Equilibrium in Endogenous Technological Change

In a complete science of functional flows – whether they be hydrodynamic flows or macroeconomic flows – the formulation of dynamic continuity and of dynamic equilibrium is central.  How do we keep the vital interdependent flows going, and how do we keep them properly balnced?  A dynamic heuristic will insist upon a specification of dynamic equilibrium.

(Functional Macroeconomic Dynamics) is “a general theory of dynamic equilibria and disequilibria.” [McShane 1980, 117]

Schumpeter acknowledged that dynamic analysis called for a new light on equilibrium.  Such new light arises when, over and above, the (microeconomic) equilibria  of supply and demand with respect to goods and services, there are recognized further equilibria that have to be maintained…..Moreover, such macroequilibria are more fundamental than the microequilibria assembled by Walras.  The (macroeconomic equilibria) are the conditions of a properly functioning economy [CWL 15, 92]

To better compare and appreciate Romer’s and Lonergan’s systematics, it may help to view both from the perspective of equilibrium.

For Romer, equilibrium consisted in all functionings growing at the same rate in the very long run.

Romer’s and Nordhaus’s prize-winning contributions belong to the field of long-run macroeconomics.  In textbooks, macroeconomic analysis is usually defined over different time horizons. Most well-know is the short-run perspective on the macroeonomy: the study of business cycles – the ups and downs of output over, say, a 10-year horizon.  In the midst of such ups and downs, it is easy to forget the long-run perspective: the study or economic growth – development of output, and more broadly human welfare, over decades or even centuries. [Nobel Prize.org, Romer and Nordhaus; Press Release, 2018, page 2

Equilibrium was an equilibrium of growth rates.  Romer states that his strategy is to solve for an equilibrium which consists of constant exponential rates of equal growth for

  • the pool of knowledge available to all researchers, A
  • total capital, K
  • output, Y, and
  • consumption, C.

despite inevitable differences in the timing of growth and in the rates of growth of these aggregates in all transitional expansions of the short term or intermediate term.

The strategy for characterizing the model that is followed here is to solve for an equilibrium in which the variables A, K, and grow at constant exponential rates.  This is generally referred to as a balanced growth equilibrium.  The intuition from the Solow model suggests that such an equilibrium will exist if Agrows at a constant exponential rate. The intuition from the Uzawa model suggests that it is possible for Ato grow at an exponential rate  because equation (3) for Å is linear in A. It will grow at a constant rate if the amount of human capital Hthat is devoted to research stays constant. Verifying that a balanced growth equilibrium exists therefore reduces to the problem of showing that prices and wages are such that HYand HAremain constant as Y, K, C, and grow.  [Romer, 1990, S90]

Lonergan made precise analytic distinctions at an adequate level of abstraction to identify basic macroeconomic terms as interdependent functional flows which, by their functional relations to one another, explain the process.  Romer, on the other hand,  operates in the thicket of the microeconomic interactions of income-receiving households deciding how to allocate their human capital and labor, and of these same households as profit-seeking owners deciding whether to do research, produce durables, or produce consumables  Romer outlines what, for him, constitutes equilibrium:

An equilibrium for this model will be paths for prices and quantities such that i) consumers make savings and consumption decisions taking interest rates as given; ii) holders of human capital decide whether to work in the research sector or the manufacturing sector taking as given the stock of total knowledge A, the price of designs PA, and the wage rate in the manufacturing sector wA; iii)final goods producers choose labor, human capital, and a list of differentiated durables taking prices as given; iv) each firm that owns a design and manufactures a producer durable maximizes profit taking as given the interest rate and the downward sloping demand curve it faces, and setting prices to maximize profits; v) firms contemplating entry into the business of producing a durable take prices for designs as given; and vi) the supply of each good is equal to the demand. [Romer 1990, S88]

In Romer’s formalism of constant growth in a finite world, economic advance cannot be convex such that it tapers and comes to a halt; nor can it increase quadratically tending to infinity; it must be of a constant exponential rate. (S71, 72, 73, 78, 80)

Romer’s use of the phrase “paths for prices and quantities” [Romer 1990, S88] implies an intuition of channels containing pretio-quantital flows.  Thus Romer implicitly intuits that a) interdependent functional flows are explanatory constituents of the macroeconomic process, and b) the intelligibility of the process is immanent in, and must be somehow formulated isomorphic with the pattern of its explanatory flows.  But, because his circuits are constituted by firms rather than firm-indifferent functioning, his flows he forced himself into semimicroeconomic interfirmal forms rather than purely macroeconomic, interfunctional forms.

Remaining conscious of Romer’s interfirmal flow dynamics vs. Lonergan’s interfunctional flow dynamics, we may place Romer’s flows in Lonergan’s framework, the Diagram of Rates of Flow, to shed light on, so as to better understand, both persons’ formalisms. But we must also keep in mind that Romer’s essay has a more limited purpose and scope than Lonergan’s essay; it is not a systematization of all aspects of interdependent aggregate functional flows of both products and money within an economy.  It does not include the transitional dynamics of economic “revolutions”;  it does not allow for the facts that a) not all income recipients are owners, b) income recipients are free to decide for themselves when and how to spend their money, c) short and intermediate economic advances are intrinsically cyclical, and d) advances may be disequilibreated in aberrant, violative booms, slumps, inflation, and deflation.  Income recipients are not owners spending all that they earn robotically.

In a previous section, “Sectors,” Circuits, Explanatory Conjugates, Multiplier and Lagged Temporalty, we provided eight lists which the reader may want to review quickly.

Romer’s “sectors” are made up of proprietary organizations performing well-defined production functions; his classification of these firms according to their functionings renders his analysis satisfactorily functional and, thus, allows us to place his system in Lonergan’s framework of rates of functional flows for comparison. Lonergan’s analysis is explicitly and purely functional; it is not conceived in terms of firms and households; it recognizes that a) in the productive order, units of enterprise may produce on more than one functional level (e.g. point-to-point, point-to-line, etc.), and b) in the monetary order, the recipients of incomes – no matter in which circuit they produce – cannot be restricted to purchasing in only one functional circuit, rather they decide for themselves how to keep their money for a standard of living or to circulate it through the Redistributive Function so as to save-and-invest on some level.

Our whole structure is purely relational.  A macroeconomic functioning is not a compilation or aggregation of particular income statement categories, such as wages or interest expense.  A macroeconomic functioning is implicitly defined by its functional relation to other functionings.  The whole structure is purely relational.  “Lonergan’s analysis is concrete but heuristic.  It focuses on functional relations intrinsic to the productive process to reach eventually a general theory of dynamic equilibria and disequilibria.” [McShane 1980, 117]

I have insisted on focusing on the central issue: the need of a functional analysis of the productive process and its correlated monetary flow. [McShane 1980,200]

(Again,) Lonergan’s analysis is concrete but heuristic.  It focuses on functional relations intrinsic to the productive process to reach eventually a general theory of dynamic equilibria and disequilibria. [McShane 1980, 117]

The division is not a matter of social relations or of property or of the properties of things: it is a functional analysis. … The aim of the analysis is to reveal the possibilities of the productive process as a dynamic system.  One moves forward to that revelation in so far as one appreciates the different ways in which basic and surplus stages may relate. [McShane 1980, 119-20]

The analysis is functional and leads us to define five monetary functions which reveal a set of circulations of money. [McShane 1980, 121]

Now whatever the difficulties of measurement, the functional distinction is undeniably valid. [McShane 1980, 121]

… a massive long-term acceleration is a massive development of surplus activity.  Further, one is not to think of this increment in Q” as concentrated in firms of certain types.  The distinction between basic and surplus is not a material nor a proprietary but a functional distinction. There are types of enterprise that in themselves are indifferently basic or surplus … [CWL 15, 118]

Further to be noted is that there are two reasons for the complexity of the summation of outlays.  The one already given was that turnover frequencies varied from firm to firm.  But the full reason is the fact that the distinction between (basic outlays,) O’, and (surplus outlays,) O”, is extrinsic: it is made not by the authors of outlay but by its recipients for whom it is income. [CWL 15, 69]

In Lonergan’s science of interdependent functional flows, the major, though not the only, condition of equilibrium is the crossover balance between functional circuits.  This balance constitutes the adjustment of savings to the cyclically varying requirements of each level-circuit of the many-leveled hierarchical process.  Though, by an accounting identity, savings must always equal investment, Functional Macroeconomic Dynamics explicitly and explanatorily includes the function of credit to supplement savings, especially in the case of a geometrically increasing output in a circuit; and FMD mandates a balance of intercircuit flows for equilibrium.  Neither circuit is allowed to flood itself by draining the other

Functional Macroeconomic Dynamics has little interest in accounting identities; it is primarily concerned to understand the laws of the economic process and the precepts implied for proper management of the process.

It is a common saying that savings equals investment.  On the present showing it would be more accurate to say that the crossovers should balance, that a sustained lack of balance portends ruin, …

The advantage of such greater accuracy is that it does not suggest an immediate correlation between savings and investment.  Provided the crossovers balance, surplus income equals surplus supply. [CWL 15, 70]

Need the moral be repeated?  There exist two circuits, each with its own final market.  The equilibrium of the economic process is conditioned by the balance of the two circuits: each must be allowed the possibility of continuity, of basic outlay yielding an equal basic income and surplus outlay yielding an equal surplus income, of basic and surplus income yielding equal basic and surplus expenditure, and of these grounding equivalent basic and surplus outlay.  But what cannot be tolerated, much less sustained, is for one circuit to be drained by the other. [CWL 15, 175]

In Romer’s mathematization of profit-motivated intelligence driving continued economic advance, key assumptions include 1) that the store of economically-useful knowledge available to all researchers will increase linearly and, therefore, without bound, 2) that the rate of linear growth of inventions is, in a very-long-run concomitance, transmitted to an equal rate of growth in production and sale of producer durables and consumables, and 3) that demand equals supply because all consumers are owners buying all that they themselves produce.  While Romer’s systematics is implicitly comprised of interacting functional flows, his mathematization containing restrictive and constraining assumptions regarding intersectoral prices and wages, on one hand proceeds with faultless formal logic to proof of endogeneity but, on the other hand, bypasses the consideration of lags and intrinsic cyclicality in the transitional dynamics of short-term advances, which comprise the very long run.

The lags, multiplier effects, and intrinsic cyclicality are specified by the lagged technical accelerator.

kn[f’n(t-a)-Bn] = f”n-1(t) – An-1  [CWL 15, 37]

As one studies this section, one can become more aware of transitional dynamics by comparing and contrasting four possible ideal patterns of expansion: 1) Romer’s linear, constant exponential growth having ever expanding knowlege plus law-abiding consumers, 2) a logistic pure-cycle of growth advancing from an initial exponential growth (convex upward) to an eventual convex downward approach to an asymptote of satiation, and 3) Lonergan’s initial geometric-increase growth based upon the inner logic of productive capacities and relations followed by uniform growth to a maximum based upon technical coefficients, [CWL 15, 113-128], and 4) Peter Burley’s von Neumann models:

Burley, Peter (1989), A von Neumann Representation of Lonergan’s Production Problem, Economic Systems Research, 1 (3), [Burley, 1989]

Burley, Peter (1992) Evolutionary von Neumann Models, Journal of Evolutionary Economics 2 , 269-80 [Burley, 1992-2].

To provide an alternative perspective on Romer’s persuasive form of feasible growth in the very long run, we encourage the reader to review some of the diagrams previously shown in Introduction, Diagrams, and Framework. (Click here)   

We show again certain diagrams from that section:

Lonergan replaced the single circuit of the textbooks with the credit-centered, double circuit of Functional Macroeconomic Dynamics.

The entire tradition slipped past Lonergan’s simple move.  I describe the move as paralleling Newton’s move. Newton started within an old culture of two flows: an earthly flow and, to recall ancient searchings, a quintessential flow.  Newton went from two to one.  Lonergan started with a dominant one-flow economic analysis  –  think in terms of the household-firm diagram  –  and separated it into two flows “to form a more basic concept and develop a more general theory.” 21  [McShane 2017, viii]; also see [CWL 21, 11]

  

Lonergan’s Table of Contents might be labeled:

  • Part I              The Productive Process                                            Sections 1-11
  • Part II             The Exchange Process and Monetary Velocities   Sections 12-17
  • Part III            Phases in Expansion of the Process                         Sections 18-22
  • Part IV             Healing and Creating in History
  • Part V             Cycles, Circuits, and Monetary Circulation             Sections 23-28
  • Part VI             Superposed Circuits – Gov’t and Foreign Trade    Sections 29-31
  • Appendix: History of the Diagram, 1944-1998

Relevant to Parts I, II, III, and V (above) are diagrams (below) which show how the always current process plays out in intrinsically cyclical fashion many times over Romer’s very long term. These are easily located by their Figure numbers corresponding to section numbers in CWL 15.

In these first two diagrams, suppose that k = 1.05 and that r = .9524.

 

 

 

 

 

 

Functional Macroeconomic Dynamics specifies a process of lagged technological expansion.  For the achievement of a) continuity and b) equilibrium, – standard ideas in fluid dynamics [Giancoli, 2005, 226-55, 268-69; and L&M, 1957, 30-33]  – there is required a) a normative keeping apace of intracircuit flows, and b) a balance of intercircuit “crossover” flows, which, again, constitute the varying adjustment of savings to the varying requirements for savings in the successive phases of the expanding process. Again,

Need the moral be repeated?  There exist two circuits, each with its own final market.  The equilibrium of the economic process is conditioned by the balance of the two circuits: each must be allowed the possibility of continuity, of basic outlay yielding an equal basic income and surplus outlay yielding an equal surplus income, of basic and surplus income yielding equal basic and surplus expenditure, and of these grounding equivalent basic and surplus outlay.  But what cannot be tolerated, much less sustained, is for one circuit to be drained by the other. [CWL 15, 175]

What cannot be tolerated is an imbalance of the crossovers, i.e. one circuit to overexpand by choking off the other.

Romer’s instincts, intuitions, and formulations of the very long run are reliable, though his focus is not explicitly functional. Embedded in his treatment of interacting firms is an analysis of pretio-quantital, interdependent, functional flows.  Both Romer’s Endogenous Technological Change and Lonergan’s Functional Macroeconomic Dynamics are sets of equations specifying the relations of functionings. Both use equations for the process which can be symbolically represented by Lonergan’s Rates-of-Flow framework.

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. [CWL 3, 18-19/43]

More fully:

The analysis also reveals the importance of an apt symbolism.  ¶There is no doubt that, though symbols are signs chosen by convention, still some choices are highly fruitful while others are not. … 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, 18-19/43]

We might mention two notable aspects of Romer’s Endogenous Technological Change:  It is, on one hand, a brilliant mathematical proof, based on his assumptions and conceptual premises, of a theorem of possibility.   On the other hand, it too casually specifies an effortless supply-demand equilibrium as profit-maximizing manufacturing sectors negotiate pretio-quantital flows along intersectoral paths (channels) such that salaries of both applications of human capital, HAand HY, are the same and all sectors simultaneously grow at the same rate.  Three sectors move in very-long-run, giant lockstep.  Such a synchronous equilibrium is feasible only in the case of a) a static economy where all levels are fully developed, acting in sync, and Hequals zero, or b) in the case of change in the very long run, glossing over shorter-run cyclicality.  Romer’s title is Endogenous Technological Change and, because the change is constant exponential growthin the very long run, the title might be lengthened to Endogenous Technological Change in the Very Long Run.

The channels of Lonergan’s Diagram of Rates of Flow provide a general and universal explanatory framework of the always current process.  The channels explain– rather than merely describe or postulate – both the dynamic equilibria of the pure cycle and the dynamic disequilibria of the booms and the slumps.  As the economy expands, things can go awry.

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. [CWL 15, 17]

… positive or negative transfers to basic demand (D’-s”I’) and consequent similar transfers to surplus demand (D”-s”I”) belong to the theory of booms and slumps. They involve changes in (aggregate basic or aggregate surplus) demand, with entrepreneurs receiving back more (or less) than they paid out in outlay (which includes profits of all kinds). The immediate effect (of these aberrational monetary transfers) is on the price levels at the final markets, and to these changes (in price), enterprise as a whole responds to release an upward (or downward)  movement of the whole economy.  But the initial increased transfers to demand [that is, excess transfers along (D’-s’I’) and (D”-s”I”) ] are not simply to be supposed.  For that would be postulating without explaining the boom or slump. [CWL 15, 64]

Lonergan’s analysis of equilibrium is heuristic; guided by a scientific and dynamic heuristic, he is searching for a general and universal explanation of what constitutes equilibrium in the dynamic, intrinsically cyclical, always-current economic process – an explanation which yields the functional conditions of dynamic equilibrium.

Lonergan’s analysis is concrete but heuristic. It focuses on functional relations intrinsic tothe productive process to reach eventually a general theory of dynamic equilibria and disequilibria.   [McShane 1980, 117]

And he goes beyond the specification of the always current conditions of equilibrium in the always current process.  While the baseball diamond comprehends ever-valid instantaneous relationships between circuits, Diagrams 24-7 and 27-1 demonstrate how the always current process expands over time with a tendency towards, and an exigency for, an equilibrated pure cycle.  Again, for emphasis:

… positive or negative transfers to basic demand (D’-s”I’) and consequent similar transfers to surplus demand (D”-s”I”) belong to the theory of booms and slumps. They involve changes in (aggregate basic or aggregate surplus) demand, with entrepreneurs receiving back more (or less) than they paid out in outlay (which includes profits of all kinds). The immediate effect (of these aberrational monetary transfers) is on the price levels at the final markets, and to these changes (in price), enterprise as a whole responds to release an upward (or downward)  movement of the whole economy.  But the initial increased transfers to demand [that is, excess transfers along (D’-s’I’) and (D”-s”I”) ] are not simply to be supposed.  For that would be postulating without explaining the boom or slump. [CWL 15, 64]

Stagflation can be explained rather than merely thought mysterious.

… the U.S. economy was experiencing the phenomenon of ‘stagflation’ – a clearly discernible overturning of the conventional economic wisdom about the tradeoff between inflation and unemployment so neatly expressed in the Phillips curve.  So-called ‘Keynesian fine tuning onto the neoclassical track’ was not working; and forms of socialist planning only promised to deepen rather than resolve the anomalies of welfare economics. … (Lonergan) believed he had an explanation for what, in a statement from the essay we are editing, he described as a “situation – sometimes thought mysterious – in which consumer prices continuously inflate, new enterprise is evaded, unemployment becomes chronic, and despite inflation the value of stocks declines.” [CWL 15, Editors Introduction, xli]

Functional Macroeconomic Dynamics is not only a general theory of dynamic equilibria and disequilibria, it is a normative theory of equilibria; it defines the conditions of desirable (equilibrated) movements and it expresses “the mechanism to which classical precepts are only partially adapted; and through it again one can infer the fuller adaptation that has to be attained.” FMD provides

a closely knit frame of reference that can envisage any total movement of an economy as a function of variations in rates of payment, and that can define the conditions of desirable (equilibrated) movements as well as deduce the causes of (disequilibria called) breakdowns. Through such a frameof referenceone can see and express the mechanism to which classical precepts are only partially adapted; and through it again one can infer the fuller adaptation that has to be attained. [CWL 21, 111]

At greater length, with repetition in part:

On such a methodological model (i.e. both explanatory definition and implicit definition superseding nominal definition)…classes of payments (correlated with the productive process by projection of the structure of the productive process onto classes of payments) quickly become rates of payment standing in the mutual conditioning of a circulation; to this mutual and, so to speak, internal (monetary) conditioning there is added the external (monetary) conditioning that arises out of (crossover) transfers of money from one circulation to another; in turn this twofold conditioning in the monetary order is correlated with the conditioning constituted (in the hierarchical productive order) by productive (and sequential) rhythms of goods and services;[1]and from the foregoing dynamic configuration of conditions during a limited interval of time, there is deduced a catalogue of possible types of change in the configuration over a series of intervals. There results a closely knit frame of reference that can envisage any total movement of an economy as a function of variations in rates of payment, and that can define the conditions of desirable (equilibrated) movements as well as deduce the causes of (disequilibria called) breakdowns. Through such a frame of reference one can see and express the mechanism to which classical precepts are only partially adapted; and through it again one can infer the fuller adaptation that has to be attained. [CWL 21, 111]

Macroeconomic equilibria “are the conditions of a properly functioning economy.” [CWL 15, 92]

In Burley, Peter (1989), A von Neumann Representation of Lonergan’s production problem, Economic Systems Research, 1 (3), [Burley, 1989], Burley speaks of a new paradigmof disequilibrium macrodynamics:

Sufficient … has been done here, at least in a heuristic way, to show that the von Neumann tool-kit can be used to represent the Lonergan production analysis.  This provides a basis for a new paradigm of disequilibrium macrodynamics which, inter alia, responds to Schumpeter’s challenge that, … “has not taken any special cognizance of the process of creative destruction which we have taken to be the essence of capitalism.” (Schumpeter, Capitalism, Socialism, and Democracy. P.104) [Burley, 1989, 120-21 ]

 

[1]… In figure 14-1 the reader will notice five circles representing the monetary functions. … I would add that the aims and limitations of macroeconomics (that is, the macroeconomic circulations presented here) make the use of a diagram particularly helpful, …  For its basic terms are defined by their functional relations.  The maintaining of a standard of living is attributed to a basic process (distinct process 1), an ongoing sequence of instances of so much every so often.  The maintenance and acceleration (positive or negative) (distinct process 2) of this basic process is brought about by a sequence of surplus stages, in which each lower stage is maintained and accelerated by the next higher.  Finally, transactions that do no more than transfer titles to ownership are concentrated in a redistributive function, whence may be derived changes (distinct process 3) in the stock of money dictated by the acceleration (positive or negative) in the basic and surplus stages of the process. … So there is to be discerned a threefold process in which a basic stage is maintained and accelerated by a series of surplus stages, while the needed additions to or subtractions from the stock of money in these processes is derived from the redistributive area. … it will be possible to distinguish stable and unstable combinations and sequences of rates in the three main areas and so gain some insight into the long-standing recurrence of crises in the modern expanding economy. [CWL 15, 53-54]