Is The Order Of Efficiency Unique At A Given Rate Of Profits In Models With Multiple Agricultural Commodities?

1.0 Introduction

This post puts forth two research questions that I think I will never get to. And it puts forth one I have started on.

2.0 Is the Order of Efficiency Well-Defined with Mutliple Agricultural Commodities?

I have worked through an example with absolute, extensive, and intensive rent. The orders of efficiency and rentability are uniquely defined in this example. The example has an industrially produced commodity and one commodity, 'corn' produced on land.

Suppose more than one agricultural commodity exists. For example corn and barley can both be produced on land. But assume that no joint production, other than the use of land, exists. Would the order of efficiency still be uniquely defined at a given rate of profits? Would it depend on the composition of corn and barley in net output, as well as the level of net output?

I see even in my example, which techniques are feasible depend on the amount of iron and corn in net output. But would multiple agricultural commodities create more issues for defining the order of efficiency?

3.0 Can Competive Marginal Products Rank Inputs in the Opposite Order of their Productivity?

Frank Hahn argues that marginal productivity, rightly understood, is entirely consistent with Sraffa's model. He concentrated on the case of single production. with a discrete technology, the value of the marginal product of labor, for example, is an interval formed out of the right-hand and left-hand derivatives of production functions.

Hahn considers intertemporal equilibrium paths in which endowments are not given. Rather, they are found as part of the solution for steady state paths. I would rather take them as limit points of non-steady state paths, perhaps with saddle-point stability. But setting these points aside, I cannot see that Hahn is otherwise wrong. Marginal productivity by itself is not a theory of income distribution.

But how does marginal productivity apply to a combination of intensive and extensive rent? In my example, I find a range of the rate of profits in which three types of land are ordered by efficiency in exactly the opposite order as rent per acre. This does not seem consistent with J. B. Clark's idea that, with marginal products, you get rewarded for your contributions (or rather the contributions of the factors you own) to production.

4.0 Which Isues Arising From General Joint Production Arise In Models Combining Extensive Rent and Fixed Capital?

I give an example. In such models, the wage frontier for the cost-minimizing technique is not the outer fronter for wages curves. So I guess, it can be upward-sloping. Can the cost-minimizing technique be non-unique away from switch points? Can I find Bidard's market economy converging to a cycle, with no cost-minimizing technique existing? D'Agata has examples in a model of inetensive rent.