Intensive Rent And The Order Of Rentability

I have thought about what would be the minimal structure of an example that combines extensive and intensive rent. I want to include a commodity produced without land, as well as an agricultural commodity.

This post considers a simpler example. An analysis of extensive rent includes the identification of the order of efficiency and the order of rentability, given the wage or the rate of profits. I take the concept of these orders from Alberto Quadrio Curzio. Can these orders be defined in a model of intensive rent? What would the minimum structure of an example be in which to explore this question? I continue to insist on including an industrial commodity with negligible inputs of land.

I suggest Table 1 provides the technology for such an example. Each column specifies the quantities of labor, iron, wheat, and rye needed to produce a unit output of the commodity produced by the corresponding industry. The table also specifies the quantity of land that must be rented to operate that process. Constant returns to scale are assumed, with the limitation that the endowments of each type of land are givens.

Table 1: The Coefficients of Production

Input	Industry
	Iron	Wheat		Rye
	I	II	III	IV	V
Labor	a0,1	a0,2	a0,3	a0,4	a0,5
Type 1 Land	0	c1,2	c1,3	0	0
Type 2 Land	0	0	0	c2,4	c2,5
Iron	a1,1	a1,2	a1,3	a1,4	a1,5
Wheat	a2,1	a2,2	a2,3	a2,4	a2,5
Rye	a3,1	a3,2	a3,3	a3,4	a3,5

I show each type of land as specialized to produce a different kind of agricultural commodity. I am unsure if that specialization is needed for my point. If not, the table defining the techniques below would contain four more techniques. In each, only one of the processes producing the agricultural commodity would be operated.

As noted, the givens include the amount of each type of land available. Let t₁ be the acres of type 1 land available and t₂ be the acres of type 2 land available

The vector d representing the numeraire has components:

• d₁: The quantity of iron in the numeraire.
• d₂: The quantity of wheat in the numeraire.
• d₃: The quantity of rye in the numeraire.

Let net output y consist of a multiple of the numeraire:

y = c d

Net output is among the givens.

Table 2 specifies the techniques. Non-zero coefficients of production in Table 1 should be such that all three commodities are Sraffa basics in all techniques. Not all techniques are feasible for any level of net output.

Table 2: Is Process Operated By Technique?

Input	Industry
	I	II	III	IV	V
Alpha	Yes	Yes	No	Yes	No
Beta	Yes	Yes	No	No	Yes
Gamma	Yes	No	Yes	Yes	No
Delta	Yes	No	Yes	No	Yes
Epsilon	Yes	Yes	No	Yes	Yes
Zeta	Yes	No	Yes	Yes	Yes
Eta	Yes	Yes	Yes	Yes	No
Theta	Yes	Yes	Yes	No	Yes
Iota	Yes	Yes	Yes	Yes	Yes

One can examine which processes are introduced in the cost-minimizing technques as the level of net output expands. That is, is process II adopted before process III or vice versa? Is process IV or process V operated first? Presumably, the answer to these questions depends on the wage or the rate of profits, whichever variable is taken as given in solving the system of equations for prices of production. This model is a model of intensive rent in that, for example, Epsilon or Zeta is cost minimizing, Type 2 land will be fully farmed and obtain a rent. The scarcity of land is shown by having two processes operating side-by-side on a single type of land. Anyways, the analysis outlined here corresponds to determining the order of efficiency in a model of extensive rent.

Suppose the Iota technique is feasible and cost-minimizing. The solution of the equations for prices of production yields the rent per acre for each type of land. Which type of land obtains the larger rent per acre? Does this order vary with the given wage or rate of profits? Is reswitching of this order possible? Does postulating a stable ratio of the rate of profits among industries change the answers, at least in detail? I suggest that this analysis corresponds to determining the order of rentability in a model of extensive rent.

I assume that the order of rentability varies with distribution and that reswitching of this order is indeed possible. As far as I know, nobody has answered these questions or presented a numerical example. I always think that nothing I say would surprise Betram Schefold, Heinz Kurz, or Neri Salvadori, for example. What I try to do is present concrete examples of their more abstract analyses. My identification of fluke cases, of extending the analysis to markup pricing, and presentation of graphs to aid visualization of the results are my own tweaks, I guess.