Primary Functional Relativities in the Diagram of Rates of Flow

As represented below in the Diagram of Rates of Flow, in Functional Macroeconomic Dynamics the “basic terms are defined by their functional relations.”  The basic terms are precise analytical terms upon which a superstructure of explanatory relations can be constructed. Thus, the terms are of scientific and explanatory significance.

Diagram of Rates of Flow 2

Diagram of Rates of Flow

The Diagram constitutes a technique, tool, and aid to understanding.

I would add that the aims and limitations of macroeconomics (that is, the circulation analysis presented here) make the use of a diagram particularly helpful, …  For its basic terms are defined by their functional relations.  [CWL 15, 54]

The Diagram is explanatory, and it is a frame of reference for understanding and criticism.

(The diagram is) a closely knit frame of reference that can envisage any total movement of an economy as a function of variations in rates of payment, and that can define the conditions of desirable (equilibrated) movements as well as deduce the causes of  breakdowns.  Through such a frame of reference one can see and express the mechanism to which classical precepts are only partially adapted; and through it again one can infer the fuller adaptation that has to be attained. [CWL 21, 111]

I have spoken of the analysis as revealing channels and bringing to light an undertow.  My meaning may become clearer by referring to the distinction sometimes made between general equilibrium (Walras, Wicksell) and partial equilibrium (Marshall).  The channels of circulation replace the overall dominance claimed for general equilibrium theory, but they reveal the conditions under which partial equilibria can exist … 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, the relief given by deficit spending, and the variant provided by multinational corporations and their opposition to the welfare state. [CWL15, 17]

On such a methodological model (i.e. explanatory definition and implicit definition superseding nominal definition)… classes of payments quickly become rates of payment standing in the mutual conditioning of a circulation;  … and from the foregoing dynamic configuration of conditions during a limited interval of time, there is deduced a catalogue of possible types of change in the configuration over a series of intervals. There results a closely knit frame of reference. [CWL 21, 111]

The context for the Diagram of Rates of Flow is found on page 53 ff. of  CWL 15. Depending on one’s momentary interest and point of view, this schematic may alternatively be entitled:

  • The Diagram of Two Operative Circuits Connected by Operative Crossovers
  • The Diagram of Functional Monetary Interdependencies
  • The Configuration of Monetary Conditions
  • The Diagram of Operative Functional Flows of Products, Payments, and Financings
  • The Diagram of Monetary Channels
  • The Diagram of Monetary Transfers
  • The Diagram of Monetary Circulations
  • The Diagram of the Monetary Correlates of the Productive Process
  • The Diagram of interdependent, implicitly-defining, mutually-conditioning velocitous functionings
  • The Double-Circuited, Credit-Centered Diagram which Sublates, Supervenes, and Replaces the Single-Circuit, Credit-Centered Diagram of Macroeconomics Textbooks
  • The Functional Framework
  • (Colloquially) The Way the Process Works
  • (Colloquially, because of its shape) Lonergan’s Baseball Diamond

The diagram prescinds from a) trade imbalances, b) government surpluses and deficits, and c) other collective surpluses and deficits, which can be imaged by superposed circuits lacking vital c’O’ and c”O” flows.

 The diagram depicts abstract  primary dynamic relations which are general and universally relevant in any instance – even in a change of secondary basis resulting from earthquakes, hurricanes, zephyrs, sudden shocks or gradual long-term economic developments.  The abstract primary relation may be applied to concrete secondary determinations of prices, quantities, and velocities in the non-systematic manifold so as to reach concrete relations. These abstract primary relations and concrete secondary determinations are the two components of real concrete relations.

The diagram is credit-centered and contains two monetary circuits connected by crossovers.  The arrows of the diagram represent channels of monetary flows; i.e. flows of so much per standard interval; i.e. velocities and accelerations.

  • Equality of interdependent flows mandates concomitance of flows for continuity and equilibrium.
  • Interdependent functional relations of flows constitute the mutual defining, mutual conditioning, mutual supporting, and mutual constraining among flows.

The paragraphs under the Diagram are as follows:

Per interval, surplus demand [function], I”, pays E” for current surplus products, and receives dividends i”O” from surplus production [i.e. surplus supply function] and i’O’ from basic production [i.e. basic supply function].

Per interval, basic demand [function, I’, pays E’ for current basic products and for its services receives c”O” from surplus supply [function] and c’O’ from basic supply [function].

Vertical arrows represent transactions between the redistributional area and surplus and basic supply [functions]; horizontal arrows the dealings of demand [functions] with the redistributional area. [CWL 15, 55] [11]

Diagram of Rates of Flow 2

Diagram of Rates of Flow

The primary normative relativities of the circulations:

  • O’ = c’O’ + (c”O” = i’O’)
  • M’ = (S’-s’O’) + (D’-s’I’) + G    Money added to the pt.-to-pt. circuit
  • I’ = (O’ + M’)
  • M” = (S”-s”O”) + (D”-s”I”) – G Money added to the pt.-to-line circuit
  • I” = (O” + M”)
  • I’ = E’
  • I” = E”
  • E’ = R’
  • E” = R”
  • Therefore, O’ + M’ = I’ = E’ = R’
  • and,             O” + M” = I” + E” = R”
  • Therefore, I’ = c’O’ + c”O” + (S’-s’O’) + (D’-s’I’) + G
  • and I” = I”O”Expansionary+ I”O” R&M to self + (S”s”O”) + (D”-s”I”) – G

So, by the principle of practical concomitance evident exemplarily in electric circuits and by the laws of continuity and equilibrium ascribed to stable fluid flows, Current Demand = Current Income = Current Supply + Credit.

Therefore re Gross Domestic Functional Flows, and letting Π”Κ” stand for P”Q”pt.-to-pt. basic R&M, and letting  Π”Κ” =π”α”Κ”Expansionary+ π”α”Κ”R&M to and for itself:, descriptive Gross Domestic Product

GNP = Y = C + I + G + (Fex – Fim)

Is replaced by explanatory Gross Domestic Functional Flows

GDFFt= (P’Q’)t+ (ΠΚ”)t= (R’t-1+ M’t) + (R”t-1+ M”t) = I’t+ I”t= E’t+ E”t

 … it will be well at once to draw attention to J.A. Schumpeter’s insistence on the merits of the diagram as a tool. (Schumpeter, History240-43, on the Cantillon-Quesnay tableau.) … First, there is the tremendous simplification it effects.  From millions of exchanges one advances to precise aggregates, relatively few in number, and hence easy to follow up and handle. … Next come the possibilities of advancing to numerical theory.  In this respect, despite profound differences in their respective achievements, the contemporary work of Leontieff may be viewed as a revival of Francois Quesnay’s tableau economique. Most important is the fact that this procedure was the first to make explicit the concept of economic equilibrium.  All science begins from particular correlations, but the key discovery is the interdependence of the whole.… While it is true that a tableau or diagram cannot establish the uniqueness of a system or rigorously ground its universal relevance, it remains that the diagram (of the interconnections of a few precise aggregates) has compensating features that Quesnay’s system of simultaneous equations may imply but does not manifest. … There is the tremendous simplification (a diagram) effects the aims and limitations of macroeconomics make the use of a diagram particularly helpful, …  For its basic terms are defined by their functional relations.  The maintaining of a standard of living (distinct process 1) is attributed to a basic process, an ongoing sequence of instances of so much every so often.  The maintenance and acceleration (distinct process 2) of this basic process is brought about by a sequence of surplus stages, in which each lower stage is maintained and accelerated by the next higher.  Finally, transactions that do no more than transfer titles to ownership (distinct process 3) are concentrated in a redistributive function, whence may be derived changes in the stock of money dictated by the acceleration (positive or negative) in the basic and surplus stages of the process. … So there is to be discerned a threefold process in which a basic stage is maintained and accelerated by a series of surplus stages, while the needed additions to or subtractions from the stock of money in these processes is derived from the redistributive area. … it will be possible to distinguish stable and unstable combinations and sequences of rates in the three main areas and so gain some insight into the long-standing recurrence of crises in the modern expanding economy. [CWL 15, 53 and 177]

Diagram of Rates of Flow 2

Diagram of Rates of Flow