## Differential Rent II. First Case: Constant Price of Production

Marx, in this chapter examines a number of scenarios in which the price of production is constant, and so is determined by the worst land type, A.

Firstly, if additional capital is invested in any of the soil types, A-D, but produces an additional output only equal to what would be produced by A, then the effect is the same as if additional land type A had been brought into cultivation. In that case, because A produces no rent, the total rent does not increase. Nor is there any change in the relative productivity of lands B-D, compared with A, so not additional rent arises, on these lands.

Secondly, if additional capital is invested in lands B-D, but the marginal productivity of capital is constant, the increase in output will be proportional to the particular level of fertility of the soil in which it is invested. So, if the capital invested in land type B is doubled, the output of B doubles, but what effect this has relatively, on total output, depends on the fertility of B compared to A, C and D. What effect it has on output absolutely depends on the fertility of B, i.e. if an hectare of B produces 2 Kilos, with £2.50 of capital, it will produce 4 Kilos with £5 of capital. If total production was 10 Kilos, the additional capital causes output to rise 20%. If the additional capital had been invested in D, which produced 4 Kilos, an additional 4 Kilos would now be produced, which means total output rises by 40%.

The effect of doubling the capital on each land type is shown in the following table.

Table 1.

 Type of soil Hectares Capital £'s Profit £'s Price of Prod. Output Kilos Selling Price £ Proceeds £'s Rent Surplus Profit £'s Kilos £'s A 1.00 2.50 + 2.50 = 5 1.00 6.00 2.00 3.00 6.00 0.00 0.00 0 B 1.00 2.50 + 2.50 = 5 1.00 6.00 4.00 3.00 2.00 2.00 6.00 120% C 1.00 2.50 + 2.50 = 5 1.00 6.00 6.00 3.00 18.00 4.00 12.00 240% D 1.00 2.50 + 2.50 = 5 1.00 6.00 8.00 3.00 24.00 6.00 18.00 360% Total 4.00 20.00 4.00 24.00 20.00 60.00 12.00 36.00

Compared with the original position.

Table 2.

 Type of soil Hectares Capital £'s Profit £'s Price of Prod. £'s Output Kilos Selling Price £'s Proceeds £'s Rent Rate of Surplus Profit Kilos £'s A 1.00 2.50 0.50 3.00 1.00 3.00 3.00 0.00 0 0 B 1.00 2.50 0.50 3.00 2.00 3.00 6.00 1.00 3.00 120% C 1.00 2.50 0.50 3.00 3.00 3.00 9.00 2.00 6.00 240% D 1.00 2.50 0.50 3.00 4.00 3.00 12.00 3.00 9.00 360% Total 4.00 10.00 2.00 12.00 10.00 30.00 6.00 18.00

The rent is doubled on each type of land, where the capital is invested. The increase is due solely to the proportional increase in output. The effect here is the same as arose when the area of land under cultivation of each type was doubled.

The difference then was that although the total rent, and the rent on each type of land doubled, the rent per hectare remained constant. Here, because no more land is cultivated, but the capital per hectare is doubled, the rent per hectare doubles, but the rate of rent remains constant.

Although the proportional difference remains constant, there would be absolute differences, if additional capital were only invested in particular land types.

Table 3.

 Type of soil Hectares Capital £'s Profit £'s Price of Prod. £'s Output Kilos Selling Price £'s Proceeds £'s Rent Rate of Surplus profit Kilos £'s A 1.00 2.50 0.50 3.00 1.00 3.00 3.00 0.00 0.00 0 B 1.00 2.50 +2.50 1.00 6.00 4.00 3.00 12.00 3.00 9.00 180% C 1.00 2.50 0.50 3.00 3.00 3.00 9.00 2.00 6.00 240% D 1.00 2.50 +2.50 1.00 6.00 8.00 3.00 24.00 7.00 21.00 420% Total 4.00 15.00 3.00 12.00 18.00 48.00 12.00 36.00

This means that D now produces 8 Kilos, whilst A still produces 1, so the difference is now 7 Kilos, compared to just 3 previously. Land B now produces 4 Kilos rather than 2, so the difference with A is 3 Kilos rather than 1. In other words, these absolute differences now more than double. Land type C still produces produces 3 Kilos, which means it now produces 1 Kilo less than B, whereas before it produced 1 Kilo more.

“But this arithmetic difference, which is decisive in differential rent I in so far as it expresses the difference in productivity with equal outlays of capital, is here quite immaterial, because it is merely a consequence of different additional investments of capital, or of no additional investment, while the difference for each equal portion of capital upon the various plots of land remains unchanged.” (p 687)

Thirdly, Marx assumes that an investment in land type B-D is doubled, but with falling marginal productivity of capital, of different rates, for each land type.

Table 4.

 Soil Hectares Capital £'s Profit £'s Price of Prod. £'s Output Kilos Selling Price £'s Proceeds £'s Rent Rate of Surplus profit Kilos £'s A 1.00 2.50 0.50 3.00 1.00 3.00 3.00 0.00 0.00 0 B 1.00 2.50 + 2.50 = 5.00 1.00 6.00 2.00 + 1.50= 3.50 3.00 10.50 1.50 4.50 90% C 1.00 2.50 + 2.50 = 5.00 1.00 6.00 3.00+ 2.00 =5.00 3.00 15.00 3.00 9.00 180% D 1.00 2.50 + 2.50 = 5.00 1.00 6.00 4.00 + 3.50 = 7.50 3.00 22.50 5.50 16.50 330% 4.00 17.50 3.50 21.00 17.00 51.00 10.00 30.00

Table 4 indicates an equal investment in B-D, but as with the previous example, it does not matter if this is the case, or whether additional investment is made on only some of B-D. Nor does it matter whether marginal productivity falls unevenly, as in this example, or by some proportion in each case.

This remains the case other than as previously specified, where any additional investments on any type of land, must result in an additional output greater than 1 Kilo, i.e. greater than the output of land type A. This example corresponds to the situation considered with Differential Rent I, where additional lands were brought into cultivation whose fertility ranged between that provided by A and D. An additional investment in land type D, that produces only an additional 3 Kilos rather than 4 would have the same effect as if an additional hectare of land type C were cultivated. The additional 3.5 Kilos, seen produced here, is the same as if an hectare of some new land type C' were brought into cultivation.

It will then depend on which lands the additional investments are made what effect this will have. For example, with falling marginal productivity, an additional £2.50 of capital, invested in land type D, may produce an additional 3.5 Kilos, but invested in land type C could only produce something less than 3, and B something less than 2. A further investment in D would then produce something less than 3.5 Kilos and so on.

“But this is the law: The rent increases absolutely upon all these soils, even if not in proportion to the additional capital invested.” (p 688)