Peter Burley constructed von Neumann matrix-game models of a Schumpeter-Lonergan, creative-destruction process.  As models, they aid understanding of the principles and laws of the dynamics of the economic process.  Though linear and simplified, they demonstrate clearly important relationships of the transitional dynamics of economic expansion. The careful student sees, images, and understands the pattern in the game-theoretic interplay of production and exchange that constitutes the models. The models demonstrate the relativities among the quantifiable, velocitous interactions of the interdependent functional aggregates of the economy; and they confirm, via each’s mathematical formalism, Lonergan’s explanation of the economic process. The models are a spur to the eventual implementation of Lonergan’s economics in academe, industry and commerce, journalism, political economy, and personal finance. 

Von Neumann’s multiple-dimension joint production function would appear to be especially suited to representing a twentieth (and twenty-first) century economy.  Further its allowance for alternative processes would seem to provide a natural opening for technological change in such economies. [Burley, 1992-2, 269]

The models present quantified interrelations within and between the circuits of both productive and monetary functionings. Consider the following list of observations available to one who, with pencil and paper or keyboard and spreadsheet, constructs a model.

• The quantification drives home the idea of finitudes and boundaries. Expansion has its normative limits and constraints.
• The models are simple and mathematically tractable
• They use time-advance methods mimicking a frequent periodic public reporting to represent velocitous change in the economy from period to period.
• By filling invariant formal relationships with variable magnitudes, they symbolize any and all key possible dynamic configurations, equilibrated and disequilibrated, of a dynamic economy. The invariant relativities constitute a theory of equilibria and disequilibria.
• One “sees” that the purpose of dummy money is to circulate in such a way as to buy, now or later, goods and services endogenous to the operative process, rather than to be hoarded.
• One “sees” that the extraction of money from a previously equilibrated system systematically forces reduced production and employment.
• The models suggest that norms for adaptation by human agents will vary in the series of periods beginning with an initial stationary state; followed by a proportionate-expansion phase; followed by a surplus-expansion phase; followed by a basic-expansion phase; followed by a series of periods in a higher stationary state.
• The models thus make it clear that the priora quoad nos of employment, prices, quantities, interest rates, and inflation rates are coincidental values in a non-systematic manifold, i.e. boundary values to be inserted subsequent to the prior discovery of the differential intelligibility or primary relativity or formal cause of the modeled economy. That is, particular employment, prices, and quantities are not explanatory conjugates; rather they are the boundary-condition data of particular differential equations constituting the most general explanation at the basis of Burley’s von Neumann formalism and in Lonergan’s differential price-spread ratio, differential pure surplus income ratio, and differential basic income formula.

dJ = da’ + a”dR +Rda”  [CWL 15, 160]

df = vdw + wdv[CWL 15, 148-49]

dI’₌ Σ(w_idn_i+ n_idw_i+dn_idw_i)y_i [ CWL 15,134]

• The models provide Lonergan’s hypothesis and a ground for verification of the hypothesis in the data of the revised and explanatory matrices of the Bureau of Economic Analysis’ National Income Accounts and The Federal Reserve Bank’s Flow of Funds.
• The models demonstrate and help us understand the nature and the consequences of the current (2017) struggles of and among four primary parties:
  • the Central Bank which seeks, to manage the money supply and monitor banking activities
  • the fiscal authorities who seek to balance their budget
  • the lender-producer combination which may seek a disequilibrating rate of return greater than β-1, when β-1 may equal zero
  • the households selling productive services and wishing to a.) become or stay employed, b.) improve their standard of living, and c.) ensure their long-term financial security, even when the growth of the economy, α-1, may equal zero.
• The models point out that physical equilibrium is conditioned by proper relative production intensities and a proper money supply for transactions and that financial equilibrium is conditioned by proper relative pricing intensities, proper monetary distribution, and proper money supply.
• By pointing out the existence of norms and of the precepts associated with the norms, the models demonstrate the possibility of halcyon days and of miserable days as possible consequences of violation of these norms.
• The models help us to understand that the triple of loan values, interest rates, and maturities provide information about the expectations of borrowers vis a vis production opportunities.
• The models demonstrate the effect of a balance-sheet loss for the risk-takers whose capital becomes obsolete in the creative-destructive process
• One can witness the role of banks and investors allocating money in a system characterized by risk of a) obsolescence resulting from competitors’ innovation, and b) loss resulting from incompetent mismanagement.
• The model forces us to understand that the government is the collective “we all” – not an exogenous entity – attempting to manage an economy constituted by the interdependent functionings constituting interdependent operative circuits.
• We view clearly the migrations of workers from sector to sector in a creative-destructive economy characterized by phases of accelerations and taperings of the surplus and basic sectors
• We witness and come to understand the vital importance of new and more efficient capital equipment constituting the improvements on nature required to increase elements in the standard of living for all.
• We see in Burley [Burley, 1992-2] the criticality of recognizing when the advances of the surplus expansion must give way to implementing the basic expansion, and thus, when basic incomes in the aggregate must increase in order to fully utilize the expanded productive capacity.
• We come to understand that there are coefficients or definite measures of the functional aggregates in functional interdependence. So, to manage the process it is necessary to identify explanatory functional aggregates in the light of which to measure and assess the aggregates accurately.  While, in the model we can choose to simplify and use coefficients of convenience, in the real economy the BEA and the Fed must identify and measure our functional aggregates as precisely as practically possible.
• We understand that the formula for the basic price spread ratio (CWL 15, 158

a) is an identity based on Lonergan’s insightful definition of macroeconomic costs, and b) constitutes a relativistic definition of prices and quantities.

• The models provide clues to proper management of the money supply and credit and demonstrate how, in a growing economy, store-of-value money should enter and leave the system (along channels S’ and S” in the Baseball Diamond diagram) through the hands of producers, rather than through the hands of consumers (along channels D’ and D”)
• The models provide clues to a theoretic of mismanagement of credit implied by Burley’s combination of  β and w-c, [2]wherein w-c money is drained from the circuits into the Redistributive Function to damp or reduce employment and economic activity.

This ongoing growth in unemployment would seem important to note in a world of high rate of interest debt problems….it would seem important for analysis to be clear about the growing cost of an ongoing extraction of surpluses when living standards of employed workers are downward rigid.   [Burley and Csapo 2002-1, 140]

• We come to understand and appreciate the monetary aspects of expansion, such as the entrepreneurs’ realizing the circulation of return of what they invest, the balance-sheet and market-value losses of obsolete equipment, and the balance-sheet and market-value appreciation of new and more efficient machines.
• We come to understand the functional meaning of general interest, AKA pure surplus income, as the return “of” current investment rather than the return “on” past investment
• We achieve a new macroeconomic method and model for the present value of aggregate of bonds and stocks based on current interrelations, rather than the textbook capital asset valuation based upon future income streams.
• We come to understand the difference between widening and deepening, and between a short-term acceleration constituted by taking up slack and a long-term acceleration constituted by the installation of new and better capital equipment.
• We discover that the real macroeconomic interest rate α-1 is an internal relation among functional flowings determined by the collocation of several real functional flows, not by the market’s estimation or the Fed’s manipulations.
• We learn that this real interest rate is a mathematical function of several dynamical variables rather than derived from some historical rule of thumb.
• We discover that the real ownership value is determined by the collocation of several real endogenous factors, not by the Fed’s manipulation of interest rates and flooding of the money market or the market’s feckless optimism or pessimism.
• In [Burley, 1992-2], we see the credit money needed for a) the capital expansion of stages 1-3, b) the basic expansion of stage 4, and c) the static economy of stage 5.
• And we see that expansion of the money supply should go through the supply channels.
• That is, we develop a theoretic of credit.
• We identify factors, such as price levels and quantity levels, whose fixing by a central authority would be equivalent to and equally as improper as the manipulation of interest rates by the Fed.
• We learn how to assess a) fiscal policy, b) monetary policy, and c) adjustments of savings to the demands of the process.
• We enjoy a display of Burley’s brilliance
• We enjoy achieving enriching understanding of the intelligibility of the economic process.