Equations for Expansion of the Interest-Involving Money Supply

We have introduced a new meaning for the utterance “macroeconomic return” in the cycle of pure surplus income.  We have affirmed that savings devoted to capital expansion are classified as pure surplus income for still more expansionary investment and circulate as a “macroeconomic return”.

Pure surplus income 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 and relations of the equations below, the reader should consult the texts indicated in the references beside the equations.

In microeconomic terms, additional principal may be borrowed through S’-s’O’ and S”-s”O” by the basic and surplus production functions for an expanded supply.  The production is performed by compensated humans which tends to support demand within and between circuits for goods and services – as theorized by the normative concomitance and conjoinment of Outlays-Incomes and Expenditures-Receipts.  This purely additional money will be loaned through the horizontal channels in the Diagram, and “interest” will be charged for rental of the money.

This charged interest, which is first seen as a simple microeconomic type of return to the lenders rather than a pure surplus return, is conceptually distinct from the circulating savings for investment called “macrodynamic return” as we have defined it.

The microeconomic detail of the increase of flows in the point-to-point basic circuit constituted by initial payments, transfer payments, and final payments in two periods is formulated as

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

Next, by assimilating the macroeconomic expression for the additional money required by the basic circuit in the aggregate for expansion of consumer goods production from turnover to turnover proceeds through (S’-s’O’) for outlays in the basic supply function.

ΔM’ = (S’ – s’O’) = ΔT’ + ΔR’ + (O’ – R’)(See CWL 15, pp. 66-7)

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

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 bottom first covers the initial payments of the firm prior to or “beneath” it by transitional payments, and the final seller also picks up his own payroll through his pricing of the completed project.  Thus, the sequence of these initial incremental outlays for incremental products requires a loan until a stack of simultaneous outlays by all contributing firms in a fully developed supply chain (CWL 15, 30: ΣΣqi = qijk) makes the process self-financing, except for the (O’ – R’) lag symbolized in the macro formula above.

Σsij= Σvirij  (See CWL 21, 170)

It is the increment in a total flow of basic products and money which must be incrementally financed by incremental money through the (S’-s’O’) channel when an economy expands.

Thus, an enlarged economy requires an enlargement of the money supply symbolized above as sij, and ΔM’ through the monetary supply functions (S’-s’O’) and (S”-s”O”).  This additional money originates in the Central and multi-bank banking system and enters the economy normatively as credit to be justified 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 yet 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 descriptions and explanations of the phenomenon of interest we may put forth, all of us will agree that interest is the price paid by borrowers for a social permit to acquire new productive 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. Interest is the fee paid for new money to finance new (expanded) production.  The loan is, in some sense, the fee charged for a “social permit” to conduct expansion.  (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 .