Variation Of Cost-Minimizing Technique With Increased Net Output And Extensive And Intensive Rent

Figure 1: Cost-Minimizing Techniques

1.0 Introduction

This post is an extension of one of my examples with extensive and intensive rent. I do not expect this to make sense unless you have read that post. I struggle to easily visualize details of that example.

David Ricardo distinguishes between extensive and intensive rent. He seems to put more emphasis on extensive rent. Even so, he considers the combination of extensive and intensive rent:

"It often, and, indeed, commonly happens, that before No. 2, 3, 4, or 5, or the inferior lands are cultivated, capital can be employed more productively on those lands which are already in cultivation. It may perhaps be found, that by doubling the original capital employed on No. 1, though the produce will not be doubled, will not be increased by 100 quarters, it may be increased by eighty-five quarters, and that this quantity exceeds what could be obtained by employing the same capital, on land No. 3." - David Ricardo, Principles

Ricardo does not recognize that the order of efficiency, also known as the order of fertility, differs from the order of rentability. Nor does he recognize that these orders depend on the distribution between workers and capitalists. Nevertheless, analysis of rent by Ricardo and his contemporaries is the starting point for many interesting analyses.

2.0 Some Repetition

Assume that net output in the example consists of a numerically identical number of tons iron and bushels corn. After different levels of net output, a different set of techniques are feasible. Table 2 here defines the techniques, and Table 3 specifies which techniques are feasible as net output expands.

I think I want to repeat at least the wage curves for the example. Accordingly, Figure 2 plots the wage curves for the cost-minimizing techniques, when net output is almost as large as it can be. Figure 3 is an enlargement. The figures also show the wage curve for Delta.

Figure 2: Wage Curves for Feasible Techniques

Figure 3: Wage Curves for Feasible Techniques (Detail)

3.0 Cost-Minimizing Techniques

Figure 1, at the top of the post, depicts which techniques are cost-minimizing at which rate of profits, as net output expands. The dashed lines are points at which the order of efficiency changes, while the cost-minimizing technique does not change. They are intersections of wage curves above the wage curves for the cost-minimizing technique. The dotted lines are points at which the order of rentability changes. They are intersections of rent curves for the cost minimizing technique. Figure 4 is an enlargement.

Figure 4: Cost-Minimizing Techniques (Detail)

3.1 Extensive Rent Alone

The range of the rate of profits for which Tau is cost-minimizing, when net output is near its maximum, illustrates the analysis of extensive rent. The order of efficiency can be calculated by working downwards from the wage curves in this range. Type 3 land is partially farmed under Tau, using the same process on type 3 land as in the Gamma process. The wage curves for Alpha and Beta intersect at approximately 48 percent. This switch point corresponds to a change in the order of efficiency. When Alpha is cost-minimizing, at the lowest output region for net output, the order of efficiency for Tau is Type 1, 2, and 3 lands. When Beta is cost-minimizing, the order of efficiency is type 2, 1, and 3 lands.

The order of rentability does not vary in the range in which Tau is cost-minimizing. The rent curves for Tau do not intersect. Consequenty the orders of efficiency and rentability differ in part of the range for which Tau is cost-minimizing. Type 1 land can obtain greater rent per acre, even though type 2 land is more fertile at the given range of the rate of profits. These results echo the analysis of extensive rent in Alberto Quadrio Curzio (1980).

When net output is small enough such that Alpha and Beta are feasible, the switch point at which the order of efficiency changes for Tau exhibits capital-reversing. A higher wage is associated with firms hiring more workers, given net output. But this intersection of the Alpha and Beta wage curves is not associated with any real Wicksell effects for Tau. Quantity flows do not vary around the switch point when Tau is cost-minimizing. Both above and below the switch point, Type 1 and 2 lands are fully farmed, with the same processes be operated on each land.

Consider regions of net output for which Epsilon and Theta are feasible. Theta requires a greater input of labor for a given net output. So here too, this switch point exhibits capital-reversing, while arising in an example with extensive rent.

3.2 Extensive and Intensive Rent

The range of the rate of profits for which Omicron or Omega are cost-minimizing illustrates effects of a combination of extensive and intensive rent. Process V is operated on type 3 land for the Phi, Kappa, Chi, Pi, Xi, and Upsilon techniques. On the other hand, process IV is operated on type 3 lands for Type 3 land for the Iota and Omicron techniques. Even though process V is not operated, when net output is towards its maximum, in the range of the rate of profits where Omicron is cost-minimizing, process V contributes towards determining the order of efficiency. The switch point between Beta and Gamma has no effect on the order of efficiency. A combination of intensive and extensive rent is needed to see the possibility of non-operated processes impacting the order of efficiency.

When the Omega technique is cost-minimizing, both processes are operated on Type 3 land. Nevertheless, the switch point between Alpha and Gamma has no effect on the order of efficiency in this range.

The order of efficiency happens to match the order of rentability when Omicron is cost-minimizing. The rent curves for Omega intersect three times in the range of the rate of profits is cost-minimizing. And the order of efficiency also changes. Sometimes these orders diverge when Omega is cost-minimizing. In examples with both intensive and extensive rents, lands that are less fertile at a given rate of profits can obtain greater rents per acre.

Marginalism is a generalization of Ricardo's theory of extensive rent and its application to all factors of production. Perhaps this mismatch of the orders of efficiency and rentability is another indication of how the generalization is unwarranted.

4.0 Conclusion

Alberto Quadrio Curzio put a lot of work into investigating the theory of rent in Sraffa's approach to political economy. This post can be said to be a clarification of this comment:

"Even when the intensive rent disappears, the effects of intensive cultivation persist in the different productive processes applied to the different lands, which affect the extensive differential rents." - Alberto Quadrio Curzio & Fausta Pellizzari (2010: 46)

The process on type 3 land that goes into the system of equations for Omicron differs from the process on type 3 land used in calculating the order of efficiency. This contrast reflects the phenomenon of intensive rent, even though no intensive rent is obtained when Omicron is cost-minimizing.

The example emphasizes the need to consider technical change. Net output cannot be increased after a hard limit, imposed by land-like natural resources. Increased production is only possible with the introduction of new processes and techniques or decreases in some coeficients of production for existing processes.

The most surprising finding, for me, is that types of lands cannot generally be ordered by efficiency (also known as fertility), from most fertile to least, by observing the processes operated on the lands at a given rate of profits. This result is in tension with Sraffa's methodology. Sraffa had an aversion to counterfactuals (Sen 2003). He wanted to not not use data - for example, on processes available in the technology but not currently operated - that cannot be obtained by the 'man from the moon' (Kurz & Salvadori 2004) or in a snapshot of an ongoing economy (Roncaglia 1975).