Rent in Tons TR Total Rent £'s TR in T Total Rent in Tons II 100 65 113.750 1.750 1.846 - 0.096 1.692 3.750 0 2.142 0 3.75 2.142 III 100 75 131.250 1.750 1.600 0.150 1.466 10 11.250 5.714 6.428 21.250 12.142 IV 100 92.5 161.875 1.750 1.297 0.493 1.189 10 41.875 5.714 23.928 51.875 29.642 Total 300 232.5 406.875 23.750 53.125 30.357 30.357 76.875 43.928

By establishing the category of differential value, which can appear as a negative amount, Marx avoids the problem that arises from having to present a situation where the absolute rent falls below the normal level, as a negative differential rent, as was the case in Table C.

Marx restates some basic concepts and principles in explaining the basis of differential value. He begins by explaining the difference between individual value and individual price of production. If, in each mine, £100 of capital is employed, with the same organic composition of capital, say 80:20, then, with the same rate of surplus value, in each mine, say 100%, the individual value of output from each mine will be the same, that is £120, made up 80:20:20.

This caused some confusion for some economists, because it seemed perverse that the value of output from one mine, producing 60 tons of coal could be the same as the value of another mine producing 90 tons of coal. And, of course, in terms of the social value, or market value, of the output that is correct. But, in terms of the individual value it is not. This is a difference between an embodied labour theory of value, and a social theory of value.

Looking at a mine that produces 60 tons of coal, the value embodied in the coal is, here, £80, representing the dead labour, in the constant capital, and £40 of new value, created by the living labour, £20 of which reproduces the workers' wages, and £20 of which goes to surplus value. But, this is the value, irrespective of the quantity of coal produced. On this basis, each ton embodies 120/60 = £2 of value. If another mine produces 90 tons of coal, but similarly uses £80 of constant capital, and £20 of variable capital, with £20 of surplus value, the individual value of its output is also £120, but the value embodied in each ton is 120/90 = £1.33.

But, its obvious that Mine I does not sell its output at £2, whilst Mine II sells its output at £1.33. A commodity's value is not determined by its individual value, reflecting the embodied labour, but by its social value, a market value based upon the labour-time socially necessary for its production. In this case, we might say that the labour-time required is reflected in a value of £240 – the total value of output, which amounts to 240/150 = £1.60 per ton. On this basis, it can be seen that the individual value of Mine I's production is £0.40 per ton more than its social value, whereas Mine II's production has an individual value that is £0.66 per ton less than its social value. Put another way, the individual value of output of both mines is £120, but the market value of Mine I's output is £96, whereas the market value of Mine II's output is £144.

But, also, the individual value of output is not the same as the individual price of production. In each case, £100 of capital produces £120 of output value – individual value, i.e. 80 c + 20 v + 20 s. But, if the average rate of profit is 10%, then in each case, the individual price of production will be £110, i.e. £100 k + £10 p.

“If, therefore, the capital advanced equals £100, the value of the total product must be £120. Supposing furthermore that the average profit is 10 per cent, then £110 is the cost-price of total product, in the above example, of coal. With the given rate of surplus-value or surplus-labour, the £100 capital transforms itself into a value of £120, whether poor or rich mines are being exploited; in a word: The varying productivity of labour—whether this variation be due to varying natural conditions of labour or varying social conditions of labour or varying technological conditions—does not alter the fact that the value of the commodities equals the quantity of labour materialised in them.” (p 262)

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