Uncertainty and Velocity

In this chapter the two features of uncertainty and the variability of the velocity of money are considered. Both of these are fundamental to considering the more subtle features of a monetary economy. They are interlinked and both add further complex features to the information, perception and control mechanisms of modern monetary systems. There has been an explosive development in the study of both the qualitative and quantitative properties of risk. The power of careful modeling and sophisticated stochastic analysis has already shown itself in the context of the stockmarket and other financial markets, but as the various qualitative aspects of risk are being uncovered and made well-defined, the scope of a useful econo-physics stretches far beyond the confines of the dynamics of paper traded on paper in the financial markets to the broad control mechanisms of the economy as a whole.

Minimal Institutions: Game Theory and Gaming

The General Equilibrium system provides a pre-institutional modeling structure appropriate to studying many allocative properties of the price system. The economies we live in ere encompassed by their polities and societies. The task laid out here is to indicate how to build process models of the economy that are consistent with the General Equilibrium system, but build out in a systematic manner towards the multitude of institutions that are the carriers of process in an ongoing society. It is argued here that this can be done in such a manner that there is a natural cascade of process models consistent with General Equilibrium: but these become progressively more complex as new functions are required to support the dynamics of the society. The first step into a mathematical institutional economics involves the invention of markets and money and the endogenization of price formation.

The Context of Competition

This chapter sets the context for the book. We note the purpose of economics should be to describe concepts and models that can be made consistent with sound scientific understanding of the other aspects of life. At a minimum economic behaviour is embedded within the organic system we call the society: it affects extraction, production, utilization, exchange, consumption and disposal of physical entities and services. We consider the main questions about how to contextualize economics. It can be argued that the economy is a mechanism to organize a subset of decisions in a larger highly distributed society. The social organization obeys no simple model of control; its dynamics is often evolutionary at many scales of time, space and material content; and with these it is subject to both historical contingency and great complexity.

Mathematical Institutional Economics and the Theory of Money and Financial Institutions

Chapter 11 raises the question of what is meant by our usage of “theory”. Different disciplines utilize the word theory differently. Furthermore model and theory appear on occasion to be used interchangeably. Aristotle contrasted theory to practice. Praxis is the Greek term for doing. Mathematical theory is deductive. The sensory or empirical content is implicit in the axioms. The logical consequences of the axioms provide theorems. A semantic view stresses the connection between the axioms and the abstraction of some aspect of reality. We stress that the natural preliminary step before dynamics is to construct process models based on general equilibrium. This can be done utilizing single simultaneous move games. This is sufficient to show the critical roles of money and financial institutions without even having to discuss complication in information and behaviour. The evolution of money and many financial institutions does not even call for the presence of exogenous uncertainty. A single random variable is sufficient to illustrate innovation. We develop a general modeling methodology leading to the construction of models as playable games. Staying with the one move structure leads to describing a manageable number of minimal institutions (below 100). When we consider more moves and information the number of logically feasible and plausible institutions becomes hyperastronomical and we are forced into considering not merely structure but many variants of behaviour even within the simple scope of rational expectations. This problem is taken up in Chapter 12.

The Economy: Time, Size, and Complexity

The first five chapters have been devoted to reformulating a pre-institutional static theory of general equilibrium, into considering an economy in terms of process where markets and other institutions exist embedded within and interacting on different timescales with the polity and society. This embedding of the economy within the framework of government and society provides both a natural formal and informal control system. The government provides the formal rules with the laws and their enforcement and the society and polity on different timescales provide the pressure on the government for rule formation and the direct pressures on the economy to conform to custom as well as law. The price system where it exists provides a perception device where the pressures of disequilibrium are signalled by the shadow prices that develop both on the price of commodities and on loans and other financial instruments. We deal here with the production and exchange economy in a process setting.

Supporting Attainable Solutions: Symmetry and Complexity in One-Period Exchange Mechanisms

In this chapter we compare economies at the least-structured level of dynamics: market systems characterized by one-shot clearing and hence a single timescale for strategic choices. We choose that timescale to coincide with the social “day” that is the natural cycle of production and consumption. We compare different clearing mechanisms according to a number of structural properties that can be used as a measure of complexity. We use a measure of allocative efficiency to illustrate distortions from competitive equilibrium for each mechanism. Much of the importance of process analysis can be illustrated with a single dilemma: the meaning and determination of the value of the numéraire for exchange. This is explored here. Six market models are presented to illustrate the constraints on rational action from asymmetry of the market mechanism or from strategically ambiguous degrees of freedom. The models have sufficiently many shared features that they roughly represent successive stages in the elaboration of a few common ideas. These are laid out in the chapter.

The Guidance of an Enterprise Economy

This final chapter splits naturally into two parts. The first part presents the basic overview of a theory of money and financial institutions that covers the abstract pre-institutional structure of the price system as an allocation device in a tightly defined structure with no need for money or financial institutions to be specified in the illustration of the efficient equilibrium condition. It stresses that by merely following well defined precepts of basic physics and game theory, at the same level of abstraction process models can be completed and force a discipline on the models where items such as money, default laws, grid size, loose coupling, specification of clearance rules, and time lags are all logical necessities.. These steps convert a static pre-institutional set of models into their natural minimal institution monetary and institutional models. . The utilization of these for application still requires the addition of ad hoc physical facts and relevant understanding of behavior. Our broader goal is directed towards a general theory of organization about which this work is only a narrow part. The second part of this chapter concludes with our Nostrodamus section where we conjecture about the future. This includes the need for supranational organizations especially for weapons control. We also suggest that the fundamental problem of the control of dangerous fluctuations in an enterprise economy is predominately a politico-bureaucratic problem and calls for a stress on the design of flexible coordinating devices within the politico-economic system. A sketch of such a device is presented. In a free society the stress should be less on control and forecasting than on guidance and flexibility.

Process, Strategy, and Behavior

The previous chapters have developed structure and provided proofs in principle as to how to build and analyse multistage models with simple assumptions about behavior. The hyper-astronomical explosion of special cases is to be welcomed as indicating that the initial timeless tight system, when converted to a loosely coupled process model, calls for both the specification of ad hoc questions and the supply of ad hoc model building of the detail needed to make it feasible to provide useful answers in any applications. We summarize the five dynamic models we analysed; but stress that in application there is no substitute for knowing both the relevant details and the behavioral considerations of the situation at hand. The dynamics of the steel industry requires details concerning both structure and behavior, as these are contrasted for example with selling high end art. In this chapter we examine the functioning of the double auction market and comment on trading mechanisms. Finally we discuss the relationship among solutions, structure and behaviour, closing with observations on dynamics and complexity and the false dichotomy between “Rational” or “Behavioral Agents”. For most individuals without deep psychological problems “context rationality” may provide a reasonable description.

Innovation And Breaking The Circular Flow

Chapter 9 has a basic theme that even the simplest venture into innovation takes us into the realms of disequilibrium where the study of behaviour in transient states of any length is unavoidable, even if one sticks to the mantra of the rational economic agent. The very nature of the complexity involved in the study of innovation provides the curse of high dimensions. It is our belief that the utilization of low dimensional models in order to be able to obtain some analytical results, while of great value for exploration of basic problems, must be viewed in application as dealing with parable and metaphor intermixed with applied macroeconomics. Even with the gross behavioral simplifications of rational expectations these models can provide answers or at least raise precise questions in economic theory that remove the mystery from items such as “Bills only” by requiring specification of details such as grid size.

Endogenizing the Choice of a Monetary System1

In this chapter we introduce our first multi-timescale models of an economy. Longer timescales are associated with commitment to product specialization and to discounting and depreciation of durable goods. We compare an economy mediated by a durable commodity money, such as gold, with one with a fiat money implemented through a bureaucracy. The inefficiency costs associated with asymmetric strategic roles between money-providers and producers of consumption goods are compared with explicit losses of material productivity due to labor costs required to maintain a bureaucracy needed to manage a fiat money system. It is shown how a stable trade system can emerge. We discuss material and institutional capital stock in an economy and note that capital stock acts much like the stock of catalysts used to enable chemical reactions. In a framework such as General Equilibrium, capital stock vanishes from the net input-output relations in an abstract production correspondence.