Sunday, 24 July 2016

Capital III, Chapter 40 - Part 7

Suppose relative fertility of the different land types remains constant. Output is doubled, on each land type, as a result of the capital invested doubling, from £10 to £20, £5 now being invested in each land type. This would be the same as if two hectares of each land type had been cultivated instead of one.

The general rate of profit remains the same, and the rate of profit on each type of land remains the same. If A now produces two Kilos, B four, C six, and D eight, the price of production remains £3 per Kilo, provided demand remains high enough that land type A continues to determine the price, “... because the invested capital was doubled.” (p 683)

Because the total profit has doubled, the rent has also doubled. Measured in wheat it is now B – 2 Kilos, C – 4 Kilos, D – 6 Kilos, which at £3 per Kilo gives money rents of £6, £12, and £18 respectively. And, because the rent per hectare is doubled, the price of the land, as capitalised rent, will also have doubled.

There is no change in the rate of rent, because rent has doubled and the capital invested has also doubled. Total rent is £36, whereas the capital invested is £20, which is the same proportional rate as previously, when rent was £18 and capital invested was £10.

This same proportional relation applies to each individual type of land. Rent on land type C is £12 as against £5 of capital invested, which is the same ratio as £6 of rent with £2.50 of capital invested.

Under the conditions described here, of constant returns, i.e. the marginal productivity of capital is neither rising nor falling, but produces the same amount of output as previous investments, on that type of soil, it does not matter if all of the added investment occurs on one type of soil. If all the additional investment occurred on land type C, for example, (as in Table 5) this would not change the relative return from C, compared to A, B, or D. The additional investment would have the same effect as if additional hectares of land type C were brought under cultivation (as in Table 6).

Table 5

 Land Type Capital Per Hectare £'s Ha. Output Kilos Price per Kilo £'s Total Revenue £'s Price of Production of Output £'s Profit £'s Surplus Profit £'s D 2.50 1.00 4.00 3.00 12.00 3.00 9.50 9.00 C 5.00 1.00 6.00 3.00 18.00 6.00 13.00 12.00 B 2.50 1.00 2.00 3.00 6.00 3.00 3.50 3.00 A 2.50 1.00 1.00 3.00 3.00 3.00 0.50 0.00 Total 10.00 4.00 13.00 39.00 26.50 24.00

Table 6

 Land Type Capital Per Hectare £'s Ha. Output Kilos Price per Kilo £'s Total Revenue £'s Price of Production of Output £'s Profit £'s Surplus Profit £'s D 2.50 1.00 4.00 3.00 12.00 3.00 9.50 9.00 C 2.50 2.00 6.00 3.00 18.00 6.00 13.00 12.00 B 2.50 1.00 2.00 3.00 6.00 3.00 3.50 3.00 A 2.50 1.00 1.00 3.00 3.00 3.00 0.50 0.00 Total 10.00 4.00 13.00 39.00 26.50 24.00

“This shows that the amount of rent in produce and money per acre, and therefore the price of land, may rise, while the price of production, the rate of profit, and the differences remain unchanged (and therefore the rate of surplus-profit or of rent, calculated with respect to capital, remains unchanged).” (p 684)

But, this also applies where there is diminishing marginal productivity of capital.

Table 7.

 Land Type First Investment Second Investment Capital £'s Output in Kilos Revenue £'s Rent £'s Capital £'s Additional Output in Kilos Additional Revenue £'s Rent £'s B 2.50 2.00 6.00 3.00 2.50 1.50 4.50 1.50 C 2.50 3.00 9.00 6.00 2.50 2.00 6.00 3.00 D 2.50 4.00 12.00 9.00 2.50 3.00 9.00 6.00

The additional output on land type B from the second investment is only 1.50 Kilos, because of falling marginal productivity. The additional revenue from these 1.50 Kilos is then £3 x 1.50 = £4.50. But, the price of production of these 1.50 Kilos is £3, leaving an additional rent from the second investment of £1.50. Similarly, the increased revenue from land type C is £6, and with a price of production of £3 for this output, that leaves an additional rent of £3. For land type D, the additional revenue is £9, giving an additional rent of £6.

The rate of return to capital declines, but the total return rises. Similarly, the rate of rent declines, but the total rent on each hectare rises. The price of production, determined by it, remains the same, but the difference between the return on A, to that on B, C and D will have diminished. The rent per hectare has risen, and so the price of land also thereby rises.

Table 8.

 Land Type First Investment After Second Investment Capital £'s Ha. Rate of Rent % Rent Per Ha. £'s Capital £'s Ha. Rate of Rent % Rent per Ha. £'s A 2.50 1.00 0 0 2.50 1.00 0 0 B 2.50 1.00 120 3.00 5.00 1.00 90 4.50 C 2.50 1.00 240 6.00 5.00 1.00 180 9.00 D 2.50 1.00 360 9.00 5.00 1.00 300 15.00