Explanation By Gross Domestic Functional Flows To Supplement Description By Gross Domestic Product

A distinction has been drawn between description and explanation. Description deals with things as related to us. Explanation deals with the same things as related among themselves. The two are not totally independent, for they deal with the same things and, as we have seen, description supplies, as it were, the tweezers by which we hold things while explanations are being discovered or verified, applied or revised. … [CWL 3, 291/316]

The analysis of the overall dynamic functioning, which we call in nominal terms the economic process, must seek the explanation of the process. It must seek the objective immanent intelligibility among the interdependent, dynamic “functionings” which altogether constitute the process. The functionings are rates of so much or so many every so often, and, thus, they are velocities. And the scientific analysis must be in terms of abstract, implicitly-defined, explanatory conjugates rather than in terms of the descriptive accountants’ unities of merely legal or proprietary entities called “firms.”

An ‘accountant’s unity’ … is a category used in (conventional) accounting. For Lonergan, (conventional) accounting generally denotes an enterprise within common sense which uses descriptive, as contrasted with explanatory terms … . Insofar as that is true, the accountant’s unity is not an adequate index for the normative, explanatory analysis of the productive process. [CWL 15, page 26, ftnt. 26]

“Functional” is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory; Lonergan illustrates his basic meaning of ‘explanation’ by referring to D. Hilbert’s method of implicit definition: … In Lonergan’s circulation analysis, the basic (dynamical) terms are rates (implicitly defined by their functional relations to one another) – rates of mutually conditioning, and interdependent productive activities and rates of mutually conditioning, and interdependent payments. The objective of analysis is to discover the … functional (inter)relationships (which implicitly define these rates and explain the dynamics of these rates to one another). [CWL 15, 26-27 ftnt 27 slightly rearranged]

It is true that the distinction between basic and surplus is functional and that a number of activities may at one time be surplus and at another basic. So (the conventional accounts of) labor, services, power, transportation, materials can be known as contributions to the basic or surplus function only through further determinations and even special inquiries……….still the analysis itself will provide rather convincing indicators, and as expertise develops the new tricks of a new trade, there well may be discovered methods of attaining a sufficient accuracy for practical purposes. [CWL 15, 72]

The productive process is the purely current, purely dynamic process.

The productive process is, then the aggregate of activities proceeding from the potentialities of nature and terminating in a standard of living. Always it is the current process, and so it is distinguished both from the natural resources, which it presupposes, and from the durable effects of past production. … and it is a purely dynamic entity. … the current process is always a rate of activity … the basic terms are rates (velocities) – rates of productive activities and rates of payments. CWL 15, 20-21

Taking into account past and (expected) future values does not constitute the creative key transition to dynamics. Those familiar with elementary statics and dynamics (in physical mechanics) will appreciate the shift in thinking involved in passing from equilibrium analysis (of a suspended weight or a steel bridge)…to an analysis where attention is focused on second-order differential equations, on d²θ/dt², d²x/dt², d²y/dt², on a range of related forces, central, friction, whatever. Particular boundary conditions, “past and future values” are relatively insignificant for the analysis. What is significant is the Leibnitz-Newtonian shift of context. [McShane 1980, 127]

We wish to split out, so as to symbolize and formally recognize, the two accelerative and three non-accelerative functional flows in the Diagram of Rates of Monetary Flows.

let h stand for the overall long-term-acceleration coefficient of surplus rates of production (CWL 15, 116 and 206)
let h’ stand specifically for the long-term-acceleration coefficient of surplus rates of production expanding the basic circuit (116 and 206)
let h” stand specifically for the surplus long-term-acceleration coefficient of surplus rates of production expanding the surplus circuit (116 and 206)
let h = h’ + h” (116)
let (1 – h) stand for the overall non-accelerative coefficient of rates of surplus production of repair, maintenance, and replacement products, which preserve existing capacity but have no accelerative effect (116)
let β (beta) stand for the βasic circuit’s fraction of the (1 – h) non-accelerative coefficient
let σ (sigma) stand for the σurplus circuit’s fraction of the (1 – h) non-accelerative coefficient
let β + σ = 1
let Υ (gamma) stand for the fraction of the basic circuit’s Outlays that are directed by that circuit’s workers to the purchase of a standard of living
let τ (tau) stand for the fraction of the surplus circuit’s Outlays that are directed by that circuit’s workers to the purchase of a standard of living
let Q’, Q”, a’Q’, a”Q”, Κ”, ”α”Κ”_{Pure expansionary surplus},”α”Κ”_R&M_{to self,}be rates of sale or production

.1. hQ” has a long-term acceleration effect (116)
.2. h’Q” has a long-term acceleration effect in the basic circuit (116)
.3. h”Q” has a long-term acceleration effect in the surplus circuit (116)
.4. (1-h)Q“ has no long-term acceleration effect (116)
.5. β(1-h)Q“ stands for the rate of production of non-accelerative repair-maintenance-replacement producer goods produced in the surplus circuit for use by the basic circuit (116)
.6. σ(1-h)Q“ stands for the rate of production of non-accelerative repair-maintenance-replacement producer goods produced in the surplus circuit for use by the surplus circuit (116)
.7. γO’ stands for the portion of Basic Outlays directed by basic workers to the purchase of a standard of living, which “consumer goods”, by purchase, exit the purely current, purely dynamic productive process
.8. τO” stands for the portion of Surplus Outlays directed by surplus workers to purchase of a standard of living, which “consumer goods”, by purchase, exit the purely current, purely dynamic productive process
.9. let π”α”Κ”_expansionarySurplus Outlays produce at rates h”Q” + h’Q” to expand the two circuits

To identify and separate rates of expansionary and non-expansionary surplus Outlays for products to be used by the surplus circuit only:

.10. let π”α”Κ”_{R&M by and for self}Surplus Outlays produce non-accelerative repair-maintenance-replacement products for the point-to-line surplus circuit at rates σ(1-h)Q“
.11. let Π”Κ” = π”α”Κ”_expansionary + π”α”Κ”_{R&M by and for self} represent Expenditures (E” – c”O”) in the Surplus Circuit for products produced in the surplus circuit
.12. Let c”O” _{R&M by surplus for basic} Surplus Outlays produce non-accelerative repair-maintenance-replacement products for the point-to-point basic circuit

We display the familiar Diagram of Rates of Monetary Flow, whose arrows represent rates of flows in “channels” of circulation; then we annotate more fully certain parts of that Diagram of Rates of Monetary Flow:

More positively, the channels account for booms and slumps, for inflation and deflation, for changed rates of profit, for the attraction found in a favorable balance of trade, …. [CWL 15, 17]

The same table in larger print:

The numbers in the parentheses following the equations below refer either to the set of numbered equations above or to page numbers in CWL 15. Also, for simplicity, we are assuming stable prices; thus we can apply symbols β, σ, γ, and τ to both rates of monetary Outlays and rates of production of Quantities.

By concomitance and correlation of rates of outlays, rates of costs flows, and associated accelerative coefficients, we have:

c’O’ = p’a’Q’ from basic Outlays O’ to purchase γQ’ (156-59)
c”O” = p”a”Q” from surplus Outlays O” for β(1-h)Q“ directed to purchase τQ’ (5) (156-59)
i’O’ from basic Outlays is for purchase of β(1-h)Q“ non-accelerative repair-maintenance-replacement products. (5)

Note that satisfaction of the condition of equilibrium by adjustment of rates of income for dealings between the two circuits is G = c”O” – i’O’ = 0. Thus, per the assumption of stable prices, we have assigned the rate β(1-h)Q“ to both c”O” and i’O’. Thus,

β(1-h)Q“ – β(1-h)Q“ = 0

Whether by movements c”O” and i’O’ or by movements through the Redistributive Function, the two circuits must find a way to balance the flows between them so that each maintains its own continuity and equilibrium; i.e. by making sure that neither circuit drains the other, for that would be the essence of dynamic disequilibrium.

For the expansionary rate of surplus production we have:

i”O”_expansionary = π”α”Κ”_{Pure expansionary surplus}produces h”Q“ + h’Q“ (2) and (3)

For the non-expansionary rate of surplus production for the surplus circuit’s own benefit as to capacity we have:

i”O”_R&M = π”α”Κ”_{By and for itslef}produces σ(1-h)Q“ (6)

Thus, preliminary Gross Domestic Functional Flows in terms of the rates of Expenditures-Receipts (E’ = P’Q’ and E” = Π”Κ”) and of correlated rates of Outlays-Incomes (p’a’Q’ + p”a”Q” for basic products and π”α”Κ”_expansionary + π”α”Κ”_{R&M by and for self} for surplus products) would be:

P’Q’ = p’a’Q’ + p”a”Q” (156-59)
Π”Κ” = π”a”Κ” _expansionary + π”a”Κ” _{R&M by and for self}

And, thus, for Explanation by Gross Domestic Functional Flows to Supplement Description by Gross Domestic Product, we have:

GDFF = P’Q’ + Π”Κ”

Again, we display The Diagram of Rates of Monetary Flows for the reader’s convenience.

So, we have for primary normative monetary circulations in the two circuits of the Diagram, assuming

that all expansionary money enters the system through Supply (S’-s’O’) and (S”-s”O”),
that “the variables O’, O”, I’, and I” are to be regarded as aggregates that are ‘completed’ only after all redistributive transactions have been taken into account” (CWL 15, 200), and
(D’-s’I’) and (D”-s”I”) equal zero because we are prescinding here from CWL 15, 64’s “theory of booms and slumps.”
- R’ = E’ (CWL 15, 54)
- R” = E” (CWL 15, 54)
- I’ = O’ + M’ (CWL 15, 54)
- I” = O” + M” (CWL 15, 54)
- G = c”O” – i’O’ (CWL 15, 54)
- G = c”O” – i’O’ = 0 (CWL 16, 50)
- M’ = (S’ – s’O’) + (D’ – s’I’) + G (CWL 15, 54)
- M” = (S” – s”O”) + (D” – s”I”) – G (CWL 15, 54)
- (S’-s’O’) = ΔT’ + (O’ – R’) + ΔR’ (CWL 16, 67)
- (S”- s”O”) = ΔT” + (O” – R”) + ΔR” (CWL 16, 67)

Thus, for example, assuming that the crossovers balance so as to satisfy the condition of dynamic equilibrium, G = c”O” –i’O’ = 0, by the principle of concomitance and the role of credit to bridge brief time gaps, we would have for the basic circuit (denoted by single superscripts):

P’Q’: R’ = E’ = I’ = O’ +M’ (CWL 15, 54)
P’Q’: R’ = E’ = I’ = O’ +[S’ – s’O’] + [D’ – s’I’] (CWL 15, 54)
P’Q’: R’ = E’ = I’ = O’ + [ΔT’ + (O’ – R’) + ΔR’] + [D’ – s’I’] (CWL 15, 54, and 66-67)

Similarly, by changing the basic circuit’s single superscript (‘) to the surplus circuit’s double superscript (“), we would have for the surplus circuit:

Π”Κ”: R” = E” = I” = O” +M” (CWL 15, 54)
Π”Κ”: R” = E” = I” = O” +[S”’ – s”O”] + [D” – s”I”] (CWL 15, 54)
Π”Κ”: R” = E” = I” = O” + [ΔT” + (O” – R”) + ΔR”’] + [D” – s”I”] (CWL 15, 54, and 66-67)

More simply, we consider final Gross Domestic Functional Flows in a stable economy, fully funded so as to not require flows to or from the Redistributive Function, and explained in terms of receipts and outlays rather than described by GDP.

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 Functional Macroeconomic Dynamics, the Normative Pure Cycle of Expansion stands in contrast and in opposition to the trade cycle of boom and systematically-necessary, corrective slump. The pure cycle is an ideal and general conception. It is a normative theory and framework wherein a) flows in a circular conditioning within a circuit keep pace, b) crossovers flows in a crossover conditioning between circuits balance, c) money is supplied to the supply functions by the issuing authorities in proper proportion to the values of the expanded transactions, d) accelerations are properly constrained, e) the basic expansion is implemented subsequent to the surplus expansion, f) money needed in the circuits or for prudent reserves for catastrophe and retirement is not drained into idleness in the Redistributive Function, and thus f) the full potentials of production and employment are achieved.