February 2006

The A+B Theorem and the Tragedy of Human Effort

 Fish will not live where the water is too clear. But if there is duckweed or something, the fish will hide under its shadow and thrive. Thus, the people will live in tranquility if certain matters are a bit overlooked or left unheard.
-Yamamoto, Hagakure

My friend and mentor Anthony Cooney invited me to write a chapter on the A+B Theorem for the new Australian Heritage edition of his masterpiece, "Social Credit: Economics," published this month. The text of the chapter follows. See www.alor.org for details on the book.

C. H. Douglas seldom mentions his predecessors, but there is one he mentions repeatedly, Francis Bacon. Bacon founded the inductive method of investigation. Starting from phenomena freshly observed, one imaginatively forms a hypothesis to account for them. The hypothesis, if true, would predict (by deduction) other phenomena. Multiple confirming instances reinforce the hypothesis; one counter instance eliminates it. Action based on the hypothesis will further test it.
Unlike a mathematical theorem, the inductive method does not provide absolute certainty based on self-evident axioms in an abstract world. The inductive method provides abundantly reinforced hypotheses based on observed phenomena in the real world. Douglas was a pioneer in applying the true Baconian method to real human problems.

In regard to any application of the inductive method, we may ask
(1) What is the phenomenon to be accounted for?
(2) What hypothesis is proposed?
(3) What further phenomena are predicted by the hypothesis? and
(4) Are they confirmed?
I will here limit myself to (1) and (2).

The Problem

The phenomenon/problem that obsessed Douglas the engineer and to whose solution he devoted his entire life is what he calls the tragedy of human effort, the gross waste of people's labor. Douglas quotes a statement of H. L. Gantt that the U.S. industrial system was 5% efficient.1 That means 95% waste. That would mean we were at that time working twenty times harder than we had to to get the same results. Without committing ourselves to particular numbers, anyone not wearing blinkers can look around and see the same phenomenon today.
We see myriad jobs that do not actually produce any product or service for human satisfaction; whole industries that are mere unnecessary adjuncts to, or parasitic on, real production (or adjuncts to adjuncts); incomprehensible legislation providing jobs for armies of lawyers and spawning the Alice-in-Wonderland world of the civil "service"; massive labor diverted from actual production to unproductive commercial warfare; vast resources diverted to seducing the public; the absurdity of a country's "living on its exports"; the crime of product destroyed to keep prices up; the heartbreak of wonderful inventions killed in the womb; the insult of "job creation" promoted as something desirable.
We see all the cars and roads and petroleum used to get people to and from these unnecessary jobs. We see processing, packing, transport, distribution, and retail processes expended to put a jar of apple-sauce on the shelf when you could make a superior product at home by popping an apple into the oven. All this in the context of a technological capability that the engineer knows better than anyone could happily disemploy people. Yet despite all this technology at our disposal and all this investment of resources, our cities are still shamed by the specter of homeless and starving people, and even a middle-class family is but one illness away from economic ruin. The tragedy of human effort cries out for an explanation.

The Hypothesis

Douglas puts forward a hypothesis, which he says "has come to be called the A+B theorem." However, it is not meant to be self-contained like a theorem in mathematics. Taken as a whole, it is an inspired guess as to the cause of the tragedy of human effort, subject to confirmation or rejection by observations in the real world. It consists of three sentences, which I reproduce one by one and have further divided into lines to assist a slow and thoughtful reading:

1. In any manufacturing undertaking the payments made
May be divided into two groups: Group A:
Payments made to individuals
as wages, salaries, and dividends; Group B:
Payments made to other organizations
for raw materials, bank charges, and other external costs.

This premises that payments of a "manufacturing undertaking" are either to individuals or to organizations. To put flesh on Douglas's hypothesis and make it easy to follow, let's assume that the manufactures in question are chairs and that the payments to individuals are wages. B-payments cover a number of different things, but the most characteristic and interesting of these is payments to suppliers for capital goods and services.2 So let payments to a sawmill for wood arbitrarily stand for all payments to organizations (as if tools, etc. were free).

2. The rate of distribution of purchasing power to individuals
is represented by A,
but since all payments go into prices,
the rate of generation of prices cannot be less
than A plus B.

This premises that "all payments go into prices" and draws the conclusion from the two premises that the prices of the chairs on sale at each and every point in time ("rate") must be at least equal to the sum of wages and payments for wood incurred on behalf of that particular batch of chairs.

3. Since A will not purchase A plus B,
a proportion of the product at least equivalent to B
must be distributed by a form of purchasing power
which is not comprised in the description grouped under A.3

This is highly condensed and is the source of all the trouble. At face-value, it says that the employees cannot buy all the chairs - that the wages at each and every point in time are less than the sum of wages and payments for wood incurred on behalf of the particular batch of chairs on sale at that point in time. And it indicates a course of action, namely, to enable the employees to buy all the chairs by introducing "a form of purchasing-power" that does not go into prices.
The words, "A will not purchase A+B" tell us two new things. First, they imply that A is supposed to purchase A+B and since A is money in the hands of the consumer, we learn here for the first time that the "manufacturing undertaking" is a consumer manufacturing undertaking. Second, since the employees of the chair factory would not actually want to buy all the chairs, we learn here for the first time that we are not really talking about the product of a single "manufacturing undertaking." Rather, we are talking about all the consumer goods and services that the nation produces. If the economy as a whole is like the chair factory, Douglas is asking, how will individuals in the nation buy the consumer goods and services that the nation produces?
To liken the economy as a whole to the chair factory is to say the economy as a whole is one big consumer production system. In this view, capital production (like the sawmill), is conceived as merely an early stage of consumer production. The employees of the sawmill and the employees of the chair factory are together producing chairs. The sawmill produces wood that goes into chairs that are sold to individuals, and all costs of production are ultimately charged to individuals, whether as taxpayers (consumers of government) or regular consumers.
So "A will not purchase A+B" within the context of the one company states that the employees of the chair factory cannot buy all the chairs but in the context of both companies together states that the employees of the sawmill and the chair factory together cannot buy all the chairs.

The Big Picture

In other words, if the sawmill and chair factory were two divisions of the same company, nothing essential would change. At each and every point in time the price of chairs would be the same as it was before, and the total wages available to meet that price would be the same as it was before.
This means that "A will not purchase A+B" is not the tautology it appears to be, because the two A's can be different. With the sawmill and chair factory combined, the first A is the wages of all the employees at one point in time, but the second A - the one that goes into prices - is the wages of each division at different points in time. In that case, "A will not purchase A+B" states something more complex than at first appears. What it states is that the wages of all the employees at each and every point in time are less than the wages of the chair division that went into the particular batch of chairs on sale at that same point in time plus the wages of the sawmill division that went into that same batch of chairs plus a payment to, say, a logging company for the logs that went into the wood that went into that same batch of chairs.
Any company that is considered as generating prices at each and every point in time must also be considered as generating wages at each and every point of time (provided it still exists). If we pursue this process to its logical conclusion, we eventually encompass the whole economy. The B-element becomes less and less, but nothing essential changes because the A-element that goes into prices becomes correspondingly greater and greater. The most characteristic B-payment can be conceived as a reimbursement for past A-payments. Therefore, the A+B Theorem could be rewritten in terms of A over time.
We can think of the economy as a whole as a single "manufacturing undertaking" existing over time. And when we think of its life over time, we realize that we are talking about generations. And if we think of generations, we realize that we are talking about the entire history of civilization. Yet our grandchildren do not make a B-payment to us, they inherit from us. And our culture did not make a B-payment to a preceding culture, it inherited from it. In these cases, Douglas's hypothesis still has meaning, and we might even say this is where it really comes into its own.

A Chart That Works

Douglas's hypothesis proposes a simplified economic model in which each stage takes its raw materials or half-made goods from the previous stage, works them up further, and passes them on to the next stage. We can analyze the cost of the final consumer good or service produced as a simple addition of A-payments through its whole cost-history.
Thus, one company expends A1; the next company reimburses it (B1, equal to A1) and expends A2; the third company reimburses it (B2, equal to B1+A2), and so on. At each stage, A+B makes a new B; and the public makes the final reimbursement, which is just like a final B-payment, called the price. Thus, the final price could be expressed as A1 + A2 + A3 . . . + A100.
We can make a chart in which one dimension represents wages received for four different stages of chair production (I've added Retail as a separate stage) at each and every point in time and the other represents wage-payments incurred for the same four stages on behalf of the particular batches of goods on sale at those same points in time. Prices are got by adding across the columns, and wages are got by adding down the columns:

Notice that in this example, these two numbers are the same, 4A: the employees can buy all the chairs. But Douglas asserts "A will not purchase A + B," that is, the number got by adding down the columns is less than the number got by adding across the columns.
Why would it be less? The chart above shows a self-liquidating economy because wages at the logging company, wages at the sawmill, and wages at the chair factory stayed the same over time. If they became less over time, then the employees would not be able to buy all the chairs. For wages to become less over time would mean that less consumer goods and services were required as an inducement to work, either because people were disemployed or worked shorter hours or the work became easier or pleasanter.
Now this is just what it is the nature of labor-saving innovation to do, which is the running theme of all of Douglas's writings. So we allow this as Douglas's silent assumption and incorporate it into a continuation of our chart. The result is a chart of the A+B Theorem (expressed in terms of A) that is simple and straightforward, does not involve complex mathematics, is understandable by anyone, and really works:

"(A - 1)" represents a saving of labor at the chair factory starting at T5 and a saving of labor at the sawmill at T6. This could mean that someone is disemployed or relieved for half the day or takes a pay cut in return for an easier or pleasanter job.
This simplified chart doesn't capture the cost of the innovations. But it is obvious that at each and every point in time across the economy, the balance must always be increasing on the side of labor saved - innovations must be coming to more than they cost if they were not mistakes.
In addition, this chart underestimates the real difference between labor now and labor over the cost-history of the chairs, because the latter really goes back to the dawn of time. If it were possible to measure the whole cost-history of the chairs, the result would be a higher price and the need for a correspondingly bigger injection of a "form of purchasing power" that does not go into prices.

Conclusion

Douglas's inspired guess, in short, is that under the influence of (1) the accounting rule that all costs go into prices, (2) the absence of any "form of purchasing power" that does not go into prices, and (3) innovation, the money in people's pockets tends to become chronically insufficient to liquidate the costs of production and that this is the cause of "the tragedy of human effort."
The A+B Theorem is not a description of the way things are. It is a hypothesis as to the underlying cause why things are the way they are. Wages and prices are not usually falling over time in the real world - quite the contrary; but a tendency of wages and prices to fall over time could explain what we see in the real world. Similarly, money in people's pockets might not be less than prices in the real world; yet a tendency of that to happen could explain why things are the way they are. Douglas's hypothesis is that the economy reacts against the situation and thus produces the phenomena that we see.
To enumerate the various phenomena the hypothesis would predict and look for confirmation or rejection in the real world would require another chapter. But to have recognized that the A+B theorem is a hypothesis in a larger inductive investigation and to have expressed that hypothesis correctly is much.

Notes

1. Credit-Power and Democracy, p. 16.

2. Here is a handy mnemonic device:
A is for Allowances
To buy Apples and Ale,
B is for Back-Bursements
To buy Blubber and Ball-Bearings.

3. Monopoly of Credit, p. 35f.