Part I – The Exchange Solution’s Complexity and Change:
The exchange solution stands above and is indifferent to endless complexity and endless change; it stands on a level above all particular products and all particular modes of production.
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.… 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)
Functional Macroeconomic Dynamics takes a higher viewpoint and operates at a more adequate level of abstraction so as to achieve a general and universal field-theoretic explanation of the economic process.
“Functional” is a technical term pertaining to the realm of explanation, analysis, theory; it does not mean “who does what” in some commonsense realm of activity … 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”…In Lonergan’s circulation analysis, the basic terms are rates – rates of productive activities and rates of payments. The objective of the analysis is to discover the underlying intelligible and indeed dynamic (accelerative) network of functional, mutually conditioning, and interdependent relationships of these rates to one another. [CWL 15, 26-27 ftnt 27]
… It will be well at once to draw attention to J.A. Schumpeter’s insistence on the merits of the diagram as a tool. (Schumpeter, History 240-43, on the Cantillon-Quesnay tableau.) … First, there is the tremendous simplification it effects. From millions of exchanges one advances to precise aggregates, relatively few in number, and hence easy to follow up and handle. … Next come the possibilities of advancing to numerical theory. In this respect, despite profound differences in their respective achievements, the contemporary work of Leontieff may be viewed as a revival of Francois Quesnay’s tableau economique. Most important is the fact that this procedure was the first to make explicit the concept of economic equilibrium. All science begins from particular correlations, but the key discovery is the interdependence of the whole.… The aims and limitations of macroeconomics make the use of a diagram particularly helpful, … For its basic terms are defined by their functional relations. [CWL 15, 53 and 177]
Part II – The Exchange Solution’s Higher Field-Theoretic Law of Costs and Expenditures:
P’Q’ = p’a’Q’ + p”a”Q” (CWL 15, 156-62), where c’O’ = p’a’Q’, and c”O” = p”a”Q”, is a law standing above the exchange solution; it expresses the concomitance of Outlays, Incomes, and Expenditures in the basic circuit as represented in the Diagram of Rates of Flow above.
A condition of circuit acceleration was seen … to include the keeping in step of basic outlay, basic income, and basic expenditure, and on the other hand, the keeping in step of surplus outlay, surplus income, and surplus expenditure. Any of these rates may begin to vary independently of the others, and adjustment of the others may lag. But any systematic divergence brings automatic correctives to work. The concomitance of outlay and expenditure follows from the interaction of supply and demand. The concomitance of income with outlay and expenditure is identical with the adjustment of the rate of saving to the requirements of the productive process. [CWL 15, 144]
And G = c”O” – I’O’ = 0 (CWL 15, 45-54) is the condition of equilibrium between the basic and surplus circuits.
p’a’Q’ and p”a”Q” are “macroeconomic costs;” and they are defined by the impliecit equation, P’Q’ = p’a’Q’ + p”a”Q” .
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]
This theoretical abstract law stands above the particulars of “endless complexity and endless change” within the exchange solution.
Part III – The Law of Costs and Expenditures is a Classical Formulation at an Adequately Abstract Point of View:
P’Q’ = p’a’Q’ + p”a”Q” is a higher point of view.
- P’Q’ = p’a’q’ + p”a”q” (CWL 15, 156-62)
- P/p = a’ + a”R (CWL 15, 156-62)
- J = a’ + a”R (CWL 15, 156-62)
- dJ = da’ + a”dR + R da (CWL 15, 156-62)
In the above equations we should think of Q’ as the total flow of components, Qijk, formed into integral composite vendable aggregates where component factors in the integrals are a’Q’ and a”Q”. And the total exchanged flow (“outflow”) of completed products Qi is in concomitance and correspondence with the total “inflow” of the components which constitute those products. And P’, p’, and p” are prices, so that we have an abstract explanatory formulation of exchange revenues P’Q’ in a concomitance of circulation with basic costs, a’Q’ and a”Q”. Thus Outlays equal Incomes equal Expenditures equal Receipts.
A condition of circuit acceleration was seen in section 15 to include the keeping in step of basic outlay, basic income, and basic expenditure, and on the other hand, the keeping in step of surplus outlay, surplus income, and surplus expenditure. Any of these rates may begin to vary independently of the others, and adjustment of the others may lag. But any systematic divergence brings automatic correctives to work. The concomitance of outlay and expenditure follows from the interaction of supply and demand. The concomitance of income with outlay and expenditure is identical with the adjustment of the rate of saving to the requirements of the productive process. [CWL 15, 144]
Key equations in Macroeconomic Field Theory are
- R’ = E’ (CWL 15, 54)
- R” = E” (CWL 15, 54)
- I’ = O’ +M’ (CWL 15, 54)
- I” = O” +M” (CWL 15, 54)
- G = c”O” –i’O’ (CWL 15, 54)
- G = c”O” –i’O’ = 0 the condition of dynamic equilibrium (CWL 16, 50)
- M’ = (S’ – s’O’) + (D’ – s’I’) + G (CWL 15, 54)
- M” = (S” – s”O”) + (D” – s”I”) – G (CWL 15, 54)
- (S’-s’O’) = ΔT’ + (O’ – R’) + ΔR’ (CWL 16, 67)
- (S”- s”O”) = ΔT” + (O” – R”) + ΔR” (CWL 16, 67)
Thus for example, assuming G = 0, and by the principle of concomitance and by the functional role of credit to bridge time gaps, we have for the basic circuit the relations of functional flows among themselves:
- R’ = E’ = I’ = O’ +M’
- R’ = E’ = I’ = O’ +[S’ – s’O’] + [D’ – s’I’]
- R’ = E’ = I’ = O’ + [ΔT’ + (O’ – R’) + ΔR’] + [D’ – s’I’]
One can develop parallel equations for the surplus circuit, and then combine both circuits to calculate Gross Domestic Functional Flows, GDFF, to replace Gross domestic Product, GDP, as the primary reference for management of the economy.
Part IV: A New Idea of the Dynamics of the Economic Process:
When you add a new fundamental equation about Costs and Expenditures, (P’Q’ = p’a’Q’ + p”a”Q”) as Lonergan did when he equated Expenditures with Costs, you get a new idea of macroeconomic costs (p’a’Q’, and p”a”Q”) and Expenditures (P’Q’), and a new idea of the dynamics of the entire economic process.
… 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]
See CWL 3, 13 ff./37-38 ff. “The next significant step … the emergence of a higher point of view.”
Also see, CWL 3, 458 ff./484 ff. for clues to Lonergan’s thinking re Genetic Method.
 See [Strang, 1991] for the mathematics and technical meaning of divergence.