## Sunday, 7 August 2016

### Capital III, Chapter 43 - Part 3

Engels then presents his summary of conclusions relating to Differential Rent II, which breaks down into three principle cases and nine subcases, as previously described. Marx's examples, Engels says, are not really suitable as a means of elaboration, because they are based on relative fertility of the different soils of 1:2:3:4, and this results in “monstrous numerical values”.

The other reason these examples are not useful is that, because the relative soil fertility is designated 1:2:3:4, and the rent sequence is 0,1,2,3, it creates the temptation of seeing the second sequence as being directly derived from the first. In that case, it would seem that the doubling or trebling of rents is directly the result of the doubling or tripling of yields.

[“But this would be wholly incorrect. The rents are related as 0 : 1 : 2 : 3 : 4 even when the degrees of fertility are related as n : (n + 1) : (n + 2) : (n + 3) : (n + 4). The rents are not related as the degrees of fertility, but as the differences of fertility — beginning with the rentless soil as the zero point.”] (p 715)

The original tables were presented to coincide with Marx's text, but Engels now presents a series of new tables with output measured in bushels, and prices in shillings. As these same units are used throughout Engels' examples, it makes no substantive difference if output units are considered as lbs. or kilos, and prices as £'s, \$'s, €'s or whatever.

I am using Engels table numbering sequence, here, for simplicity.

Table X1 corresponds to Table I.

 TABLE XI Type ofSoil Price ofProductionShillings OutputBushels SellingPriceShillings ProceedsShillings RentShillings RentIncrease A 60.00 10 6.00 60.00 0 0 B 60.00 12 6.00 72.00 12.00 12 C 60.00 14 6.00 84.00 24.00 2 × 12 D 60.00 16 6.00 96.00 36.00 3 × 12 E 60.00 18 6.00 108.00 48.00 4 × 12 70.00 420.00 120.00 10 × 12
There are five land types A – E. Initial capital invested is 50 with an average rate of profit of 20%, thereby giving a price of production of 60 per hectare. Instead of the yield rising in multiples, as in Marx's examples, they rise arithmetically – 10, 12, 14, 16, 18 per hectare. As the least fertile land produces 10 units of output, per hectare, the regulating price is 80/10 = 6 per unit.

Engels then provides a further 13 tables, which relate to the three cases of Differential Rent II, and the various sub-cases that arise from them, as previously outlined.

Table XII presents the situation where there is a constant price of production and constant marginal productivity of capital with the second investment.

 TABLE XII TypeofSoil Price ofProductionShillings OutputBushels SellingPriceShillings ProceedsShillings RentShillings RentIncrease A 60 + 60 = 120 10 + 10 = 20 6.00 120.00 0 0 B 60 + 60 = 120 12 + 12 = 24 6.00 144.00 24.00 24 C 60 + 60 = 120 14 + 14 = 28 6.00 168.00 48.00 2 × 24 D 60 + 60 = 120 16 + 16 = 32 6.00 192.00 72.00 3 × 24 E 60 + 60 = 120 18 + 18 = 36 6.00 216.00 96.00 4 × 24 140 840.00 240.00 10 × 24

Table XIII presents the situation where marginal productivity falls with the second investment. In that case, the price of production can only remain constant if no additional investment is made in land type A – because, with falling marginal productivity, the average price of its output would rise.

 TABLE XIII TypeofSoil Price ofProductionShillings OutputBushels SellingPriceShillings ProceedsShillings RentShillings RentIncrease A 60 10.00 6.00 60.00 0 0 B 60 + 60 = 120 12.00 + 8.00 = 20.00 6.00 120.00 0 0 C 60 + 60 = 120 14.00 + 9.33= 23.33 6.00 140.00 20.00 20 D 60 + 60 = 120 16.00 + 10.66 = 26.66 6.00 160.00 40.00 2 × 20 E 60 + 60 = 120 18.00 + 12.00 = 30.00 6.00 180.00 60.00 3 × 20 110.00 660.00 120 6 × 20
Table XIII presents the situation where the consequence of this is that land type B now now becomes rentless, whereas Table XIV presents the situation where not all land type B is rentless. This is because, although there is declining marginal productivity of the second investment on land B, its average individual price of production is less than the the price of production for A. It produces 21 units of output, creating revenue of 126, a surplus profit of 6, which forms rent.

 TABLE XIV TypeofSoil Price ofProductionShillings OutputBushels SellingPriceShillings ProceedsShillings RentShillings RentIncrease A 60 10.00 6.00 60.00 0 0 B 60 + 60 = 120 12.00 + 9.00 = 21.00 6.00 126.00 6.00 6 C 60 + 60 = 120 14.00 + 10.50 = 24.50 6.00 147.00 27.00 6 + 21 D 60 + 60 = 120 16.00 + 12.00 = 28.00 6.00 168.00 48.00 6 + (2 × 21) E 60 + 60 = 120 18.00 + 13.50 = 31.50 6.00 189.00 69.00 6 + (3 × 21) 115.00 690.00 150.00 (4 × 6) + (6 × 21)
Table XV presents the situation where the price of production remains constant, but there is rising marginal productivity. This equally excludes additional investment in A, because it would reduce its price of production.

 TABLE XV TypeofSoil Price ofProductionShillings OutputBushels SellingPriceShillings ProceedsShillings RentShillings RentIncrease A 60 10.00 6.00 60.00 0 0 B 60 + 60 = 120 12.00 + 15.00 = 27.00 6.00 162.00 42.00 42 C 60 + 60 = 120 14.00 + 17.50 = 31.50 6.00 189.00 69.00 42 + 27 D 60 + 60 = 120 16.00 + 20.00 = 36.00 6.00 216.00 96.00 42 + (2 × 27) E 60 + 60 = 120 18.00 + 22.50 = 40.50 6.00 243.00 123.00 42 + (3 × 27) 145.00 870.00 330.00 (4 × 42) + (6 × 27)