Implicit Definition of Pure Surplus Income

To exist is to have real being, whether material or abstract. We are seeking to affirm the existence of pure surplus income. The concept of pure surplus income will be found by the technique of projection of expansionary capital production into its monetary correlate, pure surplus income.

As a mathematician succeeds by creative insights and the rules of logic to affirm the existence of a theorem, and as scientists have succeeded by insight and measurement to affirm the existence of electrical intensity or the curvature of space, so we seek to affirm the existence of pure surplus income. We are not seeking to affirm the existence of a rock by kicking it. We are seeking to affirm the existence of an element of a theory by insight into the intelligibility of data. The existence of pure surplus income is the real being of pure surplus income.

The scientist affirms the existence of electrical intensity by insight into the intelligibility of the data. Similarly, we seek to affirm the existence of pure surplus income by insight into the functional velocities of producing, selling, and operating expansionary capital products.

Description is to be distinguished from explanation.

Description uses terms denoting phenomena as they are related to us in our subjective sensing and perceiving. Explanation uses abstract terms related to one another in order to explain the interactive behavior of the interdependent phenomena.

Thus, explanation constitutes science. Explanation consists in explanatory relations of abstract terms to one another. Explanation goes beyond description, Explanation tells us Why and How. Explanation is a formal intelligibility. Explanation does not merely express our feelings.

The technique of implicit definition yields terms whose meaning is determined by their relation to one another. Thus implicit definition yields terms of scientific and explanatory significance. It yields terms and relations which can be expressed in the form of implicit equations. And if the pattern of symbols and relations in these equations is isomorphic with the pattern of the behavior of the economic phenomena which they represent, then we have the scientific explanation of the economy.

Please recall that postulations are not mere baseless assertions; rather they can often contain intelligibilities which constitute explanatory definition via terms related to one another; and these postulational-explanatory elements may either be contained in a definition or stated separately as postulates. Either way, the postulational elements can be foundational elements in what will become an expanded system of relations.

Lonergan makes critical distinctions between nominal definition and explanatory definition using examples from plane geometry. He cites as examples two postulational elements – two intelligibilities – upon which relationships may be derived in plane geometry:

  • Postulate 1: In any circle, all radii are equal
  • Postulate 2: In a planar line, all straight angles are equal

As Euclid defined a straight line as a line lying evenly between its extremes, so he might have defined a circle as a perfectly round plane curve. … But in fact Euclid’s definition of the circle does more than reveal the proper use of the name, circle. It includes the affirmation that in any circle all radii are exactly equal; and were that affirmation not included in the definition, then it would have to be added as a a postulate. ¶ To view the same matter from another angle, Euclid did postulate that all right angles are equal. Let us name the sum of two adjacent right angles a straight angle. Then, if all right angles are equal, necessarily all straight angles will be equal. Inversely, if all straight angles are equal, all right angles must be equal. Now if straight lines are really straight, if they never bend in any direction, must not all straight angles be equal Could not the postulate of the equality of straight angles be included in the definition of the straight line, as the postulate of the equality of radii is included in the definition of the circle? ¶ At any rate, there is a difference between nominal and explanatory definitions. … ¶ … Both nominal and explanatory definitions suppose insights. But a nominal definition supposes no more than an insight into the proper use of language. An explanatory definition, on the other hand, supposes a further insight into the objects to which language refers. … (In explanatory definition) one is making assertions about the objects (or processes) which names denote. [CWL 3, 10-11/35-36]

Just as these two postulates are precise relational foundations of an entire field of geometry, so Lonergan will be making precise relational and foundational distinctions in macroeconomics:

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

There exists, then, a point-to-point correspondence between bushels of wheat and loaves of bread, between head of cattle and pounds of meat, between bales of cotton and cotton dresses, between tons of steel and motor cars. In each case the elements in the standard of living are algebraic functions of the first degree with respect to elements in the productive process. … For in the totality of instances there is an identity of elements: the very material elements that were in the productive process enter into the standard of living; and the affirmation of a point-to-point correspondence is not more than the affirmation of the permanence of this material identity. [CWL 15 23-24]

By “algebraic functions of the first degree” is meant functions involving no exponential powers of the variables other than 1. … To give a simple example, if the number of loaves of bread is represented by the variable y, and the number of bushels of wheat by the variable x, then a relevant algebraic function might be where b represents the number of loaves of bread which can be obtained from one bushel of wheat under current technological means, and c represents any fixed loss or gain which is independent of the number of bushels. [CWL 15, 23 ftnt. 25]

(In the instances of capital products,) the point-to-point correspondence 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]

In the functional correspondences of the productive process, current-determinate-point-to-current-determinate-point   versus   current-determinate-point-to-future-indeterminate-series is the purely dichotomous division of the current productive process.[1]

Based upon

  1. a) this postulate of the functional relations of basic and surplus products with the standard of living, and
  2. b) the lagged technical accelerator giving the rate of acceleration (k), the lag of acceleration (t-a), and the levels of production (n)

there may be derived the concepts of

a.) two productive and monetary circuits connected by crossovers,

b.) a rhythmicness of productive surges and flattenings,

c.) conjunctions of velocitous and accelerative productive functionings and monetary functionings,

d.) macroeconomic definitions of real and relative vs. monetary and absolute pricings,

  1. e) norms vs. aberrations of the process, and
  2. f) the possibility of the application of boundary conditions such as specific quantities and prices to yield magnitudes and frequencies of productive and monetary flows.

That is, there may be gained – from these basic postulational core elements as expressed in definitional equations plus the logical expansion of their vast implications into a superstructure of equations – the scientific explanation of the behavior of the entire economic process.

In regard to different types of definitions and their significance, let us gather some excerpts which regard specifically a.) nominal definition vs. explanatory definition vs. implicit definition, and b.) postulational elements. Lonergan advances from the notions of nominal definition and explanatory definition to the notions of implicit definition and its scientific significance. Note the final three sentences of the next excerpt and Lonergan’s search for the generality and generalization needed to avoid a restricted, constricted imprisonment in one of an infinity of possible boundaried situations. “The significance of implicit definition is its complete generality. The omission of nominal definition is the omission of a restriction to objects which, in the first instance, one happens to be thinking about. The exclusive use of explanatory or postulational elements concentrates attention upon the set of relationships in which the whole scientific significance is contained.”[2]

A final observation introduces the notion of implicit definition. ¶ D. Hilbert has worked out Foundations of Geometry that satisfy contemporary logicians. One of his important devices is known as implicit definition. Thus the meaning of both point and straight line is fixed by the relation that two and only two points determine a straight line. ¶ In terms of the foregoing analysis, one may say that implicit definition consists in explanatory definition without nominal definition. It consists in explanatory definition, for the relation that two points determine a straight line is a postulational element such as the equality of all radii in a circle. It omits nominal definition, for one cannot restrict Hilbert’s point to the Euclidean meaning of position without magnitude. An ordered pair of numbers satisfies Hilbert’s implicit definition of a point, for two such pairs determine a straight line. Similarly, a first degree equation satisfies Hilbert’s implicit definition of a straight line, for such an equation is determined by two ordered pair of numbers. ¶ The significance of implicit definition is its complete generality. The omission of nominal definition is the omission of a restriction to objects which, in the first instance, one happens to be thinking about. The exclusive use of explanatory or postulational elements concentrates attention upon the set of relationships in which the whole scientific significance is contained. [CWL 3, 12-13/36-37]

You can define a circle as a perfectly round plane curve, and you would have the same sort of useless definition of a circle as you have of a straight line. If you define a circle, though, as a locus of points equidistant from a center, then you don’t need any postulate that all radii of the same circle are equal. You have it in your definition. So here (in the first case) you have just description of what you look at; here (in the second case) you have what’s equivalent to a description, because it enables you to pick out the proper use of the name ‘circle,’ and at the same time it gives you a postulate about circles. Now the implicit definition pulls a fast one. It drops out all descriptive reference and saves only the postulational elements. ¶ when you’re using implicit definitions, you’re solving problems with perfect generality. For example, geometers discovered that in projective geometry there are parallelisms: What will hold for a point and a plane will hold for two other things. Well, instead of working out all their theorems twice, they get some more general definition and work the whole thing out once. That’s the importance of implicit definition: it is a perfect generality. [CWL 18, 328]

Lonergan points out that it is insight which produces a set of concepts related to one another in a coherent manner, and that any functional concept-element is known through its formal functional relation to other concepts-elements. Thus it is insight which produces the explanatory concepts point-to-point (basic) and point-to-series (surplus) related to one another in a coherent manner and required for scientific significance. And, from these, by mapping and correlating may be derived implicit definition of the money flows called costs, ordinary surplus income, and pure surplus income.[3]

Let us say, then, that for 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]

Macrodynamic theory, like subatomic physics or Newtonian mechanics and later mechanics, is “a set of intelligible relations linking what is implicitly defined by the relations themselves; it is a set of relational forms. Any functional concept-elements in macroeconomics – such as basic income, ordinary surplus income, pure surplus income – are known through the functional relations among all concepts-elements.” In fact, macroeconomic dynamics is a field theory, a set of purely intelligible relations purged of human psychology and residues of efficient cause, to which human psychology must adapt.

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


… again, as to the notion of cause, academics and government officials conceive of interest rates and other fixed pricing as efficient causes, and functional macroeconomic dynamics drops the notion of interest rates and other fixed pricing as efficient causes; it gets along perfectly well without them. It thinks in terms of a field theory, the set of relationships between interdependent functionings. The functional macroeconomics 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 functioning is known through its relations to all other functionings. What is a basic product? A basic product is any composite that satisfies the fundamental equations of the first degree that regard components with their composite product exiting the process into a standard of living. Consequently, when you add a new fundamental equation about functional relations, as functional macroeconomic dynamics does when it relates functionings to one another, you get a new theory of macroeconomics. Macroeconomic field theory is a matter of the immanent intelligibility of the overall functioning process. [from CWL 10, 154]

Next, let us consider the isomorphism between the implicit definitions or implicit equations of mathematical reality and understand their usefulness to explanation of physical reality; and, thus, let us note the benefit of applied mathematics.

David Hilbert, a major figure in mathematical logic, defines point and line by this expression: ‘A straight line is determined by 2 and only 2 points.’ What is a point? A point is what two of will determine a straight line. What is a straight line? A straight line is what will be determined by two points. That is called implicit definition. The total statement defines two terms by their relations to one another, without committing you to any particular notion of point or line. … And if you can move back to a more general situation in which you use implicit definition, your straight line is something more general than either Euclid’s or Descarte’s, your point is something more general than either, and it can be either one. You are exploiting the isomorphism by these implicit definitions. CWL 18, 32

In the following we have paraphrased and we have substituted “economics” for “physics” and “economic” for “physical.” We thereby gain a good idea of Lonergan’s dynamic heuristic.

Again, to take perhaps a simpler and more familiar example, if someone is doing macroeconomics and you open his book, what do you find? You find just mathematical equations. He is solving problems, and what is it? It is more mathematics. Why do you say he is doing macroeconomics? He seems to be doing mathematics all the time. It is because there are regions of mathematics that are isomorphic with macrodynamic reality. There is the same relational structure between a given mathematical theory or system as there is between macroeconomic functionings that can be observed.   This is another case, a big case, of isomorphism: on the one hand, mathematical expressions, and on the other hand, macroeconomic functionings. There is the same relational structure. But in the mathematical case, the relational structure links symbolic expressions, or mathematical concepts, with one another, while in the economics case what are related are concrete macroeconomic dynamic functionings. ¶ So there is an isomorphism of geometry, algebra, macroeconomic dynamics; the same relational structure can be found in all three. Consequently, one’ symbolism can be given a geometrical interpretation, or an algebraic interpretation, or a macrodynamic interpretation. Paraphrase of [CWL 18, 32-33]

The scientific inquirer is stating an intelligibility of groups and relations that is expressed in a mathematical form. “For mathematics is not the science of quantity, but the science of intelligible groups and relations in quantity.” Likewise, the scientific macroeconomist is searching for an intelligibility that can be expressed in mathematical form. He is seeking insight into the concrete phenomena of production, exchange, and finance, and explaining the behavior of these phenomena in abstract terms and relations. He is formulating the intelligible form of a system.

the scientist is seeking … an intelligibility that can be expressed mathematically. We must note the meaning of that assumption. Mathematics is not the science of quantity, but the science of intelligible groups and relations in quantity, … The first basic assumption is that the purpose of science is the search for an intelligibility that can be expressed mathematically. [CWL 10, 139]

Because insights arise with reference to the concrete, mathematicians need pen and paper, teachers need blackboards, pupils have to perform experiments for themselves, doctors have to see patients, trouble-shooters have to travel to the spot, people with a mechanical bent take things apart to see how they work. But because the significance and relevance of insight goes beyond any concrete problem or application, men formulate abstract sciences with their numbers and symbols, their technical terms and formulae, their definitions, postulates, and deductions. Thus, by its very nature, insight is the mediator, the hinge, the pivot. It is insight into the concrete world of sense and imagination. Yet what is known by insight, what insight adds to sensible and imagined presentations, finds its adequate expression only in the abstract and recondite formulations of the sciences. [CWL 3, 6/30]

The macroeconomist, like any scientist, seeks an insight into an image – such as the Diagram of Rates of Flow, where symbolic representation of interdependent functional flows by channels supplies the relevant image.

mathematical operations are not merely the logical expansion of conceptual premises. Image and question, insight and concepts, all combine. The function of the symbolism is to supply the relevant image, and the symbolism is apt inasmuch as its immanent patterns as well as the dynamic patterns of its manipulation run parallel to the rules and operations that have been grasped by insight and formulated in concepts. … ¶ An apt symbolism will endow the pattern of a mathematical expression with the totality of its meaning. … The mathematical meaning of an expression resides in the distinction between constants and variables and in the sign or collocations that dictate operations of combining, multiplying, summing, differentiating, integrating, and so forth. CWL 3, 18-19/

On the production side, distinct basic and surplus production functionings are not merely described; they are defined explanatorily and theoretically by their distinctly different geometric intelligibilities as current-determinate-point-to-current-determinate-point and current-determinate-point-to-indeterminate-future-series. That is, they are defined by their distinctly different formal correspondence with elements in the standard of living, from which is derived their formal correspondence with each other. They are implicitly defined by their functional relations. They are mutually definitive and constitute a pure dichotomy. To understand basic is to understand surplus, and vice versa. To say basic is to acknowledge surplus, and vice versa.

These formal correspondences are foundational elements in macroeconomic dynamics, just as in Euclidean plane geometry “two points determine a straight line” and “all right angles are equal” are foundational postulational elements.

When qualified by the lagged technical accelerator

kn[f’n(t-a)-Bn] = f”n-1(t) – An-1[4]

as to productivity (kn), timing (t-a) and (t), and level (n), one has the systematic core of macroeconomic dynamics.

Basic and surplus productive functionings exclude one another; they do not overlap. They are Porphyrean. They make up all that there is of production; we make either consumer products which flow out of the process into a standard of living or we make producer goods which flow from being under process to being in the process to produce other goods. The two velocitous rates of production constitute the entire production operations in a pure dichotomy.

we move to a more detailed knowledge of the whole by a process of dichotomy … Porphyry’s tree divides being into material and nonmaterial. Nothing in the universe is left out when there is a division by contradictories. The material divides into the living and the nonliving, the living into the sentient and the nonsentient, and the sentient into the rational and the nonrational. As long as you proceed by dichotomies, you are constructing the whole universe. [CWL 10, 151]

Moving from the production side to the monetary side: On the monetary side, dummy money is the means of exchange in both the production and the sale of goods and services. In producing as distinguished from selling, outlays are functionally congruent with the producing of goods and services. To produce consumer goods in the same quantity as before and maintain the capacity of the system is to not invest in expansionary capital goods, and vice versa. The flows of basic and surplus outlays are conceptually distinct yet mutually definitive. These two functional monetary flows constitute an either/or, a pure dichotomy.

In selling (expenditures = receipts) as opposed to producing (outlays = incomes), the monetary flows implicitly define one another by their distinct relations of basic sales vs. expansionary surplus sales.

Further, we have a.) the basic circuit’s crosswise functional dependence on the surplus circuit for both repair and maintenance of its capital and for expansionary capital, and b) the surplus circuit’s dependence on the basic circuit for a standard of living for its employees. Purchase money flows crossoverwise between the two circuits.

Investment is a payment of money. A payment is an outflow from the investor dependent on a prior or electronically simultaneous inflow to the investor. Thus, if there is investment, there is income called pure surplus income. The income correlated exclusively with expansionary capital expenditures is called pure surplus income: pure in the sense of exclusively; surplus as a word denoting, coldly and mathematically, a dynamic though indeterminate current-point-to-indeterminate-future-series relation with future elements in the future standard of living; and in-come in the sense of money to be out-go on expansion of the capital stock. Thus, the term pure surplus income does not denote or connote a level of excess or an intention of predation. It is simply the monetary correlate of investment.

To review a critical point: Consistent with these correspondences and correlative congruencies, Lonergan cleverly takes the everyday corporate-accounting words costs and profits of microeconomics and, by the technique of implicit definition, assigns them new meanings as scientific, explanatory terms in a functional macrodynamic system. Basic expenditure – that which is spent on a standard of living – are called costs; basic income’s implicit complement in the entire process, pure surplus income, – that which is spent on investment – since it is not a cost of a standard of living, is called net profits.[5]


There is a sense in which (we) 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; for (our meaning) would include among costs the standard of living of those who receive dividends but would not include (among costs of basic production) the element of pure surplus in the salaries of managers; worse (our meaning) would not include (among costs of basic production) replacement costs, nor the part of maintenance that is purchased at the surplus final market (which are both part of the costs of surplus production and ((defined as)) ordinary surplus income which crosses over to the basic circuit) … 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’ and c”O” as costs of production, having warned the reader that the costs in question are aggregate and functional costs…. [CWL 15 156-57]

The accompanying “baseball-diamond”[6] (including possible superposed circuits[7] ) represents the relations of the system. It is a schematic of functional monetary interdependencies and of the monetary transfers satisfying these interdependencies. Insight into the relations among the dependencies and the transfers yields mathematical expressions of macroeconomic principles and laws. And these mathematical expressions of macroeconomic principles and laws constitute a theory.


Consider, first, the differential flows constituting the consumer-goods sector. Since we understand that all flows are in the same reference interval, the and operators may be eliminated and our first-order expression becomes algebraic:

Functional                              Functional                                    Functional

Monetary Flow             =     Monetary Flow        +            Monetary Flow

                                      P’Q’                  =     (p’a’Q’)Basic          +         (p”a”Q”)Ordinary Surplus[8]

Note the circularity and concomitance in this equation. The functional flows of initial outlays to consumers on the right are circling around to constitute final payments for consumer goods on the left. The consumer-goods sector of the objective economic process is being formulated in terms of monetary flows – i.e. velocitous payments – which implicitly define one another in the equation by the functional relations in which they stand with one another in the process. The form of the equation is isomorphic with the pattern of functional flows. The basic sector of the dynamic process is being defined and explained in terms of its functional interrelations and interdependencies. Its nature as a velocitous process is faithfully represented by the mathematical representation of the relations of its constituent velocities.

Left to right the equation can be read as Use equals Source.

We could reverse the sides of the equation and from left to right the equation can be read as Source equals Use.

The complementary sector is the expansionary sector. Consider, similarly, in regard to that sector:[9]

Π’’Κ” Total surplus = π’’α’’Κ’’expansionary + π’’α’’Κ’’R&M to self   [10]

Π’’Κ” Pure surplus   = π’’α’’Κ’’expansionary[11]

ΣFi   =   Π’’Κ” Pure surplus =    π’a’Κ’ expansionary =   vI”[12]

The flow of pure surplus income vI” (which is not spent on consumption or on repair and maintenance) dedicated to capital expansion Π”Κ”Pure surplus, is formulated as identical with the flow of outlays associated with capital expansion. The flows of initial payments, π”a”Κ” expansionary, circle back to be identical to pure surplus income Π”Κ”Pure surplus. Thus pure surplus outlays, pure surplus incomes, pure surplus expenditures, and pure surplus revenues form the surplus circuit of pure surplus income.

Thus, we have the formula scientifically explaining the dynamics of Gross Domestic Flows.

Expenditures/Receipts       =                             Outlays/Incomes

GDFF  =     P’Q’Basic + Π”Κ”  =        p’a’Q’Basic + p”a”Q”R+M + π”a”K”expansionary + π”α”Κ”R&M to self

Having imaged in the baseball diamond the key monetary interdependencies and transfers and having had insight into the terms and interlocking relations, we have reached the mathematical formulation of their dynamics. We have come to understand costs and pure surplus incomes as explanatory terms defined by the form of their combination in the three equations above. We have worked from phenomena to their explanatory mathematicization.

To strengthen our understanding, we may work in the opposite direction. Acting for the moment as pure mathematicians, we may wish to consider the equations as formulations of purely abstract relations without physical or economic content, i.e. as purely intelligible relations among terms. Then, removing our restrictions to pure mathematical form and filling the terms with dynamic economic content, we may appreciate that we have achieved a purely abstract, functional macroeconomic dynamics possessing scientific, explanatory significance.[13]

To conclude this subsection of Implicit Definition of Pure Surplus Income:

In brief Lonergan is looking for an explanation in which the terms (velocities) are defined by the (functional) relations in which they stand, that is, by a process of implicit definition … that specifies “things in their relations to one another”. … The exclusive use of explanatory or (implicitly-defined) postulational elements (will yield) a set of relationships in which the whole scientific significance is contained.” [ Gibbons 1987, 313]



[1] Re point to surface and point to volume

[2] The meaning is fixed by the relation. And note the pedagogical significance of the phrases “exclusive use,” “concentrates attention,” “the set of relationships,” and “whole scientific significance.”

[3] Then further superstructural relations such as the basic price-spread ratio and the pure surplus income ratio, etc. may be derived for broader understanding. In our case of macrodynamics, insight upon insight produces the cluster of insights called the theory of macrodynamics constituted by the relations among the implicitly-defined concepts. (See second excerpt immediately following)


(In fact insight is an interesting phenomenon; understanding of it and all its implications, and implementation of its vast range of implications move metaphysics from medieval ontology to modern-day gnoseology. Here we are trying to treat macrodynamics and we find ourselves compelled to treat gnoseology in order to be comprehensive.)


[4] CWL 15,37

[5] We have five equivalent names for the same phenomenon. Use would be determined by the point of view.

  1. pure surplus income, (in the sense of normatively legitimate income which is exclusively associated with capital expansion)
  2. net aggregate savings,
  3. the monetary correlate of capital expansion,
  4. the social dividend. (See CWL 15, p. 133, ftnt. 186)
  5. the aggregate return upon capital investment


Pure surplus income may be defined for present purposes as a fraction of total surplus income this fraction will be denoted by the symbol v, where v is the fraction of surplus expenditure that goes to new fixed investment. … Thus in each interval the rate of surplus expenditure E” consists of two parts: one part, (1-v)E”, goes to the replacement and maintenance of old fixed investment; the other part, vE”, goes to new fixed investment. ¶Now, when I” is keeping pace with E”, so that (D”-s”I”) is zero, one may make a parallel distinction in surplus income, naming (1-v)I” as ordinary surplus income and vI” as pure surplus income. This pure surplus income is quite an interesting object. When v is greater than zero, it is a rate of income over and above all current requirements for the standard of living, since that is provided by I’, and as well over and above all real maintenance and replacement expenditure, since that is provided by (1-v)I”. Thus one may identify pure surplus income as the aggregate rate of return upon capital investment: entrepreneurs consider that they are having tolerable success when they are not merely “making a living,” no matter how high their standard of living, and not merely obtaining sufficient receipts to purchase all the equipment necessary to overcome obsolescence, but also receiving an additional sum of income which is profit in their strong sense of the term. [CWL 15, 146]


[6] CWL 15, 55 Depending on one’s momentary interest and point of view, this schematic may alternatively be called:

  • The Diagram of Two Operative Circuits Connected by Operative Crossovers
  • The Diagram of Functional Monetary Interdependencies
  • The Diagram of Operative Functional Flows of Products, Payments, and Financings
  • The Diagram of Monetary Transfers
  • The Diagram of Monetary Channels
  • The Diagram of the Monetary Correlates of the Productive Process
  • The Diagram of Implicitly Defining, Mutually Conditioning, Velocitous Functionings
  • The Diagram Sublating, Supervening, and Replacing the Single-Circuit Diagram of Macroeconomics Textbooks
  • The Functional Framework
  • (Colloquially, because of its shape) Lonergan’s Baseball Diamond

The diagram prescinds from trade and government deficit and other collective deficit. It is usually not noticed, much less understood.


[7] CWL 15, 162-76

[8] CWL 15, 158

[9] CWL 15, 150

[10] CWL 15, 146

[11] CWL 15, 146

[12] CWL 15, 146

[13] See Scientific Significance in Survey of Key Concepts