Theorems of “Continuity” in Macroeconomic Dynamics

Because he was so expert in math, science, and scientific method, Lonergan’s early thinking in Macroeconomics in CWL 21 was more abstract, more general, and more advanced even than the thinking found in the Macroeconomics textbooks of today.  His thinking continued to develop into the explanatory systematics of CWL 15.  Here, two brief excerpts from the earlier CWL 21.

The Provisional Theorem of Continuity (CWL 21, §24, pp. 47-48)

Now if continuity is defined by equality of sales at the final markets in successive instants or turnovers, the necessary and sufficient condition of continuity is that

DA’ = DA

and

DA” = DA”.

Since equations (8) DE’ + DE” = DI’ + DI” and (9) G’DI’ = G”DI” are independent, it follows that continuity in its simplest form has a twofold condition.  First, from equation (8), total primary and secondary income must be spent.  Second, from equation (9), primary income moving to the secondary final market must equal secondary income moving to the primary final market. (CWL 21, 47-48)

The General theorem of Continuity (CWL 21, §38, pp. 73-75) 

The economic process is an organic whole.  The process can proceed only within the limits of equilibrium of the various phases. Continuity is the maintenance of organization within these limits. To step outside them is to bring about a general breakdown.

An initial and provisional theorem of continuity was enounced in a preceding chapter (§24).  Now it may be indicated in its full generality. ¶ The analysis has revealed that the economic system is a pattern of aggregate dynamic relationships arranged in different kinds of velocity and accelerator rhythms. In the real order there are the primary and secondary rhythms, with the former accelerated by the latter.  In the monetary order there are the rhythms of excess release from the redistributional area to the primary and secondary rhythms; and again, the former accelerate the latter. ¶ Now the general theorem of continuity is that this complex machine has a nature that must be respected.  Absolutely, there is no necessarily right value for the monetary accelerators DT’, DT”, DC’, DC”; again, absolutely, there is no necessarily right values for the six multipliers C’, C”, T’, T”, G’, G”.  But what is true is this: as soon as a few of these are determined, the rest become determined within narrower limits, for all form part of an organic whole; to violate this organic interconnection is simply to smash the organism, to create the paradoxical situation of starvation in the midst of plenty, of workers eager for work and capable of finding none, of investors looking for opportunities to invest and being given no outlet, and of everyone’s inability to do what he wishes to do being the cause of everyone’s inability to remedy the situation.  Such is disorganization.  Continuity, on the other hand, is the maintenance of organization, the stability of the sets and patterns of dynamic relationships that constitute economic well-being in a society. ¶ While the provisional theorem of continuity (§24) did regard the static phase, it is important to observe that the general theorem regards any phase.  There is a general historical movement of ideas, opportunities, and decisions integrating into that major rhythm in which transformations are followed by exploitations only to bring forth new and deeper transformations.  Within this broad historical scheme of things, the role of any age, and still more of any country, is but a small thing: the past was settled by our forebears, and the future will be in the hands of posterity; only the present is ours, and it is only within the limits that we make of the present what we wish.  Our starting pint is already determinate: we have to face things as they are; we may never lose sight of them or attempt to reckon without them.  But not only is there ever a broad and unalterable datum of things as they are; there are also the limitations which this datum imposes on things as we are going to make them.  ¶ The theorem of continuity is the abstract and formal aspect of such limitations in the economic order.  At the moment the exchange process is static or expanding or contracting.  We may like it so or we may wish it different.  But in any case there is some determinate range of values of the multipliers and of the monetary accelerators – of C’, C”, T’, T”, G’, G”, of DC’, DC”, DT’, DT” – that corresponds with such a decision.  Moreover there has to be an internal coherence between these values, and to violate this coherence is to rout economic organization.  Just as the movements of the controls of an airplane must be coordinated and all coordinations are not possible at all instants, so also he economic machine as its controls, which can be moved only in concert and only in a limited number of ways at any given time.  ¶ Such is the general theorem of continuity.  In the abstract and in a general way, it affirms that the economic process can proceed only within the limits of equilibrium of the various phases.  To step outside them is to bring about a general breakdown. (CWL 21 73-5)

Elements of Analysis

 

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