Further to the isolated comments and excerpts in the Introductory section:
The utterance pure surplus income designates the income which is invested in an expansion of the stock of capital.
one may legitimately project a division of expenditure into the division of income, and it is in this manner that we arrive at the concept of pure surplus income. [CWL 15, 144]
In the surplus circuit of serially conditioned monetary flows, pure surplus income is the income directed to expansionary investment. It is distinguished from ordinary surplus income which is the income directed to repair and maintenance of existing capital; i.e. toward the maintenance of current capacity rather than the expansion of current capacity.
Investment is expenditure for capital items. Expenditure does not occur without an income to expend. The expansion of the process requires an increase in the money supply. In the first instance, the source of the income-inflow is a loan extended by the banking system through (S’-s’O’) or (S”-s”O”). The money supply is increased.
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 exit of 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 (through savings) of basic income with an increase in the supply of money (for investment), – (such a reduction is a redirection, 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]
I have spoken of the analysis as revealing channels and bringing to light an undertow. My meaning may become clearer by referring to the distinction sometimes made between general equilibrium (Walras, Wicksell) and partial equilibrium (Marshall). The channels of circulation replace the overall dominance claimed for general equilibrium theory, but they reveal the conditions under which partial equilibria can exist … More positively, the channels account for booms and slumps, for inflation and deflation, for changed rates of profit, for the attraction found in a favorable balance of trade, the relief given by deficit spending, and the variant provided by multinational corporations and their opposition to the welfare state. [CWL15, 17]
(Burley re entry channel: under construction)
As so often insisted, doing the science of macroeconomics requires a scientific heuristic. That requirement drags us into the structure of the form of knowing of mathematicians and physicists. As a concept, functional pure surplus income is a constituent of an insight which relates explanatory terms to one another. Again,
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]
Pure surplus income represents a functional flow correlated with expansionary investment rather than with maintenance of capital or with production of basic goods By projection, mapping, correspondence, and correlation, basic production, R&M production, and pure-surplus production are functionally correlated with the incomes expended upon them. The division of incomes is congruent with the divisions of the productive process into interdependent, mutually defining and mutually conditioning functionings. Thus pure surplus income is defined by its functional relation to the other functional income flows correlated with the network of production and sale. If one grasps and can define velocitous pure surplus income, one grasps and can define velocitous ordinary surplus income and velocitous basic income. All are interlocked in a sweeping perspective, for a sweeping insight grasps all in a single act. “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.” Conceptually, the flows cohere with one another in the unified relations of the integral system. That coherence of concepts is constituted by their implicit definition of one another and by their functional relations to one another in the whole system.
… operative payments have been defined as standing in a network congruent with the network of the productive process; it follows that we have to deal with quantities of money congruent with the values emerging in the productive process, and with the velocities of money congruent with the velocities of the productive process. CWL 21, 135
Thus, pure surplus income is a technical term – like charge, heat, and pressure – related implicitly in an equation to other technical terms by the functional relations in which they stand with one another. And the pattern of constants, variables, operators and their collocations and equals sign faithfully reflect the pattern of their functional interdependence and their interdependent flows. Thus, the cluster of equations which contain the workings of the entire process constitutes an explanatory theory.
As explanatory, the set of technical terms and their functional relations account for the functionings of the overall process. In addition, the set of terms and relations yield norms for the proper adaptation by human agents such as consumers, producers, and investors. The relations are the relations of velocitious functionings. Recall the intelligibility of the serially-conditioned series called a circuit. Outlays become incomes; incomes are expended. Conceptually we may regard income as “in between” its outlay-source and its expenditure-use. Expenditure is serially conditioned by an income to be expended. Income for expenditure is serially conditioned by outlays for production, or, in the first instance before any recirculation, by an infusion of credit to the system.
The explanatory theory and the technical coefficients yield normative patterns for realization of full potential; the norms beg conformance with the potentialities of the finite system.
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]
The idea of one velocity in circulatory dependence with another velocity implies velocity “keeping in step” with velocity. Thus outlay, income and expenditure must keep in step within one circuit. Simply, we may rely on brief bridge loans to overcome a normal delay in the series from outlay back to final receipt.
The more difficult macroeconomic concept is the concept of the crossover dependence between two circuits. This requires a crossover balance constituted by the adjustment of the rate of saving vs. the rate of consuming according to the phase-ic requirements of the dynamic phase-ic process of creative destruction. The ratio of surplus production to basic production is always changing, requiring an ever changing ratio of saving to consuming.
The critical, normative concomitance of income with outlay and expenditure is constituted by adjustment of the rate of saving to the ever-changing requirements of the creative-destructive process. Outlays get split into basic income for a standard of living, ordinary surplus income for R&M, and pure surplus income for expansion. Each type of income, must be accelerated and decelerated according “to the (technical) requirements of the productive process,” whether the process be in a static phase or an expansionary phase. A cross-purposed, out-of-whack, draining of money needed in one circuit out to another circuit inflates one circuit and damps the other. Also, a leakage of money out of either of the productive circuits into investment in secondary markets damps real economic activity. On the other hand, a flood of consumer credit into the circuits artificially swells incomes, inflates prices and swindles those holding cash and receivables.
In particular, the flow of pure surplus income must keep in step – neither trailing to damp nor running ahead to overdo – with the requirements of the expansionary investment determined normatively by the technical coefficients of the process for a given state of culture, technology and institutions.
In summary, to understand the concept of pure surplus income is to understand its companion concepts in their proper functional interdependence and formal coherence.
 Depending upon the aspect of the process being considered, several phrases are used to designate the income used for expansionary investment:
- Pure surplus income
- Purely expansionary income
- Expansionary “macroeconomic profit”
- The monetary correlate of capital expansion
- Net aggregate savings
- Net macroeconomic “profits”
- “Macroeconomic interest”
- The social dividend
- The “over and above” what is used for consumption
- Betterment money
- Not ordinary surplus income for repair and maintenance of capital
- Not “constant normal profit” for repairt and maintenance of capital
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
 We restrict the meaning of investment to investment in capital items. It is, of course, possible to invest, so to speak, in inventory.
 The source may be initially-credit or continuously-ongoing receipts from prior operations.
 See Strang for the mathematics and technical meaning of divergence.
 The capital expansion calls for borrowing or saving; the basic expansion calls for consuming.