Why Do Mainstream Economists Not Make More Out Of The CCC?

Marx is mostly right.

That is the conclusion one should draw from capital theory. But honestly understanding how we are fed, clothed, and housed under capitalism is not what academic economics is about.

Ownership of property in, say, the United States results in the generation of income. This income takes the form of interest on debt, dividends, capital gains, rent, and so on. Many of those who are among the most wealthy often have returns to property ownership as their only source of income.

Overall, laborers work within a given environment to recreate the capital goods used up in production and to produce more. The source of the returns to property ownership comes from paying workers less than what they produce, over and above the constantly reproduced capital. The owners of capital direct and control the workers and the environment in which they work, in hierarchical structures, so as to attempt to ensure the surplus is as large as possible.

Marx provides a vocabulary to talk about the above qualitative outline, to understand the formal and real subsumption of labor.

Marx provides many details to investigate and modify. I do not think the law of the tendency of the rate of profits to fall (TRPF) can be deduced from the remainder of his system. But just like a simple labor theory of value, it seems to work surprisingly well empirically. When one tries to make sense about the stagflation of the 1970s and the transition from the post war golden age to the neoliberal era, trends in the rate of profits seem quite important.

How important is the question of labor values versus prices of production in any quantitative analysis built on this basis? One can say a lot while confining one's attention to employment multipliers and prices of production. The non-applicability and incoherence of the theory of supply and demand is a major point of the Cambridge Capital Controversy. Supply and demand functions no longer should appear in any long run theory, in any investigation of persistent trends in capitalist economies.

And, of course, Leontief figured out how to organize data for empirical and quantitative investigations along these lines. One can construct Leontief input output tables from the make and use tables that are kept for the national income and product accounts (NIPAs). I would also like price indices for each industry at the level of the available NIPAs. There are many details and conventions that one should understand in working with such data, which I think I get muddled over when I've gone into details.

And much room exists for qualitative and historical work. One could draw on institutional economics in examining capital as power.

You can start to see scholars developing economics in this direction in the 1970s and early 1980s. I think of Donald Harris' Capital Accumulation and Income Distribution, Stephen Marglin's Growth, Distribution and Prices, Michio Morishima's Marx's Economics: A Dual Theory of Value and Growth, Luigi Pasinetti's Lectures on the Theory of Production, John Roemer's Analytical Foundations of Marxian Economic Theory, or Peter Skott's Conflict and Effective Demand in Economic Growth.

But most of the economists at the supposed best schools were uninterested or too craven to accept work along these lines as valid research programs. So much of academic economics is special pleading in bad faith for their paymasters among the plutocracy, as comes out in the news every once in a while. (Disclaimer: I own stock in Amazon and Apple.)

Marx's Theory Of Value Is Consistent With And More General Than Marginalist Economics

1.0 Introduction

One inspiration for this post is stumbling across this abstract

2.0 Marx

Start with labor coefficients and a Leontief input/output matrix, in physical terms. You can construct this from make and use tables for your country, given price indices by sectors.

For any existing capitalist economy, I expect that matrix to characterize a more than viable economy. After all the capital goods used up in producing the final demand in, say, a year are reproduced, some commodities will remain for consuming and investing.

As with any other matrix, a set of n Eigenvalues and corresponding Eigenvectors can be found for that matrix. And, if I recall correctly, the maximum Eigenvalue has an associated Eigenvector in which all elements are non-negative. The components for Sraffa's basic commodities are all strictly positive. And they are in the proportions of Sraffa's standard commodity. If wages are zero (the worker's live on air) and the final demand is all invested, the final demand will be in proprortions of Sraffa's standard economy and the economy will expand at a rate of growth related to this eigenvalue. One can read von Neumann (1945) as describing this model of uniform growth.

So given the technique in use in a capitalist economy, a composite commodity of average capital composition is picked out. Georg von Charasoff called this composite commodity 'Urkapital' which, I guess, is translated as "original capital". In some sense, this urkapital is a commodity of average organic composition of capital. This numeraire is picked out by the technique in use. In the production of this numeraire:

• The rate of profits, as calculated in the system of embodied labor values, is identically equal to the rate of profits, as calculated in the system of prices of production.
• Gross output, as evaluated at embodied labor values, is equal to gross outputs, as evaluated at prices of production.
• Net output, as evaluated at embodied labor values, is equal to net output, as evaluated at prices of production.
• The division of net output between workers and capitalist makes no difference to the above invariants.

So Volumes 1 and 3 of Marx's Capital are consistent.

3.0 Marginalist Economics

If one is ill-informed and malicious these days, one could insist that Sraffa's model is a special case of a neoclassical model of intertemporal equilibrium. Consumers maximize utility, and managers of firms maximize profits. Initial endowments just happen to be so that the economy expands along a steady state growth path.

4.0 Conclusions

But, of course, utility-maximization is nonsense, especially inter-temporally. Furthermore, the von Neumann ray has saddle-point instability. As Joan Robinson showed with her models of metallic ages, one need not assume that the workforce is fully employed in the long-run.

The model that has no need of restrictive assumptions is the more general.

Where Can I Read Correspondence Between Robinson And Sraffa?

I have been looking at Sraffa's archives. Scott Carter was responsible for putting them online, as I understand it. Anyways, I know some contents has been published. What should I read for transcripts of letters between Robinson and Sraffa? Maybe something by Marcuzzo?

Anyways, here is a 18 June 1960 letter from Robinson to Sraffa (D3/12/111: 340-341)

All the work that I have been doing the last 10 years has been very much influenced by you – both our conservations in old days and by your Preface. When I went off my head I thought that the idea I had seen in a blinding flash was yours, because it came to me in terms of Ricardo’s corn economy, but it was connected with TIME and it so appears is very much akin to your point of view (though one it seems to fit perfectly well.) Since, quite apart from your worldly success, I have a lot of fun. I have a very deep feeling of gratitude to you. The fact that you reject it doesn’t affect the case at all.

A Fixed Capital System That Is Or Is Not Interlocked

I have defined patterns of switch points in considering perturbations of examples of the choice of technique. For example, I have defined three-technique and four-technique patterns. An obvious extension is to consider how these patterns arise in models of joint production. A simplification is to only consider models of fixed capital without superimposed joint production.

This post lays out an example in which, maybe, some parameter values can lead to a three-technique pattern. I am trying to consider whether I want to allow it to be an interlocked system. The question arises when I lay out a simple example in which a machine can be used for one or two years.

Accordingly, consider an example with the coefficients of production in Table 1. Corn and new machines are finished goods. An old machine is an intermediate good. Intermediate goods cannot be sold for consumption. Processes I and II constitute the machine-producing or machine sector. Processes III and IV are in the corn sector. In each sector, there is one and only one primary process, in which the only inputs are finished goods. Processes I and III are the primary processes in the two sectors. Processes II and IV are secondary processes.

Table 1: Coefficients of Production for The Technology

Input	Process
	(I)	(II)	(III)	(IV)
Labor	a0,1	a0,2	a0,3	a0,4
Corn	a1,1	a1,2	a1,3	a1,4
New Machines	1	0	1	0
Old Machines	0	1	0	1
Outputs
Corn	0	0	b1,3	b1,4
New Machines	b2,1	b2,2	0	0
Old Machines	1	0	1	0

I make the usual assumption, inappropriate for environmental economics, of free disposal. A machine can be discarded without cost after used for only one year; managers of firms can choose not to operate the secondary processes in either sector. I also make the assumption that old machines cannot be transferred between sectors. An old machine jointly produced by the first process can be either discarded or used to operate process II. It cannot be used as an input in process IV. With these assumptions, this is a pure fixed capital system without superimposed joint production. An analysis of the choice of technique must consider the four techniques in Table 2. The cost-minimizing technique can be found by constructing the wage frontier. Demand does not matter except inasmuch as coefficients of production are affected by the scale at which processes are operated.

Table 2: Techniques

Technique	Processes
Alpha	I, III
Beta	I, II, III
Gamma	I, III, IV
Delta	I, II, III, IV

Table 3: Variables with Corn as Numeraire

Variable	Definition
w	Wage, in units of bushels per person-year
r	The rate of profits
p1	Price of a new machine, in units of bushels per machine
p2	Price of an old machine in the machine sector, in units of bushels per machine
p3	Price of an old machine in the corn sector, in units of bushels per machine

Suppose, on the other hand, that an old machine can be transferred between sectors. For example, the old machine jointly produced in the first process can be used in process IV to produce corn. Its history in being used to produce new machines has no effect on its efficiency in then being used to produce corn. Then only thee techniques, Alpha, Beta, and Gamma, would exist. Delta could only arise as a switch point between Beta and Gamma. Only two types of machines would exist. And p₂ would be redefined to be the price an old machine, whatever sector it would be in. This is then an example of an interlocked system. One might think reducing the number of techniques and the number of variables would simplify the model. But a simplification of the price system is available in the non-interlocked system that I do not think is possible for the interlocked system.

I think I am convincing myself that the assumption a system cannot be interlocked is a reasonable assumption.