Logical Structure of Austrian Economics

1. Introduction. We will attempt to reconstruct the Austrian approach to economics using first-order logic.

We observe (in section 3) Austrian economists confuse deduction with introducing logically independent propositions. The general reasoning is "This doesn't directly contradict our foundational axiom, therefore it must logically follow from it" promoting the non-sequitur from fallacy to rule of inference.

Nevertheless, we bravely continue, and in section 4 discover it's impossible to deduce marginal utility from the action axiom. This spells disaster for any marginal analysis in the Austrian school.

Definition and Explication

2.1. Axiom ("Action Axiom"). Murray Rothbard's The Logic of Action One: Method, Money, and the Austrian School (1997) describes the "action axiom" as:

Praxeology rests on the fundamental axiom that individual human beings act, that is, on the primordial fact that individuals engage in conscious actions toward chosen goals. This concept of action contrasts to purely reflexive, or knee-jerk, behavior, which is not directed toward goals. The praxeological method spins out by verbal deduction the logical implications of that primordial fact. In short, praxeological economics is the structure of logical implications of the fact that individuals act. This structure is built on the fundamental axiom of action, and has a few subsidiary axioms, such as that individuals vary and that human beings regard leisure as a valuable good. Any skeptic about deducing from such a simple base an entire system of economics, I refer to Mises's Human Action. Furthermore, since praxeology begins with a true axiom, A, all the propositions that can be deduced from this axiom must also be true. For if A implies B, and A is true, then B must also be true. (58--59)

This outlines the Austrian methodology fairly faithfully (I hope).

In order to make heads or tails out of it, lets first refine the meaning of "action" (since "humans act" is ambiguous at the moment).

2.2. Definition (Action). Ludwig Mises' Human Action itself defines "action" rather vaguely:

Human action is purposeful behavior. Or we may say: Action is will put into operation and transformed into an agency, is aiming at ends and goals, is the ego's meaningful response to stimuli and to the conditions of its environment, is a person's conscious adjustment to the state of the universe that determines his life. Such paraphrases may clarify the definition given and prevent possible misinterpretations. But the definition itself is adequate and does not need complement of commentary.

Personally, I find this unsatisfactory, but I will resign myself to accept the definition of "action" as "physical and psychological processes which render a specific state". (Even then, I'm nervous.)

If it makes much of a difference, Rothbard insists that All action in the real world, furthermore, must take place through time; all action takes place in some present and is directed toward the future (immediate or remote) attainment of an end (59). I thought this went without saying, but it is good to be explicit.

Immediate "Deductions"

3.1. Corollary. Rothbard continues:

Let us consider some of the immediate implications of the action axiom. Action implies that the individual's behavior is purposive, in short, that it is directed toward goals. Furthermore, the fact of his action implies that he has consciously chosen certain means to reach his goals. (59)

Well, is "the ego's meaningful response to stimuli" necessarily "consciously chosen"? Wasn't that the point of Pavlov's dogs?

OK, lets overlook this and continue analyzing the consequences of the action axiom. (I mean, real and meaningful consequences, not tautological statements.)

3.2. Corollary. Rothbard tries to pull a fast one, insisting

Furthermore, that a man acts implies that he believes action will make a difference; in other words, that he will prefer the state of affairs resulting from action to that from no action. (59)

How does this logically follow at all? The actor's belief in his success seems irrelevant to the supposition the actor "acts" (in the Austrian sense). It seems Rothbard assumes "conscious actions toward chosen goals" implies that choosing a goal requires first belief in succeeding at accomplishing that goal. So without that prior belief in success, we would have no action?

So, if I had doubt or no belief whatsoever in my success to bring about a desired state, and I resign myself to this fate, am I still "acting"?

This is so stupid a point to make, because this has no bearing on anything at all in Austrian economics. But Rothbard insists on making it! So, I should say Rothbard will say two things: first, that I am not acting (otherwise he immediately contradicts himself); and second, I am acting, because I have belief in my success in my resignation.

My own personal belief is that this point should be disregarded, as it has no bearing on Austrian economics...nor does it illuminate the action axiom (or any other proposition "shown").

Fine, I'm willing to expand the definition of "action" to include the condition "The actor consciously believes in his or her own success".

3.3. Corollary (Uncertainty). Rothbard continues in his analysis, suggesting:

Action therefore implies that man does not have omniscient knowledge of the future; for if he had such knowledge, no action of his would make any difference. Hence, action implies that we live in a world of an uncertain, or not fully certain, future. Accordingly, we may amend our analysis of action to say that a man chooses to employ means according to a technological plan in the present because he expects to arrive at his goals at some future time. (59)

The proposition "Humans live in a world of uncertain future" is compatible with the Action axiom, but in no way does it logically follow. That is, there are no rules of inference which gets us from the Action axiom to this Uncertainty proposition. (Why? Because they're independent propositions!)

At the same time, there is no rule of inference denying this Uncertainty proposition. The two (the Action axiom and this uncertainty proposition) are compatible, like the Continuum hypothesis and ZFC set theory.

But the term "technological plan" here (introduced for the first time) Rothbard does not define.

3.4. Corollary (Scarcity). Rothbard's fifth conclusion:

The fact that people act necessarily implies that the means employed are scarce in relation to the desired ends; for, if all means were not scarce but superabundant, the ends would already have been attained, and there would be no need for action.

So if I want to read Mises' Human Action, that is only possible provided there is scarcity? This does not logically follow from anything stated thus far.

The proof Rothbard gives is a proof by contradiction, which is worse than useless.

Rothbard attempts clarifying this proposition, Stated another way, resources that are superabundant no longer function as means, because they are no longer objects of action (60). So the argument basically boils down to "Because the current state of the world is not the end-state desired by an action, there must be scarcity." This is a non-sequitur.

3.5. Observation. The "logic" Rothbard uses appears to be "Here's a proposition B. It's logically compatible with the action axiom. (But in no way does the action axiom logically imply B or its negation.) Therefore we deduce B must be true."

This is an invalid rule of inference. Why? Because you're not proving anything! You don't have a statement "If A, then B."

Instead you have a statement "We have A. And here's an independent proposition B. Therefore A implies B."

Marginal Utility

4.1. Scarcity. Thorsten Polleit "deduces"

Human action implies employing means to the fulfillment of ends, and the axiom of human action implies that means are scarce. For if they were not scarce, means would not serve as objects of human action; and if means were not scarce, there would be no action — and that is unthinkable.

But nothing in the definition of "action" necessitates the existence for any "means to the fulfillment of ends". Having such "means" exist is not necessary for the definition of "action".

If we change the definition for "action" to "employing some 'means' to achieve some 'end'", then we have problems: we have introduced two undefined terms. We can handwave 'end' as "The state of the world after the action is done" to arbitrary precision (specify how long afterwards, etc. etc. etc.).

But the term "means" here is completely ambiguous. If we take it as "physical objects", then the axiom of action collapses on itself: the argument "Trying to refute the action axiom is a contradiction" becomes false, and all the preceding "deductions" in section 3 become false.

If we weaken the meaning for "means" as both physical objects and mental processes, then we still have problems: the claim for scarcity has a metaphysical statement that needs to be shown (namely, "Mental processes are scarce").

If we ignore everything except the proposition if means were not scarce, there would be no action, then...this claim still needs to be demonstrated. Why? Because it is the contrapositive of the claim "If there is action, then the means are scarce" which has not been shown.

So, in short, this nice-sounding couple of sentences is ambiguous.

4.2. Can Scarcity Be Deduced? The statement concerning scarcity's existence (or non-existence) is necessarily an a postereori claim, since it is an empirical statement.

If we buy into this Kantian taxonomy of propositions (a priori vs a postereori, analytic vs synthetic), then there is no way to deduce an a postereori proposition from an a priori one...otherwise it would be, by definition, a priori.

Consequently, by definition, it is impossible to "deduce" anything about scarcity's existence.

4.3. Scholium. What's the consequence of this? Any proposition in Austrian economics dependent on scarcity's existence has no logical grounding. So, basically, all of Austrian economics has no logical grounding.

Conclusion

We have examined the action axiom and the definition of "action". We found it mildly ambiguous, but workable.

We have seen the "immediate consequences" are really just independent propositions that are not logically linked to the action axiom.

We tried to reconstruct the inference "action implies scarcity", and found this to be impossible (trying to deduce a postereori from the a priori is always impossible). Consequently, all Austrian economics depending on scarcity has no logical grounding.

Future research might include analyzing the Austrian business cycle, or other macroeconomic theories.

Addenda

12 May 2014, 8:23AM (PST). It dawns on me the "Action axiom" isn't a priori --- it's based on the observation that people "act", and the observation attempts to refute it are "actions". No one really cares about this in Austrian circles nowadays, it seems, as no one seriously defends Mises peculiar Kantian inclinations.

I wonder about the "synthetic-ness" of the "Action axiom", too.

NB: the fact that the "Action axiom" is a proposition that's neither a priori nor synthetic doesn't seriously alter anything in Austrian economics. Fundamentally, it's an "axiom" in the modern mathematical sense rather than the Kantian sense: a specification we expect to hold while making "deductions" (in some vague sense).

12 May 2014, 8:48AM (PST). After thinking deeply about a priori synthetic statements (in the Kantian sense), it dawns on me that Kant used Aristotlean logic. Theoretically, Austrian economics cannot use first-order logic because of their Kantian underpinnings. I suppose it would be an interesting philosophical project to re-cast Austrian economics in rigorous first-order logic, and see what happens. A project, I hope, I will not commit myself to...

But it does mean the proposition "Man acts" is not a valid proposition for Aristotlean logic. Rothbard's proposition individuals engage in conscious actions toward chosen goals is invalid within Aristotlean logic. Mises' Human action is purposeful behavior. likewise is invalid. Hence it's invalid to consider it either a priori or a postereori, analytic or synthetic. Being charitable, perhaps a better form of the action axiom would be "All humans are 'actors'". But this only confirms the previous point: this is clearly not a priori.

Notes on Sraffa's Production, Chapter 9

66. Quantity of labour embodied in two commodities jointly produced by two processes

• So what results from single-product systems generalize over to joint-product systems?
• One rule we should study: when the rate of profits is zero, the relative value of each commodity is proportional to the quantity of labor which (directly and indirectly) has gone to producing them (§14).
  • For joint-products, there is no obvious criterion apportioning the labor among individual products. It seems doubtful whether it makes any sense to speak of a "separate" quantity of labor as having gone to produce one among many jointly produced commodities.
  • We get no help from the "Reduction" approach, where we sum the various dated labor inputs weighted by the product of rate of profits. (This is further discussed in §68)
• With the system of single-product industries, we had an alternative (if less intuitive) approach using the method of "Sub-systems" (Sraffa discusses this in his Appendix A).

  It was possible to determine — for each of the commodities composing the net product — the share of aggregate labor which could be regarded as directly or indirectly entering its production.

  • This method (with appropriate adaptation) extends to joint-products, so the conclusion about the quantity of labor "contained" in a commodity and its proportionality to value (at zero profits) can be generalized to joint products.
• Consider two commodities jointly produced through each of two processes in different proportions.

  Instead of looking separately at the two processes and their products, lets consider the system as a whole and suppose quantities of both commodities are included in the net product for the system.

• We further assume the system is in a self-replacing state, and whenever the net product is changed...the self-replacing state is preserved (i.e., immediately restored through means of suitable adjustments in the proportions of the processes composing it).
• We also note: it is possible to change (within certain limits) the proportions in which two commodities are produced if we alter the relative sizes of the two processes producing them.
• If we wish to increase the quantity which a commodity enters the net product of the system (while leaving all other components unchanged), we normally must increase the total labor employed by society.

  It's natural to conclude we must increase labor for producing the commodity in question. This may go directly (i.e., directly into the process in question) or indirectly (i.e., producing the means of production).

  • The commodity added will (at the prices corresponding to zero rates of profits) be equal in value to the additional quantity of labor.
• This conclusion seems to hold for commodities jointly produced, as it holds for single-product systems.
  • The conclusion appears to hold even when we change the quantities of the means of production, since any additional labor needed to produce the latter is included as indirect labor in the quantity producing the addition to the net product.
  • Footnote. Since joint-products are present, the contraction for some processes might occur, and thus we might fall into the awkward "negative industries" scenario again...but even then, the adjustments noted include them!

    This can be avoided, provided the initial increase for the commodity in question is supposed to be "sufficiently small", and the net product for the system is assumed to comprise at the start "sufficiently large quantities" of all products...so any necessary contraction may be absorbed by existing processes, without the need for any of them having to receive a negative coefficient.

67. Quantity of labour embodied in two commodities jointly produced by only one process

• Similar reasoning holds for the case when two commodities ('a' and 'b') are jointly produced through only one process...but are used as means of production (in different relative quantities) through two processes, each produes singly the same commodity 'c'.
  • So we have two processes of the form $q_{1,a}a+q_{1,b}b\to <!--\; \to \; -->q_{1,c}c$ and $q_{2,a}a+q_{2,b}b\to <!--\; \to \; -->q_{2,c}c$ where $q_{1,a}/q_{1,b}\ne <!--\; \ne \; -->q_{2,a}/q_{2,b}$, and none of the coefficients vanish.
• We can't change the proportions which 'a' and 'b' appear in the output of their production processes (i.e., the processes producing them). But we can (through altering the relative size of the two processes using them) vary the relative quantities in which they enter as means for producing a given quantity of 'c'.

  We can vary the relative quantities of 'a' and 'b' this way, and this by itself alters the relative quantities in which they enter the net social product. (The relative quantities in which the two enter the gross product are fixed.)

  • Remark. As a childish example, we could have $$\begin{array}{r}a+2b\to <!--\; \to \; -->c\\ 3a+b\to <!--\; \to \; -->c\end{array}$$ So, suppose we have for our toy example $q_a=q_b$ (there is a one-to-one ratio between the quantity of 'a' and 'b' produced).

    The relative quantities of 'a' and 'b' seems like a strange term to me. We could consider enlarging the first process and keep the second process constant: $$\begin{array}{rl}f(\stackrel{⃗<!--\; ⃗\; -->}{x})+L_a& \to <!--\; \to \; -->5a\\ g(\stackrel{⃗<!--\; ⃗\; -->}{y})+L_b& \to <!--\; \to \; -->5b\\ 2(a+2b)& \to <!--\; \to \; -->2c\\ 3a+b& \to <!--\; \to \; -->c\end{array}$$ For simplicity, the production of 'a' and 'b' are blackbox functions which takes "some vector" of inputs. We have combined $5a+5b\to <!--\; \to \; -->3c$. The relative quantities of 'a' and 'b' are, literally, one-to-one. Observe the surplus is 3 c...and we had $L_a+L_b$ contribute.

    But if we change how we produce things, say use only the first process, then we have $$\begin{array}{rl}f(0.4\stackrel{⃗<!--\; ⃗\; -->}{x})+0.4L_a& \to <!--\; \to \; -->2a\\ g(0.8\stackrel{⃗<!--\; ⃗\; -->}{y})+0.8L_b& \to <!--\; \to \; -->4b\\ 2a+4b& \to <!--\; \to \; -->2c\end{array}$$ and hence we have the surplus be 2c. The relative proportion which 'a' and 'b' enter production change; is this what Sraffa means? We varied the size of the processes producing 'a' and 'b', without deforming the processes (i.e., changing the proportions of the coefficients, just reduced the ratio to produce a lesser amount).

    The amount of labor also changed from $L_a+L_b$ to $0.4L_a+0.8L_b$.

• It is thus possible (through an addition to total labor) to arrive at a new self-reproducing state, where a quantity for one of the two products (say 'a') is added to the net product, while all other components of the latter remain unchanged.

  We can conclude the addition to labor is the quantity which directly and indirectly is required to produce the additional amount of 'a'.

68. Reduction to dated quantities of labour not generally possible

• Sraffa claims there is no equivalent (in the case of joint-products) to the "alternative method", i.e., Reduction to a series of dated labor terms. Sraffa explains the "essence" of Reduction is that each commodity should be (a) produced separately, (b) by only one industry, and (c) the whole operation consists in tracing back the successive stages of a single-track production process.
  • Remark. I am very suspicious of this claim, and I don't follow the reasoning given. After all, consider the system given as $$(1+r)A\stackrel{⃗<!--\; ⃗\; -->}{p}+w\stackrel{⃗<!--\; ⃗\; -->}{L}=\stackrel{⃗<!--\; ⃗\; -->}{p}$$ where A is the input-output matrix, $\stackrel{⃗<!--\; ⃗\; -->}{p}$ is the price-vector, w wage, $\stackrel{⃗<!--\; ⃗\; -->}{L}$ the labor vector, and r the rate of profits. Then we have $$(I-<!--\; -\; -->(1+r)A)\stackrel{⃗<!--\; ⃗\; -->}{p}=w\stackrel{⃗<!--\; ⃗\; -->}{L}$$ where I is the identity matrix. This gives us $$\stackrel{⃗<!--\; ⃗\; -->}{p}=(I-<!--\; -\; -->(1+r)A)\cdot <!--\; \cdot \; -->w\stackrel{⃗<!--\; ⃗\; -->}{L}=\left(\underset{0}{\overset{\mathrm{\infty <!--\; \infty \; -->}}{\sum <!--\; \sum \; -->}}(1+r{)}^n{A}^n\right)w\stackrel{⃗<!--\; ⃗\; -->}{L}$$ Isn't this a Reduction-type equation?

    If so, it could be suitably generalized in the straightforward way for a joint-product. Provided the joint-product system satisfies the conditions Sraffa gives (basically, the general linear algebraic conditions that a solution exists).

  • Remark (Cont'd). Now, we are dealing with a slightly more general situation, specifically: $$(1+r)A\stackrel{⃗<!--\; ⃗\; -->}{p}+w\stackrel{⃗<!--\; ⃗\; -->}{L}=B\stackrel{⃗<!--\; ⃗\; -->}{p}$$ where the matrix B is necessary for joint-products. Without loss of generality, we may assume it is an invertible matrix. Thus we re-write this system as $$(1+r)B^{-<!--\; -\; -->1}A\stackrel{⃗<!--\; ⃗\; -->}{p}+w{B}^{-<!--\; -\; -->1}\stackrel{⃗<!--\; ⃗\; -->}{L}=\stackrel{⃗<!--\; ⃗\; -->}{p}$$ or if we introduce new symbols to stress the similarity to the previous case: $$(1+r)\stackrel{˜<!--\; ˜\; -->}{A}\stackrel{⃗<!--\; ⃗\; -->}{p}+w{\stackrel{⃗<!--\; ⃗\; -->}{L}}^{\prime }=\stackrel{⃗<!--\; ⃗\; -->}{p}.$$ We should observe this becomes the previous situation.
• Sraffa suggests we should have to give a negative coefficient to one of the two joint-production equations and a positive coefficient to the other, thus eliminating one of the products while retaining the other in isolation.

  Some of the terms in the Reduction equation would represent negative quantities of labor, which Sraffa insists "no reasonable interpretation could be suggested."

  • Sraffa insists the series would contain both positive and negative terms, so the "commodity residue" wouldn't necessarily be decreasing at successive stages of approximation. Instead, it might show steady or even widening fluctuations — the series might not converge!
  • Sraffa will investigate this in §79 ("Different depreciation of similar instruments in different uses").
• Reduction could not be attempted if the products were jointly produced by a single process, or by two processes in the same proportions, since the apportioning of the value and of the quantities of labor between the two products would depend entirely on the way the products were used as means of production for other commodities.

69. No certainty that all prices will remain positive as the wage varies

• Sraffa urges us to reconsider another proposition considered earlier: if the prices of all commodities are positive at any one value of the wage between 1 and 0, no price could become negative as a result of varying the wage within those limits (§39).
  • Sraffa denies the possibility we could generalize this proposition to joint-product systems.
• Recall, the premise underpinning this proposition: the price of a commodity could only become negative if the price for some other commodity (one of its means of production) had become negative first — so no commodity could ever be the first to do so.
  • But for joint-products, there is a way around and the price for one of them may become negative...provided the balance was restored by a rise in the price of its companion product sufficient to maintain the aggregate value of the two products above that of their means of production by the requisite margin.

70. Negative quantities of labour

• Sraffa suggests his conclusion is "not in itself very startling". He interprets the situation quite simple. Sraffa notes in fact all prices are positive...but a change in the wages may create a situation which necessarily requires prices to become negative. Since this is unacceptable, those methods giving negative prices would be discarded in favor of those giving positive prices.
• When we consider this with the previous section (concerning the quantity of labor entering a commodity), the combined effect requires some explaining...
  • What's involved is not merely something like "In the remote contingency of the rate of profits falling to zero, the price of such a commodity would (if other things remain equal) have to become negative"...but we conclude in the actual situation, with profits at the perfectly normal rate of (say) 6%, that particular commodity is in fact produced by a negative quantity of labor.
  • Caution: We will work supposing 6% is the "normal rate of profits" throughout this section, so bear that in mind...
• Sraffa says "This looks at first as if it were a freak result of abstraction-mongering that can have no correspondence in reality." He has such a way with words, sometimes!
  • If we apply it to the test employed for the general case in §66, where — under the supposed conditions — the quantity of such a commodity entering the system's net product is increased (the other components remaining constant), we shall find as a result the aggregate quantity of labor society employs has diminished.
• Nevertheless! Since the change in production occurs while the "ruling rate of profits" is 6%, and the system of prices is the one appropriate to that rate, Sraffa argues "nothing abnormal will be noticeable".

  In effect the diminution in the expense for labor will be more than balanced by an increased charge for profits, the addition to net output will entail a positive addition to the cost of production.

• So, what happened? In order bring about the required change in the net product, one of the two joint-production processes must be expanded while the other contracted.

  In the case under consideration, the expansion of the former employs (either directly or through "other processes as it carries in its train the ensure full replacement") a quantity of labor which is smaller...but means of production which at the prices appropriate to the given rate of profits are of greater value — and thus attracts a heavier charge for profits — than the contraction of the latter process "under a similar proviso".

• Sraffa concludes "It seems unnecessary to show in detail that what has been said in this section concerning negative quantities of labor can be extended (on the same lines as was done for positive quantities in §67) to the case in which two commodities are jointly produced by only one process, but are used as means of production by two distinct processes both producing a third commodity."

71. Rate of fall of prices no longer limited by rate of fall of wages

• Sraffa has one further proposition about prices which needs reconsideration for the case of joint products.
• We have seen (§49) for single-product industries, when the wage falls in terms of the Standard commodity that no product can fall in price at a higher rate than does the wage.
  • The premise underpinning this: were a product able to do so, it must be owing to one of its means of production falling in price at a still higher rate.

    Since this could not apply to the product that fell at the highest rate of all, that product itself could not fall at a higher rate than wage.

• With one of a group of joint products, there is the alternative possibility the other commodities jointly produced with it should rise in price (or suffer only a "moderate" fall) with the fall of wage so as to make up — in the aggregate product of the industry — for any excessive fall of the first commodity's price.

  To such a rise, there is no limit...and thus there is none to the rate at which one of the several joint products may fall in price.

• But as soon as it is admitted the price of one (out of two or more joint products) can fall at a higher rate than does the wage, it follows even a singly produced commodity can do so...provided it employs — as one of its means of production, and to a sufficient extent — the joint product so falling.

72. Implication of this

• This possibility — price may fall faster than the wage — has some noteworthy consequences...
• First we have an exception to the rule "The fall of wage in any Standard involves a rise in the rate of profits."
• Suppose a 10% fall in the Standard wage entails (at a certain level) a larger proportionate fall — say 11% — in the price of 'a' as measured in the Standard product.
  • This means labor has risen in value by about 1% relative to the commodity 'a'.
    • Remark. I think the ratio would be $90/89\approx <!--\; \approx \; -->1.01123595505$ or the rise of value of labor relative to 'a' is about 1.12%.
  • If we were to express the wage in terms of commodity 'a', a fall in such a wage over the same range would involve a rise in the Standard wage and consequently a fall in the rate of profits.
• Moral. We can't speak of a rise or fall in the wage unless we specify the standard, for what is a rise in one standard may be a fall in another.
• For the same reasons, it becomes possible for the wage-line and price-line of a commodity 'a' to intersect more than once as the rate of profits varies
  • Figure 5: Several intersections are possible in a system of multiple-product industries.
    

• As a result, to any one level of the wage in terms of commodity 'a', there may correspond several alternative rates of profits.
  • In figure 5, the several points intersective the solid black curve — representing the price of 'a' — with the dashed wages curve represent equality in value between a unit of labor and a unit of commodity of 'a'...i.e., the same wage in terms of 'a'.

    Of course, they represent different levels of wage in terms of the Standard commodity.

  • On the other hand, as in the case of the single-products system, to any one level of the rate of profits there can only correspond one wage, whatever the standard in which the wage is expressed.

"Metaphysics" in Economics

This is a review of the concept of Joan Robinon's "metaphysics" in economics...I suppose we might call it "economic metaphysics" or something like that. The interested reader may peruse her original book on the subject:

Joan Robinson, Economic Philosophy. Penguin books, 1962. Freely available online at archive.org.

My page numbers will refer to the Penguin edition.

Definition of Metaphysics

Robinson begins with the definition of metaphysics, saying:

The hallmark of a metaphysical proposition is that it is incapable of being tested. We cannot say in what respect the world would be different if it were not true. The world would be just the same except that we would be making different noises about it. It can never be proved wrong, for it will roll out of every argument on its own circularity; it claims to be true by definition of its own terms. It purports to say something about real life, but we can learn nothing from it. Adopting Professor Popper's [fn: See The Logic of Scientific Discovery] criterion for propositions that belong to the empirical sciences, that they are incapable of being falsified by evidence, it is not a scientific proposition. (pp. 8.75--9.1)

Question 1. Is this a good definition of a "metaphysical proposition"?

But look, we really have two different criteria for a metaphysical proposition given:

Popperian Critera: "...it is incapable of being tested. [...] they are incapable of being falsified by evidence [...]."

Logical-Positivist Criteria: "It can never be proved wrong, for it will roll out of every argument on its own circularity; it claims to be true by definition of its own terms. It purports to say something about real life, but we can learn nothing from it."

Well, okay, so we have two different criterion...is this really a bad thing? It is if they are inconsistent, i.e., we have a proposition be metaphysical in one criterion but not in the other.

We have to dissect the Popperian critera a bit further before answering our first question.

Question 2. Is "Testability" Well-Defined?

Robinson continues, asking about the Classical Economist's notion of 'value' "What is it? where shall we find it? Like all metaphysical concepts, when you try to pin it down it turns out to be just a word" (p. 29.66).

The objection raised is we cannot observe value, therefore it cannot be falsifiable or testable. (This is the subject of the second chapter.)

This seems too naive stating "observable = testable = scientific". After all, hard sciences don't use this criteria (otherwise renormalization in QFT would be "metaphysical", as well as natural selection in biology, among many other scientific concepts).

Do we "observe" the business cycle or its symptoms? Well, it's the latter (with unemployment, inflation, and other indicators reflecting the state of the cycle).

So the business cycle is not testable, according to this strict criteria. It's "metaphysics".

After all, we observe only "symptoms"...does that mean we should designate the disease as "metaphysics"?

I don't think so...

Back to Question 1: Consistency of Criteria?

Well, the business cycle isn't "observable" although its symptoms are observed. The Popperian criterion qualifies it as a "metaphysical concept".

Now, to answer our question "Are the two criteria for metaphysics consistent?" We will examine...whether the business cycle qualifies in the "Logical Positivist" sense as "metaphysics".

Really, we have two different notions here: (a) the model explaining the business cycle, and (b) the phenomenon of the business cycle [i.e., the actual process itself].

The logical positivist criteria would consider (a).

I will state here my confessed belief that the model for the business cycle is not "circular" (no more so than any other model). If pushed, I don't know if I could defend this position in a short time --- we would have to specify which model!

But we have inconsistent results from the two criteria: Popper says the business cycle is metaphysics, whereas the Logical Positivist approach disagrees.

Answer to question 1: the criteria given is inconsistent.

Addendum: On Language Games

This dawned on me after posting: Wittgenstein's "language games" and "rule-following" are important and relevant concepts when discussing "metaphysics".

Question 3. Can we classify a proposition as neither "scientific" nor "metaphysical"?

After all, the Popperian criterion boils down to "analytic proposition = metaphysical, and synthetic proposition = scientific".

This tacitly assumes that language reflects reality. (Yep, time to drop the W-bomb!)

Wittgenstein's "language-games" demolishes this assumption (for reviews, see Xanthos' Wittgenstein's Language Games and the Stanford Encyclopedia of Philosophy entry).

After all, doesn't this alleviate our anxieties Popper raised concerning the distinction between model and symptoms?

I should probably flesh this out a bit more, but I'm certain anyone could write a thesis on "Robinson's 'metaphysics' in the context of Wittgenstein's 'language games'"...

Addendum 2: Metaphysics is Metaphysical

Question 4. Is the concept of a "metaphysical proposition" itself a metaphysical proposition?

I am a bit sloppy here. I should specify: isn't the proposition "A metaphysical proposition exists" a metaphysical proposition?

What do I mean by "metaphysical proposition"? It doesn't matter. Lets consider both criterion for a "metaphysical proposition".

Using Popperian Criterion. We can't observe a "metaphysical proposition", since it's entirely a human construct. So, I guess that means it is metaphysical.

I fear I am using a caricature of the Popperian criterion, so critical comments would be welcome!

Using Logical-Positivist Criterion. "It can never be proved wrong, for it will roll out of every argument on its own circularity; it claims to be true by definition of its own terms. It purports to say something about real life, but we can learn nothing from it."

Isn't this vacuous?

After all, regarding the proposition "A metaphysical proposition exists" — well, we "cannot say in what respect the world would be different if it were not true."

Hence, we conclude the existence of metaphysical propositions...is a metaphysical notion.

Question 5. Does "metaphysics" contribute to economics? More precisely, does is this a useful dichotomy [a proposition is "scientific" or "metaphysical"] or not?

I wonder about this, because what are we left with when we examine only "scientific propositions" in economics?

We're left with what may be observed. Isn't this merely econometrics?

Whenever discussing econometrics, someone ivariably invokes the Lucas Critique.

Tangential Question: Is the Lucas Critique a metaphysical proposition? [We'll have to consider this another time...]

Categorizing a proposition as either "scientific" or "metaphysics" implicitly gives it a positive or negative connotation (respectively).

Denoting propositions as "metaphysics" boils down to using loaded terms.

What's worse, Robinson notes "Yet metaphysical statements are not without content" and "Metaphysical propositions also provide a quarry from which hypotheses can be drawn" (9.1--9.5).

The only positive twist I could put is if Robinson meant "metaphysical propositions" belong to an Althusserian problematic...a background "idea-logical" [ideological] framework an economist brings to the game.

Is that even useful to know?

Question 6. If we weaken "testability", can we get a good notion of "metaphysics"?

I think we're being too strict with our notion of "metaphysics". We should use a slightly different criterion, a little weaker than either given.

It seems "testability" is too strict for economics. We should be a little weaker...if the concept produces "accurate predictions", we should consider it scientific.

Joan Robinson says the notion of "Value" [in Classical Economics] is metaphysical since we cannot "observe" it...we don't find it living under a rock.

BUT we can predict prices using "values". If the predicted prices are "wrong", then the concept of "value" would be incorrect.

Although this is a more realistic criterion for "testability", it would violate the understanding that metaphysical propositions constitute the ideological framework an economist uses to analyze phenomena.

Notes on Sraffa's Production, Chapter 8

Ch. 8. The Standard System with Joint Products

53. Negative Multipliers: I. Proportions of Production Incompatible with Proportions of use

• When we consider in detail how we construct a Standard system with joint products, it becomes obvious some of the multipliers may be negative.
• Consider two products jointly produced, each through two different methods.
  • The possibility that varying the extent to which one or the other method is used ensures a certain range of variation in the proportions in which the two goods may be produced in aggregate.
  • For each commodity, its two methods limits the range of proportionality. The limits are reached as soon as one or the other method is exclusively employed.
• Now suppose in all cases which two joint products 'a' and 'b' are used as means of production, the proportion in which 'a' is employed relatively to 'b' is invariably higher than the highest of the proportions in which it is produced.
  • In such circumstances we may say some process must enter the Standard system with a negative multiplier: but whether such a multiplier will have to be applied to the low producer or high user of commodity 'a' cannot be determined a priori—it can only be discovered through the solution of the system.

54. Negative Multipliers: II. Basic and non-basic jointly produced

• Non-basic products are "the most fertile ground" for negative multipliers.
  • (NB: non-basic goods needs a new definition under these new circumstances…but we may say that the main class, i.e. products altogether excluded from the means of production, will still be non-basic; see §60)
• Consider again the case of two commodities (jointly produced in different proportions by two processes). One is to be included in the Standard product while the other — not entering the means of production for any industry — must be excluded from the Standard product.
  • This will be effected by giving a negative multiplier to the process which produces relatively more of the second commodity, and a positive one to the other process.

    The two multipliers being so proportioned when the two equations are added up to the two quantities produced of the non-basic exactly cancel out…while a positive balance of its companion product is retained as a component of the Standard commodity.

55. Negative Multipliers: III. Special raw material

• Once negative multipliers have been admitted for some processes, others (which shine with a reflected light) are liable to appear.
• Hence, suppose we have a raw material be directly used in only one process. Suppose that process has a negative multiplier. Then the industry which produces the raw material will itself follow suit and enter the Standard system with a negative multiplier.

56. Interpretation of negative components of the Standard commodity

• Since no meaning could be attached to "negative industries" which such multipliers entail, it becomes impossible to visualize the Standard system as a conceivable rearrangement of the actual processes.
• We must therefore (in the case of joint-products) be content with the system of abstract equations, transformed by appropriate multipliers, without trying to think of it as having a bodily existence.
  • Remark. I'm sure many marginalist economists howl out in frustration over this, which is amusingly ironic.
• The Standard system's purpose is to provide a Standard commodity. When it has negative components, there is no difficulty interpreting them: they are liabilities or debts. This is analogous to accounting (negative numbers = liabilities/debts; positive numbers = assets).
• Hence a Standard commodity which includes both negative and positive quantities may be adopted as money of account without straining the imagination, provided the unit represents a fraction of each asset and each liability (like a share in a company)…with the liability in the shape of an obligation to deliver without payment certain quantities of particular commodities.

57. Basics and non-basics, new definition required

• We have another difficulty we must tackle before constructing the Standard commodity: the criterion distinguishing basic and non-basic goods fail…since it's ambiguous whether a product entering the means of production for only one industry producing a given commodity should or should not be regarded as entering directly the means of production for that product.
  • Footnote: The trouble lies deeper, and as we shall see presently there would be uncertainty even if the commodity entered directly the means of production of all the processes in the system! See §59.
• And the uncertainty would naturally extend to the question whether it did or did not enter "indirectly" the production of commodities, into which the latter entered as means of production.

58. Three types of non-basics

• All three distinct types of non-basics are met in the single-product system will find their equivalents in the case of multiple-product industries.

  Taking advantage of this circumstance, we begin defining for the latter case the three types of non-basics, each as the extension of the corresponding single-product type (cf. §35).

  1. Products which do not enter the means of production for any industry. This type can be immediately extended to the multiple-product system without modifying anything.
  2. Products each of which enters only its own means of production. The equivalent would be a commodity which enters the means of production for each of the processes by which it is itself produced, and no others — but enters them to such an extent that the ratio of its quantity among the means of production to its quantity among the products is exactly the same in each of the processes concerned.
  3. Products which only enter the means of production for an interconnected group of non-basics; in other words, products which (as a group) behave in the same way as a non-basic of the second type does individually.
• In order to define (in the multiple system of k processes) the type which corresponds to the third case (with the interconnected group consisting of 'a', 'b', and 'c'), we arrange the quantities in which these commodities enter any one process, as means of production, and as products, in a row. We shall thus obtain k rows ordered in 2×3 columns as follows: $$\begin{array}{r}{A}_1{B}_1{C}_1{A}_{(1)}{B}_{(1)}{C}_{(1)}\\ A_2{B}_2{C}_2{A}_{(2)}{B}_{(2)}{C}_{(2)}\\ \dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\\ A_k{B}_k{C}_k{A}_{(k)}{B}_{(k)}{C}_{(k)}\end{array}$$
  • Footnote: Some of these quantities may be zero, of course.
• The condition for the three products being non-basic: not more than three of the rows should be independent, and the others should be a linear combination of those three. (For the general definition, see §60.)

59. Example of the third type

• This third type gives us "curiously intricate patterns". Sraffa demonstrates this with an example.
• Given a system of four processes and four products, two commodities ('b' and 'c') are jointly produced by one process and are produced by no other.

  But while 'b' does not enter the means of production for any process, 'c' enters the means of all four processes.

  Supposing the process producing 'b' and 'c' corresponds to the equation $$(A_1{p}_a+C_1{p}_c+K_1{p}_k)(1+r)+L_{1}w=A_{(1)}{p}_a+B_{(1)}{p}_b+C_{(1)}{p}_c+K_{(1)}{p}_k$$ the "rows" for the two commodities will be $$\begin{array}{cccc}-<!--\; -\; -->& C_1& B_{(1)}& C_{(1)}\\ -<!--\; -\; -->& C_2& -<!--\; -\; -->& -<!--\; -\; -->\\ -<!--\; -\; -->& C_3& -<!--\; -\; -->& -<!--\; -\; -->\\ -<!--\; -\; -->& C_4& -<!--\; -\; -->& -<!--\; -\; -->\end{array}$$ Only the first row and any other are independent, the remaining two rows are linear combinations of the first pair. So both 'b' and 'c' are non-basic.

• If we look at the matter from constructing the Standard system, we see: (a) it's obvious 'b' can't enter the Standard commodity, (b) 'c' looks like it could be a suitable component.
  • However, since 'b' occurs only in one process, the only way to eliminate 'b' is omitting that process altogether.
  • But that process was the exclusive producer of 'c', so it only appears as means of productions…not as a produced commodity. So 'c' cannot possibly enter the Standard commodity, and must be dropped.

60. General Definition

• The formal definition given is not as satisfying as the intuition "entering (or not entering) the means of production for all commodities", which it supercedes. BUT it has the advantage of greater generality.
• Lets observe the first two types of non-basics may be considered as special cases of the third.
• The definition covers the three types of the single-product system.
  • (It is quite general, and as the example in §59 suggests, it includes a final type of non-basic, which is introduced subsequently…namely commodities which enter the means of production but are not produced — a type which land is the outstanding example.)
• We can give this general formulation between the distinction between basic and non-basic goods:
• Critera. In a system of k productive processes and k commodities (no matter whether produced singly or jointly), we say that a commodity — or more generally a group of n linked commodities (where 1≤ n< k) — are "Non-Basic" if:

  of the k rows (formed by the $2n$ quantities in which they appear in each process) not more than n rows are independent, the others being linear combinations of these.

  Or, in linear algebraic terms, the matrix of k rows and $2n$ columns is of rank less than or equal to n.

• All commodities which do not satisfy this condition are "Basic" (Note that, as has been stated in §6, every system is assumed to include at least one basic product.)

61. Elimination of non-basics

• It follows we can (through linear transformations) entirely eliminate non-basic commodities from the system…both on the side of the means of production and the products.
• This operation achieves the same result as we obtained in the single-products system by the much simpler method of crossing out equations of industries producing non-basics (§35).

62. The system of Basic equations

• If the number of basic products is j, the system thus obtained will consist of j equations: these may be described as Basic equations.
• Supposing the j basic commodities are a, b, …, j we shall denote the net quantities in which they appear using the "barred-quantities" $\stackrel{ˉ<!--\; ˉ\; -->}{A}$, $\stackrel{ˉ<!--\; ˉ\; -->}{B}$, …, $\stackrel{ˉ<!--\; ˉ\; -->}{J}$ to distinguish them from the quantities in the original processes.
• The Basic equations will accordingly be as follows:

$$\begin{array}{rl}({\stackrel{ˉ<!--\; ˉ\; -->}{A}}_1{p}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_1{p}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_1{p}_j)(1+r)+{\stackrel{ˉ<!--\; ˉ\; -->}{L}}_{1}w& ={\stackrel{ˉ<!--\; ˉ\; -->}{A}}_{(1)}{p}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_{(1)}{p}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_{(1)}{p}_j\\ ({\stackrel{ˉ<!--\; ˉ\; -->}{A}}_2{p}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_2{p}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_2{p}_j)(1+r)+{\stackrel{ˉ<!--\; ˉ\; -->}{L}}_{2}w& ={\stackrel{ˉ<!--\; ˉ\; -->}{A}}_{(2)}{p}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_{(2)}{p}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_{(2)}{p}_j\\ \dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->& \dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\\ ({\stackrel{ˉ<!--\; ˉ\; -->}{A}}_j{p}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_j{p}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_j{p}_j)(1+r)+{\stackrel{ˉ<!--\; ˉ\; -->}{L}}_{j}w& ={\stackrel{ˉ<!--\; ˉ\; -->}{A}}_{(j)}{p}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_{(j)}{p}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_{(j)}{p}_j\end{array}$$

• This system is equivalent to the original one inasmuch as the values it determines for R and the prices will also be solutions of that system.
• It differs from the original system (aside from obviously excluding non-basics):

  (a) A basic equation does not represent a productive process — it merely is the result of combining the equations of a number of processes.

  (b) It may contain negative quantities as well as positive ones.

63. Construction of the Standard system

• The basic equations are designed for the construction of the Standard product.
  • Footnote. It would be possible to construct the Standard product directly from the original equations, and the final result would have been the same. Why it has seemed simpler to go through the intermediate step of the Basic equations, well, Sraffa explains it in Appendix C.
• The multipliers $q_1$, $q_2$, …, $q_j$ which applied to the $j$ Basic equations give the Standard system are determined by the following equations:

$$\begin{array}{rl}({\stackrel{ˉ<!--\; ˉ\; -->}{A}}_1{q}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_1{q}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_1{q}_j)(1+r)& ={\stackrel{ˉ<!--\; ˉ\; -->}{A}}_{(1)}{q}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_{(1)}{q}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_{(1)}{q}_j\\ ({\stackrel{ˉ<!--\; ˉ\; -->}{A}}_2{q}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_2{q}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_2{q}_j)(1+r)& ={\stackrel{ˉ<!--\; ˉ\; -->}{A}}_{(2)}{q}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_{(2)}{q}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_{(2)}{q}_j\\ \dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->& \dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\dots <!--\; \dots \; -->\\ ({\stackrel{ˉ<!--\; ˉ\; -->}{A}}_j{q}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_j{q}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_j{q}_j)(1+r)& ={\stackrel{ˉ<!--\; ˉ\; -->}{A}}_{(j)}{q}_a+{\stackrel{ˉ<!--\; ˉ\; -->}{B}}_{(j)}{q}_b+\dots <!--\; \dots \; -->+{\stackrel{ˉ<!--\; ˉ\; -->}{J}}_{(j)}{q}_j\end{array}$$

• The equations give an equation for R of the j-th degree, so there may be up to j possible values of R and corresponding sets of values of the q's. Each set will represent a Standard commodity of different composition.

64. Only the lowest value of R economically significant

• When deciding which (among the j possible sets of values) is the relevant one, we can not rely on there being a value of R which corresponds to an all-positive Standard commodity. Why? Because in a system with joint-production all possible Standard commodities may include negative quantities among their components.
• If we reconsider the matter from the perspective of single-product systems, we find while an all-positive Standard makes sense, its superiority is due to it corresponding to the lowest possible value of R (as we shown in §42).
  • We shall see the possession of this last property is — by itself — sufficient to make the Standard net product, endowed with it, the one eligible for adoption as unit of wages and prices.

    This is regardless of whether the Standard commodity with this crucial property consists of all positive quantities or otherwise.

• Suppose that $R^{\prime }$ being the lowest possible value of $R$, we adopted as unit the Standard product corresponding to another value (say $R^{\prime \prime }>R^{\prime }$).
  • As the wage $w$ measured in this Standard was gradually reduced from 1 it would (before vanishing) arrive at a level $w^{\prime \prime }$ such that $$R^{\prime \prime }(1-<!--\; -\; -->w^{\prime })=R^{\prime }$$ when the rate of profits would be equal to $R^{\prime \prime }$.
  • If at such a level of $w$, we suppose on the basis of $R^{\prime }$, then the wage must be zero (since the rate of profits is at its maximum). While on the basis of $R^{\prime \prime }$ the wage must be positive since the rate of profits is below its maximum.
  • We reconcile this through the wage $w^{\prime }$ be a positive quantity of a composite commodity who's exchange value is zero. This is because (as we shown in §41) the exchange value for a Standard commodity the composition corresponds to one solution of $R$ (in our case $R^{\prime \prime }$) at the prices that correspond to another solution of $R$ (for us, $R^{\prime }$) is zero.
  • This implies, under these circumstances, the prices of all commodities would — in terms of the chosen Standard — be infinite(!).

    Economically, such a result is meaningless.

    This anomaly, however, can be avoided if we adopt as unit the Standard net product corresponding to the lowest value of $R$.

    This is the only Standard product in terms of which, at all the levels of wage from 1 to 0 (and so at all the levels of the rate of profits from 0 to its maximum), it is possible for the prices of commodities to be finite.

65. Tax on non-basic product leaves rate of profits and prices of other products unaffected

• The distinction between Basics and Non-Basics has become so abstract in the multiple-product system, we may wonder if it has become void of meaning.
• The chief economic implication of the distinction was the basics have an essential part in determining prices and the rate of profits, while Non-Basics have none. And this remains true under the new definition.
• For single-product systems this implies: if an improvement took place in the method of production for a basic commodity, then the result would necessitate a change in the rate of profits and the prices of all commodities.

  Whereas a similar improvement for a Non-Basic would affect only that particular Non-Basic's price.

  • This cannot be directly extended to a system with multiple products, where both basics and non-basics may be produced through the same process.
  • We can find an equivalent in a tax (or subsidy) on the production for a particular commodity.

    Such a tax is best conceived as a tithe, which can be defined independent of prices and has the same effect as a fall in the output for the commodity in question all other things (viz., the quantities of its mean of production and its companion products) remaining unchanged.

• A tax on a basic product will affect all prices and cause a fall in the rate of profits corresponding to a given wage, while if imposed on a Non-Basic…it will have no effect beyond the price of the taxed commodity, and those other Non-Basics linked with it.
  • Footnote. The effect which tax has on the price for Non-basics will vary with the type of Non-Basics.

    If it does not enter any of the means of production, its price will rise by the amount of the tax.

    If it enters its own means of production, its price will change to the extent required to maintain the original ratio of the value for the aggregate product of the process (after deduction of the wage and tax) to the value of its aggregate means of production.

    If it belongs to a group of interconnected non-basics, the prices of all or some of the components of the group will change s oas to maintain that ratio.

    (In the example of §59 if the production of commodity 'c' were taxed, the price of 'c' itself would be unaffected and the brunt would be borne by the price of 'b' which would have to rise to the necessary extent.)

• This is obvious if we consider the transformed system of Basic equations (which by itself determines the rate of profits and prices of basic products) cannot be affected by changes in the quantity or prices of Non-basics which are not part of the system.