Lonergan’s Laws of Economic Motion

Newton’s Laws of Motion are laws of efficient cause.  In brief:

  1. A body at rest or in uniform motion remains at rest or in uniform motion unless acted upon by an(external, efficient-causal) force
  2. F = ma; force equals mass times acceleration
  3. When one object exerts a force on a second object, the second exerts an equal and oppositely directed force of equal magnitude on the first.

And, masses are defined by F = Gm1m2/d2; i.e. masses are defined implicitly by an equation and are purely relational one to another.

 as to the notion of cause, Newton conceived of his forces as efficient causes, … (CWL 10, 154)

Functional Macroeconomic Dynamics is not a theory of an external efficient cause in a rigidly mechanical system.  It is a theory of the immanent intelligibility of a dynamic process.  This intelligibility is conceptually independent of the efficient-causal agency of the participants.  FMD is a theory of that formal cause of the dynamic process.  FMD is the explanatory theory constituted by explanatory laws of motion.  Its basic explanatory conjugates are precisely-analytical classes of velocitous functional flows, mutually defined by the functional dynamical relations in which they stand internally with one another in the dynamic process.  Its normatively is grounded in the equilibrium which is conceptually primary, operationally mandatory, and processwise diffuse among product and payments flows.  The terms and their interrelations constitute a field theory of relations among n interdependent aggregate and functional flows.This field theory is relevant in any instance.

Unexpected changes in prices and in quantity flows, such as those of the IS-LM and AD-AS efficient-cause models, are not the primary analyzands.  Prices and quantity changes in pretio-quantital flows must be interpreted in the light of the explanatory interdependencies among these functional pretio-quantital flows, of which the prices and quantities constitute the purely relational, pretty-quantital, components, one to another.

In Lonergan’s circulation analysis, the basic terms are ratesrates of productive activities and rates of payments.  The objective of the analysis is to discover the underlying intelligible and dynamic (accelerative) network of functional, mutually conditioning, and interdependent relationships of these rates to one another.  [CWL 15, 26-27  ftnt 27]

The economic process always is the current, purely dynamic economic functioning.  It is intrinsically a process of production and value.  Its immanent intelligibility is constituted by aggregate and functional flows of a) goods and services and b) payments for goods and services.  There is an immanent duality; flows of goods and services meet with and mate with flows of payments. The flows in the productive and monetary order are of so much or so many every so often; i.e. mathematically, they are velocities or rates.

To pique wonder, we list, in brief, bullets of particular key ideas, which we will soon use to characterize and qualify Lonergan’s Laws of Motion explaining the dynamic process.  Key words and phrases will include point-to-point, point-to-line, implicit definition, productive function, monetary function, duality, interdependence, concomitance, continuity, correspondence, correlation, equilibrium, constancy, magnitude, frequency, pretio-quantital, relativity, and non-systematic manifold.  Note that we will be putting words signifying motion in boldface.

  • Factors of production are always moving towards integration in a rectilinear series of applications at rates (velocities): qi = ΣΣqijk and Qi = ΣΣQijk (CWL 15, 30)
  • Payments of dummy money move in circuits at circular velocities; e.g. O = I = E = R (CWL 15, 54) and O’ + O” = I’ + I” = E’ + E” = R’ + R” (CWL 15, 54)
  • The integral composites (completed goods and services) are sold at a velocity of so much or so many per interval.
  • Explanatory, velocitous productive functionings are classified according to the correspondence of their component factoral elements with the factors of composites being sold.  The correspondences are point-to-point, point-to-line, point-to-surface, point-to-volume, or higher. (CWL 15, 23-28)
  • The entire process of velocities and accelerations of products and payments is unitary, endogenous, and purely relative. FMD is a field theory, relevant in any instance, of the immanent intelligibility of internal relations among n objects.
  • In the basic circuit of aggregate and functional pretio-quantital velocities, monetary movements, p’a’q’ + p”a”q” = P’Q’ (CWL 15, 158) implicitly define and condition one another. The implicit equations may be read from left to right or right to left; and the equals sign mandates compromising and compensating adjustments among prices and quantity velocities.
  • There is a normative principle and condition of Concomitance among the velocitous flows; i.e. a normative keeping pace.  Concomitance is quintuply-conditioning with respect to the normative theoretical requirements for 1) continuity, 2) equilibrium, 3) constant value, 4) flows in and out of reserves, and 5) flows of credit in a geometrically increasing surplus expansion.
  • Continuity requires concomitance of circularly-conditioned flows within their circuits.
  • Dynamic Equilibrium within the system requires a concomitant balance of flows between circuits of the unitary system. The condition of dynamic equilibrium is G = c”O” – i’O’ = 0 (CWL 15, 54)
  • Constancy of exchange value requires concomitant and proportionate flows of products and their payments.
  • The financing of geometrically-increasing surplus expansion requires a geometric increase in incomes for investment, which is, at heart, an adjustment of the distribution of incomes.  And similarly for a geometrically increasing basic expansion.
  • Indexes of prices and quantity velocities are vectors.
  • By the inner logic of a long-term, major expansion, the productive flow of point-to-line (capital) items initially increases (accelerates) in a geometric progression.
  • In a long-term expansion, an increase in production of point-to-line capital items gives rise to a later acceleration of point-to-point (consumables) items in a lagged process.

k[fn(t-a) – Bn] = f”n-1(t) –An-1 (CWL 15, 37)

  • The dramatic motion of long-term expansion of production consists of a series of accelerative phases defined by the comparison of the accelerations dQ”/Q” and dQ’/Q’.  The phases may be named proportionate, surplus, basic, and static.
  • The flow of pure surplus income for expansionary investment, vI”, ascends to a maximum and returns to zero. (CWL 15, 144-56)
  • An acceleration of productive transactions implies a accelerating flow of money into the money supply through (S’-s’O’) and (S”-s”O”) for expeditious transacting.
  • Infusions of money through (D’-s’I’) and (D”-s”I”) are intrinsically inflationary.
  • The magnitude and frequency of production turnovers (turnover-period product flows) is correlated with the magnitude and frequency of payments (money flows).
  • The ratio of sales price to cost price, P’/p’ [derived from from p’a’q’ + p”a”q” = P’Q’] (CWL 15, 158), is constantly changing over the course of a long-term expansion. (CWL 15, 156-62)
  • The pretio-quantital flows in the exchange process are explained by the scientist’s formulation of Gross Domestic Functional Flows, replacing the accountant’s, conventional, descriptive Gross Domestic Product.
  • The Hamiltonian function of the kinetic energy of the dynamic process plus the potential energy to be realized is not fixed. Invention keeps increasing the potential of the deepening of the process.  The system is not conservative.

Macroeconomics textbooks deal mostly in static or comparatively static, Walrasian, supply-demand economics.  In New Keynesian Theory, the economic process experiences efficient-causal shocks of unexpected changes in prices, productivity, scarcity, government spending, Federal Reserve manipulations.  In all this, except for changes in scarcity, the ultimate efficient-causal factor is human agency; and in most cases the shock is deleterious; and the so-called theory may be characterized as particular sporadic catastrophism rather than as a unitary, field-theoretic, dynamics relevant in any instance.

To be sure, the economic process has an efficient cause, namely, the human agents in the process, who cause shocks and reactions as a result of our ignorance or malice.  But, in contrast to traditional efficient-cause economics, Functional Macroeconomic Dynamics is a field theory of the immanent intelligibility or formal cause of the process prior to and independent of human psychology.  And FMD is a normative field theory, yielding precepts for adaptation to its laws by plain people.

It is the viewpoint of the present inquiry that, besides the pricing system, there exists another economic mechanism, that relative to this system man is not an internal factor but an external agent, and that the present economic problems are peculiarly baffling because man as external agent has not the systematic guidance he needs to operate successfully the machine he controls. [CWL 21, 109]

… modern mechanics drops the notion of (efficient-causal) force; it gets along perfectly well without it.  It thinks in terms of a field theory, the set of relationships between n objects.  The field theory is a set of intelligible relations linking what is implicitly defined by the relations themselves; it is a set of relational forms.  The form of any element is known through its relations to all other elements. … Field theory is a matter of the immanent intelligibility of the object. (CWL 10, 154)

In Functional Macroeconomic Dynamics, the objective immanent intelligibility of the economic process is conceptually prior to and independent of the subjective human psychology expressing itself in the microeconomic pricing system.  The economic process has an objective mechanical structure.

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]

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]

The point I wish to make is that modern science is not simply an addition to what was known before.  It is the perfecting of the very notion of science itself, of knowing things by their causes, by analysis and synthesis.  What are the causes?  The field of intelligible relations that implicitly define the objects.  The objects with which a science deals are whatever is defined by its field of intelligible relations, whatever falls into that field.  The causes are formal causes; it is only applied science that is concerned with agents and ends. [CWL 10, 155]

Ought there not to be introduced a technical term to denote this type of intelligibility?  … The intelligibility that is neither final nor material nor instrumental nor efficient causality is, of course, formal causality…What we have called the intelligibility immanent in sensible data and residing in the relations of things to one another might be named more briefly formal causality … [CWL  3, 78/101-102]

We now list Lonergan’s Laws of Economic Motion more fully, then, expanded in elaboration buttressed by excerpts.

More fully:

  1. The economic process always is the current, purely dynamic economic functioning.
  2. Factors of production always are moving towards integration in the current productive process from being components to being completed composites in a rectilinear series of applications at rates (velocities) of so much or so many factors every so often: qi = ΣΣqijk and Qi = ΣΣQijk (CWL 15, 30)
  3. Payments of dummy money move in circuits at circular velocities; e.g. O = I = E = R (CWL 15, 54) and O’ + O” = I’ + I” = E’ + E” = R’ + R” (CWL 15, 54)
  4. The component factors of production are velocitously combined into final composites, which are sold at a velocity of so much or so many per interval, so as to be no longer under process.
  5. Explanatoryvelocitous productive functionings are classified according to the correspondence of their component factoral elements with the factors of the composites being sold.  The correspondences are either point-to-point, point-to-line, point-to-surface, point-to-volume, or higher. (CWL 15, 23-28) 
  6. The entire process of velocities and accelerations of production and pretio-quantital flows is unitary, endogenous, and purely relative. The process is explained by the relations of the terms among themselves.  FMD is a field theory, relevant in any instance, of the immanent intelligibility of the internal relations among n objects
  7. In the basic and surplus circuits of aggregate and functional pretio-quantital velocities, monetary movements, p’a’q’ + p”a”q” = P’Q’ (CWL 15, 158) and π”α”Κ”Surplus R&M + π”α”Κ”Pure surplus outlays = Π”Κ”. Outlays on the left and Expenditures on the right implicitly define and condition one another. The implicit equations may be read from left to right or right to left; and the equals sign mandates compensating adjustments among prices and quantity velocities.
  8. There is a normative principle and condition of Concomitance, among the velocitous flows; i.e. a normative keeping pace.  Concomitance is quintuply-conditioning with respect to 1) continuity, 2) equilibrium, 3) constant value, 4) flows in and out of reserves, and 5) flows of credit to a geometrically increasing surplus production.  In particular, Income taken as the flow of payments for productive services must keep pace with Expenditures taken as payments for the flows of products themselves; and vice versa.
  9. Continuity requires concomitance of circularly-conditioned flows from period to period within their circuits. Prescinding from the concept of credit, all Incomes currently received as compensation for productive services (including rent and dividends) are to be spent concomitantly to purchase point-to-point consumables or point-to-line capital items.  And all Receipts currently received as payments for final products are to be spent concomitantly to produce point-to-point consumables or point-to-line capital items.
  10. Dynamic equilibrium within the system requires a concomitant balance of flows between circuits of the unitary system. The condition of dynamic equilibrium is G = c”O” – i’O’ = 0 (CWL 15, 54)
  11. Constancy of exchange value requires concomitant and proportionate flows of products and their payments from period to period.
  12. The immanent intelligibility of the dynamic process reveals a Pure Productive Cycle of expansion for which the process has an exigence.  The cycle is characterized by phases, all of which must be implemented to achieve the pure cycle.  Deviations bring about a systematic necessity for corrective adjustments.
  13. The financing of geometrically-increasing surplus expansion requires a geometric increase in incomes for investment, which is, at heart, an adjustment of the distribution of incomes.  And similarly for a geometrically increasing basic expansion.
  14. Indexes of prices and of quantity velocities are vectors. Goods and services are built up of component factors for money then sold as composites for money. They are either currently under process or, when sold, they are no longer under process.
  15. The product of vectoral indices representing pricing, P, and velocitous composing of quantities of factors, Q, – whether during the productive process of making or at the final vending constituting exit from the productive process – is given by the dot product: P’Q’ = PQ cosA
  16. The periodic expansions of the circulatory flows of pure surplus income for investment effect a mounting stock of capital, which competes against a greater requirement for velocity of Repair and Maintenance Outlays, B. And capital expansion is limited by a finite desire for consumables.  Among other concerns, consumers have to watch their weight.
  17. By the inner logic of a long-term expansion, the productive flow of point-to-line (capital) items initially increases (accelerates) in a geometric progression.
  18. In a long-term expansion, an increase in production of point-to-line capital items gives rise to a later acceleration of point-to-point (consumables) items in a lagged process.     k[fn(t-a) – Bn] = f”n-1(t) –An-1  (CWL 15, 37)
  19. The “dramatic motion” of a long-term expansion of production consists of a series of accelerative phases defined by comparison of the accelerations dQ”/Q” and dQ’/Q’.  The phases may be named proportionate, surplus, basic, and static.
  20. The curves representing the velocitous course of a) pure surplus income for investment, vI”, b) average pure surplus income, F/O, and c) the pure surplus income ratio, f = vw of a circumscribed process ascend to a maximum and return to zero.
  21. An acceleration of productive transactions implies a accelerating flow of money into the money supply through (S’-s’O’) and (S”-s”O”) for expeditious transacting.
  22. In a stable economy. large Infusions of money through (D’-s’I’) and (D”-s”I”) are intrinsically inflationary.
  23. The magnitude and frequency of production turnovers (turnover-period product flows) is correlated with the magnitude and frequency of payments (money flows).
  24. The ratio of P’/p’ (selling price index/cost price index) (Income-expenditure prices/ Outlay – cost prices) is constantly changing over the course of a long-term expansion. (CWL 15, 156-62)
  25. The pretio-quantital flows in the exchange process may be explained by the scientist’s formulation of Gross Domestic Functional Flows, replacing the accountant’s conventional, descriptive, Gross Domestic Product.
  26. The Hamiltonian function of kinetic energy of the dynamic process plus potential energy to be realized is not fixed. Invention keeps increasing the potential of the deepening of the process. The economic system is not conservative.

Expanded and Buttressed by excerpt or by simple reference:

  1. The economic process always is the current, purely dynamic economic functioning.

The productive process is, then, the (current) 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. [CWL 15, 20]

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 for example 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]

  1. Factors of production always are moving towards integration in the current productive process – from being components to being composites – in a rectilinear series of applications at rates (velocities) of so much or so many factors every so often: qi = ΣΣqijk and Qi = ΣΣQijk (CWL 15, 30) (Click here)

 

  1. Payments of dummy money move in circuits at circular velocities as shown inthe Diagram of Rates of Flow ; e.g. O = I = E = R (CWL 15, 54) and O’ + O” = I’ + I” = E’ + E” = R’ + R” (CWL 15, 54)  We point out that the arrows represent functional flows, represented mathematically as velocities in channels.  The dynamic functionings are completely defined by the functional relations in which they stand with one another.  Early versions of the diagram were titled Diagram of Transfers between Monetary Functions, indicating that it is a diagram of flows or of Monetary Transfers.

  1. The component factors of production are velocitously combined into final composites, which are sold at a velocity of so much or so many per interval so as to be no longer under process.

Thus the productive process is a purely dynamic entity.  We began by saying how broadly the term was to be taken.  But it is also necessary to insist how narrowly.  It is not wealth, but wealth in process. … It is none of its own effects, if by effects are understood what has been completed.  It is neither the existence nor the use of durable consumer goods, of clothing, houses, furnishings, domestic utensils, personal belongings, or indeed any item of private or public property that can be listed as a consumer good and has passed beyond the process to become an element of the community’s standard of living.  On the other hand, with regard to producer goods a distinction has to be drawn: they are in the process as a means of production; they are in the process in the sense that labor is in the process or that management is in the process, namely, their use forms part of the process; but once they are completed they are no longer under process, any more than labor or management is under process and being produced. … factories and machinery, railways and power units, warehouses and offices are in the productive process only while being produced; once they are produced, they themselves have passed beyond the process to enter the category of static wealth, even though their use remains a factor of production. CWL 15, 21-22

.5. Explanatory velocitous functionings are classified according to the correspondence of their factoral component elements as either point-to-point or point-to-line with the factors of composites being sold. Basic terms must be precisely defined and questions must be put in their right order.(See CWL 15, pages 23-28)

.6. The entire process of velocities and accelerations of production and of pretio-quantital flows is unitary, endogenous, and purely relative. It is explained by the relations of the terms among themselves.  FMD is a field theory, relevant in any instance, of the immanent intelligibility of the internal relations among n objects.

as to the notion of cause, Newton conceived of his forces as efficient causes, and the modern mechanics drops the notion of force; it gets along perfectly well without it.  It thinks in terms of a field theory, the set of relationships between nobjects.  The field theory is a set of intelligible relations linking what is implicitly defined by the relations themselves; it is a set of relational forms.  The form of any element is known through its relations to all other elements. … Field theory is a matter of the immanent intelligibility of the object. (CWL 10, 154)

The process is unitary.  It is an organic whole with organic interconnections.

Now the general theorem of continuity is that this (organic whole) has a nature that must be respected. … to violate this organic interconnection is simply to smash the organism, to create the paradoxical situation of starvation in the midst of plenty, of workers eager for work and capable of finding none, of investors looking for opportunities to invest and being given no outlet, and of everyone’s inability to do what he wishes to do being the cause of everyone’s inability to remedy the situation.  Such is disorganization.  Continuity, on the other hand, is the maintenance of organization, the stability of the sets and patterns of dynamic relationships that constitute economic well-being in a society. [CWL 21, 74]

(In) every basic insight there is a circle of terms and relations, such that the terms fix the relations, the relations fix the terms, and the insight fixes both.  If one grasps the necessary and sufficient conditions for the perfect roundness of this imagined plane curve, then one grasps not only the circle but also the point, the line, the circumference, the radii, the plane, and equality.  All the concepts tumble out together, because all are needed to express adequately a single insight.  All are coherent, for coherence basically means that all hang together from a single insight.  [CWL 3, 12/36]

Paraphrasing: … If one grasps in a single insight the necessary and sufficient conditions for the continuity, equilibrium, and normative functioning of the interdependent flows of goods and services, as represented by the double-circuited, credit -centered Diagram of Rates of Flow, then one grasps point-to-point relations, point-to-line relations, interdependent functional-flow velocities, basic incomes, ordinary surplus incomes, pure surplus incomes, the normativity of concomitance within circuits, the normative role of credit, etc.  All the explanatory concepts tumble out together, because all are needed to express adequately the single sweeping insightgrasping all in a single viewThe terms fix the relations, the relations fix the terms, and the insight fixes both All concepts and equations are coherent, for coherence basically means that all hang together from a single insight.  (CWL 3, 12/36)

… such a property as invariance is a property, not of a geometrical entity, but of an expression regarding geometrical entities. [CWL 3, 148/171]

 And we say that such a property as invariance is a property, not solely of any particular macroeconomic process, but of a set of expressions explaining all macroeconomic processes.  The theory represented by this full system is a purely-relational field theory; and it is an invariant relevant to explanation of any economic process in any instance.  Transformation equations would preserve the primary relativities of the flows

  1. In the basic and surplus circuits of aggregate and functional pretio-quantital velocities, monetary movements, p’a’q’ + p”a”q” = P’Q’ (CWL 15, 158), and π”α”Κ”Surplus R&M + π”α”Κ”Pure surplus outlays = Π”Κ”. Outlays on the left and Expenditures on the right implicitly define and condition one another. The implicit equations may be read from left to right or right to left; and the equals sign mandates compensating adjustments among prices and quantity velocities.

The concomitance of outlay (p’a’Q’ and p”a”Q”) and expenditure (P’Q’) follows from the interaction of supply and demand.  The concomitance of income (I’) with outlay and expenditure is identical with the adjustment of the rate of saving to the requirements of the productive process. (CWL 15  144).

(d’Inverno 1992, 169): Before attempting to solve the field equations we shall consider some of their important physical and mathematical properties in this chapter.  The full field equations (in relativistic units) are
Gab= 8πTab
  1. The field equations are differential equations for determining the metric tensor gab from a given energy-momentum tensor Tab. Here we are reading the equations from right to left.  … one specifies a matter distribution (on the left by the energy-momentum tensor on the right) and then solves the equations to ascertain the resulting geometry.
  2. The field equations are equations from which the energy-momentum tensor can be read off corresponding to a given metric tensor gab. Here we are reading the equations from left to right.
  3. The field equations consist of ten equations connecting twenty quantities, namely, the ten components of gab and the ten components of Tab. Hence, from this point of view, the field equations are to be viewed as constraints on the simultaneous choice of  gab and Tab.  This approach is used when one can partly specify the geometry and the energy-momentum tensor from physical considerations and then the equations are used to try and determine both quantities completely. [d’Inverno, 1992, 169]

 

  1. There is a normative principle and condition of Concomitance, among the velocitous flows; i.e. a normative keeping pace.  Concomitance is quintuply-conditioning with respect to 1) continuity, 2) equilibrium, 3) constant value, 4) flows in and out of reserves, and 5) flows of credit to a geometrically-increasing surplus expansion.  In particular, Income taken as the flow of payments for productive services must keep pace with Expenditures taken as payments for the flows of products themselves; and vice versa.

Concomitance is, I would claim, the key word in Longergan’s economic thinking.  See the index to For a New Political Economy, where it is the largest entry, and also the comment on it in the conclusion to the Introduction to the Index    Philip McShane, www.philipmcshane.com, Fusion 1,  page 4, ftnt 10

My other extravagance is to bring into focus, by entries under ‘Concomitance,’ the total challenge of the new political economy.  Are we to respect the heart-pulses of the productive machine, or are we to continue the ‘absurdity’ of counterpulsing, locally and globally? (CWL 21, 326 Editor’s Introduction to the Index.)  See also in the Index entries for ‘concomitance’ and ‘absurdity of eliminating cycles.’

Schumpeter, Canton, Quesnay, Leontieff: … 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, History 240-43, 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] [#66]

.9. Continuity requires concomitance of circularly-conditioned flows from period to period within their circuits. Prescinding from the concept of credit, all Incomes currently received as compensation for productive services (including rent and dividends) are to be spent concomitantly to purchase point-to-point consumables or point-to-line capital items.  And all Receipts currently received as payments for final products are to be spent concomitantly to produce point-to-point consumables or point-to-line capital items. (See Provisional Theorem of Continuity (CWL 21, 47-49; and General Theorem of Continuity (CWL 21, 73-75)

The concomitance of outlay and expenditure follows from the interaction of supply and demand.  The concomitance of income with outlay and expenditure is identical with the adjustment of the rate of saving to the requirements of the productive process. CWL 15  144[1]

Paraphrasing: … If one grasps in a single insight the necessary and sufficient conditions for the continuity, equilibrium, and normative functioning of the interdependent flows of goods and services, as represented by the double-circuited, credit -centered Diagram of Rates of Flow, then one grasps point-to-point relations, point-to-line relations, interdependent functional-flow velocities, basic incomes, ordinary surplus incomes, pure surplus incomes, the normativity of concomitance within circuits, the normative role of credit, etc.  All the explanatory concepts tumble out together, because all are needed to express adequately the single sweeping insight grasping all in a single view.  The terms fix the relations, the relations fix the terms, and the insight fixes both All concepts and equations are coherent, for coherence basically means that all hang together from a single insight.  (CWL 3, 12/36)

[1] Equivalent statements of this idea of concomitance are those of “the crossovers balancing” and “the adjustment of the rate of saving to the phase of the process”

… without further clarification Schumpeter acknowledged that dynamic analysis called for a new light on equilibrium.  Such new light arises when, over and above (DSGE’s) equilibria of supply and demand with respect to goods and services (classic microeconomics), there are recognized further equilibria (crossovers balancing, concomitance of outlays with income and income with both outlays and expenditure) that have to be maintained if an economy chooses to remain in a stationary state, to embark on a long-term expansion, to distribute its benefits to the vast majority of its members, and so to return to a more affluent stationary state until such further time as further expansion beckons. … Moreover, such macroequilibria are more fundamental than the microequilibria assembled by Walras.  (FMD’s macroequilibria) are the conditions of a properly functioning economy. (CWL 15, 92)

Now the general theorem of continuity is that this (organic whole) has a nature that must be respected. … to violate this organic interconnection is simply to smash the organism, to create the paradoxical situation of starvation in the midst of plenty, of workers eager for work and capable of finding none, of investors looking for opportunities to invest and being given no outlet, and of everyone’s inability to do what he wishes to do being the cause of everyone’s inability to remedy the situation.  Such is disorganization.  Continuity, on the other hand, is the maintenance of organization, the stability of the sets and patterns of dynamic relationships that constitute economic well-being in a society. [CWL 21, 74]

.10. Dynamic equilibrium within the system requires a concomitant balance of flows of incomes between circuits of the unitary system. The condition of dynamic equilibrium is G = c”O” – i’O’ = 0 (CWL 15, 54)  Also, dynamic equilibrium requires a concomitant balance of flows between the operative circuits and the secondary markets. One circuit must not drain the other, and a secondary pool of excess reserves must not be built up by draining in the operative circuits.

Need the moral be repeated?  There exist two circuits, each with its own final market.  The equilibrium of the economic process is conditioned by the balance of the two circuits: each must be allowed the possibility of continuity, of basic outlay yielding an equal basic income and surplus outlay yielding an equal surplus income, of basic and surplus income yielding equal basic and surplus expenditure, and of these grounding equivalent basic and surplus outlay.  But what cannot be tolerated, much less sustained, is for one circuit to be drained by the other. That is the essence of dynamic disequilibrium. [CWL 15, 175]

This complete explanation yields a normative theory and a set of laws, the normative theory and laws which men themselves administrate in the personal conduct of their lives.  Also, the normative theory explains both dynamic equilibrium and dynamic disequilibria. It defines the objective situation with which man has to deal, and it defines the psychological attitude that has to be adopted if man is to deal successfully with economic problems.  (reference?)

.11. Constancy of exchange value requires concomitant and proportionate flows of products and their payments from period to period.

The third condition is that the dummy must be constant in exchange value, so that equal quantities continue to exchange, in the general case, for equal quantities of goods and services.  The alternative to constant value in the dummy is the alternative of inflation and deflation.  Of these famous twins, inflation swindles those with cash to enrich those with property or debts, while deflation swindles those with property or debts to enrich those with cash; in addition to the swindle each of these twins has his own way of torturing the dynamic flows; deflation gives producers a steady stream of losses; inflation yields a steady stream of gains to give production a drug-like stimulus. [CWL 21, 37-38] 

the real issue is the value of the dummy (money in divided exchange rather than barter)… The (1) relative value (of money) is its usefulness….the scarcity of the (useful) dummy is attended to by the technicians (The Central Bank and the banking system) of the technical rules governing its issuance.  Whether it issues from the printing press or from the credit structure makes no difference.  The (2) economic value (of money as a means of exchange) lies in the human effort against scarcity… the (3) exchange value is the ratio or proportion in which are exchanged the different categories of objects for which men strive because they are useful and scarce….It is now necessary to state the necessary and sufficient condition of constancy or variation in the exchange value of the dummy.  To this end we compare two flows of the circulation: the real flow of property, goods, and services, and the dummy flow being given and taken in exchange for the real flow….Accordingly, the necessary and sufficient condition of constant value in the dummy lies in its concomitant variation with the real flow….More briefly, if there is concomitance between the two flows, then the proportion in which dummies and goods exchange remains the same.  If there is lack of concomitance, then this proportion changes.  But exchange value is a proportion.  Therefore, the concomitance of the two flows is the condition of constant exchange value. [CWL 21, 37-39]

.12. The immanent intelligibility of the dynamic process reveals a Pure Productive Cycle of expansion for which the process has an exigence.  The cycle is characterized by phases, all of which must be implemented to achieve the pure cycle.  Deviations bring about a systematic necessity for corrective adjustments.

.13. The financing of a geometrically-increasing surplus expansion requires a geometric increase in incomes for investment, which, at heart, is an adjustment of the distribution of incomes.

.14. Indexes of prices and of quantity velocities are vectors. Goods and services are built up of component factors for money then sold as composites for money. They are either currently under process or, when sold, they are no longer under process. (See CWL 15, 120-28)

.15. The product of vectoral indices representing pricing, P, and velocitous composing of quantities of factors, Q, – whether during the productive process of making or at the final vending constituting exit from the productive process –is given by the dot product

    • PŸQ = PQ cosA, and
    • (p)Ÿ(a’Q) = (p)(aQ) cosA, and
    • PQ + ΔPQ = (P + dP)(Q + dQ) cos (A + dA), and
    • ΔPQ = PQ[(dP/P + dQ/Q + dPdQ/PQ) cos (A + dA) – 2sin(dA/2)sin(A + dA/2)]
    • (CWL 15, 107-113)

.16. The periodic expansions of the circulatory flows of pure surplus income for investment effect a mounting stock of capital, which competes against a greater requirement for velocity of Repair and Maintenance Outlays, B. And capital expansion is limited by a finite desire for consumables.  Among other concerns, consumers have to watch their weight.

… economic developments are finite, and so no economic development will accelerate indefinitely.  They operate against an increasing resistance, to justify Juglar’s celebrated pronouncement: “the only cause of depression is prosperity.” (as quoted in Schumpeter, History 11240

Now in any expansion it is inevitable that quantities under production run ahead of quantities sold.  Current production is with reference to future sales, and if there is an expansion, then future sales are going to be greater than current sales.  But in the free economies the acceleration factors are not held down to the minimum that results from this consideration.  During the surplus expansion the basic price-spread ratio J will increase from an increase of R, of a”, and also of a’The advance of the price-spread ratio will work out through a rise of the basic price level, and selling prices generally will mount.  Now, when prices are rising and due to rise further, the thing to be done is to buy now when prices are low and sell later when they are high.  There results a large amount of liquid investment.  Each producer orders more materials, more semifinished goods, more finished goods, than he would otherwise.  Moreover, he makes this speculative addition to a future demand estimated upon current orders received, so that the further back in the production series any producer is, the greater [will be] the speculative element contained in the objective evidence of current orders received, the more rosy the estimate of future demand, and the greater the speculative element he adds to this estimate when he places orders with a producer still further back in the series. Thus an initial rise in prices sets going a speculative expansion that makes the acceleration factors quite notable, expands the price spread still more, and stimulates a pace of further acceleration that it will be quite impossible to maintain.  Etc. [CWL 15, 160]

At the root of the depression lies a misinterpretation of the significance of pure surplus income. In fact it is the monetary equivalent of the new fixed investment of an expansion…..our culture can not be accused of mistaken ideas on pure surplus income as it has been defined…; for on that precise topic it has no ideas whatever………However the phenomena referred to by …”pure surplus income” are well known.  Entrepreneurs are quite aware that there are times of prosperity in which even a fool can make a profit and other mysterious times in which the brilliant and the prudent may be driven to the wall……….Thus pure surplus income may be identified best by calling it net aggregate savings and viewing them as functionally related to the rate of new fixed investment. (CWL 15 152-53)

Now it is true that our culture cannot be accused of mistaken ideas on pure surplus income as it has been defined in this essay; for on that precise topic it has no ideas whatever. [CWL 15, 153]

(In a capital expansion,) unless the quantity of money in circulation expands as rapidly as prices rise and, as well, as rapidly as the productive expansion of quantities requires, there will result a contraction of the process: then, instead of adjusting the rate of saving to the requirements of the productive cycle, the productive cycle is arrested to find adjustment to the rate of saving. (CWL 15, 135-37)

.17. By the inner logic of the long-term expansion, the productive flow of point-to-line (capital) items initially increases (accelerates) in a geometric progression.

Now, when the surplus stage of the process is effecting a long-term acceleration of surplus activity but as yet not affecting basic activity, one may expect successive values of Q” to increase in geometrical progression.  This gives an initial period, in which the graph of dQ”/Q” is approximately a level straight line.  Next, as the surplus expansion develops and devotes more and more of its activity to the long-term acceleration of the basic stage, one may expect no more than a uniform acceleration of the surplus stage.  This gives a second period in which dQ”/Q” is curving downwards with successive values in decreasing geometrical progression.  Thirdly, as the expansion approaches its maximum in the surplus stage, dQ”reverts to zero and Q” becomes constant.  In this third period dQ”/Q” is again a level straight line but now coincidental with the x-axis; h” is zero, but h’Q” may be great for a notable period to effect a long-term acceleration of the basic stage which, however, gradually declines as replacement requirements begin to mount. [CWL 15, 122-24]

Now, when the acceleration of Q” is uniform, the long-term potential of the surplus stage is increasing, and so the surplus stage is devoting more and more of its efforts to the long-term acceleration of the basic stage; then Q’ will be increasing at an increasing rate, and time series of its values may stand in a geometrical progression to make dQ’/Q’ a level straight line.  When, however, Q” becomes constant, the acceleration of Q’ becomes uniform, and then dQ’/Q’ will curve downwards; and as replacement requirements begin to mount, this downward curve is accentuated until dQ’ reverts to zero.  Thus, both dQ”/Q’ and dQ’/dQ’ are described as initially straight level lines that eventually curve downwards till the acceleration ratios become zero.  One may well ask for an account of the movement of the acceleration ratios  from their initial zeros to the level straight lines.  ¶ There are two factors in such a movement: short-term acceleration and the period of generalization of a long-term acceleration. … [CWL 15, 126]

.18. In the long-term expansion, an increase in production of point-to-line capital items gives rise to a later acceleration of point-to-point (basic consumables) items in a lagged process

k[fn(t-a) – Bn] = f”n-1(t) –An-1  (CWL 15, 37)

.19. The “dramatic motion” of a long-term expansion of production consists of accelerative phases defined by comparison of the accelerations dQ”/Q” and dQ’/Q’.  The phases may be named proportionate, surplus, basic, and static.

.20. The curves representing the velocitous course of a) pure surplus income, vI”, b) average pure surplus income, F/O, and c) the pure surplus income ratio, f = vw of a circumscribed process ascend to a maximum and return to zero.

.21. An acceleration of productive transactions implies a accelerating flow of money into the money supply through (S’-s’O’) and (S”-s”O”) for expeditious transacting.

While there is no simple and even perhaps no ascertainable correlation between the quantity of money and the volume of exchange activity, it remains true that variations in the volume, if not to result in inflation or deflation, postulate some variations in the quantity.  Now in the long run these variations in quantity can be had only by the introduction of a money of account, … [CWL 21, 104]

.22. In a stable economy, large  Infusions of money through (D’-s’I’) and (D”-s”I”) are intrinsically inflationary.

.23. The velocity of money theories must be based upon the fact that the measurables of magnitude and frequency of production turnovers (product flows) are correlated with the magnitude and frequency of payments (money flows).

This would be the beginnings of a new economics of measurable flows, one that would yield norms of financing, of profit in both normal and innovative economies, etc., etc. [McShane, 1995, v]

money performs a circuit of work moving, say, from expenditure through receipts, outlay, income back to expenditure. [CWL 15, 56]

the work for money to do is to move, say, wheat from the western plains to the householder’s table, and increasing the number of owners that intervene in the process gives no more than a phenomenal increase in the velocity of money. … the velocity of money in the main circuits is tied to the velocity with which goods are produced and sold. …the velocity of money in the main circuits coincides with the velocity, the time interval, between the initiation of production and the moment of final sale. [CWL 21, 61-62]

Thus, the production period has its correlative in the monetary order, namely, the turnover period; and similarly the value of the goods processed or the services rendered in the production period has its monetary correlative in turnover size (magnitude). [CWL 21, 136]

Now, if in each unit of enterprise the magnitude and frequency of payments depend upon the magnitude and frequency of turnovers, it follows that with respect to the aggregate of basic units and again with respect to the aggregate of surplus units we have quantities and circuit velocities of money determined by turnover magnitudes and frequencies.  [CWL 15, 59]

Now every unit of enterprise involves a turnover magnitude and a turnover frequency.  The statement would be merely a truism if it meant no more than that the rates of payment received and made by the unit of enterprise involved quantities and velocities of money.  But the statement is not a truism, for it involves a correlationbetween the quantities and velocities of rates of payment and the quantities and velocities of goods and services. [CWL 15, 57]

the quantity alternative in the rates of payment is conjoined with the quantity alternative in the rate of production, and the frequency alternative in the rate of payment is conjoined with the frequency alternative in the rate of production (and sale).  The two cases of quantity-velocity are not only parallel but also correlated. [CWL 15, 57]

.24. The ratio of P’/p’ (selling price index/cost price index) (Income-expenditure prices/ Outlay – cost prices) is constantly changing – expanding, then contracting – over the course of a long-term expansion. (CWL 15, 156-62)

  • P’Q‘ = p’a’Q’ + p”a”Q”
  • P’/p’ = a’ + a”p”Q”/p’Q’
  • J = a’ + a”R
  • dJ = da’ + a”dR + Rda”

(the model and the analysis) involves an enlargement of perspective and a proper ordering of assumptions.  But I must note immediately how intimately the ordering is within the perspective: “as the hypothesis is the principle in mathematics so the end is the principle in praxis.” (Lonergan: Theology and Praxis) The movement of Lonergan’s analysis might be described as a paradigmatic descent from a concrete heuristic of the productive process determined by the end of that process.  The monetary order is conditioned by, and correlated to, the rhythms of production adequate to the end.  Only later in the analysis can one arrive at an adequate account of the monetary distributions commonly called wages and profits.  That account springs from a characterization of possible types of productive rhythms…Thus, for example, one determines the oscillations of basic income which may be briefly described as anti-egalitarian during basic expansions.  Again, distinctions are required within surplus income: what requires attention during expansion is that fraction of I”, which we may call pure surplus income, that goes to new fixed investment.  It is evidently subject to cyclic variation. [McShane 1980, 125-126]

To increase the rate of saving (in a capital-goods-expansion phase), increase the income of the rich (who have a lower average propensity-to-consume percent). … to decrease the rate of saving (in a consumer-goods-expansion phase), increase the income of the poor (who have a higher average propensity-to-consume percent). … The foregoing is the fundamental mode of adjusting the rate of saving to the phases of the productive cycle.  It reveals that the surplus expansion is anti-egalitarian, … but it also reveals the basic expansion to be egalitarian, for that expansion postulates that increments go to low incomes … [CWL 15, 135-37]

To increase the rate of saving (in a capital-goods-expansion phase), increase the income of the rich (who have a lower average propensity-to-consume percent). … to decrease the rate of saving (in a consumer-goods-expansion phase), increase the income of the poor (who have a higher average propensity-to-consume percent). … The foregoing is the fundamental mode of adjusting the rate of saving to the phases of the productive cycle.  It reveals that the surplus expansion is anti-egalitarian, … but it also reveals the basic expansion to be egalitarian, for that expansion postulates that increments go to low incomes … [CWL 15, 135-37]

.25. The pretio-quantital flows in the exchange process may be explained by the macroeconomic  scientist’s formulation of Gross Domestic Functional Flows, replacing the accountant’s conventional, descriptive Gross Domestic Product. (Click here)

the set of terms and relations capable of explaining the phenomena of the business or trade cycle would not be the same as any given pricing system that automatically coordinates a vast coincidental manifold of decisions of demand and decisions of supply,  Such a system comes to sight as bookkeeper’s entities that form the basis of the preliminary descriptive classifications that need to be explained: they are the similarities “first-for-us.”  The relevant set of explanatory terms and relations would have to expose similarities that reside in the relations of things to one another or what is “first-in-itself”: namely both the dynamic elements (distinct, implicitly-defined, productive and monetary functionings)and the differentials (velocities and accelerations) of the economic mechanism which reveal the significance of aggregate changes in prices that by themselves are in need of interpretation……prices as a concern for the bookkeepers or accountants are known- first-to-us by description and commonsense classification; and that (Lonergan’s) own functional analysis of production and circulation reveals an explanatory system known-first-in-itself (continue to lvii “significance”) CWL 15  lvi

  • 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

.26. The Hamiltonian function of kinetic energy of the dynamic process plus potential energy to be realized is not fixed. Invention keeps increasing the potential of the deepening of the process. The economic system is not conservative.