Two Summaries in Functional Macroeconomic Dynamics

.I.   Summary of the Analysis:  Heuristic, Observations, and Discoveries

.II.  Summary of the Argument (verbatim from CWL 15, 5-6)

.III. Supplement to the Summaries

.I.  Summary of the Analysis:  Method, Observations, and Discoveries

.I.a.  Heuristic

  1. Scientific analysis of the objective economic process prescinds from the merely subjective human psychology of the participants.
  2. The process must be understood as always the current, purely dynamic economic process.  It is an overall velocitous functioning whose real components are interdependent, mutually defining functional activities.
  3. Thus, in order to explain a dynamic process the analyst must adopt a scientific and dynamic heuristic. The explanation will be constituted by an interrelated and fully coherent set of differentials with respect to time; i.e. a set of velocities and accelerations of interdependent constituent functionings.
  4. Money is understood as a dummy invented by humans to enable efficient operation of a vast and complicated exchange process. And money properly circulates in abstract circuits of Outlays, Incomes, Expenditures, and Receipts.
  5. Explanation is in the form of terms related to one another rather than in terms related to us. The velocitous functions will be implicitly defined by the relations in which they stand with one another.  These explanatory terms will be mutually defining and mutually conditioning.
  6. Also, since the economic process is a concrete functioning, the explanation will consist of primary abstract relativities applied to secondary concrete determinations from the non-systematic manifold.
  7. The complete set of abstract terms-in-relation will be unitary; as abstract it will constitute an invariant, a field theory applicable in any instance.
  8. Since the process is dynamic, the abstract explanatory terms are rates (velocities), and the explanatory relations are relations of velocities to correlated velocities and of accelerations to correlated accelerations.  By implicit definition, the terms will define the relations, and the relations will define the terms, and insight into the correlations among the measured data will fix both the terms and the relations.
  9. The analysis will result in an explanation of the process rather than in a description or statistical aggregation of accountant’s terms. The interdependent terms of explanation will be called explanatory conjugates.
  10. The completely coherent explanation must be a generalization at an adequate level of abstraction, so as to sublate all the disputes among incomplete, psychopolitical, non-explanatory, conflicting, and multiply flawed isms and schools of macroeconomics.

.I.b.  Observations

  1. Real analysis must begin with analysis of the structure of the production function, which is served by dummy money invented by humans to enable expeditious transactions, rather than dominated by money to be hoarded.
  2. As a dynamic functioning, the process is observed to consist of rates or velocities: a) rates of production, b) rates of exchange using money, and c) rates of finance supplying new money.
  3. It is observed that products are produced over time in a rectilinear series of additions of value by compensated humans; and the rate of a compensated contribution is a quantum of the dynamic process. qi = qijk, pi = pijk (CWL 15, 30)
  4. It is also observed that phenomena described as “trade cycles” consist of excessive capital investment accompanied and fueled by excessive credit, then followed by declines of investment, increased contraction and liquidation, higher unemployment, and tightening of the granting of credit.
  5. The sciences of electromagnetics, hydrodynamics, and macroeconomics regard radically different phenomena and, thus, are radically different sciences. However, each involves flows in circuits.  So, clues to adequate abstraction and general explanation in macroeconomic flows in circuits may be gleaned in the formulae expressing concomitance, continuity, and equilibrium of flows in electric circuits and in variable hydrodynamic systems.  The principles of identity and non-contradiction will apply.  Similars are similarly understood.

.I.c  A Mix: Heuristic, Observations, and Discoveries

  1. The particular methodology of the analyst and econometrician will be guided by a dynamic heuristic; the analysis identifies classes of point-to-point (“basic”) and point-to-line (Surplus”) velocities, which are of precise analytical significance; their coherent relations among themselves constitutes a complete theory and complete explanation, in accordance with the Canon of Complete Explanation.
  2. In a stable, non-increasing process, the implicitly-defined explanatory conjugates and their relations among themselves include, by the principle of concomitance, O’ = E’ = p’a’Q’ + p”a”Q”, O’ = I’ = E’, E’ = I’ = P’Q’ = p’a’Q’ + p”a”Q”.
  3. This complete explanation yields a normative theory and a set of laws, the normative theory and laws which men themselves are bound to 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.
  4. It is “Insight,” which yields terms related to one another as required for explanation of the process. The terms are defined by the relations; the relations determine the meaning of the terms; and it is insight that discovers the immanent intelligible unity consisting of terms and their defining relations.  All the interrelated and mutually defining concepts of an act of understanding (an insight) tumble out together.  To know one term is to know all terms.
  5. Abstraction is the attainment of insight that reveals in the data what is variously named as the significant, the relevant, the important, the essential, the idea, the form. (CWL 3, 88/) … intelligence concentrates on the significant to abstract from all else. (CWL 3, 356/) To abstract is to grasp the essential and to disregard the incidental, to see what is significant and set aside the irrelevant, to recognize the important as important and the negligible as negligible. (CWL 3, 30/)  Check out  CWL 3, 141, 160, 130-31, 175-76
  6. Insight yields and reveals implicit definition. The technique of implicit definition is used to discover explanatory terms implicitly–defined by their functional relations to one another.  Thus, familiar terms — even though their utterance may be familiar to us as concrete and descriptive — can be assigned abstract and explanatory meanings.
  7. Since the process is an overall dynamic functioning, the explanation will be constituted by an interrelated and fully coherent set of differentials with respect to time; i.e. a set of velocities and accelerations of interdependent constituent functionings. “Coherent” means they hang together and are consistent with one another.
  8. The concrete economic process exists in a non-systematic manifold consisting of scattering or diverging series of conditions. Thus, prediction is impossible in the general case.
  9. Thus, explanation of the concrete process will contain two components: first, an invariant primary component consisting of abstract, invariant, primary relativities, relevant in any instance; plus, second, a secondary component of concrete determinations incidently decided upon in the non-systematic manifold – such as prices – to which the abstract and primary relativities can be applied to reach explanation of the particular concrete instance.
  10. Thus prices are understood in the light of the significant and invariant abstract primary relativities which explain the process in any instance. Prices are not first in the analysis (as in the AD-AS and the IS-LM, DSGE Models); they are elements to be explained and, thus, last in the analysis.
  11. These differences and correlations (of the productive process of a hierarchical, advanced economy) are projected into their monetary correlates to set up classes of payments.  occurring in an exchange economy. [CWL 15, 39]
  12. Price changes may be real and relative or monetary and absolute.
  13. Negatively speaking, since the explanatory terms and relations will be abstract and purely relational, the terms will contain no residues describing things in their relations to us. Scientific analysis of the objective process refuses to admit descriptive, non-explanatory terms such as personal wealth, social class, or interest charges as they affect one personally.
  14. The primary function of credit is to bridge the gap in time between payments made and payments received. Thus, for example, the three-years of Outlays-Incomes for construction of a new and additional large factory increases supply of the factory’s products and the associated basic Expenditures-Receipts only after the three years are correlated.
  15. The lagged technical accelerator is the general formulation of expansion ………………………..kn[f’n(t-a)-Bn] = f”n-1(t) – An-1 [CWL 15, 37]
  16. Lags requiring credit are notable in a vast and complex long-run expansion consisting of, first, innovation and its time-consuming, credit-requiring implementation, and, only later, production and delivery of basic goods and services.
  17. Thus, there are two (or more)circuits of Outlays, Incomes, Expenditures, Receipts. The theory is a two-circuit theory.  These circuits have dealings with one another, but a condition of dynamic equilibrium is that neither may be allowed to drain the other; i.e. crossovers must balance in any phase of an expansion..
  18. Again, money is understood as a dummy invented by humans to enable efficient operation of a vast and complicated exchange process; and money properly circulates in abstract circuits of Outlays, Incomes, Expenditures, and Receipts requiring a keeping apace (concomitance) and intercircuit balance as conditions of continuity and equilibrium.
  19. The turnover magnitudes and frequencies of production are correlated with the turnover magnitudes and frequencies of payments.  Recognition and formulation of such replaces a vague quantity theory of money or velocity theory of money.
  20. The issuance of new money for expansionary transactions should be through expanding supply functions so that the money is “justified” by production of goods and services of value.
  21. The abstract and purely relational set of terms and relations that are discovered constitute a relativistic field theory, universally relevant and applicable in any instance. Examples of such purely relational field theories in physics are Clerk-Maxwell’s electromagnetic equations (absent the descriptive residue of force with its connotation of concrete muscular effort) and Einstein’s Special Relativity
  22. The Canon of Parsimony will be honored by explanation by means of only a few implicitly-defined terms easily handled
  23. The interest rate will be revealed as an inner intrinsic relation among the explanatory functionings constituting the economic process. Its manipulation by the Fed is double edged; it is neither an external single-effect magic lever nor an effective corrective of distortive divergence from the norms of monetary flows.
  24. The scientific analysis reveals an immanent set of intelligible relations modeled in the Diagram of Rates of Flow.  The analysis of economic expansion reveals a set of general relations between the production of capital goods and consumer goods as the process expands.  The Diagram of Rates of Flow provides the scheme of intelligible and normative interdependencies and the condition of equilibrium to Lonergan’s diagrams of the phases of expansion; simultaneously, the diagrams of the phases of expansion provide magnitudes and frequencies back unto the Diagram of Rates of Flow.
  25. Again, the phenomena of electromagnetics, fluid dynamics, and macroeconomics are radically different phenomena, and, thus, constitute radically different fields of inquiry. However, each involves flows in circuits.  Clues to adequate abstraction and general explanation in macroeconomic flows in circuits may be gleaned in the formulae expressing concomitance, continuity, and equilibrium of flows in electric circuits and in variable hydrodynamic systems.  Similars are similarly understood.
  26. A. Einstein discovers general, explanatory significance in a ratio of velocities; γ = (1 – v2/c2)½ in his Field Theory of Special Relativity. In his Macroeconomic Field Theory, B. Lonergan discovers general, explanatory significance in ratios of a) prices: P’/p’, b)  velocities: (p”Q”/p’Q’) and vI”/(I’ + I”), and c) accelerations dQ’/Q’ and dQ”/Q” and their comparison with one another.

.II.  Summary of the Argument  (verbatim from CWL 15, 5-6)

The present inquiry is concerned with relations between the productive process and the monetary circulation.  It will be shown 1) that the acceleration of the process postulates modifications in the circulation, 2) that there exist ‘systematic,’ as opposed to, windfall profits, 3) that systematic profits increase in the earlier stages of long-term accelerations but revert to zero in later stages – a phenomenon underlying the variations in marginal efficiency of capital of Keynesian General Theory, 4) that the increase and decrease of systematic profits necessitate corresponding changes in subordinate rates of spending –  a correlation underlying the significance of the Keynesian propensity to consume, 5) that either or both a favorable balance of trade and domestic deficit spending create another type of systematic profits, 6) that while they last they mitigate the necessity of complete adjustment of the propensity to consume to the accelerations of the process, 7) that they cannot last indefinitely, 8) that the longer they last, the greater the intractability of ultimate problems.  From the premises and conclusions of this analysis it will the be argued 9) that prices can not be regarded (by the stewards of the economy) as ultimate norms guiding strategic economic decisions, 10) that the function of prices is merely to provide a mechanism for overcoming the divergence of strategically indifferent decisions or preferences, and 11) that, since not all decisions and preferences possess this indifference, the exchange economy is confronted with the dilemma either of eliminating itself by suppressing the freedom of exchange or of certain classes of exchanges, or else of effectively augmenting the enlightenment of the enlightened self-interest that guides exchanges.   [CWL 15, 5-6]

.III. Supplement to the Summaries

We supplement and substantiate elements of the Two Summaries by reference to other sections of this website and by excerpts, which are not sequenced in any special order.

See related entries on this website.

… Special Relativity is primarily a field theory, that is, it is concerned not with efficient, instrumental, material, or final causes of events, but with the intelligibility immanent in data; but Newtonian dynamics seems primarily a theory of efficient causes, of forces, their action, and the reaction evoked by action. … Special Relativity is stated as a methodological doctrine that regards the mathematical expression of physical principles and laws, but Newtonian dynamics is stated as a doctrine about the objects subject to laws.  [3, 43/67]

In Clerk-Maxwell’s laws of electromagnetism, the electric intensity and the magnetic intensity are implicitly defined by a pattern of relationships, not by verbal description.  And the pattern of relationships is explanatory and of scientific significance.

  • ∇ X E = (-1/c)H’
  • ∇ X H = (+1/c)E’
  • ∇•H = 0
  • ∇•E = 0

Similarly, the law of cosines: c2 = a2 + b2 -2ab(cos C) is both purely relational and more general than the Pythagorean formula; it contains the Pythagorean Theorem as a mere special case in which the angle C between sides a and b happens to equal 90o  and, therefore, (cos C) happens to equal 0.  Mere special cases , whether in mechanics or macroeconomics are of little instance to the theorist operating a a sufficiently general level of abstraction.

again, 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 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.  What is a mass?  A mass is anything that satisfies the fundamental equations that regard masses.  Consequently, when you add a new fundamental equation about mass, as Einstein did when he equated mass with energy, you get a new idea of mass.  Field theory is a matter of the immanent intelligibility of the object. [CWL 10, 154]

Maxwell, at first, did not adopt the modern concept of a field as a fundamental quantity that could independently exist. … the situation was resolved by the introduction of the Special Theory of Relativity by Albert Einstein in 1905.  This theory changed the way the viewpoints of modern observers were related to each other.  They became related to each other in such a way that velocity of electromagnetic waves in Maxwell’s theory would be the same for all observers.  By doing away with the need for a background medium, this development opened the way for physicists to start thinking about fields as truly independent entities. [Wikipedia (3), Field (Physics), page 3 of 11]

Those familiar with elementary statics and dynamics will appreciate the shift in thinking involved in passing from (static) equilibrium analysis … to an analysis where attention is focused on second-order differential equations, on  d2θ/dt2,  d2x/dt2,  d2y/dt2,  on the primary relativities of a range of related forces, central, friction, whatever.  Particular secondary boundary conditions, past and future pricings and quantities, are relatively insignificant for the analysis of the primary relativity immanent in, and applicable to, every instance of the process.  What is significant is the Leibnitz-Newtonian shift of context. [McShane, 1980, 127]

Lonergan is alone in using this difference in economic activities to specify the significant variables in his dynamic analysis… no one else considers the functional distinctions between different kinds of productive rhythms prior to, and more fundamental than, wealth, value, supply and demand, price levels and patterns, capital and labor, interest and profits, wages, and so forth….only Lonergan analyzes booms and slumps in terms of how their (explanatory) velocities, accelerations, and decelerations are or are not equilibrated in relation to the events, movements, and changes in two distinct monetary circuits of production and exchange as considered both in themselves (with circulatory, sequential dependence) and in relation to each other by means of crossover payments. [CWL 15, Editors’ Introduction, lxii]

(Lonergan) approaches the focus armed with precise analytic distinctions between basic and surplus activities, outlays, incomes, etc. [CWL 21, xxvi]

…  the productive process (is) a purely dynamic entity, … It is to be shown that the correspondence between elements in the productive process and elements in the standard of living may be a point-to-point, or a point-to-line, or a point-to-surface, or even a higher correspondence. (CWL 15, 23)

All science begins from particular correlations, but the key discovery is the interdependence of the whole.  (CWL 15, 53 and 177)

(the) whole structure (of Functional Macroeconomic Dynamics) is purely relational.  A macroeconomic functioning is not a compilation or aggregation of particular income statement categories, such as wages or interest expense.  A macroeconomic functioning is implicitly defined by its functional relation to other functionings. The whole structure is purely relational.  “Lonergan’s analysis is concrete but heuristic.  It focuses on functionalrelations intrinsic to the productive process to reach eventually a general theory of dynamic equilibria and disequilibria.” [McShane 1980, 117]

“Functional” is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory;  … Lonergan (identified) the contemporary notion of a “function” as one of the most basic kinds of explanatory, implicit definition – one that specifies “things in their relations to one another” … [CWL 15, 26-27  ftnt 27]

Lonergan makes precise analytical distinctions between point-to-point vs. point-to-line relations.  A point-to-point relation  is represented by an algebraic function of the first degree.  A point-to-line relation is represented by the correspondence of a point to a series of points.  Since scientific explanation deals with the things among themselves, the pure relations of point-to-point and point-to-line may prove to be of scientific significance.  And if they are a basis one can construct a superstructure of relations serving as first, a hypothesis, and if verified, a theory which – like Clerk-maxwell’s and Einstein’s equations – constitute an explanation of certain phenomena, and, further, of the laws governing electricity in our homes or our GPS location.

These differences and correlations (of the productive process of a hierarchical, advanced economy) have now to be projected into their monetary correlates to set up classes of payments.  Thus a restrictive supposition is introduced into the argument.  The productive process is now envisaged as occurring in an exchange economy.  It will be supposed to be an economy of notable size, complexity, and development, with property, exchange, prices, supply and demand, money.  [CWL 15, 39]

The sentence explaining the arrows surrounding the ‘redistributional area’ [sic] drops the term ‘savings’ altogether, perhaps in an effort to remove residual descriptive connotations.  (CWL 15, 196)

Lonergan … was seeking the explanatory intelligibility underlying the ever-fluctuating rhythms of economic functioning.  To that end he worked out a set of terms and relations that ‘implicitly defined’ that intelligible pattern.  When all was said and done the relations, and the terms they implicitly defined, were markedly different from either the terms of ordinary business parlance or the terms of neoclassical and Keynesian economic theory.  Moreover, not only did Lonergan’s terms differ, but he also indicated that these aforementioned terms (of neoclassical and Keynesian economic theory) were permeated, as were the terms of Newton’s theory of gravitation, with descriptive, nonexplanatory residues.  Hence, just as a mathematical equation may be said to be the most adequate expression of purely intelligible relations among explanatory terms in certain instances – for example, Einstein’s gravitational field tensor equations – something closely akin to Lonergan’s diagram (and the equations it represents) seems necessary for the realm of dynamic economic functioning.  So, for example, the existence and manner of dynamic mutual interdependence of the two circuits of payment, basic and surplus, is not adequately expressed either by descriptive terms (since this pattern does not directly relate to the senses of anyone operating in a common-sense way in a concretely functioning economy) nor by the series of (simultaneous) equations that do not explicitly manifest the interchanging of ‘flows.’ [CWL 15, 179]

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) which, in the first instance, one was thinking about.   [Michael Gibbons, Economic Theorizing in Lonergan and Keynes]

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 1980, 124][2]

(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 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)

Lonergan’s intention was to formulate the laws of an economic mechanism more remote and, in a sense, more fundamental than the pricing system…laws which men themselves administrate in the personal conduct of their lives. In 1978 he began to refer to Nicholas Kaldor in support of his judgment that the significance traditionally accorded to price theory by conventional economics since Adam Smith’s Wealth of Nations (1776) amounted to a virtual derailment of economic theory. [CWL 15, Editors’ Introduction xlv]

Our aim is to prescind from human psychology that, in the first place, we may define the objective situationwith 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]

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.  …  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]

Lonergan defines the basic stage of the process analytically as an aggregate of rates in some determinate, though not immutable or unvarying, algebraic function of the first degree with respect to elements in the standard of living.

… let the basic stage of the productive process be defined as the aggregate of rates of production of goods and services in process and in a point-to-point correspondence with elements in the emergent standard of living.  As explained in Section 6, goods and services are in process when they are neither the mere potentialities of nature nor on the other hand finished products.  As explained in Section 7, goods and services are in a point-to-point correspondence with elements in the standard of living when they are some determinate, though not immutable or unvarying, algebraic function of the first degree with respect to elements in the standard of living.  Finally, just as the aggregate of rates constituting the emergent standard of living is an aggregate of instances of ‘so much every so often,’ so also is the aggregate of rates of production in the basic stage of the process [CWL 15, 28-29]

(In the instances of capital products as distinguished from consumable products,) the point-to-point correspondence (between the factors of production and emergent consumer goods) is escaped because it is not the product but some ulterior effect of the product that enters into the standard of living.  Spears, nets, ships, factories, machines end up as means of production.  They enter the standard of living, not in themselves, but in their (ulterior) effects of pounds of meat, (etc.) …. Such a correspondence may be named point-to-line: (capital) elements in the productive process correspond not to single elements in the standard of living but to indeterminate series of the latter. [CWL 15, 24]

Lonergan’s more comprehensive scope allowed different functioning to increase at different rates.  He treated extensively the implications of the different timing of payments on the different levels of production and the role of credit to a) bridge gaps in time, and b) support a greater volume of transactions.  He recognized in particular the gap in time between the initiation of the manufacture of capital goods and their resulting later acceleration of the production of consumer goods, as expressed in the general law of accelerator and accelerated, called the lagged technical accelerator.

kn[f’n(t-a)-Bn] = f”n-1(t) – An-1   [CWL 15, 37]

This familiar formula, allowing for slack and depreciation, expresses the intrinsically cyclical relationship of point-to-line velocities accelerating point-to-point velocities in a Schumpeterian creative-destructive economy.

Further, these two differently timed levels a) have their own circuits of payments and b) purchase from and sell through “crossovers” to one another such that the textbooks’ single circuit must be replaced by two circuits connected by crossovers.  Also, only by understanding the intrinsic cyclicality of the double-circuited process and the conditions of continuity and equilibrium can one explain technically the distortions, divergences, and maladaptations colloquially described as booms, slumps, recessions., depressions, and crises.  All this is beyond the ken of Endogenous Technological Change.

Re abstraction: One can throw and feel a discus, but one cannot kick and feel the concept of a planar circle.  Similarly, one can suffer an electrical shock, but one can’t suffer a shock from the concept of electric intensity, E, in Δ X E = (-1/c)H.  One can suffer boredom in his/her experience, but one cannot suffer boredom from the concept of space-time.

While we agree with Schumpeter that Walras’s system implicitly includes the aggregates commonly considered in macroanalysis, (Walras’s system) can hardly be credited with distinctions between basic and surplus Expenditure, Receipts, Outlay, Income, and much less with an account of their various dynamic relations.  But until such distinctions are drawn and their dynamic significance understood, the aggregates and relations cannot be contained implicitly in any (explanatory) system. [CWL 15,  91-92]

An advanced economy is constituted by production and exchange for money rather than by production and barter.  The production and exchange for money is called the exchange solution.

… the exchange solution is a dynamic equilibrium resting on the equilibria of markets. … every product of the exchange economy must mate through exchange with some other product, and the ratio in which the two mate is the exchange value.  The generality of this equilibrium makes it indifferent to endless complexity and endless change; for it stands on a level above all particular products and all particular modes of production.  While these multiply and vary indefinitely, the general equilibrium of the exchange process continues to answer with precision the complex question, Who, among millions of persons, does what, among millions of tasks, in return for which, among millions of rewards?  Nor is the dynamic solution unaccompanied by a continuous stimulus to better efforts and more delicate ingenuity.  For the uniformity of prices means that the least efficient of those actually producing will at least subsist, while every step above the minimum efficiency yields a proportionately greater return. [CWL 21, 34-35]

Analysis of the economic process must distinguish two economic mechanisms: 1) the microeconomic mechanism called the pricing system, 2) the macroeconomic mechanism constituted by aggregate surgings and taperings whose “mechanics” are explained by Functional Macroeconomic Dynamics.

Further, without further clarification Schumpeter acknowledged that dynamic analysis called for a new light on equilibrium.  Such new light arises when, over and above the 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 outlays and expenditure) that have to be maintained if an economy chooses to remain in a stationary state, (or) to embark on a long-term expansion (and) to distribute its benefits to the vast majority of its members (in a basic expansion), and so to return to a more affluent stationary state until such further time as further expansion beckons.

No doubt Keynes was an economist first and a methodologist second but he was none the less very articulate about his theorizing……..Lonergan, for his part, is perhaps a methodologist first and an economist second, but, as we shall see, he was able to push his economic reflections further than Keynes because he had a firmer grasp of the essentials of an effective theory.   [Gibbons, 1987]

Those familiar with elementary statics and dynamics will appreciate the shift in thinking involved in passing from (static) equilibrium analysis … to an analysis where attention is focused on second-order differential equations, on d2θ/dt2, d2x/dt2, d2y/dt2, on the primary relativities of a range of related forces, central, friction, whatever.  Particular secondary boundary conditions, past and future pricings and quantities, are relatively insignificant for the analysis of the primary relativity immanent in, and applicable to, every instance of the process.  What is significant is the Leibnitz-Newtonian shift of context. [McShane, 1980, 127]

… the dummy (money) 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. [CWL 21, 37-38]

(We) 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]

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]

Proviso: Our analysis … acknowledged the existence of schemes of recurrence in which a happy combination of abstract laws and concrete circumstances makes typical, further determinations recurrent, and so brings them under the domination of intelligence.  Moreover, it acknowledged that concrete patterns of diverging series of conditions are intelligible; granted both the requisite information and mastery of systematic laws, it is possible in principle to work from any physical event, Z, through as many prior stages of its diverging and scattering conditions as one pleases; and it is this intelligibility of concrete patterns that grounds the conviction of determinists, such as A. Einstein. … However, we agree with the indeterminists inasmuch as they deny in the general case the possibility of deduction and prediction.  For while each concrete pattern of diverging conditions is intelligible, still its intelligibility lies not on the level of the abstract understanding that grasps systems of laws but on the level of the concrete understanding that deals with particular situations.  Moreover such concrete patterns form an enormous manifold that cannot be handled by abstract systematizing intelligence for the excellent reason that their intelligibility in each case is concrete. There results the peculiar type of impossibility that arises from mutual conditioning. Granted complete information on a totality of events, one could work out from knowledge of all laws the concrete pattern in which the laws related the events in the totality.  Again, granted knowledge of the concrete pattern, one could use it as a guide to obtain information on a totality of relevant events.  But the proviso of the first statement is the conclusion of the second; the proviso of the second statement is the conclusion of the first; and so both conclusions are merely theoretical possibilities.  For the concrete patterns form a non-systematic aggregate, and so it is only by appealing to the totality of relevant events that one can select the concrete pattern; on the other hand, the relevant totality of events is scattered, and so they can be selected for observation and measurement only if the relevant pattern is known already  [CWL 3, 650/672-73]

CWL 3, 31-32  It follows that for the story of Archimedes … average reader.

[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.

[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]