The flows of pure surplus income, ordinary surplus income, basic income, and expansionary credit are explanatory elements in the production-and-exchange process.

Pure surplus income – whether initially borrowed from outside the operative circuits or saved within the operative circuits- is income for investment, i.e. non-consumption income. As such, the aggregate circling-round , period after period, of the pure surplus principal to entrepreneurs-investors as a group may be identified as the *return *of outlays of investment principals to this group. The circling round and round, period after period, for repeated use is a *returning *period after period.

Pure surplus income is, as money for investment,[1]implicitly defined as the income correlated with investment rather than with consumption or repair and maintenance. It will rise and fall as demonstrated by the elements of the pure surplus-income ratio in Figure 27-1. [CWL 15, 150]

It is essentially a circulating principal. It is a precisely defined functioning. It may be called by many names, but all names will refer to the same phenomenon. One name might be the current recircling *social **dividend *of the process. It is the return flowing each moment or interval to risk-taking participants as a group for their further expansion of capital. As a quasi-dividend and functional “returning”, we may include it in the genus of “returns,” being careful to not identify it as corporate inflows still attributable to investments of the past. For we are not doing corporate financial accounting; we are doing functional analysis called Functional Macroeconomic Dynamics. This macrodynamic return is an explanatory functioning.

In contrast to the repeated returnings of principal investment amounts, contractual interest payments are payments negotiated by participants as a rental payment for temporary use of money. They are payments for one particular service – the money rental service – among the myriad of services constituting the dynamic process. They are understood in the realm of bookkeepers and accountants in terms of accounting principles applicable to income statements and in the realm of financial analysts in terms of the money-rental charges; retained earnings and dividends being less secure types of rental charges.

Pure surplus income – as a type of current return received by entrepreneurs-investors as a group – is naturally part and parcel of the process. Mathematically, its rate is given by the tangent or first derivative with respect to time of the mathematical function expressing the current accumulation of value of new consumer goods or new capital. It is the change in the accumulation; and, since it is with respect to time, it is a *velocity*. And its change in velocity is an acceleration (or deceleration) of monetary investment values.

In Burley and Csapo’s von Neumann model, *Money Information in Lonergan-von Neumann Systems,*[2] the rate of flow in pure surplus income in their von Neumann model of the transition from one level of production to a higher level is given by the Newton-Raphson method as[3]

and in Burley’s *Evolutionary von Neumann Models*[4]*, *the growth factor α,interest factor β, growth rate α-1, and interest rate β-1, in an expanding economy as given by the two roots of the characteristic equation of the game matrix are;

*α _{1}= *

*β*

_{1}= 1;*α– 1 =*

*β– 1 = 0*

and

*α _{2}= *

*β*

_{2 }= 1 + {(lk^{N }– l^{N}k )/ kl’^{N}} – d^{N}and in Burley’s *A 3-Level Lonergan von Neumann Model *[Burley, 2002-1,p.71],using the same Newton-Raphson method:

(Due to formatting problems with large formulae we must refer the reader to:

Burley, Peter (2002), *A 3-Level Lonergan-von Neumann Model*, Australian Lonergan Workshop 2, ed. Matthew C. Ogilvie and William J. Danaher, Sydney: Novum Organum Press 68-74 [Burley, 2002-1,p.71])

Note that, even in Burley’s simple, full-employment linear models, the macroeconomic interest rate is neither a simple contractual rate nor a speculative, bond-market rate; rather it is an intrinsic aspect of the process defined by real velocities of basic goods, surplus goods, depreciation, repair and maintenance, and productivity of existing and new investments. If any single technical rate, or combination of rates, of dynamic flows changes, the intrinsic macroeconomic rate of return would change.[5] Each production rate grounding its correlated payments rates is constituent to the productive flows constituting the whole dynamic process. (And, if Burley departed from an assumption of full employment of a stable population, the formula would become even more complicated.)

In simple terms, whether we call it pure surplus income, circulating principal, macroeconomic social dividend, macroeconomic return, etc, it is a single phenomenon; and its quantity normatively and systematically would rise, peak, decline, and return to zero in the pure cycle of expansion.

We harken back to the comments about insight yielding the definition of a circle:

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/

In the grasp of the general intelligibility of the macroeconomy, all the concepts, including the interest rate, identified with the functional flows tumble out together because “All are coherent, for coherence basically means that all hang together from a single insight.” Thus, basic outlays, basic incomes, ordinary surplus outlays, ordinary surplus incomes, pure surplus outlays, and pure surplus incomes are all grasped together in a relational coherence in the sweeping general insight grasping the immanent intelligibility of the current, purely dynamic, process.

As part of the explanation of a normative circulation at a particular point in time, the marginal increase in mounting investment expenditure has marginal pure surplus income as its source. In functional principle, in an initial geometric expansion, pure surplus income will return each period as an ongoing source to be supplemented by further borrowing to support its convex curvature. As the expansion approaches its technical limits and the curvature changes, a)repair and maintenance requirements mount to claim more and more of the money in the system, and b) the need for new money for expansionary investment declines.

Thus, the normal source of pure surplus income for expansion in the surplus circuit is not the draining of money from the consumer-goods circuit. Rather the credit function supplies money for expansion to the surplus supply function. If money for expansion were drained from the basic circuit, barring rapid selling-price reductions or initial reliance on stored basic inventories, this would only lead to less basic income chasing the same quantity of consumer goods, falling basic prices, and a diminished surplus expansion. There would result a reduction of basic flows, layoffs, an idling of machinery, and a discouraging of investment.

As a productive expansion proceeds, the quantity of money in the operative circuits must expand accordingly. Principal must be borrowed.

the supposition that circuit acceleration to some extent postulates increments in the quantity of money in the circuits … points to excess transfers to supply, to (S’-s’O’) and (S”-s”O”), as the mode in which increments in quantities of money enter the circuits. [CWL 15, 61]

Further, the

normal entry and exitof quantities of money to the circuits or from them is by the transfers from the redistributive to the supply functions. [CWL 15, 64]One cannot identify a reduction of basic income (by savings) with an increase in the supply of money (for investment), – (such a reduction is normally a misdirective drain of the basic circuit, not an increase) – for a reduction of basic income is only one source of such supply; moreover, it is neither the normal nor the principal source of such supply; … principally the increase in the supply of money is due to the expansion of bank credit, which is necessary to provide the positive (S’-s’O’) and (S”-s”O”) needed interval after interval to enable the circuits to keep pace with the expanding productive process. [CWL 15, 142]

Also, on this website we demonstrate the general principles of the rhythmic, creative-destructive process by both a logistic growth model (S-curve) and Burley’s von Neumann linear model. Not any old model will suffice. A model is a model, not just an excessively simplified demonstration of principle. Each expansion process has an inner logic. Each expansion will have its own technical quantities and technical relations; expansion is not willy nilly. The S-curve may be tall or extended, but it will be an S-curve. Capital expands first, then the fruits of the capital expansion are produced in greater abundance. The secondary determinations of particular multipliers and time lags applied to the primary relativity of surplus acceleration causing basic acceleration yield the laws in particular configurations. Though some simplification is necessary, one’s mathematical model must represent faithfully the general form that is the immanent intelligibility of the process. The mathematical formalism must be isomorphic with the dynamic form of the concrete process. And, the correlated credit money financing an expansion will circulate to meet the pattern of accumulation and curvature of the productive expansion which it finances.

once long-term acceleration is underway, rates of production increase increasingly; their graphs are concave upward; but the curvature moves from being flatter to being rounder as the acceleration is generalized from one section (of the capital sector) to another throughout the productive process. During this period of generalization, rates of production are not merely increasing in geometrical progression but moving from less to more rapid geometrical progressions. … This situation, however, is bound to be temporary; its existence is the lag between the generalized long-term acceleration of the surplus stage and that of the basic stage. When that is overcome, dQ’/Q’ moves again to a peak and remains there; and by the same token, dQ”/Q” will begin to decline. [CWL 15, 126]

Throughout our logistic growth model – which begins with an exponential expansion of the stock of capital – the monetary expansion, the normative macroeconomic rate of returning is given by the *logistic differential equation *in either of two equivalent formulations with which the reader might be familiar:[6]

*dP/dt = kP(1 – P/K)* or alternatively *dP/dt = kP(K – P)*

where P is the “population” of machines,[7]*k *is the “absorbability” or “gestation” constant,[8]and *K *is the limiting carrying capacity determined by the natural resources, technical coefficients, and human techniques and skills. Thus the velocity or rate of change of a population of people or machines (for *machines *we might use the letter *Q*for quantity, as in Q_{i}= ΣΣQ_{ijk}[9] (rather than *P *for *population*) with respect to time depends jointly on the absorbability constant and the existent population’s relation to an ultimate limiting carrying capacity.

In the following examples at time zero, with *P *at 80 and *K *at 100, note that in the first formulation *k *= .30 and, in the second formulation, *k *= .0030:

*dP/dt = (.30)(80)(1 – 80/100) = 4.8* or alternatively *dP/dt = (.0030)(80)(100 – 80) = 4.8*

Let us proceed with the first of the two versions. The solution to the first order equation gives the quantity at any time *P(t)*.

where

A = (K – P_{0})/P0

Given the amount of capital *P*at *t = 0 *as 80, then *P *at *t=1 *equals 83.7. The quantity of capital expands geometrically, first in more rapid geometrical progression, then in a less rapid geometrical progression; i.e. first concave upward to an inflection point, then concave downward towards the asymptote *K*.

Now, curvature in general is given by

*C = d T/ds*

Where ** T **is the unit tangent vector and

*s*is the arc length given by (using a tall “S” as the integration operator):

*s(t) = **S*^{t}_{a}*|r’(u)|du*

Thus curvature is given by

c(x) = |f”(x)|/[1 + (f’(x)^{2}]^{3/2}.[11] [12]

The reader can apply other initial, limiting, and absorbability values to verify that, at first, “the graph of *P *is concave upward, but then it becomes concave downward and approaches the limiting population *K*.”[13] This path resembles the general path described by Lonergan for Q” in the surplus expansion and for Q’ in the subsequent basic expansion.

Lonergan’s model in CWL 15, p 121 is a slight departure. He describes exponential growth succeeded by uniform growth to a maximum capacity rather than exponential growth throughout. The curve of the bottom of the S is retained, but thereafter uniform growth forms a straight line to the limit of the carrying capacity. Innovative though the stagecoach might have been to carry the strong box, mail, and trekkers west, stagecoaches are no longer produced for use, even in fractions near the asymptote.

Each stage of the long process is ushered in by a new idea that has to overcome the interests vested in old ideas, that has to seek realization through the risks of enterprise, that can yield its full fruit only when adapted and modified by a thousand strokes of creative imagination., And every idea, once it has borne its fruit, has to reconcile itself to death. A new idea is new only when it first appears. It comes to man not as a possession forever but only as a transient servant; it has its day glorious or foul; it lives for a period that is long or short according to its generality; but it may be succeeded by other alternatives, and in any case it will be transformed, perhaps beyond recognition, by higher generalizations. Thus the stagecoach disappeared before the train, … money changers yielded to bill brokers, brokers to banks and financiers. [CWL 21, 20]

Again, in correspondence with each advance of practical intelligence, there is a technological obsolescence of capital equipment. The old shops still have their shelves and counters; the old machines may suffer no material or mechanical defect. But the new models produce better goods more efficiently; and trade now walks on different streets. [CWL 3, 207-208/233]

Examples relevant to Figures 24-1 and 24-2 [CWL 15, 121]

Lonergan’s model suggests exponential growth followed by uniform growth, until the carrying capacity is reached.

[1]savings in the sense of withheld from use for consumption. Money borrowed from the money-creating credit system of banks for investment is, thus, “saved” or “kept safe” from being used for consumption; then it keeps returning for investment by those who invest; it is a “return of prior expansionary investment funds.”

[2]Burley, P. and Csapo, Laszlo, (1992) *Money Information in Lonergan-von Neumann Systems*, Economic Systems Research, Vol 4, No. 2, 1992

[3]We need not here identify the constants and variables of the formula, since our only purpose is to demonstrate that the interest rate is a.) intrinsic to the process, and b.) interrelated to all the constants and variables of the process.

[4]Burley, P. (1992) *Evolutionary von Neumann Models*, Journal of Evolutionary Economics 2 , p. 277

[5]unless all changes offset and net to zero

[7]or, more analytically, the quantity of capital composites of factors of production

[8]For many reasons it takes much time to produce and coordinate vast amounts of capital.