Rent With Multiple Agricultural Commodities

1.0 Introduction

My next problem might be to explore how to apply an analysis of the orders of efficiency and rentability to a model of rent with multiple agricultural commodities. I would like the possibility of both extensive and intensive rent. This post outlines the structure of a simople numeric example. I have not written down the price systems for each technique. I need to do that to be sure Table 2 is correct.

I should prioritize submitting an article with my most recent model of rent. I should also work through examples in the problems for the approriate chapter in Kurz and Salvadori (1995). As I understand it, nobody has investigated the orders of efficiency and rentability in a model like this. I think Kurz and Salvadori have an existence proof in a special case of joint production, different from the special case I would develop.

Table 1 shows the structure of the technology I am thinking of investigating. Each agricultural commodity can be produced by two processes. The processes differ in which of the two types of land they are operated on, as well as in other coefficients of production.

Table 1: Processes Comprising the Technology

Inputs	Industries
	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	0	c1,4	0
Type 2 Land	0	0	c2,3	0	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
OUPUTS	1 ton iron	1 bushel wheat	1 bushel wheat	1 bushel rye	1 bushel rye

Table 3 lists the techniques of production.

• Alpha, Epsilon, and Zeta have the same solving subsystem. Epsilon and Zeta pay extensive rent on type 2 land.
• Delta, Eta, and Theta have the same solving subsystem. Eta and Theta pay extensive rent on type 1 land.
• Iota pays intensive rent on type 1 land. The solving subsystem has joint production.
• Kappa pays intensive rent on type 1 land. The solving subsystem has joint production.
• Lambda pays intensive rent on type 2 land. The solving subsystem has joint production.
• Mu pays intensive rent on type 2 land. The solving subsystem has joint production.
• Nu pays intensive rent on both types of land. The solving subsystem has joint production.

I do not seem to have a technique that pays both extensive and intensive rent. If type 1 land were fully farmed under Epsilon, would the price system not be overdetermined?

Table 2: Technique

Name	Processes	Type 1 Land	Type 2 Land
Alpha	I, II, IV	Partially Farmed	Fallow
Beta	I, II, V	Partially Farmed	Partially Farmed
Gamma	I, III, IV	Partially Farmed	Partially Farmed
Delta	I, III, V	Fallow	Partially Farmed
Epsilon	I, II, III, IV	Partially Farmed	Fully Farmed
Zeta	I, II, IV, V	Partially Farmed	Fully Farmed
Eta	I, II, III, V	Fully Farmed	Partially Farmed
Theta	I, III, IV, V	Fully Farmed	Partially Farmed
Iota	I, II, III, IV	Fully Farmed	Partially Farmed
Kappa	I, II, IV, V	Fully Farmed	Partially Farmed
Lambda	I, II, III, V	Partially Farmed	Fully Farmed
Mu	I, III, IV, V	Partially Farmed	Fully Farmed
Nu	I, II, III, IV, V	Fully Farmed	Fully Farmed

Anyways, this post presents some thoughts about future research I might explore.