Equations for Expansion of the Interest-Involving Money Supply

We have introduced a new meaning for the utterance “return.”  We have affirmed that credit and savings devoted to capital expansion circulate to become pure surplus income for still more expansionary investment. This circular returning is a distinct species of “return.”  It is a type of current circulatory return to entrepreneurs in the aggregate who might unfortunately, with their mistaken understanding of the current circular monetary order, perceive and classify this pure surplus income naively as a boon attributable solely to past investment.

For the full context and denotation of terms of the equations below, the reader should consult the texts indicated in the footnotes.

In microeconomic terms, additional principal may be borrowed by the basic and surplus production functions for an expanded supply and demand for goods and services.  This additional money will be loaned and “charged interest” will be charged.

This charged interest, which is a type of return to the lenders, is conceptually distinct from the continually circulating principal called “macrodynamic return” as we have defined it.

The microeconomic detail of the flows among initial and transfer payments in two periods is formulated as

Σi’Σ0n-1(fij+ Tij) = Σi’Σ1n(oij+ tij – sij)   [CWL 15, 66]

Next, the macroeconomic expression for the additional money required by the basic circuit in the aggregate for expansion of consumer goods production proceeds through (S’-s’O’) for outlays in the basic supply function. At least temporarily it will be pure surplus income.

ΔM’ = (S’ – s’O’) = ΔT’ + ΔR’ + (O’ – R’)

The additional money required in the surplus circuit, which also becomes pure surplus income (or the current return of current investment, or the macroeconomic return) is similar in form with the single superscript being replaced by the double superscript.

Also, it is highly instructive to review and understand Lonergan’s mathematical formalism in CWL 21 representing the pattern of sequential initial and transitional payments destined to circulate into final payments for goods and services.  In a spreadsheet scheme[3]wherein the “bottom” unit of enterprise is first in the sequence of additions of value culminating in the final sale of the composite product, each unit of enterprise except the first covers the initial payments of the firm beneath it by transitional payments, and the final seller also picks up his own payroll through his pricing.  Thus, the sequence of these initial outlays requires a loan until a stack of simultaneous outlays by all contributing firms makes the process self-financing,  except for the (O’ – R’) lag symbolized in the macro formula.

Σsij= Σvirij [4]

It is the increment in this total which must be financed through the (S’-s’O’) channel when an economy expands.

An enlarged economy requires an enlargement of the money supply symbolized above as sij, and ΔM’through the supply functions (S’-s’O’) and (S”-s”O”).  This additional money originates in the multi-party banking system and enters the economy normatively as credit to be justified as real by its use in the supply functions.  And, of course, the banking system charges what is called in microeconomics “charged interest” for its services in the supplying of the money.

Schumpeter notes that interest, in its narrower meaning, is the price charged by the lending function for the temporary use of money which has not been earned by the needful borrower through past production.  That is to say that the borrowed money will bridge the temporary gap between production outlays made first and sales revenues received later.

Whichever of the many explanations of the phenomenon of interest we may hold, all of us will agree to the following definition, although some of us may think it very superficial:  Interest is the premium on present over future means of payment or, as we will say a posteriori, balances.  Interest is the price paid by borrowers for a social permit to acquire commodities and services without having previously fulfilled the condition which in the institutional pattern of capitalism is normally set on the issue of such a social permit, i.e. without having previously contributed other commodities and services to the social stream.  Joseph A. Schumpeter, Business Cycles (New York: McGraw-Hill, Inc., 1964) p. 98

[1]CWL 15, 66 and surrounding context

[2]CWL 15, 67 “Transfers to or from supply, (S’ – s’O’), tend to equal the sum of the increments of aggregate turnover magnitudes in final payments (ΔR’) and transitional payments (ΔT’).  Of these, two, the increment in transitional payments will be the larger, since for each sale at the final market there  commonly is a sale at a number of transitional markets.”  CWL 15, 67

The history of the development of money points to a preponderant role of increasing turnover magnitude in circuit accelerations.  CWL 15, 68

[3]The “bottom” firm is here the first firm in the compositing and value-adding process of production.  This bottom firm is the first of the jfirms in .

[4]CWL 21, 170