An analysis of rent, where these proportions vary, is also a means of examining the conditions under which the rate of rent may rise, even though prices are not rising, and there is no change in relative fertility when prices are falling.
Marx provides four tables based on those provided previously. To conform with the amendments I made of them, I have amended the figures accordingly. Where he uses Acres, I have changed this to Hectares.
TABLE I
Type of Soil

Hectares

Price of Production
£'s

Product
Kilos

Rent in Grain
Kilos

Rent in Money
£'s

A
B C D 
1.00
1.00 1.00 1.00 
60.00
60.00 60.00 50.00 
1.00
2.00 3.00 4.00 
1.00
2.00 3.00 
0.00
60.00 120.00 180.00 
Total

4.00

230.00

10.00

6.00

360.00

Assuming the area under cultivation doubles in each category.
TABLE Ia
Type of Soil

Hectares

Price of Production
£'s

Product
Kilos

Rent in Grain
Kilos

Rent in Money
£'s

A
B C D 
2.00
2.00 2.00 2.00 
120.00
120.00 120.00 100.00 
2.00
4.00 6.00 8.00 
0.00
2.00 4.00 6.00 
0.00
120.00 240.00 360.00 
Total

8.00

460.00

20.00

12.00

720.00

TABLE Ib
Here the production is expanded on the two poorest soil.
Type of Soil

Hectares

Price of Production
£'s

Product
Kilos

Rent in Grain
Kilos

Rent in Money
£'s


Per Hectare

Total


A
B C D 
4.00
4.00 2.00 2.00 
60.00
60.00 60.00 60.00 
240.00
240.00 120.00 120.00 
4.00
8.00 6.00 8.00 
0.00
4.00 4.00 6.00 
0.00
240.00 240.00 360.00 
Total

12.00

720.00

26.00

14.00

840.00

In the final table production is expanded on each type of land in different proportions.
TABLE Ic
Type of Soil

Hectares

Price of Production
£'s

Product
Kilos

Rent in Grain
Kilos

Rent in Money
£'s


Per Hectare

Total


A
B C D 
1.00
2.00 5.00 4.00 
60.00
60.00 60.00 60.00 
60.00
20.00 300.00 240.00 
1.00
4.00 15.00 16.00 
0.00
2.00 10.00 12.00 
0.00
120.00 600.00 720.00 
Total

12.00

720.00

36.00

24.00

1440.00

The second table, Ia, shows that the area cultivated in each category is doubled. The third, Ib, that it is quadrupled on the two worst lands, and doubled on the two better lands, and the final table shows where it increases by different proportions in each category.
In each example, the rent per hectare remains the same in each category – nil in A, £60 in B, £120 in C, and £180 in D. The amount of rent produced by each category differs in each example, because the amount of land in each category is different.
The second example shows the amount of rent in each category, and therefore, in total, doubling, because the amount of land in each category doubles.
In the third example, the total rent more than doubles, because land type B quadrupled, whilst C and D doubled, but the total area trebled.
In the last example, the total rent quadruples because the largest rises in the land under cultivation occurs in those land types that pay the highest rent per hectare – C and D. But, again the total area trebled.
In Example 2, the rent doubles, whether measured in grain or money. But, because in the other examples, the proportions of each type of land increase by different amounts, the increase in the total product varies compared with the increase in the total area cultivated. So, where the more fertile types of land increase compared to the less fertile, the total product increases by a bigger proportion than the increase in the total area cultivated, and vice versa.
In Example 3, therefore, the total area cultivated trebles, but the total product only increases to 2.6 times, because it is the least fertile areas that increase by the biggest proportion.
In Example 4, however, the total area cultivated trebles, but the product is 3.6 times the original.
The price of grain remains the same in each case. Where the total area cultivated increases by the same proportion, in each category, the total rent increases by that proportion. If the increase in cultivation is proportionately greater in the less fertile soils, the increase in the total rent will be proportionately less than the increase in total cultivation. Where the increase in cultivation is proportionately greater in the better types of soil, rents will increase proportionately more than the total increase in cultivation. Only where all of the increase in cultivation is on the worst soil, paying no rent, will an increase in cultivation, not result in an increase in total rent.
“Thus, given two countries in which soil A, yielding no rent, is of the same quality, the rental is inversely proportional to the aliquot part represented by the worst soil and the inferior soil types in the total area under cultivation, and therefore inversely proportional to the output, assuming equal capital investments on equal total land areas. A relationship between the quantity of the worst and the quantity of the better cultivated land in the total land area of a given country thus has an opposite influence on the total rental than the relationship between the quality of the worst cultivated land and the quality of the better and best has on the rent per acre and — other circumstances remaining the same — on the total rental. Confusion between these two points has given rise to all kinds of erroneous objections raised against differential rent.” (p 6645)
Total rental increases as a result of an extension of cultivation and increase in capital invested on the land. If we take Example 1, the total area cultivated is 4 Hectares, which produces a rent of £360 or £90 per Hectare. In Example 2, where everything is doubled, the rent per Hectare is still £90.
Now, if we assume that in Example 1, £200 of capital must be invested to farm the land, and thereby enable this rent to be paid, we can determine a rate of rent, which is the relation of the rent to the capital that must be advanced to produce it. Here a rent of £360 is produced by a capital of £200, giving a rate of rent of 180%. Because in Example 2, each category of land has doubled, the capital invested also doubles to £400, and so the rate of rent remains constant at 180%.
However, in Example 3, 12 Hectares are cultivated, giving a rent of £840, or £70 an Hectare, reflecting the fact that it is the worst land whose cultivation has risen most. With £600 of capital invested on these 12 Hectares, the rate of rent falls to 140%. Total rental has risen due to the increase in cultivation, but the average rent per Hectare, and rate of rent has fallen, even though the rent per Hectare, for each type of land has remained constant.
Looking at Example 4, the total area cultivated trebles, and so the total capital trebles also to £600. But, the total rent rises to £1,440, an average rent of £120 per Hectare, whilst the rate of rent now rises to 240%.
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