Monday, 1 January 2018

Theories of Surplus Value, Part II, Chapter 12 - Part 3

If £100 of capital is employed, comprising £80 c + £20 v, and producing £20 s, the total value is £120. If the average rate of profit is 10%, the price of production is £110, which means £10 can be charged in absolute rent. But, it doesn't matter whether this capital is employed on more or less fertile land, in respect of this absolute rent. If this was Mine I, it may produce 90 tons of coal, whereas in Mine IV it produces 120 tons of coal. In terms of the capital employed, the cost of production, price of production, and the value of production, nothing is changed, and so the absolute rent is the same. The only thing that is different is the value and price of production per ton of coal.

“Besides, the amount [of rent] must be the same, because—at a given rate of rent—capitals of the same magnitude would have been employed. But, since the [market] -value of the coal is not determined by the [individual] value of the coal derived from IV, it would bear an excess rent, or an overplus over its absolute rent; a rent derived, not from any difference between value and cost-price, but from the difference between the market-value and the individual value of the produce No. IV.” (p 254-5)

In other words, because the rate of rent remains constant, and the amount of capital employed remains constant, at £100, the amount of rent remains constant. The difference is again that the amount of rent per ton is reduced. If previously £100 produced 100 tons, and the rent was £10 that is £0.10 rent per ton. If now, £100 produces 120 tons, rent is still £10, but that is £0.085 rent per ton.

But, now, as Marx sets out, in addition to this absolute rent, an additional differential rent arises, because the individual value of this production, from Mine IV, is lower than the market value of coal, and this difference derives from the greater fertility of Mine IV, compared to the other mines.

The absolute rent is the same in Mines I-IV, because the composition of capital, and amount of capital, in each, is the same. Although the value and price of production, per ton, is different, in each, the proportion remains the same.

 c v s Value K R' 10% Price of Production Absolute Rent Tons Price per Ton I 80 20 20 120 100 10 110 10 100 1.10 II 80 20 20 120 100 10 110 10 110 1.00 III 80 20 20 120 100 10 110 10 120 0.92 IV 80 20 20 120 100 10 110 10 130 0.85

“This difference in their values is, therefore, exactly equal to the difference in their cost-prices, in other words to [the difference in] the relative amount of capital expended to produce one ton of coal in I, II and III. The variation in the magnitudes of value in the three groups does not, therefore, affect the difference between value and cost-price in the various classes. If the value is greater, then the cost-price is greater in the same proportion, for the value is only greater in proportion as more capital or labour is expended; hence the relation between value and cost-price remains the same, and hence absolute rent is the same.” (p 255)

That is not the case with the differential rent. Marx assumes that the £100 employed in Mine IV not only replaces all of the production from Mine I, but also half the production of Mine II. As the total production is now effected with less capital, its clear that the price of production itself has fallen. Total investment has fallen by the amount of half the half of capital invested in Mine II. The investment in Mine I has been replaced by an investment of the same amount in Mine IV. The rent from Mine I disappears, but is replaced by the absolute rent from Mine IV. Half of the rent from Mine II disappears, because only half the capital is now invested in it. If previously, £100 was invested in each of Mines I-III, that is £300, but now we have £50 in II, £100 in III, and £100 in IV, making £250 in total.

Because the total amount of coal is now produced with £50 less capital, its clear that the market value of coal must, thereby, have fallen, even though the individual value of the coal produced by mines II and III remains the same. The reason the market value has fallen, is because Mine IV produces coal with a lower individual value, and its production has replaced all of the higher value production of Mine I, and half the production of Mine II.

Marx assumes that £100 invested in Mine I produces a value of £120. The absolute rent is £10, and £10 is profit. £100 invested in Mine II produces a product with a market value of £130. That is because the price per ton is determined by the market value, which is higher than the individual value per ton of Mine II's output. So, Mine II provides the average profit of £10, plus £20 rent (£10 absolute, £10 differential).

Mine III produces output with a market value of £150, including £10 profit and £40 rent.

The actual output of the mines is I 60 tons; II 65 tons; III 75 tons. The market value per ton is then £2. Total output is 60 + 65 + 75 = 200 tons.

When Mine IV opens, I closes, and half the capital employed in II is removed. Mine IV produces 92.5 tons, equal to all of Mine I's output, and half of Mine II. At the old market value of £2 per ton, it would have a market value of £185, comprising £10 profit and £75 rent. The rent would be 7.5 times the absolute rent of £10. But, now the market value of coal must have fallen. It is Mine II that now determines the market value. Mine II produces 32.5 tons of coal with £50 of capital. On £100, the average profit is £10, and the absolute rent is £10. On £50, therefore, both are £5. So, the market value of this 32.5 tons is £60, or £1.846 per ton.

The amount of rent paid by II has fallen, because less capital is employed, but also because it now pays only the absolute rent, and not an amount of differential rent.

With the market value now set at £1.846 per ton, the value of output of III is 75 tons x £1.846 = £138.45, and where previously it paid rent of £40, this now falls to £28.46. Previously, the difference between this rent and the absolute rent was £30, and now it is only £18.46. In other words, previously it was 4R, and is now only 2.846R.

“As the amount of capital invested in III has remained the same, this fall is entirely due to the fall in the rate of differential rent, i.e., the fall in the excess of the market-value of III over its individual value. Previously, the whole amount of the rent in III was equal to the excess of the higher market-value over the price of production, now it is only equal to the excess of the lower market-value over the cost-price; the difference is thus coming closer to the absolute rent of III.” (p 258)

Mine III produces 75 tons with an individual value of £120, giving a value per ton of £1.60. Previously it sold each ton at the old market value of £2, giving a surplus over the market value of £0.40 per ton, which means on 75 tons, a total of £30, equal to the differential rent. The new market value is £1.846, which is £0.246 above the individual value per ton for Mine III. On 75 tons that is a total of £18.45, “and this is exactly the differential rent, which is thus always equal to the number of tons multiplied by the excess of the market-value of the ton over the [individual] value of the ton.” (p 258)

Mine IV produces 92.5 tons with an individual value of £120, giving an individual value per ton of £1.297. But it sells the output at the market value of £1.846 per ton giving an excess over the market value of £0.549. On 92.5 tons that gives a total of £50.783, which is equal to the differential rent on Mine IV.

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