Intensive Rent, Extensive Rent, And Absolute Rent

1.0 Introduction

I have decided that this previous post is inadequate. If intensive rent exists on some type of land, the system of equations for prices of production cannot include a process that only partially cultivates some other type of land producing the agricultural commodity.

So to form an example with both intensive and extensive rent, I need the technology to specify the possibility of cultivating at least three types of land. I might as well include markup pricing so as to maybe create an example with intensive, extensive, and absolute rent all existing. If this example works out, it would provide a refutation, in some sense, of this paper.

2.0 Technology, Endowments, Requirements for Use, and Relative Markups

Table 1 presents coefficients of production defining technology. Three types of land exist, and four processes are known for producing corn on land. Each corn-producing process is operated on one type of land. A negligible amount of land is used in producing iron, the industrial commodity.

Table 1: The Coefficients of Production

Input	Industry
	Iron	Corn
	I	II	III	IV	V
Labor	a0,1	a0,2	a0,3	a0,4	a0,5
Type I Land	0	c1,2	0	0	0
Type II Land	0	0	c2,3	0	0
Type II Land	0	0	0	c3,4	c3,5
Iron	a1,1	a1,2	a1,3	a1,4	a1,5
Corn	a2,1	a2,2	a2,3	a2,4	a2,5

The givens include the amount of each type of land available. Let t₁ be the acres of type 1 land available, t₂ acres of type 2 land, and t₃ acres of type 3 land.

Following Sraffa, I take requirements for use as parameters. In my understanding, requirements for use specify the net product. Let d₁ be the tons iron and d₂ the bushels corn required for net output.

Finally, I want to allow for industry or agriculture to have some sort of market power. So let s₁ r be the rate of profits obtained in operating the first (industrial) process. Let s₂ r be the rate of profits obtained in operating any of the agricultural processes. (I am actually going to solve this model, if I do, with parameters for the markups of each type of land.)

The above has set out the givens for what I think is a minimal model with heterogenous capital goods and the possibility of intensive, extensive, and absolute rent arising.

3.0 Techniques

I can define various techniques (Table 2) with this technology. This is an example of the Sraffian combinatorial explosion. (Omega is the only greek letter not listed.) Not all techniques are feasible, given technology, endowments, and requirements for use. Which technique(s) are cost-minimizing varies with, say, the wage. The cost-minimizing technique need not be unique, even away from switch points. Land is not scarce for the Alpha, Beta, Gamma, and Delta techniques, and ownership of land pays no rent. The Epsilon through Upsilon techniques are examples of extensive rent. Phi is an example of intensive rent. Chi and Psi are examples of the combination of intensive and extensive rent.

Table 2: Techniques of Production

Technique	Processes	Land
		Type 1	Type 2	Type 3
Alpha	I, II	Partially farmed	Fallow	Fallow
Beta	I, III	Fallow	Partially farmed	Fallow
Gamma	I, IV	Fallow	Fallow	Partially farmed
Delta	I, IV	Fallow	Fallow	Partially farmed
Epsilon	I, II, III	Partially farmed	Fully Farmed	Fallow
Zeta	I, II, IV	Partially farmed	Fallow	Fully Farmed
Eta	I, II, V	Partially farmed	Fallow	Fully Farmed
Theta	I, II, III	Fully Farmed	Partially farmed	Fallow
Iota	I, III, IV	Fallow	Partially farmed	Fully Farmed
Kappa	I, III, IV	Fallow	Partially farmed	Fully Farmed
Lambda	I, II, IV	Fully Farmed	Fallow	Partially farmed
Mu	I, III, IV	Fallow	Fully Farmed	Partially farmed
Nu	I, II, V	Fully Farmed	Fallow	Partially farmed
Xi	I, III, IV	Fallow	Fully Farmed	Partially farmed
Omnicron	I, II, III, IV	Partially farmed	Fully Farmed	Fully Farmed
Pi	I, II, III, V	Partially farmed	Fully Farmed	Fully Farmed
Rho	I, II, III, IV	Fully Farmed	Partially farmed	Fully Farmed
Sigma	I, II, III, V	Fully Farmed	Partially farmed	Fully Farmed
Tau	I, II, III, IV	Fully Farmed	Fully Farmed	Partially farmed
Upsilon	I, II, III, V	Fully Farmed	Fully Farmed	Partially farmed
Phi	I, IV, V	Fallow	Fallow	Fully Farmed
Chi	I, III, IV, V	Fallow	Fully Farmed	Fully Farmed
Psi	I, II, IV, V	Fully Farmed	Fallow	Fully Farmed

4.0 To Do

The above sets out a model to solve. Thw first step is to find levels of operation needed to satisfy requirements for use, given the technique. One should then identify which techniques are feasible. An infeasible technique is one in which some processes must be operated at a negative level or in which more of a type of land must be cultivated than exists. Then one can, given the wage w or the scale factor r for the rate of profits, find prices of production, including rent, for each feasible technique. Finally, one can determine the cost-minimizing technique(s) at each wage.

I do not necessarily expect to find examples in which more than one cost-minimizing technique exists at a given wage. Nor do I expect to find a case with the non-existence of a cost-minimizing technique. Even if one cannot find such examples, one should discuss their possibility in any write up of this model. One should discuss the orders of efficiency and rentability. The Chi and Psi techniques are examples in which no cultivated land pays no rent. When either is cost-minimizing, it is not a fluke case. I have some interesting graphs, I think, that can show how the dependence of the cost-minimizing technique on the wage varies with the ratio of markups in industry and agriculture. The point is to identify the variation in rent with that ratio as variation in Marx's absolute rent.

This post is an example of my attempt to find something interesting hitherto not clearly explained between models of circulating capital and fully general models of joint production.