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| Figure 1: A Part of a Parameter Space |
This post revisits my numerical examples in which I demonstrate the possibility of the reswitching of the order of fertility and of the reswitching of the order of rentability. Each of those posts presents a numeric example. In each, different ranges of the coefficients of production a0,2 and a1,2 are considered. This post combines those ranges, while still not considering the full parameter space, even for the slice for these coefficients.
In the example, reproduction of a capitalist economy requires the production of two commodities, iron and corn. Managers of firms know one process for producing iron and three processes for corn. Each corn-producing processes operates on a different quality of land. The given endowments of land and the requirements for use are such that all three types of land must be farmed. In each of three techniques of production, Alpha, Beta, and Gamma, the decisions of managers of firms result in two types of land being completely farmed. The third type of land is only partially farmed. Being in excess supply, it pays no rent (the rule of free goods). Which type of land pays no rent varies among the three techniques.
I consider the analysis of the choice of technique in this example. Following Sraffa, I assume wages and rents are paid out of the surplus product after the harvest. In this analysis of prices, extra profits cannot be obtained at prices of production by operating any available process. The difference between the revenues and wages and charges on capital goods for processes that produce agricultural goods are compensated for the rents obtained by landlords.
Figure 1, at the top of the post, illustrates, a part of a slice of the parameter space. Reswitching of the order of rentability occurs in region 3. Reswitching of the order of fertility occurs in region 7. Table 2 summarizes the result of the analysis of the choice of technique in each section. For this range of paramters, the Alpha technique, in which type 3 land pays no rent, is always cost-minimizing. The maximum rate of profits is the maximum rate of profits for the Alpha technique. The range of the rate of profits is partitioned into intervals where either the order of fertility or the order of rentability do not vary. And these orders are also listed.
| Region | Range of Rate of Profits | Order of Fertility | Order of Rentability |
| 1 | 0 ≤ r ≤ r1 | Type 2, 1, 3 | Type 1, 2, 3 |
| r1 ≤ r ≤ rα,max | Type 2, 1, 3 | ||
| 2 | 0 ≤ r ≤ rα,max | Type 2, 1, 3 | Type 2, 1, 3 |
| 3 | 0 ≤ r ≤ r1 | Type 2, 1, 3 | Type 2, 1, 3 |
| r1 ≤ r ≤ r2 | Type 1, 2, 3 | ||
| r2 ≤ r ≤ rα,max | Type 2, 1, 3 | ||
| 4 | 0 ≤ r ≤ rα,max | Type 2, 1, 3 | Type 1, 2, 3 |
| 5 | 0 ≤ r ≤ r1 | Type 2, 1, 3 | Type 2, 1, 3 |
| r1 ≤ r ≤ rα,max | Type 1, 2, 3 | ||
| 6 | 0 ≤ r ≤ r1 | Type 1, 2, 3 | Type 1, 2, 3 |
| r1 ≤ r ≤ rα,max | Type 2, 1, 3 | ||
| 7 | 0 ≤ r ≤ r1 | Type 2, 1, 3 | Type 1, 2, 3 |
| r1 ≤ r ≤ r2 | Type 1, 2, 3 | ||
| r2 ≤ r ≤ rα,max | Type 2, 1, 3 | ||
| 8 | 0 ≤ r ≤ rα,max | Type 1, 2, 3 | Type 1, 2, 3 |
| 9 | 0 ≤ r ≤ r1 | Type 2, 1, 3 | Type 1, 2, 3 |
| r1 ≤ r ≤ rα,max | Type 1, 2, 3 |
Technical progress can be seen as a reduction in coefficients of production. For this example and the chosen coefficients of production, technical progress is a movement from the northeast to the southwest in the figure at the top of the post. Initially, the order of rentability is the same as the order of fertility, and neither order varies with the rate of profits (region 2). At some point, the order of rentability has reversed, for lands that pay a rent (region 4). Even later, the order of fertility has reversed, so the orders of fertility and rentability once again match, whatever the rate of profits (region 8). The reswitching of these orders appear at intermediate regions of time between each reversal.
This example is another example showing why biotechnological determinism is unfounded. One can see that one type of land is simultaneously more and less fertile than another type, depending on the rate of profits or the wage. And this ranking can be reversed and then switched back with, say, an increase in the rate of profits. Furthermore, owning the more fertile type of land need not allow its owner to obtain a larger rent per acre than a less fertile type of land that pays a rent. And whether or not these orders match also varies, possibly non-monotonically, with the distribution between wages and profits.
It is meaningless to claim that economic agents earn the worth of the contributions (of the goods that they own) to production.
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2 comments:
«One can see that one type of land is simultaneously more and less fertile than another type, depending on the rate of profits or the wage.»
Fertile in what sense? In my understanding the "fertility" of a parcel of land is the ratio of seeds of corn that it produces at harvest given the number of seeds of corn used to sow it. Does that depend on the rate of profits or the wage?
In farming or mining reality the number of harvested seeds also depends on other inputs than the parcel of land, such as inputs of fertilizer, capital (e.g. deep ploughs) and labour, and random factors like weather, but I would not then say that the varying quantities of the other inputs change the fertility of that parcel of land itself.
But then what is the "intrinsic" fertility of the land becomes a difficult cost accounting investigation, as usual :-).
« This example is another example showing why biotechnological determinism is unfounded [...] It is meaningless to claim that economic agents earn the worth of the contributions (of the goods that they own) to production»
My way of saying this is that the optimization landscape has several different lowest "energy" points, each in general yielding both a different distribution of income and different ratios between contributions and incomes.
The only reason why (some) neoclassical models have a single lowest "energy" point (unique "concavity") is that any premises that don't yield that result have been intentionally expunged, even at the cost of consistency.
My reading of Sraffa is that he wanted ("prelude to a critique") to show that even in a very simplified but consistent class of (input-output) models there can be multiple lowest "energy" points. That to me seems unsurprising if not obvious, but it is interesting that he demonstrated it so simply (and that he derived a "standard commodity" in that class of simplified models).
The order of fertility is the order in which types of land are introduced into cultivation as requirements for use expand. The most fertile land is the first cultivated. If the rate of profits is given, the order of fertility is downward from the highest wage curve.
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