A Contrast: Understanding Pricing in Macrostatic DSGE vs. Macrodynamic FMD

.I.  Introduction: Contrasting Diagrams and What They Represent

.II.  The Dynamic Process Consists of Interdependent Rates of Flow

.III.  The Treatment of Prices as Constituents of Explanatory Flows

.IV. Primary Relativities and Secondary Determinations; an Excursus and Repetition

.I.  Introduction: Contrasting Diagrams and What They Represent

We contrast an assumption and description with an explanation and interpretation.  We contrast the Dynamic Stochastic General Equilibrium (DSGE) assumption and description of pricing as exogenously given and acceptable as a lead item in analysis of economic problems with Functional Macroeconomic Dynamics’ (FMD’s) explanation and interpretation of pricing in the light of the significant functional pretio-quantital flows which explain the dynamic economic process.

We conclude that pricing is an endogenous element of pretio-quantital explanatory flows; and pricing is understood last, rather than passively accepted as first, in one’s search for the immanent intelligibility of the process.  Also. the heuristic tracing of the continually changing Basic Price-Spread Ratio through the phases of an expansion reveals a radically different understanding of pricing from that of the Walrasian textbooks of Abel and Bernanke, Krugman and Wells, Mankiw, Blanchard, Baumol and Blinder, et al.  The difference is startling.  There is a contrast, but there is hardly any basis for comparison.

From the premises and conclusions of this analysis it then will be argued (9) that prices can not be regarded 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 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]

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

Lonergan agreed with Schumpeter on the importance of systematic or analytic framework in order to explain, rather than merely record or describe, the aggregate phenomena of macroeconomics; … to be able to explain the booms, slumps, and crashes of the trade or business cycles the economist’s analysis had to be as dynamic as the subject matter under investigation; and he agreed that the economist had to know what are the significant variables in the light of which price changes are to be interpreted.  According to Lonergan, standard economic theory had successfully achieved none of these desiderata. [CWL 15, Editors’ Introduction liii]

Also, we emphasize that real analysis is analyzing what money buys.  Money in the operative circuits buys what is produced in the productive order.  The production process is a process of surges and taperings in an advance from a lower to a higher level of abundance.  Thus, analysis of the structure and timing of the productive process is more fundamental than, and must occur prior to, an analysis of the payments correlated with the productive process.  In fact, the structure of the productive process of making and selling must be projected onto payments in general to get the specific classes of payments – – Outlays-Incomes, Expenditures-Receipts, basic receipts and “macroeconomic costs”, pure surplus incomes and investments – –  correlated with production and, so, forming circulations in basic and surplus circuits.

In order to illustrate and explain some differences between DSGE and FMD, we focus on the basic (point-to-point) circuit and we contrast, as our example, different views of supply-demand pricing in the basic  circuit of the economic process.  First, we display two graphs: an AD-AS graph of a basic-circuit static momentary balance and, beside it, a FMD diagram of basic-circuit dynamic flows.  For further perspective on the flows in the basic circuit, below those two diagrams we display three versions of the Diagram of Rates of Flows: the leftmost diagram truncated so as not to show basic-circuit dealings with the Redistributive Function; the center diagram showing the possible lending and borrowing dealings with the Redistributive Function; and the rightmost diagram representing basic-circuit velocities in the full context of an equilibrated, closed, field-theoretic and invariant two-circuit system of interdependent flows.  Finally, for the reader’s convenience, we show an enlarged and clearer version of the full-context Diagram of Rates of Flow.  The theory represented by this full system is a purely-relational field theory; and it is an invariant relevant to explanation of the economic process in any instance.

The leftside AD-AS supply-demand diagram makes one a master of the obvious – transactions are effected at a price!  At any moment pricing, all by its isolated self, is assumed to determine curvatures of the effective subjective willingness of buyers and sellers of “basic” goods and services.  The rightside FMD diagram represents the “basic” part ofa dynamic process; it is a diagram of interrelated rates of monetary flow which have conditions of continuity and equilibrium; it represents a set of velocities implicitly-defined by the relations in which they stand with one another; the rates are mutually-conditioning, implicitly-defining rates (dynamic velocities) of monetary supply-and-demand flows in the basic-circuit channels.  The key contrasts embedded in the passages to follow, are:

  • at rest vs. in motion: snapshot intersections absent time subscripts contrasted with evolutionary velocities of differential or difference pretio-quantital flows
  • inadequate heuristic vs. adequate heuristic: satisfaction with a Walrasian static heuristic contrasted with dissatisfaction mandating a Newtonian, Einsteinian dynamic heuristic
  • efficient cause vs. formal cause: description by static pricing as efficient cause contrasted with explanation by normative formal cause
  • serial shifts vs. concomitant equilibration:  shocks and reactions vs. a new basis of concomitance, continuity, and equilibrium among dynamic flows
  • the non-systematic concrete vs. the formally abstract: secondary determinations of prices and quantities from the non-systematic manifold distinguished from primary relativities of abstract terms and relations which explain the process
  • money as master of the process vs. money as servant of the process: money assumed to be the ventriloquist distinguished from money properly understood as the ventriloquist’s dummy
  • explanation attempted on sand or on rock: careless grounding in the shifting sand of random and “shocking” exogenously-determined pricing contrasted with solid grounding on the invariant rock of the formal structure of production and exchange
  • incoherent vs. coherent: seriation of descriptive aspects of the economic process mistaken for unitary explanation by an invariant set of functional relations; the terms in the equations cohere and the equations themselves cohere; they hang together in an intelligible unity.
  • single circuit or double circuit: a single-flow theory contrasted with a two-flow theory

The analyst should put all interrelated velocitous elements together in a single schematic or view and, thus, come to understand the unitary whole in a single sweeping act of understanding in which all the concepts tumble out together. (Click here)

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

I have spoken of the analysis as revealing channels … . The channels of circulation replace the overall dominance claimed for general equilibrium theory, but they reveal the conditions under which partial equilibria can exist … More positively, the channels account for booms and slumps, for inflation and deflation, for changed rates of profit, for the attraction found in a favorable balance of trade, the relief given by deficit spending, … . [CWL15, 17]

A shift in thinking is required. The analyst must employ a scientific, dynamic heuristic. He/she must be searching for a set of differentials or differences with respect to time which are adequate to explain what is always the current, purely-dynamic process.

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]

The AD-AS supply-demand diagram represents a static balance at a particular moment; the Diagram of Rates of Flow represents a set of general, field-theoretic relations constituting an invariant, which is relevant in any and every instance.  Like the equations of Electromagnetics and Special Relativity, the terms and relations of purely-relational FMD do not change.  Particular concrete values from the non-systematic manifold, such as chosen electric current in Electromagnetics, ratio of vehicle speed to light speed in Special Relativity, or prices and quantities in Macroeconomic Field Theory, may change, but the set of abstract primary relativitionships explaining the phenomena do not change.  They constitute an invariant, applicable in any instance.

.II.  The Dynamic Process Consists of Interdependent Rates of Flow 

The analysis prescinds from human psychology to discover the objective laws of the process to which participants must adapt. In the Diagram of Rates of Flow, Outlays which are Incomes become Expenditures which are Receipts.  O = I = E = R.  The four dynamic elements are in a continuing circular dependence round after round.  By the principle of concomitance they are unitary, and for continuity and equilibrium they must keep apace.  They define and condition one another by the functional relations in which they stand with one another.

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[1]

The structure applies in any case of psychological disposition.  Just as Clerk-Maxwell’s electromagnetic equations underlying the flow of electricity do not change depending upon the mood of the person operating the controls, so the relativistic invariant of the laws relating the economic flows of  basic and surplus incomes and expenditures do not depend on the mood, preferences, utility, or rationality of the persons operating the economic controls.  The laws prescind from, and are both prior to and more fundamental than, human psychology.  The system of laws is an objective invariant.

We seek to understand the objective conditions of a properly functioning economy.

… such macroequilibria are more fundamental than the microequilibria assembled by Walras.  The (macroequilibria) are the conditions of a properly functioning economy. (CWL 15, 92)

The analyst’s heuristic must be adequate to a dynamic exchange process. Again,

Lonergan agreed with Schumpeter on the importance of systematic or analytic framework in order to explain, rather than merely record or describe, the aggregate phenomena of macroeconomics; he agreed with Schumpeter that to be able to explain the booms, slumps, and crashes of the trade or business cycles the economist’s analysis had to be as dynamic as the subject matter under investigation; and he agreed that the economist had to know what are the significant variables in the light of which price changes are to be interpreted. According to Lonergan, standard economic theory had successfully achieved none of these desiderata. [CWL 15, Editors’ Introduction liii]

We are not seeking to describe the microeconomic exchange process; rather we seek to explain the phenomena of the macroeconomic business or trade cycle.

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, Editor’s Introduction  lvi]

Again, there is required a shift in the economist’s thinking.  The economist must construct his/her explanation of the dynamic process in second-order differential equations.

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]

.III.  The Treatment of Prices as Constituents of Explanatory Flows

Monetary flows, such as Outlays-Incomes and Expenditures-Receipts, are pretio-quantital flows.  An advanced treatment would be in terms of pretio-quantitality reminiscent of Special-Relativity’s spatio-temporality.

… tensors are defined by their transformation properties and it can be shown that, in the present case, if the coefficients gij are any instance of a covariant tensor of the second degree, then the expression for the interval will be invariant under arbitrary transformations. … Thus in the familiar Euclidean instance, gij is unity when equals j; it is zero when does not equal j; and there are three dimensions.  In Minkowski space, the gij is unity or zero as before, but there are four dimensions, and xequals ict. In the General Theory of Relativity, the coefficients are symmetrical, so that gij equals gji; and in the Generalized Theory of Gravitation, the coefficients are anti-symmetrical.   [CWL 3, 146 -147/170-71]

Outlays-Incomes and Expenditures-Receipts implicitly define one another.

There is a sense in which one may speak of the fraction of basic outlay that moves to basic income as the “costs” of basic production.  It is true that that sense is not at all an accountant’s sense of costs; … But however remote from the accountant’s meaning of the term “costs,” it remains that there is an aggregate and functional sense in which the fraction… is an index of costs.  For the greater the fraction that basic income is of total income (or total outlay), the less the remainder which constitutes the aggregate possibility of profit.  But what limits profit may be termed costs.  Hence we propose ….to speak of (c’O’  = p’a’Q’) and (c”O” = p”a”Q”) as costs of production, having warned the reader that the costs in question are aggregate and functional costs…. [CWL 15, 156-57]

The Diagram of Rates of Flow implicitly contains the principle of concomitance informing the implicit definition of Outlays-Incomes and Expenditures-receipts.  Again,

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[1]

Employing the principle of concomitance and the technique of implicit definition, we advance beyond the simplistic AD-AS scheme; we seek, with a) the aid of the Diagram of Rates of Flow, and b) per CWL 15, pages 107-113, and 156-58, to discover the primary, abstract, field-theoretic relativities which explain the evolutionary economic process:

(c’O’  = p’a’Q’)     (41)

(c”O” = p”a”Q”)     (42)

Whence, by equation (4)

I’ = p’a’Q’ + p”a”Q”     (4) (page 49) and (43)

Now, when (D’-s’I’) satisfies general conditions of circuit acceleration by being zero, so that E’ = I’, then since E’ = P’Q’ one may write

P’Q’ = p’a’Q’ + p”a”Q”     (44)

In implicit equations, Expenditures, P’Q’,  and “costs”, p’a’Q’ + p”a”Q”, are implicitly-defined by the relations in which they stand with one another.

P’Q’ = p’a’Q’ + p”a”Q”

Since the equation expresses implicit definition, we may read from left to right, right to left, or back and forth between right and left.  From left to right, expenditures-receipts P’Q’ define  and determine concomitant macroeconomic costs, p’a’Q’ and p”a”Q” as they are defined (CWL 15, 156-58)  From right to left,  basic and surplus costs-outlays constitute the incomes which define and determine the limit and norms of what is concomitantly spent for basic products.  Travelling back and forth between left and right, the equals sign mandates the reciprocal constraining influence on one another of pretio-quantial expenditures-receipts and pretio-quantital costs-outlays constituting basic incomes.

We may then proceed to define the Basic Price-Spread Ratio in terms of accelerations and costs flows and trace its path of expansion and contraction in the evolution from lower to higher levels of abundance.

Dividing through by p’Q’ one may write

P’/p’ = a’ + a”(p”Q”)/(p’Q’)     (45)

Letting J represent P’Q’, and R represent (p”Q”)/(p’Q’), we have

J = a’ + a”R,     (45)  

and, thus,   dJ = da’ + a’d + R’da”     (47)

As seen, understood, and appreciated, we have finally attained the intelligibility of prices.  We get to understand prices last in the analysis.  Note in particular the two equations labeled (45) above: the ratio of the index of selling price to the index of cost price.  The prices are boundary values from the non-systematic manifold to which the governing primary relativities are applied.  They are understood in light of the flows of Outlays (p’a’Q’ and p”a”Q”) and Expenditures (P’Q’) of which they are constituent elements.  Further, macroeconomic “costs” (p’a’Q’ + p”a”Q”) and macroeconomic “revenues” (P’Q’)  implicitly-define and mutually-determine one another; and the equation (44), P’Q’ = p’a’Q’ + p”a”Q” can be read from right to left or from left to right.  And note in particular the implicit mutual determination of P’ and p’ and p”.  The level of p’ and p” must be in satisfaction of the level of P’, and vice versa.  I’ is, so to speak, the middle term.  Again, for the third time,

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[2]

These flows of costs and revenues are, by the principle of concomitance in the implicit equation, purely relational, mutually definitive, mutually determinative, and, thus, by this mutuality of definition and determination, they are specially relative.  We have a relativistic general specification of the dynamics of the two-circuit economic process, in which prices are explained by the interdependent flows of two circuits correlated ultimately with the structure of the flows of point-to-point and point-to-line products.

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[3] are last in analysis: they require explanation. [McShane, 1980,124]

Paraphrasing: One might be reminded here of a parallel in hydrodynamics: if what is at issue is a general specification of the dynamics of pretio-quantital monetary flows, a premature introduction of general boundary conditions, (happenstantial prices and quantities) … botches the analytic possibilities….the analysis is hampered … by building the economic priora quoad nos of quantities, prices, interest rates etc., into explanation, when in fact the priora quoad nos[5] are last in analysis: they require explanation in the form of general, dynamic, functional interrelations.

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

DSGE’s simplistic AD-AS model takes the psychological demand curve (composed of utility, time preferences, and irrationality) and the psychological supply curve (profit maximization) as isolated and independent elements of analysis.  And, because transactions do occur, it is a truism that the price paid is the price received; the curves intersect at a price and, thus, the guessed-at and merely-postulated psychological curves are determined by the pricing.  And, thus, pricing on the vertical axis can be said to determine the point of output on the horizontal axis.

Thus, in Walrasian analysis, exogenously-determined prices may be taken as first in the analysis, and said to determine the level of a standstill output supplied and demanded at a moment in time.  FMD, on the other hand, understands prices in terms of the interdependent velocitous and accelerative pretio-quantital flows which constitute and explain the process in a  purely relational field theory.  Prices are understood in the light of the significant variables which constitute the process.  And this understanding of prices is not reached until the end of the analysis.  Note that the intelligibility of prices,

P’/p’ = a’ + a”(p”Q”)/(p’Q’)

J = a’ + a”R

is reached in the third last chapter, before the two appended treatments of exceptional superposed circuits.

.IV. Primary Relativities and Secondary Determinations; an Excursus and Repetition

In CWL 21, Lonergan treats separately “the Normative Proportion” and “The Crossover Ratio.”  There is always a “size” of price, a “size” of quantity, a “size of pretio-quantital monetary flow.  One particular concrete size suggests comparison and relation to other concrete sizes.  And the primary relations of one price to another, one quantity to another, one magnitude of flow to another would be primary abstract relations of proportion, while the secondary determinations themselves from the non-systematic manifold would happen to be in some numerical ratio such as 1:1, 2:1; 3.5:1, 8:1, etc..

… it is necessary to distinguish in concrete relations between two components, namely, a primary relativity and other secondary determinations.  Thus, if it is true that the size of A is just twice the size of B, then the primary relativity is a proportion and the secondary determinations are the numerical ratio, twice, and the two observable sizes.  Now ‘size’ is a descriptive notion that may be defined as an aspect of things standing in certain relations to our senses, and so it vanishes from an explanatory account of reality.  Again, the numerical ratio, twice, specifies the proportion between A and B, but it does so only at a given time under given conditions; moreover, this ratio may change, and the change will occur in accord with probabilities; but while probabilities will explain why objects like A and B every so often have sizes in the ratio of two to one, they will not explain why A and B are in fact in that relation here and now; and so the numerical ratio, twice, is a non-systematic element in the relation.  However, if we ask what a proportion is, we necessarily introduce the abstract notion of quantity and we make the discovery that quantities and proportions are terms and relations such that the terms fix the relations and the relations fix the terms.  For the notion of quantity is not to be confused with a sensitive or imaginative apprehension of size; a quantity is anything that can serve as a term in a numerical ratio; and, inversely, a proportion, in the present context, is a numerically definable ratio between two quantities. [CWL 3, 491]

The distinction of primary relativity and its secondary “coincidental” and absolute determinations separates the systematic and the non-systematic.

The point, then, to our distinction between the primary relativity of a relation and its secondary determinations is that it separates the systematic and the non-systematic.  If A and B are things of determinate kinds, then they must be quantitative; and if they are quantitative, there must be some proportion between their quantities.  But just what that proportion will be at any given time, will depend on the manifold of factors that form the non-systematic pattern of a diverging series of conditions, and so there is within the limits of human science no ultimate and fully determinate explanation of why A happens to be just twice B at a given moment. [CWL 3, 491]

So, we distinguish the primary, abstract, purely relative relation from the non-systematic secondary determinations to which it can be applied.

There is a further point to our distinction.  As it separates the systematic from the non-systematic, so also it separates the relative from its absolute determinations.  All that is relative in the notion, twice, is also found in the notion, proportion; the difference between them is that ‘twice’ is a proportion specified by a pair of quantities such as one and two, or two and four, etc.; and such pairs of quantities, simply as pairs of quantities, prescind from the relations of one to the other. [CWL 3, 492]

Again,

General laws contain a primary relativity and are applied to the concrete “only through the addition of further determinations, and such further determinations pertain to a non-systematic manifold. … it is not enough to think about the general law; one has to add further determinations that are contingent from the very fact that they have to be obtained from a non-systematic manifold. [CWL 3, 492/516]

In Functional Macroeconomic Dynamics, a simple, yet fundamental and explanatory, relation of proportion is the Aggregate Basic Price-Spread Ratio (CWL 15, 156-60):

P’/p’ = a’ + a”p”Q”/p’Q’  or

J = a’ + a”R

Its differential is

dJ = da’ + a”dR + Rda”

 

The heuristic tracing of the continually changing Basic Price-Spread Ratio through the phases of an expansion necessitates a radically different macroeconomic understanding of pricing from that of the Walrasian textbooks of Abel and Bernanke, Krugman and Wells, Mankiw, Blanchard, Baumol and Blinder, et al.  The difference is startling.  There is a contrast, but there is scarcely any basis for comparison.

This variable ratio of the indexes of selling price to cost price has vast implications for understanding and interpreting the ever-shifting, evolutionary, economic process.  The variable ratio, since it is a variable, changes.  And that primary relation of  proportion is, in this case, defined by the collocation of significant explanatory variables of acceleration, surplus productive outlays and basic productive outlays.  Functional variables implicitly define other variables by the relations in which they stand with one another.  The discovery of this central, purely-relational, key intelligibility of the economic process is last in the analysis.  The gem, called the Basic Price-Spread Ratio, is hidden in the process until it is finally discovered and becomes the capstone of the process.

One may easily get disoriented by everyday words such as “costs”, “outlays”, “profits” used to describe concrete experiences; and one may fail to grasp that Lonergan has applied new meanings and is using these terms as abstract, explanatory conjugates, ultimately grounded in precise analytic distinctions such as point-to-point and point-to-line in the production-and-sale process, for which the money suggested by “costs” etc. is a dummy servant. …

FMD is concerned with equilibrium among the flows constituting payments in the dynamic productive 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 maintainedif 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)

[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”

[2] 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”

[3] 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.

[4] 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[4]

[5] 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.