The Fundamental Quantum of Political Economy is Denoted by the Subscript k

 

Taking a cue from Descartes, Lonergan advised that we attend to the simple things that anyone can understand.

Again and again, in his regulae ad directionem ingenii, (Descartes) reverts to this theme.  Intellectual mastery of mathematics, of departments of science, of philosophy, is the fruit of a slow and steady accumulation of little insights.  Great problems are solved by being broken down into little problems.  The strokes of genius are but the outcome of a continuous habit of inquiry that grasps clearly and distinctly all that is involved in the simple things that anyone can understand.  (CWL 3, 3/27)

Perhaps, though we are not doing quantum mechanics, nor forcing economics into any Procrustean form of physics, we can, nevertheless, find a fundamental “quantum” that anyone can understand.

Let us agree provisionally that, for us, the utterance “quantum” denotes the most fundamental element or parcel of the productive process; it is the velocitous contribution by a human in a unit of enterprise of an elemental factor of production.  And as the most elemental, we should not be surprised that Lonergan’s first quasi-equation in his analysis of the productive process is the “statement of composition” of an individual product, qi,  and of the total flow of products, Qi.

qi = ΣΣqijk

where k represents 1 through k factors of production, j represents 1 through j contributors [CWL 15, 29-31] (1), and for the total flow of products,

Qi = ΣΣQijk

But if the ultimate product qi is related by a double summation to the contributions of factors of production qijk, then the total flow of ultimate products Qi is also related by a double summation to the rates of the contributions of the factors of production Qijk, where both Qi and Qijk are instances of the form ‘so much or so many every so often.’ (CWL 15, 30)

where k represents 1 through k factors of production, j represents 1 through j contributors [CWL 15, 29-31] (1), and

The most elemental item is the first in the analysis.

Thus, the total of real basic and surplus incomes, I = I’ + I”, which are either spent on a cost of living or invested, are contingent upon the compensated productive outlays, ΣΣpiki. That is, the consumption and investment in a properly managed economy ultimately depend upon the velocities productive contributions ΣΣqijk.  And in an expanding economy, the incremental expansionary transactions would be financed by proportionately increasing credit directed into the supply function.  Thus the expanding credit is justified by its being used to finance expanding supply in the productive order.

What must be analyzed first is the dynamic process of producing and selling those things which correlated dummy money finally buys.  And what will be understood last in the analysis is what traditional economic analysis routinely takes as first in the analysis – prices.  (Click here and here)

Questions cannot be put in any order whatsoever.  Some questions simply cannot be answered until others have been resolved.  And sometimes the answers to one question immediately provide the answers to others. [CWL 12, 23]

… the questions are put in such an order that, once the first is solved, the solutions to the others follow with almost no difficulty.  Therefore, because the later solutions are connected to the first as conclusions are connected to some principle, all solutions after the first seem to be the proper province of knowledge. [CWL 12, 25]

… if solving the first problem virtually solves all the others, the concepts and terms in which the first problem and the first solution are defined and expressed cannot be significantly changed if they are to serve to define and express the later problems and solutions.  Clearly, then, it is not the arbitrary malice of professors but the interconnected questions and solutions themselves that demand both systematically formed concepts and a technical terminology that corresponds not to any concepts whatsoever but to systematic concepts. [CWL 12, 25]

Contrary to the textbooks and the pronouncements and actions of the Federal Reserve Bank, money and prices are not the ultimate masters of the economic process.

… money is an instrument invented to fulfill a definite task; it is not the ultimate master of the situation.  … Accordingly money has to conform to the objective exigencies of the economic process, and not vice versa. (CWL 21, 101)

“The ‘basic’ stage of the process is, in its pure form, an aggregate of rates of labor, of managerial activity, of the use of capital equipment for the sake of the goods and services that enter the standard of living.”  Thus, the fundamental “aggregandum”  is a rate of productive contributions.  We state how some ultimate product, qi,  is composed:

qi is the individual product composed at the rate of composition ΣΣqijk [CWL 15, 29-31]

Why did we use the term “quasi-equation”?

It is to be noted that the emergent standard of living and the basic stage of the process are not identical aggregates of rates.  …  Since the form of the relation between them is a double summation, the emergent standard of living and the basic stage of the process are not identical aggregates of rates.  On the other hand, precisely because the relation is a double summation, they are equivalent aggregates of rates.  However, this statement requires three qualifications. [CWL 15, 29-31]

The third qualification is with regard to the meaning of the equivalence: the symbolic expression (1) is not a mathematical equation and it cannot be until a common measure is found for the ultimate products and contributions to ultimate products; such a common measure is not had until the measure of exchange value is introduced. [CWL 15,31]

The phenomenology of that little subscript, ki, is as follows:

  • It is a rate of application of a factor of production by humans, a so much or so many per interval
  • As such, it is a velocity, which in calculus would be symbolized as instantaneous d/dt or difference Δ/Δt
  • Each unit of enterprise (subscript j, 1-j) in the product’s supply chain makes several contributions of factors such as
    • operating a machine
    • various types of direct labor
    • supervision
    • purchasing and receiving of materials
    • accounting
    • sales
    • management
  • Each individual application of a factor by a human is compensated. Money is taken by a human in exchange for productive services to the unit of enterprise.  That is, monetary Outlays by each unit of enterprise are Incomes to the recipients.

So, in a rectilinear series of contributions in the producing of each and every product (or service), qi, (i = 1-n), component factors, ΣΣqijk, are velocities of so much every so often until the composite product is completed and finally sold.  And this sale constitutes the exit from the current, velocitous, purelydynamic, productive process.  After exiting the process, the integral or composite goes into either use as a unit of capital or into enjoyment in a standard of living.  The good or service is no longer “under process.”  It is no longer an element of consideration in the current, dynamic, productive process.

It is worth repeating, regarding first things first.

… if solving the first problem virtually solves all the others, the concepts and terms in which the first problem and the first solution are defined and expressed cannot be significantly changed if they are to serve to define and express the later problems and solutions.  Clearly, then, it is not the arbitrary malice of professors but the interconnected questions and solutions themselves that demand both systematically formed concepts and a technical terminology that corresponds not to any concepts whatsoever but to systematic concepts. [CWL 12, 25]

And last things last.  Prices are last in the analysis, rather than first as in the textbooks’ AD-AS models.  In and of their individual or aggregate selves they cannot completely explain the dynamic economic process.  They are not, all by themselves, a set of abstract formal relativities of complete explanation.  They are merely secondary concrete determinations from the non-systematic manifold. (Click here and here and here ) They require explanation in the context of the significant variables and relations which do in fact explain the economic process of production and sale.

One might be reminded here of a parallel in hydrodynamics: if what is at issue is a general specification of the dynamics of free water waves, a premature introduction of general boundary conditions or worse, specific channel conditions, botches the analytic possibilities….the Robinson-Eatwell analysis is hampered … by their building the economic priora quoad nos of profits, wages, prices, etc., into explanation, when in fact the priora quoad nos[1] are last in analysis: they require explanation. [McShane, Philip (1980) Lonergan’s Challenge to the University and the Economy, (Washington, D.C.: University Press of America) P. 124][2]

Lonergan agreed with Schumpeter on the importance of a systematic or analytic framework in order to explain, rather than merely record or describe, the aggregate phenomena of macroeconomics; he agreed with Schumpeter that to be able to explain the booms, slumps, and crashes of the trade or business cycles the economist’s analysis had to be as dynamic as the subject matter under investigation; and he agreed that the economist had to know what are the significant variables in the light of which price changes are to be interpreted. According to Lonergan, standard economic theory had successfully achieved none of these desiderata. [CWL 15, Editors’ Introduction liii]

Lonergan’s critique (shows that) by using the technique of implicit definition, the emphasis shifts from trying to define the relevant variables to searching heuristically for the maximum extent of interconnections and interdependence; and that the variables discovered in this way might not resemble very much the objects (or the aggregates) (such as prices) which, in the first instance, one was thinking about.   [Gibbons, 1987; Economic Theorizing in Lonergan and Keynes]

Two issues should be noted: First, we discard the use of some imaginary universal quantum, η, of which all things are composed, as in qi = aη with “a” being the individual composite product’s coefficient for the quantity of the component η’s.

Second, each contributor’s application of a factor ki in each unit enterprise j is compensated at a wage or salary rate unique to that enterprise.  And each contribution and its cost-price are concrete.  Prices do not stand as abstract laws; rather they are secondary concrete determinations from the non-systematic manifold.  Thus, while FMD’s analysis of the primal productive process yields formal distinctions of point-to-point and point-to-line, and while its primary field-theoretic relativities are purely abstract and relevant in any instance, the complete explanation of the concrete process has two components; it consists of 1) primary abstract relations applied to 2) secondary concrete determinations from the non-systematic manifold. (CWL 3, 494-95/515-16)

… it is necessary to distinguish in concrete relations between two components, namely, a primary relativity and other secondary determinations.  Thus, if it is true that the size of A is just twice the size of B, then the primary relativity is a proportion and the secondary determinations are the numerical ratio, twice, and the two observable sizes.  Now ‘size’ is a descriptive notion that may be defined as an aspect of things standing in certain relations to our senses, and so it vanishes from an explanatory account of reality.  Again, the numerical ratio, twice, specifies the proportion between A and B, but it does so only at a given time under given conditions; moreover, this ratio may change, and the change will occur in accord with probabilities; but while probabilities will explain why objects like A and B every so often have sizes in the ratio of two to one, they will not explain why A and B are in fact in that relation here and now; and so the numerical ratio, twice, is a non-systematic element in the relation.  However, if we ask what a proportion is, we necessarily introduce the abstract notion of quantity and we make the discovery that quantities and proportions are terms and relations such that the terms fix the relations and the relations fix the terms.  For the notion of quantity is not to be confused with a sensitive or imaginative apprehension of size; a quantity is anything that can serve as a term in a numerical ratio; and, inversely, a proportion, in the present context, is a numerically definable ratio between two quantities. [CWL 3, 491]

Again,

One might be reminded here of a parallel in hydrodynamics: if what is at issue is a general specification of the dynamics of free water waves, a premature introduction of general boundary conditions or worse, specific channel conditions, botches the analytic possibilities….the Robinson-Eatwell analysis is hampered … by their building the economic priora quoad nos of profits, wages, prices, etc., into explanation, when in fact the priora quoad nos[3] are last in analysis: they require explanation. McShane, Philip (1980) Lonergan’s Challenge to the University and the Economy, (Washington, D.C.: University Press of America) P. 124[4]

Advancing from the contexts of (CWL 15, Sections 7-9, pp. 23-35) and (CWL 15, Section 13, pp. 45-55) to (CWL 15, Section 23, p. 108, and with reference to the Diagram of Rates of Flow):

let pi be the compensation of worker(s) applying factor ki at a velocity in an individual contributing unit of enterprise.  Then the total of basic and surplus Outlays for productive services are symbolized as O’ + O” = ΣΣpiki , which, by the principle of concomitance, gives us for a stable economy  ΣΣpik=  O’ + O” =  I’ + I” = E’ + E” = R’ + R”.  Thus, total incomes, I = I’ + I”, which are either spent on a cost of living or invested, are contingent upon the compensated productive outlays, ΣΣpiki. That is, the consumption and investment in a properly managed economy ultimately depend upon the productive contributions qijk.  And in an expanding economy, the incremental expansionary activities would be financed by proportionately increasing credit, which, of course, is justified in turn by its being used to finance production rather than as a supplement to not-earned expenditures.

Pausing to gather ourselves and our symbols, in the general case the analytical “cost price” in the period and the quantity per the period in the Outlays of the productive order are given by vectors in an n-dimensional Cartesian coordinate framework for pi and aqi.  In total, where the sales price and quantity, P and Q, are each vectors (CWL 15, 107-113) in an n-dimensional Cartesian coordinate framework,

Σ(pi)(aqi) = PQ = PQcosA =(pi)(aqi) = (pi)(aqi)cosB,

 And the change in PQ is given by

ΔPQcosA = PQ[(dP/P + dQ/Q + dPdQ/PQ) cos (A + dA) – 2 sin(dA/2) sin(A + dA/2)] (CWL 15, 109)

And, in simpler non-vectoral terms, and superscripts, ‘, for basic and, “, for surplus, we derive the implicit equations for the Basic Price Spread Ratio, P’/p’ or J :

P’Q’ = p’a’Q’ + p”a”Q”  (CWL 15, 156-62) (44)

P’/p’ = a’ + a”p”Q”/p’Q’   (CWL 15, 156-62) (45)

i.e.,   J = a’ + a”R   (CWL 15, 156-62) (45)

so,  dJ = da’ + a”dR + Rda”   (CWL 15, 156-62) (47)

There is a sense in which one may speak of the fraction of basic outlay that moves to basic income as the “costs” of basic production.  It is true that that sense is not at all an accountant’s sense of costs; … But however remote from the accountant’s meaning of the term “costs,” it remains that there is an aggregate and functional sense in which the fraction… is an index of costs.  For the greater the fraction that basic income is of total income (or total outlay), the less the remainder which constitutes the aggregate possibility of profit.  But what limits profit may be termed costs.  Hence we propose ….to speak of (c’O’  = p’a’Q’) and (c”O” = p”a”Q”) as costs of production, having warned the reader that the costs in question are aggregate and functional costs…. [CWL 15, 156-57]

Thus, the productive process is constituted by workers contributing applications of factors at rates per period across the nation and getting paid so much per period to do so.

Based upon these elements, ki , one can proceed to

  • discover the formal structure of the rectilinear process of surplus production and time-lagged basic production
  • make precise analytical distinctions, based upon the correspondence between those composites of k  that enter directly into the standard of living and those that remain in the process as capital items, between point-to-point (“basic”) and point-to-line (“surplus”) correspondences
  • formulate the lagged technical accelerator for two levels of the productive order

k[fn(t-a) – Bn] = f”n-1(t) –An-1

  • by reasoning to the heuristic structure of the normative geometric and linear accelerations of the surplus circuit and, then, the basic circuit, identify phases of the long-term expansion constituted by the relations of dQ”/Q” to dQ’/Q’ in the productive order

And, by adding consideration of cost-price Outlays, pi , and by recalling that money is a dummy invented by humans to enable the conducting of a vast and intricate process of exchange

  • understand
    • the condition of continuity
    • circular conditions of keeping pace within circuits, where O1 = I1 = E1 = R1 and O2 is dependent on the occurrence of R1; and
    • crossover conditions between circuits requiring that G = c”O” – I’O’ = 0
  • formalize the Pure Surplus-Income Ratio, f = vw , and its differential df = vdw +wdv (CWL 15, 144 ff.)
  • finally, understand, affirm, and verify that pricing in the dynamic process can be understood only in the light of the purely-objective, scientifically-significant variables of production acceleration, a’ and a”, and of the ratio of surplus activity to basic activity, p”Q”/p’Q’.  Starting with the equation E’ = P’Q’, we have imp0licit equations :

P’Q’ = p’a’Q’ + p”a”Q”  (CWL 15, 156-62) (44)

P’/p’ = a’ + a”p”Q”/p’Q’   (CWL 15, 156-62) (45)

i.e.,   J = a’ + a”R   (CWL 15, 156-62) (45)

so,  dJ = da’ + a”dR + Rda”   (CWL 15, 156-62) (47)

(The implicit relations of equation (44) remind one of Special Relativity’s field-theoretic, implicit relations among space, time, (space-time), and the ratio of the variable vehicle speed in the observer’s reference frame to the constant of light speed in any inertial reference frame)

By such a process of observation, insight, hypothesis, and verification, one can identify the norms in the process of expansion to which participants must adapt in the personal conduct of their lives.  A set of purely objective relations constitutes the objective mechanical structure of economic activity.  And in particular, at its time and for proper management of the economic process, the basic expansion must be implemented. (Click here)

We set out to indicate the existence of an objective mechanical structure of economic activity, of something independent of human psychology, of something to which human psychology must adapt itself if economic activity is not to become a matter of standing in a tub and trying to lift it. [CWL 21, 56]

Our aim is to prescind from human psychology that, in the first place, we may define the objective situation with which man has to deal, and, in the second place, define the psychological attitude that has to be adopted if man is to deal successfully with economic problems.  Thus something of a Copernican revolution is attempted: instead of taking man as he is or as he may be thought to be and from that deducing what economic phenomena are going to be, we take the exchange process in its greatest generality and attempt to deduce the human adaptations necessary for survival. [CWL 21,42- 43]

Academic macroeconomists must adopt a scientific, dynamic heuristic in order to explain the economic process and dispel their own, their students’, their clients’, the fiscal authority’s, and the monetary authority’s ignorance.

Academic macroeconomists must dispel their own, their students’, and their clients’ ignorance

In equity (the basic expansion following the surplus expansion) should be directed to raising the standard of living of the whole society.  It does not.  And the reason why it does not is not the reason on which simple-minded moralists insist.  They blame greed.  But the prime cause is ignorance.  The dynamics of surplus and basic expansion, surplus and basic incomes are not understood, not formulated, not taught….. [CWL 15, 82]

When intelligence is a blank, the first law of nature takes over: self-preservation.  It is not primarily greed but frantic efforts at self-preservation that turn the recession into a depression, and the depression into a crash. [CWL 15, 82]

Finally, one can explain the normative, stable process (Click here) as properly-managed Gross Domestic Functional Flows.

GDFF = P’Q’ + Π”Κ”  

GDFF = P’Q’ + Π”Κ” = p’a’Q’ + p”a”Q” + π”a”Κ” expansionary + π”a”Κ” R&M by and for self

In summary:

What traditional economic analysis routinely takes as first in the analysis – prices – is analytically last in the analysis.  (Click here and here)  What must be analyzed first is the dynamic process of producing and selling those things which correlated payments of dummy money finally buy.

We accept that, for us, the utterance “quantum” means the most fundamental element or parcel of the productive process; it is the velocitous contribution by a human in a unit of enterprise of an elemental factor of production.  And as the most elemental, we should not be surprised that the statement of composition qi = ΣΣqijk is the first quasi-equation in Lonergan’s analysis.

Total incomes, I = I’ + I”, which are either spent on a cost of living or invested, are ultimately contingent upon the compensated productive outlays, ΣΣpiki. That is, the consumption and investment in a properly managed economy ultimately depend upon the productive contributions qijk.  And in the case of an expanding economy, the incremental expansionary activities are to be financed by proportionately increasing credit, which, of course, is justified by its being used to finance production rather than as a supplement to contributionless expenditures.

 

 

xxx 

(Romer equation for η:  Once it owns the design, the firm can convert η units f final output into one durable unit of good i. S81.  ¶ In parallel with the usual one=sector model and in conformity national income accounting conventions. It is useful to define an accounting measure of total capital K as cumulative foregone output.  Thus K(t) evolves according to the rule

K°(t) =  Y)t) –C(t) (2) S82

where C(t)  denotes aggregate consumption at time t.  because it takes η units units of foregone consumption to create one unit of any type of durable, this accounting measure K is related to durable goods that are actually used in production by the rule K = ηΣi=1xi = ηΣAi=1xi.  Thus H and L are fixed, and K grows by the amount of foregone consumption. S82)

[1] The priora quoad nos – first for us – are the things which we notice first because they are related to our sensitive selves, e.g. hot and cold, fast, slow.  The priora quoad se – first among themselves – are the things or terms which are related to each other, e.g. pressure, volume, temperature, space, time, mass, etc.

Thus the system is an overall functioning explained in terms of interdependent correlated monetary functioning.  Functions represent a deeper level of abstraction that do bookkeepers’ entities.  As correlated, these functions are related to each other rather that related to us; they are priora quoad se rather than priora quoad nos; they are explanatory rather than merely descriptive; they are implicitly defined by the co-relations in which they stand with each other.

[2] More fully, the quote is: One might be reminded here of a parallel in hydrodynamics: if what is at issue is a general specification of the dynamics of free water waves, a premature introduction of general boundary conditions or worse, specific channel conditions, botches the analytic possibilities….the Robinson-Eatwell analysis is hampered, not only by an absence of paradigmatic heuristic thinking in a field whose principles involve ends, but also by their building the economic priora quoad nos of profits, wages, prices, etc., into explanation, when in fact the priora quoad nos are last in analysis: they require explanation. McShane, Philip (1980) Lonergan’s Challenge to the University and the Economy, (Washington, D.C.: University Press of America) P. 124[2]

[3] The priora quoad nos – first for us – are the things which we notice first because they are related to our sensitive selves, e.g. hot and cold, fast, slow.  The priora quoad se – first among themselves – are the things or terms which are related to each other, e.g. pressure, volume, temperature, space, time, mass, etc.

Thus the system is an overall functioning explained in terms of interdependent correlated monetary functioning.  Functions represent a deeper level of abstraction that do bookkeepers’ entities.  As correlated, these functions are related to each other rather that related to us; they are priora quoad se rather than priora quoad nos; they are explanatory rather than merely descriptive; they are implicitly defined by the co-relations in which they stand with each other.

 

[4] More fully, the quote is: One might be reminded here of a parallel in hydrodynamics: if what is at issue is a general specification of the dynamics of free water waves, a premature introduction of general boundary conditions or worse, specific channel conditions, botches the analytic possibilities….the Robinson-Eatwell analysis is hampered, not only by an absence of paradigmatic heuristic thinking in a field whose principles involve ends, but also by their building the economic priora quoad nos of profits, wages, prices, etc., into explanation, when in fact the priora quoad nos are last in analysis: they require explanation. McShane, Philip (1980) Lonergan’s Challenge to the University and the Economy, (Washington, D.C.: University Press of America) P. 124[4]

 

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