The Relativistic Invariant: The Ideal Pure Cycle at the Root of the Aberrant Trade Cycle

The heart of the normative theoretical framework that can actually explain business and trade cycles is what (Lonergan) calls the ‘Pure Cycle’ (§10, §24, 114).  This cycle generalizes into clearly articulated relationships the ideal phases characteristic of major economic transformations as they depart from a stationary phase and move through phases first of surplus expansion and then of basic expansion, only to return to a new stationary phase. … (CWL 15, Editors’ Introduction, lxiii)

Though all expansions are different, in every expansion there is an invariant: the abstract normative primary relativities of interdependent functions to one another, including the conditions of continuity and equilibrium.   Further, as in the invariant formulation of Special Relativity, the abstract primary relativities are purely relative; and they constitute a macroeconomic field theory.  Thus the title of this section: The Relativistic Invariant; … .  Justification of the title can also be found in Explanatory Macroeconomic Dynamics: Relevant in Any Instance, and Field Theory in Physics and Macroeconomics, which are included herein by this reference.

Special Relativity is primarily a field theory, that is, it is concerned not with efficient, instrumentalmaterial, 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]

Paraphrasing [CWL 10, 154]: … as to the notion of cause, macroeconomists mistakenly conceive of subjective preferences as formal causes.  Functional Macroeconomic Dynamics drops the notion of subjective preferences; it gets along perfectly well without it.  It thinks in terms of a field theory, the set of relationships between interdependent, implicitly-defined functional activities.  The field theory of FMD 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 functioning is known through its relations to all other functionings.  ….  Macroeconomic field theory is a matter of the immanent intelligibility of the objective phenomena. [See CWL 10, 154]

Thus it is that in the history of human societies there are halcyon periods of easy peace and tranquility  that alternate with times of crisis and trouble.  In the periods of relaxed tension, the good of order has come to terms with the intersubjective groups.  It commands their esteem by its palpable benefits; it has explained its intricate demands in some approximate yet sufficient fashion; it has adapted to its own requirements the play of imagination, the resonance of sentiment, the strength of habit, the ease of familiarity, the impetus of enthusiasm, the power of agreement and consent.  Then a man’s interest is in happy coincidence with his work; his country is also his homeland; its ways are the obviously right ways; its glory and peril are his own. (CWL 3, 216/241)

The abstract primary relativities are applied to the secondary determinations of prices and quantities  to reach the concrete relations of the concrete process.  These abstract primary relativities are explanatory and relevant in any instance, and they yield normative relations for which any concrete pretio-quantital expansion has a fundamental exigence.

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

Negatively speaking, the pure cycle of expansion must not be converted into the trade cycle of a boom followed by a systematically-necessary corrective slump. And In the early period of a surplus expansion, the participants must not fail to distinguish between real and relative price increases vs. general and absolute price increases.  And the participants must not fail to understand the economic significance of pure surplus income.

Previously I have suggested a lack of adaptation in the free economies to the requirements of the pure cycle.  What that lack is can now be stated.  It is an inability to distinguish between the significance of a relative and an absolute rise or fall of monetary prices.  A relative (i.e. “real”) rise or fall is, indeed, a signal for a relatively increased or reduced production (of one product relative to another) … Inversely, the rising prices of the surplus expansion are not real and relative but only monetary and absolute rising prices; to allow them to stimulate production is to convert the surplus expansion (of the ideal pure cycle) into a (trade cycle of) boom (which must be followed out of systematic necessity by a correlative and devastating slump).  This I believe is the fundamental lack of adaptation to the productive cycle that our economies have to overcome. [CWL15, 139-140]

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… 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]

Different expansions are different in character.  Their technologies, techniques, and human skills are different.  Their potentials and realizations are different.  Their technical coefficients and time-to-completion are different. The train revolution, the automobile revolution, the applied-science revolution, and the hardware-software-information revolution have all been different with respect to technology, time lags, degrees of efficiency, long-term potential.

This dynamic structure has now to be connected with the idea of cycles.  Let us distinguish two totally different types.  There is the familiar trade cycle which is characterized by a succession of positive and negative accelerations of the productive process; there are booms and there are slumps.  Quite different from this trade cycle one may conceive a pure cycle or wave that has no necessary implications of negative acceleration.  A pure cycle of the productive process is a matter, simply, of the surplus stage accelerating more rapidly than the basic, then of the basic stage accelerating more rapidly than the surplus.  (CWL 15, 38)

The trade cycle is a succession of expansions and contractions. … The contention of the present analysis is that there is a pure cycle at the root of the trade cycle. … Of itself, it would not involve any contraction. … It can further be shown that the lack of such adaptation transforms the pure cycle into a trade cycle: the free economies of the present day are overadapted to the surplus expansion, which they exaggerate into booms, but underadapted to the basic expansion, which they convert into slumps.[1] [CWL 15, 115]

Again, though all expansions are different, in every expansion there is an invariant: the abstract normative primary relativities of interdependent functions to one another, including the conditions of continuity and equilibrium.  These primary relativities are applied to the secondary determinations of prices and quantities from a non-systematic manifold to reach the concrete relations of the concrete process.  The abstract primary relativities are explanatory and relevant in any instance and they yield relationships for which any concrete pretio-quantital expansion has a fundamental exigence.  Further, as in the invariant formulation of Special Relativity, the abstract primary relativities are purely relative; and they constitute a macroeconomic field theory.  Thus the title of this section: The Relativistic Invariant; … .  Justification of the title can be found in Explanatory Macroeconomic Dynamics: Relevant in Any Instance, and Field Theory in Physics and Macroeconomics  ,which are included herein by this reference.

Paraphrasing: … as to the notion of cause, macroeconomists mistakenly conceive of subjective preferences as formal causes.  Functional Macroeconomic Dynamics drops the notion of subjective preferences; it gets along perfectly well without it.  It thinks in terms of a field theory, the set of relationships between interdependent, implicitly defined functional activities.  The field theory of FMD 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 functioning is known through its relations to all other functionings.  ….  Macroeconomic field theory is a matter of the immanent intelligibility of the objective phenomena. [See CWL 10, 154]

The Editors of CWL 15 are careful to point out:

Lonergan has introduced certain assumptions about rates of growth and acceleration.  These assumptions constitute something of a ‘model’ of a pure cycle.  That model is a four-phase cycle, where successive phases are characterized by parameters

  1. dQ’/Q’ = dQ”/Q” = 0
  2. dQ’/Q’ = 0,  dQ”/Q” = k – 1
  3. dQ’/Q’ = k – 1; dQ” =  (1/r – a)Q”1
  4. dQ’ = (1/r – a)Q1; dQ” = 0;

followed by a repetition of phase 1.  See Figures 24-3 through 24-7.)

Such a model represents only one possible instance of a pure cycle; there are a manifold of other possible pure cycles, and a still larger set of possible aberrant ‘trade’ cycles.  Lonergan’s use of this model at this point in the text merely illustrates his more general principles, and is not central to his argument.  In later sections of this essay, where other graphs have been supplied to illustrate Lonergan’s points (for example, in §27, ‘The Cycle of Pure Surplus Income’), an effort has been made to stay as close as possible to the assumptions Lonergan introduced here. (CWL 15, 125-26, ftnt 165)

For a fuller interpretation of the four-phase cycle the reader should consult  CWL 15, pp. 120-28, especially pp. 125-28, which includes footnote 165 on pp. 125-26.

Economists in academe speak of “smoothing out the process of expansion; but, first, it is difficult to calculate the acceleration ratios dQ’/Q’ and dQ”/Q”, and second, the process is intrinsically cyclical.

Without urging the necessity of such a (particular) cycle, one may say that it is solidly grounded in a dynamic structure of the productive process; and one has only to think of the practical impossibility of calculating the acceleration ratios dQ’/Q’ and dQ”/Q” to smile at the suggestion that one should try to ‘smooth out the pure cycle.’ (CWL 15, 128)

The schemes of recurrence and expansion in a vast and intricate economy must be managed properly in order to avoid the drift to totalitarianism and the decline of civilization.

The present point is a very simple point.  Just as the surplus expansion is anti-egalitarian in tendency, postulating an increasing rate of saving, and attaining this effectively by increasing, in the main, the income of those who already spend as much as they care to on basic products, so the basic expansion is egalitarian in tendency; it postulates a continuously decreasing rate of saving, a continuously decreasing proportion of surplus income in total income; and it achieves this result effectively by increasing, in the main, the income of those who have a maximum latent demand for consumer goods and services. [CWL 15, 139]

The economic process has an exigence for satisfaction of its own intelligible laws.  The stretched spring must contract; the compressed spring must expand.  The set of coherent laws constituting the pure cycle exerts a grave push or pull on the trade cycle’s boom or economic slump.

Instead of moralizing about profit, Lonergan’s analysis of the natural intelligibility of the pure cycle reveals how profit as ‘constant and normal’ is related to profit as ‘pure surplus income,’ which is a social dividend.  It is intrinsic to the intelligibility of capitalist process that there be an exigence for the ‘anti-egalitarian’ requirements of the major surplus expansion to yield eventually to the ‘egalitarian’ requirements of the major basic expansion. (CWL 15, Editors’ Introduction, lxv)

Thus it is that in the history of human societies there are halcyon periods of easy peace and tranquility  that alternate with times of crisis and trouble.  In the periods of relaxed tension, the good of order has come to terms with the intersubjective groups.  It commands their esteem by its palpable benefits; it has explained its intricate demands in some approximate yet sufficient fashion; it has adapted to its own requirements the play of imagination, the resonance of sentiment, the strength of habit, the ease of familiarity, the impetus of enthusiasm, the power of agreement and consent.  Then a man’s interest is in happy coincidence with his work; his country is also his homeland; its ways are the obviously right ways; its glory and peril are his own. (CWL 3, 216/241)

Clearly schemes of recurrence exist and function.  No less clearly, their functioning is not inevitable.  A population can decline, dwindle, vanish.  A vast technological expansion, robbed of its technicians, would become a monument more intricate but no more useful than the pyramids.  An economy can falter, though resources and capital equipment abound, though skill cries for its opportunity and desire for skill’s product, though labour asks for work and industry is eager to employ it; then one can prime the pumps and make X occur; but because the schemes are not functioning properly, X fails to recur.  As the economy, so too the polity can fall apart. … in a twilight of straitened but gracious living men await the catalytic trifle that will reveal to a surprised world the end of a once brilliant day. [CWL 3, 209-210/235]

In the nineteenth century democracy was the successful political form, he wrote, but times have changed and modern economics aims at replacing democracy with the totalitarian state.  The regimenting of the Russians by the Soviets, of the Germans by the Nazis, and of the Italians by the Fascists are moves towards making the whole world conform.  In contrast the power of the old political economists was solely that of argument, the aim to release the creativity that resides in human beings rather than in ideologies or parties or bureaucracies.  What is needed in economic thinking is a ‘scientific generalization of the old political economy and of modern economics that will yield the new political economy that we need.’ It will be a new point of departure, not unlike that established by Newton in relation to the science of mechanics.  It will seek to understand most generally the patterns of relations among certain human activities that make up the economy.  This Lonergan will break down into questions about production, exchange, and finance. {Mathews 2005, 113]

The excellence of the exchange solution becomes even more evident when contrasted with the defects of a bureaucratic solution.  The bureaucrat … (gives the people) what he thinks is good for them, and he gives it in the measure he finds possible or convenient; nor can he do otherwise, for the brains of a bureaucrat are not equal to the task of thinking of everything; only the brains of all men together can even approximate to that. … when a limited liability company has served its day, it goes to bankruptcy court; but when bureaucrats take over power, they intend to stay. … when the pressure of terrorism is needed to oil the wheels of enterprise, then the immediate effect is either an explosion or else servile degeneracy. [CWL 21, 34-35]

With reference to Figure 27-1, Rate of Change of v, w, and f during a Pure Cycle, Ideal Maximum f:

On the assumption of the pure cycle, Q” does not decrease but reaches a maximum and then levels off into a straight line parallel to the time axis; in that case, the maximum of v arises subsequently to the maximum of w when, during the basic expansion, the rate of replacements begins to rise or, if Q” were still increasing, when the rate of replacements begins to increase more rapidly than Q”.  If, however, the surplus expansion was over-ambitious and expanded the surplus stage of the process excessively, then Q” is bound to fall sharply at some time or other. (CWL 15, 149)

… the surplus expansion is only an acceleration lag.  The greater it is and the longer it lasts, the greater the potential for basic expansion that is created.  Obviously, it is not created and then left unused.  It is put to work as rapidly as possible, and so the basic stage accelerates at an ever greater pace while the surplus stage begins to realize that it has acquired as great a potential as possibly can be used.  There results the basic expansion, with the basic stage accelerating, proportionately, more rapidly than the surplus: w has passed its maximum. (CWL 15, 151)

[1] Lonergan is commenting on his table of “the possibility of different types of phases. CWL 15, 113-14.

Fully:

The significance of the table is that it makes possible a distinction between different types of cycle.  The trade cycle is a succession of expansions and contractions: it certainly is a movement up and down the table, and it may or may not also involve movements across the table.  The contention of the present analysis is that there is a pure cycle at the root of the trade cycle.  By a pure cycle is meant a movement across the table with no implication of a movement up or down the table.  Thus the succession of surplus expansion, basic expansion, proportionate expansion, repeated as often as you please, would give a pure cycle. Of itself, it would not involve any contraction. … I can further be shown that the lack of such adaptation transforms the pure cycle into a trade cycle: the free economies of the present day are overadapted to the surplus expansion, which they exaggerate into booms, but underadapted to the basic expansion, which they convert into slumps. (CWL 15, 115)