The Meanings of “Function”

Our first subsection after the Introduction was Function as a Descriptive Term. Let us review and clarify some particular meanings of the word function:

In doing economics we might bounce the wordfunction around and use the term in several senses:

(1) in a narrow mathematical sense, the form one studies in pure calculus

(2) in a general descriptive or nominal sense, an economic function, such as supply or demand, without specification of any explanatory significance

(3) in the scientific macroeconomic sense, a definite economic activity whose definition is determined strictly by its functional relation to other economic activities and expressed in the equations of an explanatory macrodynamics.

The scientific functioning with meaning (3) can be stated and defined mathematically; the economic functioning may then be a technical term in the expression of a mathematical function with meaning (1).

Meaning (1) in the purely mathematical, purely relational sense: In the calculus we may write the expression

y = x3

We say, “is a function of x,” with no physical or economic meaning given to yor xand without a trace of xbeing an efficient cause of ythrough some sort of muscular effort.  We are stating a purely mathematical co-relation of yto x.

Meaning (2), with barely more understanding of relations than that of a parrot: We may speak of the monetary supply function as the functional flow of money from units of enterprise into the hands of supplier-workers or the monetary demand function as the functional flow of money from the hands of purchasers to the hands of units of enterprise, without any consideration of possible explanatory significance in a comprehensive theory.

Meaning (3): We may use function as a technical term in an equation representing tghe intelligibility in an explanatory theory of macroeconomic dynamics.  The purely abstract mathematical function may then be applied to the economic content of the concrete economic process. Conversely, the secondary determinations of the concrete process finds the primary relativity in a general mathematical form.

In our formalization of the circular flow in the basic circuit we have the simple equating of flow elements, thus defining and giving the normative keeping pace of the circular flows;

O’ = I’ = E’ = R’

and because these flows consist of the money required by the price-quantity being exchanged, the scientific definition and explanation of both prices and quantities are achieved. Consider:

P’Q’ = (p’a’Q’)Basic+ (p”a”Q”)OrdinarySurplus

In discussing the circular flows in the basic circuit we may use the word “function” in both the first and third senses, but we must be careful to distinguish our meanings. First, we may “channel” the pure mathematician, put on an “I’m a pure mathematician,” cap, and consider solely the mathematical function apart from any economic content; we may focus on the purely mathematical form of the collocation of the operations of adding, multiplying and equating.

In the third sense, this formula expresses the content of an insight into the purely objective functional interconnections of velocitous demand and supply monetary functionings.  On the left, P’Q’ represents the flow of money constituting the basic monetary demand functioning which sends consumer goods out into a standard of living and terminates basic productive supply of these goods.  The two terms on the right represent the flows to workers of compensation  for productive services, which flows are directed to the purchase of a standard of living.

Monetary demand flows are identified with monetary supply flows.  Macroeconomic revenuesare functionally equal to macroeconomic costs.  The rate of flow of final payments for purchase of consumer goods equals the sum of the rates of flows of income emanating from the production of both consumer goods and R&M capital goods.  The expression identifies and defines in and by an equation the functional monetary interrelations of basic demand and basic supply. The form of the terms and their collocations is isomorphic with, or conformsto, and faithfully represents the form of the functionings in the economic process.

The functional terms define each other implicitly by their functional relations in the economic process. They are mutually definitive. Conversely the relations define the terms, i.e. the meaning of the terms is implied by their relations to one another. And this implicit-mutual definition is cast in mathematical terms and confers scientific significance on the equation of functions in relation.

The abstract and recondite terms of our mathematical function representing the economic functioning are not income-statement terms, nor are they terms of  fuzzy psychology (e.g. “utility”) or politically-stained sociology (e.g. “working class,” “proletariat,” “bourgeoisie”).  They define one another by their purely objective functional relation to one another in the economic process, apart from and prior to the thoughts and feelings of participants.  The technical interrelations are grasped by insight, formulated, and verified by repeated common experience.

Then this and other explanatory postulates and theorems are formalized and related to one another to form a coherent and comprehensive theory.