## Introduction

We assume that the reader has read the previous section, *A Short Introduction to Selected Key Notions *containing the subsection *Functions *and the section entitled *Further re Functions .*** **If so, he/she has already been confronted with a new science of macroeconomics and with new sets of explanatory equations containing new terms and relations.

In this section, *Functions, Velocities, and the Achievement of Scientific Economics*, this first subsection, *Introduction, *formally introduces the science of functional macroeconomic dynamics. We recommend that the reader read this Introduction without pause just to get a sense of where we are headed. Subsequent sections will provide clarity of significant issues one by one.

The *basic terms *of the explanatory equations in functional macroeconomics will be interdependent rates, i.e. *velocities*. In the economic process, there are movements at rates of so much every so often of 1) products and 2) payment-money to enable the production and sale of these products. Movements of products and money may also be viewed and referred to as “flows.” And these movements or flows of products and money at rates or velocities are called *functionings *or *functions*. Thus, the basic explanatory terms of functional macroeconomics will be the velocities of interdependent functionings.

Since products are constituted by factors of production, one set of fundamental rates is the rates of application of the factors of production in a period; i.e. the rate of use of materials, labor, management, capital, etc. These rates of application are flows (so much every so often) of the components into composite products; thus they are the flows of productive factors. A second set of rates is the rates of exit of final composite products out of the productive process and into the standard of living.

The basic stage of the process is, in its pure form, an aggregate of rates of labor, of managerial activity, of the use of capital equipment for the sake of the goods and services that enter the standard of living. Let us say that some ultimate product … [CWL 15, 29-31]

It is to be noted that the emergent standard of living and the basic stage of the process are not identical aggregates of rates. … Since the form of the relation between them is a double summation, the emergent standard of living and the basic stage of the process are not identical aggregates of rates. On the other hand, precisely because the relation is a double summation, they are equivalent aggregates of rates. However, this statement requires three qualifications. [CWL 15, 29-31]

The application of factors of production, the sale of finished products, the correlated payments to humans for productive services, and the correlated payments to units of enterprise to purchase these products, are all effected at rates of so much per period. These functionings will be regarded as flows or as velocities. Just as there are flows of water or electric current, so there are flows of products and payments. Just as flows of water or electric current are understood as velocities, so flows of products and payments are understood as velocities.

As flows, the movements are *functionings*.

The occurrence of some flows condition the occurrence of other flows. The flow of B is conditioned by the flow of A. There is a connection of functional dependence.

The flows may initially be described and categorized based on our everyday commonsense experience, but flows will finally be defined implicitly by their functional relations to other flows. The entire structure of the dynamic process is purely relational.

Science consists in the relating of terms to one another so as to explain the data of the phenomena under investigation. The terms can be called *explanatory conjugates*. This implicit definition of explanatory conjugates by their functional relations to one another confers *scientific significance *upon these explanatory conjugates. It will, of course, be necessary that the terms and relations of the dynamical equations represent faithfully the form of the interconnected constituent movements of the economy. There must be an isomorphism between the form of the constants and variables and in “the sign or collocations that dictate operations of combining, multiplying, summing, differentiating, integrating, and so forth”and the dynamical relations within the economic process.

The major premise postulates a correspondence between the insights of (scientists) and the form of the mathematical expression of (scientific) principles and laws; in other words, it requires that the content of acts of understanding be reflected faithfully by the form of the mathematical expressions. [CWL 3, 24/ ]

Because functional macroeconomic dynamics will apply to all advanced exchange economies regardless of their political institutions, Lonergan states a similar key idea of general relativity: the form of an equation is independent of a nation’s political institutions.

The analysis also reveals the importance of an apt symbolism. … ¶Why is this so? It is because 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. It follows that, as long as the symbolic pattern of a mathematical expression is unchanged, it’s mathematical meaning is unchanged. Further, it follows that if a symbolic pattern is unchanged by any substitutions of a determinate group, then the mathematical meaning of the pattern is independent of the meaning of the substitutions. [CWL 3, 18-19/ ]

Functional macroeconomics is the science of the flows of products and money.

As Newtonian mechanics is the science of motion constructed on the basis of the terms of space, time, and density per unit volume (mass), so functional macroeconomics is the science of the interdependent functional flows in the process from the potentialities of nature to a standard of living; thus, our science will be in terms of interdependent product flows per unit of time and the conjoined and correlated money flows per unit of time.

In this section entitled *Functions, Velocities, and the Achievement of Scientific Economics*, we will begin with the subsection treating the notion of a functioning as something we merely experience and describe as observers or participants; then, by insight, we will advance to the concepts of an interdependent functional flow as a purely abstract terms in an system of terms and relations which explain the concrete process. This system of terms and relations will explain the how concrete process actually works.

This section is rather long. Rather than entering the forest at its edge only to get lost in the trees, let us descend upon the forest and allow its more prominent features to become clearer and clearer as we do so.

Prominent aspects or features – in our case, the important topics or issues – interact and overlap, so we encounter some minor problems of sequence and cannot avoid redundancy altogether. But, for expositor and student, redundancy or repetition as forms of drill are beneficial to learning. The following outline from an altitude of 30,000 ft. indicates the general ordering of this section:

- Introduction
- Function as a descriptive term
- Production Flows or Rates
- Monetary Flows or Rates

- The Threefold Process – intracircuit and intercircuit interdependence and conditioning
- Scientific explanation
- The Redistributive Monetary Function
- Implicit definition and scientific significance
- “Functionally Related”
- Rates as the Basic Terms
- Rates of production activities
- Conjoined and correlated rates of payments

- Functional relation and implicit definition of basic and surplus, costs and profits
- Formulation of functionally related, macroeconomic flows
- Implicit norms
- The Achievement of Explanation

Let us descend to 20,000 ft. A slight expansion of the outline above gives a clearer overview and preview of the main lines of the argument:

**Introduction**: The aims and key ideas of the section are stated**Function as a descriptive term**: The word “function” has various meanings and may be used as a descriptive term or as an explanatory term. We give a nominal definition of the term and describe functions in the economic process- Production Flows or Rates
- Monetary Flows or Rates

**The Threefold Process**– constituted by intracircuit and intercircuit interdependence and conditioning: The objective economic process consists of the productive activities of the consumer-goods and capital-goods sectors leading ultimately to the emergence of a standard of living. Productive activities of making and selling have monetary correlatives. Among the productive activities and their monetary correlates there is interdependence. The two production processes depend upon a financing process.**The Redistributive Monetary Function**– the source of money for the two productive circuits**Scientific****explanation**: We state what constitutes science and explanation – in economics as well as in physics, chemistry, etc.**Implicit definition and scientific significance**: Implicit definition consists of terms mutually defining one another.This relation of terms to one another – rather than to our everyday selves – conveys scientific significance upon an analysis.**Rates as the Basic Terms**: The basic terms of the explanation of the current dynamic process are functional rates, either being kept in pace with one another according to intelligible norms or being forced out of keeping pace and constituting maladaptation and dysfunctions such as booms and slumps.- Rates of production activities
- Conjoined and correlated rates of payments

**Interdependence and conditioning as objective from the nature of the process****Function as a Technical Term:**The functional relations of the aggregate velocities of productive and monetary activities within the economy are specified. Functional relation and implicit definition of a.)*basic*and*surplus*, and b.)*costs*and*profits*:**Formulation of functionally related, macroeconomic flows**: The functional relations are stated in a coherent set of equations to comprise a fully explanatory theory.**Implicit norms**: The norms of proper functioning are specified.**The Achievement of Explanation**: By formulating the dynamic interrelations among interdependent functionings, functional macroeconomics successfully explains the dynamics, demonstrates how the economy actually works, and gives the theorems, theory, and systematics of what are colloquially called booms and slumps.

Now, let us descend to 10,000 ft. and bring into view the elements of Lonergan’s pedagogical sequence. This presentation of this view may seem to be a machine-gun fire of totally foreign points, more confusing than enlightening or inspiring. If so, the reader should jump to the next subsection, **Function as a Descriptive Term**(URL).

Analysis is “an examination of a complex, its elements, and their relations.” Functionalism is a theoretical orientation that systematizes the interdependence and mutual conditioning of functional velocities or velocitous functionings. And the functionings are the flows of goods and services and the flows of the money to enable these flows of goods and services.

In CWL 15,

Macroeconomic Dynamics: An Essay in Circulation Analysis, Lonergan proceeds deliberately. The importance and aptness of his pedagogical sequence can hardly be overestimated. Money is to buy things. Therefore the purpose of money is to support or be servant to the process of production and sale. Production and sale of basic and consumer goods have a rhythm and structure. Therefore it is critical to understand, first, the rhythm and structure of the productive process. Lonergan begins his analysis with an analysis of the structure of the productive process and its interdependent flows. From this he advances to and concludes with a systematic understanding of how money must function in interdependent circuits of flow if the overall process is to be continuous and fully realized. In broad outline, the analytical-pedagogical sequence of CWL 15 is as follows:

**Lonergan’s Sequence**

- The constitution of a good or service in a modern, developed, complex, exchange economy by the accumulation of contributions of factors of production by units of enterprise in a series
- The limits of the production of products by the finitudes and mutual conditioning of their factors of production
- The precisely-analytical point-to-point relationship of consumer-goods’ production factors to the elements of the produced products which comprise a standard of living. The aggregates of rates of application of these production factors producing a standard of living is called the “basic stage” of the process.
- The point-to-indeterminate-future-series relationship of lowest-stage capital goods to basic-stage consumer goods; and the point-to-higher-dimensions relationship of deeper and deeper-stage capital goods to basic-stage consumer goods, i.e. the “hierarchy” of the process. These point-to-line or point-to-surface or point-to-volume productive activities make up the “surplus stage” of the process.
- The dependence of the flows of consumer (basic) goods upon the necessary flows of maintenance and repairs of the existing capital stock.
- The installation of more of the same capital goods as a widening of the economy without a change of basis or formula.
- The invention and installation of more efficient capital goods as a deepening of the economy and a putting the economy on a new basis with a new formula.
- The dependence of the flows of capital goods of a given level or stage upon the flows of maintenance and repairs of higher-level capital goods
- The intrinsic successively-surging rhythms associated with the above flows as, first, new capital is produced and installed and, only later, a greater quantity of consumer goods is produced
- The inevitably diminishing returns on capital as an increasing resistance is created by a.) the finitudes of materials and other factors of production, b.) the rising repair and maintenance requirements, and c.) the maxima allowed by technical coefficients among interdependent elements.
- A model sequence of exponential growth, constant growth, and inevitable zero growth of capital expansion resulting from the existence of finitudes and the associated impossibility of continued exponential growth
- The classification and pattern of the associated money flows, i.e. monetary functionings, necessary to enable and continue this successive-surgings productive process as
*basic*,*ordinary**surplus*, and*pure**surplus*

** **

- Financing requirements determined by the magnitudes and frequencies of the turnovers of units of enterprise operating simultaneously with respect to a standard interval
- The dependence of the continuity of the objective economic process on a) the concomitance of the flows of money within a productive-monetary circuit, and b) between mutually dependent circuits

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[3]

Further, without further clarification Schumpeter acknowledged that dynamic analysis called for a new light on equilibrium. Such new light arises when, over and above the equilibria of supply and demand with respect to goods and services (classic microeconomics), there are recognized further equilibria (crossovers balancing, concomitance of outlays with income and income with outlays and expenditure) that have to be maintained if an economy chooses to remain in a stationary state, (or) to embark on a long-term expansion (and) to distribute its benefits to the vast majority of its members (in a basic expansion), and so to return to a more affluent stationary state until such further time as further expansion beckons.

In this highlighted pedagogical sequence, Lonergan treats appropriately as to emphasis and timing the following additional issues:

- A nation really earns only what it really produces. Its product is its income. Its National Product is its National Income.
- The aggregates of consumable and capital products sold in a period are represented by the vector quantities Q’ and Q” respectively. Since the magnitudes of these products are magnitudes per period of time, these symbols stand for velocities or rates Q/t
_{n}. - If the velocities are Q’ and Q”, the accelerations are dQ’/Q’ and dQ”/Q”. (These accelerations suggest a second-order differential equation.)
- Accelerations may be compared to determine which type of aggregate of goods – capital goods or consumer goods – is accelerating at a greater rate, and thereby define phases of the process requiring adjustments of income levels and savings rates.
- Table of possibility of different types of phase

dQ”, dQ’ | |||

I. Unspecified | Surplus Advantage | Proportionate Phase | Basic Advantage |

II. Neither negative | Surplus Expansion | Proportionate Expansion | Basic Expansion |

III. Neither positive | Surplus Contraction | Proportionate Contraction | Basic Contraction |

IV. Both zero | — | Mixed Phase | — |

V. One positive,
one negative |
Mixed Phase | — | Mixed Phase |

- Quantities under production may differ from quantities sold in a period. These quantities under production may be represented by a’Q’ and a”Q” where a’ and a” range above and below 1.0 as more is produced than sold or more is sold than produced.
*Costs*of production and*profits*from production are defined from a macroeconomic point of view rather than from a bookkeeper’s point of view.

There is a sense in which one may speak of the fraction of basic outlay that moves to basic income as the “costs” of basic production. … 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

functionalcosts…. CWL 15 156-57

- P’ and P” are vector quantities representing selling price indices of basic and capital goods respectively
- p’ and p” are vector quantities representing cost price indices and, consistent with the previous quote and with this project of explanation by implicit definition of terms reperesenting functions in functional relations, defined implicitly and explicitly by the equations:

c’O’ = p’a’Q’ p’ = c’O’/a’Q’

c”O” = p”a”Q”_{Basic Circuit Repair and Maintenance }p” = c”O”/a”Q”_{Basic Circuit R&M}

- Therefore, the dot product of the price vector and the quantity vector represents the flow of money in a demand or supply functioning.
- However, the money of a circuit may be diverted from its requirement in one circuit into another circuit or into the redistributive function to drain or flood, deflate or inflate, damp or swell the normative pattern of functionings.That is, the human-agent driver may, out of ignorance or malice, turn the wheel of the economy in the wrong direction! Or step on the accelerator of one pair of wheels and simultaneously step on the brake of the other pair of wheels, thus putting the pairs at cross purposes with one another.
- A heuristic analysis of the series of stages of the cyclical process over the long term confirms the scientific achievement of functional macroeconomics

Now, having descended gradually into macroeconomic dynamics and noticed its important features as a science, though blurriness and confusion still remain, let us proceed to achieve a better understanding of functional macroeconomic dynamics.

** **

[1]Where *k*stands for factors of production and *j*stands for units of enterprise in the series of value-adding units of enterprise.

[3]Equivalent statements of this idea of concomitance are those of “the crossovers balancing” and “the adjustment of the rate of saving to the phase of the process”