Extensive And Intensive Rent

This post begins the presentation of an example in which extensive and intensive rent can both arise. I do not consider external intensive rent or joint production in general. Kurz and Salvadori (1995), in section 2.2 of Chapter 10, have a more general model that includes external extensive rent and joint production. It does not allow for more than one agricultural commodity, although they treat that in problems, with examples from the literature.

Perhaps developing this example will help me find a insightful way of presenting some of the fluke cases I have found in the theory of rent.

Table 1 presents coefficients of production for the simplest example I can think of in which more than one commodity is produced, intensive and extensive rent are possible, and general joint production does not arise. Here, multiple types of land (that is, two types) exist. Only one agricultural commodity, corn, can be produced on the processes in which land is used. For one type of land, more than one process can be operated on land. Only one process is known for producing each (that is, one) industrial commodity.

Table 1: The Coefficients of Production

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

Table 2 lists the available techniques of production available. Not all may be feasible. Which are feasible depends on requirements for use (that is, required net output) and how much of each type of land is available. Rent is zero for the Alpha, Beta, and Gamma techniques, since neither type of land is fully used. That is, land is not scarce. Techniques Delta, Epsilon, Zeta, and Eta are examples of extensive rent since only one process is operated on each type of land. The Theta technique resembles an example of intensive rent. Finally, if the Iota technique is adopted, one will observe both extensive and intensive rent.

Table 2: Techniques of Production

Technique	Processes	Type 1 Land	Type 2 Land
Alpha	I, II	Partially farmed	Fallow
Beta	I, III	Fallow	Partially farmed
Gamma	I, IV	Fallow	Partially farmed
Delta	I, II, III	Fully farmed	Partially farmed
Epsilon	I, II, III	Partially farmed	Fully farmed
Zeta	I, II, IV	Fully farmed	Partially farmed
Eta	I, II, IV	Partially farmed	Fully farmed
Theta	I, III, IV	Fallow	Fully farmed
Iota	I, II, III, IV	Partially farmed	Fully farmed

Here are some questions I expect to answer:

• How should the input-output matrices a₀, A, B, and C be characterized in general for a case of extensive and intensive rent without full joint production?
• How are prices of production defined for this example, following Kurz and Salvadori's direct method?
• Can one extend the concepts of the order of fertility and the order of efficiency from extensive rent proper to this combination of extensive and intensive rent?
• Can one find numerical examples of 'perverse' behavior with these orders, as in models of extensive rent? Maybe I would want to postulate the availability of a third type of land.
• Can one find numerical examples of non-existence and nonuniqueness of cost-minimizing techniques, as in models of intensive rent?
• Can one find numerical examples of fluke cases?