## Martin Shubik and Eric Smith

Print publication date: 2016

Print ISBN-13: 9780262034630

Published to MIT Press Scholarship Online: May 2017

DOI: 10.7551/mitpress/9780262034630.001.0001

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# Innovation and Evolution: Growth and Control

Chapter:
(p.395) 10 Innovation and Evolution: Growth and Control
Source:
The Guidance of an Enterprise Economy
Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262034630.003.0010

# Abstract and Keywords

In connecting Walras and modern General Equilibrium theory with Keynes and Schumpeter we have confined ourselves to 1-ply games with government and a central bank and initial and terminal conditions specified. Pandora’s Box is opened at 2-ply or more. Then the whole world of learning, teaching, signalling, non-symmetric information and habit, herd and rule-of-thumb behavior open up . In this chapter previous approaches are noted, including large econometric models, simulations and possible operational games. Innovation in an asset rich economy is considered. The need for at least three levels of banking and a national debt is discussed. The institutions required are a central bank, commercial banks, and investment financiers, and a treasury or other named manager of a national debt. The chapter ends with a consideration of related complexities in biology and economic dynamics.

# 10.1 Preamble

In connecting Walras and modern general equilibrium theory with Keynes and Schumpeter we have confined ourselves to one-ply games with a government and a central bank and initial and terminal conditions specified. One can take the fundamental first step in going from no-process to full-process models with only one strategic move per player and minimal information. A case can be made for considering the noncooperative equilibrium as a reasonable solution concept. With a few reasonable restrictions, there are not that many behavioral solutions that can be suggested for a one-shot game. Pandora’s box is opened at two-ply or more. Then the whole world of learning, teaching signaling, nonsymmetric information and habit, herd and rule-of-thumb behavior must all be specified in order to be able to take the description of the institutional carriers of process1 and add behavioral rules that lead to specifying the equations of motion.

In chapter 9, although we have broad misgivings about the application of the rational-expectations solution concept to growth models with even a reasonable amount of complexity, we solved several examples, in part to be able to formulate fully experimental games that could be used to test the behavioral validity of rational expectations, but even more importantly to show that a one-shot Schumpeterian breaking of the circular flow of capital could be completely mathematized within an initial and terminal equilibrium framework, and acheived with minimal control by the government.

Disequilibrium and the full force of evolution emerges with period-by-period strategic ability to innovate (see section 9.12). Here our concern is more (p.396) with government guidance, the mechanisms, instruments, and institutions and their control functions, rather than with the computation of another rational-expectations solution.

There is such a plethora of reasonable but complex models that can be specified and so few hard facts on behavior that the full development and analysis of a completely specified dynamic model is heavily dependent upon both context and specific questions to be answered.

The era of the large macroeconomic many-equation structural model of the economy with many parameters reestimated frequently appears to have passed, but technology has changed, and economic knowledge and computational and simulation ability have increased. The early advocates of the large mechanistic simulation such as Jay Forester of MIT [134] or the vast databank-organizing simulation such as Guy Orcutt of Yale [279] advocated have gone and are, for the most part, forgotten, but the data gathering and processing and the feasibility of manipulating large models have completely changed in the last 40 years. We have reserved most of our comments, recommendations, and obiter dicta concerning practice and the intersection between theory and practice to chapter 13; here we make an exception concerning simulation and experimental gaming.

## 10.1.1 Science, policy, and truth in packaging

Neither these authors nor anyone else has achieved the dynamic theory of economic behavior; but it is well worth the theorist’s time to simplify assumptions about both structure and behavior to obtain as low-dimensional a context and parameter-free a representation of structure and behavior as she deems plausible and to analyze the implications of such a model. One may then wish to switch roles and behave as an advisor or advocate claiming that the low-dimensional analysis provides the best advice available. The politics and sociology of the melding of science and policy advice may be such that this is about all that is feasible; however, we suggest a politically naive alternative.

The coordination problem is central to many aspects of a complex economy, as it is to any complex evolving organism. The government as a whole as well as the central bank in particular must provide much of the coordination and conflict resolution for the economy. We propose the creation of an operational gaming section in any national central bank. This would be done in concert with the economics research departments of universities and policy and (p.397) research institutions. Several economic models varying in size from large such as the Ray Fair macroeconomic model [120] down to smaller specialized models devised to answer only one or two specific questions would be utilized and reformulated as parts of an overall playable game open to modification during the game. This would provide a structured debate aimed at examining jointly the political, bureaucratic, and economic feasibility of proposed policies.

A large war game may use small formal operations research models such as a damage exchange model between submarines and destroyers to predict tactical outcomes that feed back to the strategic game. An economic game might use a formal small model to calculate the first-order outcomes of a change in taxation.

In a central-bank-hosted econo-political exercise (EPE) the players would consist of bank and other government bureaucrats, selected politicians, and business executives. There would be three playing teams and the referee team. The playing teams would be the central bank, an aggregate of other government agents concerned with fiscal problems, and the private business sector. The consumers’ demand and many other aspects of the overall economy would be parts of the simulation. The largest model and the smaller ones would bear a relationship to each other similar to that between the special operations research models and the overall game in a major war game, such as those employed in the politico-military exercises at the Naval War College in the United States and in other military establishments. There the key aspects of the game are decisions of the teams, possibly rejected by the referee team as implausible, then modified and accepted in joint discussion and utilized as inputs into the overall simulation. Thus the game combines an operational debate evaluating intangibles with a period-by-period formal simulation where not just the technical parameters are being updated but the assumptions and concepts behind the game are being challenged. The design calls for the utilization of financial historians much in the same way that the military gaming scenarios employ military historians [82].

The gaming facility responsible for producing these operational “war games” would provide a link between operational applications and research in the sense that as a product incidental to the operational purpose there is an implicit or explicit ongoing critique of the formal economic models and simulations involved.

A major weakness with this proposal is its political feasibility. It is not axiomatic that a political stakeholder welcomes operational clarification.

# (p.398) 10.2 Aspects of an Innovating Economy

The last chapter on innovation stressed the breaking of the circular flow of funds and an attempt to vary the money supply via a passive central bank. This chapter notes some of the problems that appear with innovation in a financial system that has commercial banks, a national debt, and other loci of control.

In particular, items to be covered are:

1. 1. Utility and/or wealth optimization,

2. 2. The role of many assets and side payments,

3. 3. Financing and control of innovation,

4. 4. Financing and two-way causality,

5. 5. Bankruptcy as the delimiter of risk in a loosely coupled system,

6. 6. Bankruptcy and the money supply as public goods controlling mutation,

7. 7. Failure as involving the destruction of credit, not government money,

8. 8. The locus of innovation finance whether public or private.

## 10.2.1 Utility and/or wealth optimization

The utility function was devised, developed, and replaced by the map of preferences in the study of consumption under certainty. One of the earlier and elegant developments of mathematical economics was the theory of consumer choice. Glued together with a theory of production, cleverly closed, this produced general equilibrium theory. The utility function went out of fashion with theorists, who observed that consumer choice under certainty utilized only ordinal properties of preference. This apparent great generality dies, however, when we are dealing with decision making under uncertainty.

The axiomatization of measurable utility introduced by von Neumann and Morgenstern in 1944 [411] was not at first well received by the profession, as is evinced in the commentary by Baumol [40], but in the next two decades, especially with the development of a theory of finance, it became a centerpiece. Interest was renewed in the work of Bernoulli, and Menger [258] considered problems with and solutions to the Bernoulli paradox and the utility of money, from which some open questions remain to this day.

The measurement of the utility of money began to be used in finance within the development of a set of partial equilibrium models in an open economy with no concern with the details of consumer choice. Since the 1970s there has been a development both in macro- and microeconomics of the use of dynamic (p.399) programming and rational expectations. Bewley [31], Lucas [232], Shubik and Whitt [366], Stokey and Lucas [394], and Karatzas, Shubik, and Sudderth [199] provide examples. In both the macro- and microeconomic applications noted, essentially for reasons of mathematical tractability the commodity set was aggregated into a single aggregate commodity, thereby obliterating the structure’s suitability for the study of any of the details of consumption, but stressing its use for the study of income and wealth measured in terms of money.

We suggest that the picture of the consumer painted in Hicks [184] or in Debreu [79] is a mathematical picture of consumers who have to ration their wealth over consumption goods, and certainly is not descriptive of the entrepreneurs or financiers with plutomania whose mantra may be “the player who dies with the most chips wins,” or the many fiduciaries whose performances are measured in money returns.

At the level of abstraction adhered to in this book, the assumption that the natural persons within a society all have the same preferences is a useful approximation. It is reasonable to consider several different segments of a wealth-utility function that determine behavior as a function of wealth. Table 10.1 based on the study of Edward Nathan Wolff [421] displays the distribution of income and wealth in the United States in 2010.

Those with incomes in the bottom two quintiles have essentially a hand-to-mouth existence. As the income flows in, it is spent on consumption. The net wealth of households at an income level of around $30,000 or less a year, such as it is, is in real consumer goods such as clothing, furniture, consumer durables, automobiles, and housing. The financial wealth of these families is negligible, and for many negative.2 As the family’s income rises, the utilization of income for subsistence consumption starts to weaken. More goods and better-quality goods may enter into consumption, and the holding of real consumption assets grows. The rented Table 10.1 Wealth and income in the United States, 2010 W or I M Inc (2009) M N W M F W Top 1%$1,318,200

$16,439,400$15,171,600

Top 20%

$226,200$2,061,600

$1,719,800 Bottom 80%$72,000

$216,900$100,700

Bottom 60%

$41,000$61,000

$12,200 Bottom 40%$17,300

−$10,600 −$14,800

Note: W or I = Wealth or Income; M Inc = Mean Income; M N W = Mean Net Wealth; M F W = Mean Financial Wealth.

(p.400) apartment may be replaced by the house. As income continues to rise, financial saving in the form of savings accounts and holdings in money market or mutual funds starts to appear. Somewhere between incomes of say $1,000,000 and$20,000,000 the disconnect between marginal income and consumption becomes more or less complete.3 The extra money is no longer consumption money but is primarily investment money (after status and ego money uses have been accounted for). At the lower end of the income scale we have the poorer consumers who devote their total income and time to consumption. At the upper end of the scale some extra income may be spent to aid in the mechanics of consumption, delegated to interior decorators, caterers, chauffeurs, servants, and others; but the bulk is primarily for investment.

In order to formalize this heuristic sketch we need to take into account the considerations noted below.

### 10.2.1.1 Goods, services, financial instruments, and wealth

As we sweep over income levels, the consumers are concerned with:

• Consumables and services,

• Consumer durables,

• Simple financial instruments such as mutual fund shares, land, possibly gold,

• More complex financial assets and structures,

• Political and social power and prestige.

### 10.2.1.2 The economics of pure consumer choice without uncertainty

Pure consumer choice `a la Hicks [184] has the economic agent purchase the services of perishables and consumer durables subject to an income constraint. In the presentation the distinction between stocks and flows is hardly made. Suppose:

• M1 is a set of consumables,

• |M1| = m1 is the number of consumables,

• M2 is a set of consumer durables,

• |M-2| = m2 is the number of consumer durables,

• $u( x 1 ,..., x m 1 ; y . 1 ,..., y . m 2 )$ is the utility of consumption,

• (a1, , am1 ; b1, , bm2) are initial resources,

• (p1, , pm1) are prices of consumables,

• $( p ⌢ 1,..., p m1 )$ are prices of services of consumer durables,

$( p ˜ 1,..., p ˜ m2 )$ are prices of consumer durables,

• xj is the consumption of a consumable j,

• $y ˙ j$ is the consumption of the services of a durable j.

• (p.401) The consumer optimization is given by

$Display mathematics$

subject to

$Display mathematics$

One of the crowning joys of the 1930s–1940s exposition of consumer choice was to observe that the optimization subject to wealth constraint did not need to involve a utility function. It was often stated that the utility function could be defined up to an arbitrary ordinal transformation. However, if one were to enlarge the domain of choice to include contingent commodities, then under the von Neumann axioms it could be defined only up to an arbitrary linear transformation.

Even without the extra axiom on gambles, if convexity of the utility function were lost the market would endogenously introduce gambling.

### 10.2.1.3 Finance and the von Neumann utility

Uncertainty is the key to the von Neumann treatment of utility. He enlarged the choice set and added one extra axiom beyond the axioms for a preference ordering to give a utility function defined up to a linear transformation. The axiom was the equivalence of a certainty outcome to a lottery ticket. Given abc, there exists a probability η‎ such that η‎a+(1 - η‎) cb. Given this condition, the utility function u is determined up to two parameters such that α‎u+β‎ will also serve as a representation of the utility function.4 If there is a natural zero point, such as the worth of no trade, the modeler may select β‎ = 0 and the utility is defined up to an affine transformation. If interpersonal comparisons are possible then the α‎ may be fixed.5

An individual is deemed to be risk-neutral if

$Display mathematics$

implies that

$Display mathematics$

The development of much of finance such as portfolio theory, the analysis of options, and the construction of derivatives has taken place in a world where lottery tickets are the primary reality. Implicitly in studying any market the economic reality of the actual corporation together with its management and physical product is replaced by a lottery ticket measured in money. Due (p.402) diligence, securities evaluation, and other aspects of evaluation are abstracted away from the financial analysis. Depending on the question being asked, this may be deemed to be an excellent or highly inadequate abstraction.

In finance the stress is on the utility of wealth of the individual measured essentially in terms of money. Thus “how much is X worth” is answered by adding up all assets deemed to be liquid, then adding the other assets, with estimates or guesstimates of the orderly liquidation worth of the other assets, with haircuts given to reflect any market imperfections.

In utilizing the overall utility function for wealth one must take care to avoid a post hoc ergo propter hoc fallacy, confusing the induced valuation of producer assets at an equilibrium solution with the intrinsic valuation by individual consumers who can neither eat nor evaluate steel mills. Investment bankers and deal makers may do this evaluation as part of the ongoing money game. The major study of finance is within the development of an open and not full feedback model; thus in those models the influence of the government on the utility for money may be regarded as exogenously given, and previous prices are hard evidence but not sufficient alone to provide the behavioral basis for the formation of expectations.

### 10.2.1.4 The rich consumer-investor

At the lower end of the wealth scale consumer choice is concerned with hand-to-mouth existence, with finance appearing as a more or less tight constraint on the procurement of consumption goods and services. This contrasts with the richer end where consumption goods and services are merely part of the real goods allocation and monetary wealth. By conservation, all goods have to be somewhere. The steel plants, the industrial farms, hotels, the buildings and factories have owners who do not derive direct utility from the vast array of large durable assets.

In a modern society the government may own anywhere between 10 and 50 percent of the physical infrastructure such as roads, land, public buildings. Few individuals own large assets in a direct manner. They own the public or private shares of the institutions that own the assets.

## 10.2.2 The utility-wealth function

Nowadays people know the price of everything and the value of nothing.

—Oscar Wilde, The Picture of Dorian Gray

Wilde’s rhetoric is closer to the basic problems in finance than he conceived. In a complex society the evaluation of the worth of many assets and their prices may require considerable skill and perception.

(p.403) If we view the utility-wealth function that the individual is meant to optimize as the sum over all expected consumption streams until death, then at any point we are forced to include current valuations of his long-term physical and financial assets. The discussion presented here is related to but different in detail and emphasis from the Friedman permanent income hypothesis (see [144] and others).

The study of finance is about equities, debt, and hybrid instruments such as corporate shares, bonds, and derivatives and how they connect with real means of production, durable assets, and other financial instruments and are evaluated in terms of money. In contrast consumption theory is usually discussed over a high-dimensional commodity space, and the mapping into one dimension which is meant to represent a utility function is of little interest in the study of most questions in consumer choice. Finance theory tends to deal just with a single-good “money” and complex lottery tickets involving valuations of institutions and processes in terms of money bets.

If we look at a rich individual both consuming and investing, it is reasonable to deal with two representations. The first deals with consumption preferences, emphasizing choice among consumption goods and services subject to an investment decision constraint which may easily be lower than either the wealth or the income constraint. The second representation deals with a utility-of-wealth function for investment that has, in essence, allocated consumption to a separate anaylsis connected to it by the lower bound reflected in the implicit or explicit decision on what to spend this year.6 The financial decision payoff function is reasonably represented by a one-dimensional utility for wealth.

For many operational questions in finance and consumption theory it is most convenient to use the two different representations.

The individual or family is at least two agents, and this unit illustrates the roles of aggregation, disaggregation, and money faced by a single decision maker. Depending on the aggregation used, the goods and services space may vary from a few dozen to a few thousand dimensions. When running a house, going to a movie, or buying groceries, several alternative goods and services are considered. When buying a major consumer durable such as a new car or a house the problem may be framed as: Can we afford it (or do we have enough money)? The investment and ownership side of the family is primarily represented in money.

If we try to model the behavior of the rich, we need to consider context and usually select a different representation for production and consumption, with a money representation dominating production and the acquisition of the ownership of direct or indirect production assets.

(p.404) A way to investigate some of the implications of an asset-rich economy is to consider as a first-order approximation that most individuals have a utility-wealth function that consists of a concave function up to some level of wealth followed by an unbounded linear utility function, where the concave segment represents the level of wealth at which one is still concerned about consumption. Beyond that point the additional wealth is for chips at the investment table.

## 10.2.3 Fiduciary behavior and utility

We know that the vast majority of financial decisions are made by fiduciaries. The fiduciaries are legal but not natural persons. They are for the most part clearly owned by natural persons.7 The social psychology of formal group decision making is a topic that is not completely terra incognita, but even with agency theory what the firm maximizes has many answers. Minimal complexity and ease in analysis call for expected discounted profits as a goal, or the “utility function” of the firm. There are some questions for which this may be a reasonable approximation, but, as has already been noted in chapter 5, large bureaucracies may have many other goals.

## 10.2.4 Risk-neutral rich and fiduciaries and the risk-averse others

Even if all natural persons were considered as having the same preferences, in an economy with considerable uncertainty the rich and the fiduciaries may be expected in aggregate to assume most of the investment risk and to earn accordingly. However, in a complex economy with an information processing division of labor in finance as well as an industrial division of labor, this nonsymmetry could be even larger. Those not in the financial world may be unaware of many of the risks that are there. Furthermore there are many risks they may be aware of but do not understand. The nonprofessional does not have the training, skills, perceptions, or time to perceive and evaluate risk. The rich professionals not only buy and sell the risky assets, but expend much of their energy in minimizing the risk to themselves by selling off the parts they deem to be too dangerous to those who may be less perceptive than themselves. This is all part of the politicoeconomic valuation process.

## 10.2.5 An aside on quasi–side payment cooperative games

Side payment cooperative-game theory offers a way to study phenomena such as cartels or mergers and acquisitions among oligopolistic players. The use of the characteristic function to consider oligopolistic structures and solutions (p.405) such as the core was first considered [346] as early as 1956. No further analysis to this approach is given here;8 but the central observation is made that in an economy with innovation, a nonsymmetric, oligopolistic form of industry is to be expected from the dynamics. This combined with the presence of many nonconsumption real assets and their financial instrument representations leads naturally to a quasi-cooperative structure in deal making in the oligopolistic “market” for firms.

# 10.3 Innovation in an Asset-Rich Economy

In chapter 9 we treated innovation in an asset-poor economy. Like many of the studies employing dynamic programming, we utilized a single aggregate consumption/production good. A far more felicitous but more difficult model requires the presence of producer durables to reflect the real wealth of a developed economy.

## 10.3.1 A discussion on an asset-rich economy

We could extend the example provided of the asset-poor economy in chapter 9 by adding extra durable commodities in the form of land and producer goods as part of production. Rather than provide an extra calculated example, a verbal sketch is given to stress the new feature and why it is worth considering.

In the previous model Crusoe had to expose himself to considerable loss in consumption in order to risk innovation. There was only one real commodity that served both as the input of the production processes and the only output available for both production and consumption in the society. A richer array of assets could change his risk.

Embellishing the classical land, labor, and capital trinity, we assume the existence of:

• A consumption good C;

• Labor E (which splits into labor and leisure);

• Land L which is an infinitely lived nonreproducible asset that plays a catalyst role in production;

• Reproducible capital goods9 that do not appear in the utility function directly. Depending on ownership and use, they are more or less categorized as (a) producer durables and (b) consumer durables. For the purposes of illustrating the point, just the addition of land and labor is sufficient.

## (p.406) 10.3.1.1 Consumption

We assume that Crusoe has preferences $u( c, e ˙ , l ¯ )$ for the consumption good and the services of leisure and land, where:

• c is the consumption of an individual,

• ė is the amount of leisure, and

• $l ¯$ is the value derived from consumption use of land.

Historically in the opening up of new terrain, the new land was primarily owned by the emperor, monarch, nobility, or other forms of government and eventually was awarded or sold to the public.

Even if Crusoe were deemed to own his island, except for the land in immediate use such as his hut and cultivated area it is difficult to attribute consumption worth to his nondirect utilization of the other land.10

Crusoe, being his own monarch with unutilized land, may attribute no direct worth to it, but if it along with other productive assets that may be present on the island serve as the prime inputs to his new activities, they then assume production worth and may require that he risk few if any consumption assets beyond his own labor.11

If we go beyond Crusoe to the competitive economy, the presence of many producer assets and land and other basic resources employed in active processes justifies a positive price for them. Governments such as the United States may still hold a substantial amount of the land and natural resources as the monopolist, referee, and participant in the economy.

As the implementation of an innovation is, in essence, the utilization of a new process with the existing resources, the resources required are culled out of the economy to be put to a higher expected utilization. In a rich economy almost all of the resource reallocation can fall on production goods and labor services and not current consumption. In economic activity, the context of the polity is always present; thus, for example, in virtually any society in wartime the political conditions and the financing possibilities may be more favorable to production and innovation than in peacetime. The choice is made decisively for guns and weapons innovation rather than butter.

## 10.3.2 Financing and control of innovation

The need to finance innovation may not only require borrowing but may involve elements of control and valuation. In figure 9.2 of chapter 9 an economy with six actors was shown:

• Nonfinancial firms,

• Stockholders,

• (p.407) Savers,

• Commercial bankers,

• Financiers or financial firms,

• The central bank and government.

In an economy with a given configuration of physical resources, the financing of an innovation can take place in many different ways depending not merely on the physical and financial resources available but on the structure of their control.

A large corporation such as a General Electric is in a sufficiently powerful position to be self-financing. A more or less unknown startup, depending on the nature of the innovation involved, may have its principals borrow from friends and family or try to obtain financing from a venture capitalist or other financial institution. Depending on the nature of the innovation, government funding may be available.

The key observation is that the financing of new businesses and innovation requires not merely the availability of funds but the availability of a group or institution with the requisite knowledge and evaluation abilities. The nature of the market involved is far different from the ideal exchange of the stock market.

In the stock market anonymity is, in essence, the rule, and the two evaluations involved in a trade are independent and have been performed (if at all) before coming to the market. The existence of a previous market price permits the institution of the stock market to serve at any instant as an exchange device, not as a microeconomic evaluator. At best it can be regarded as outputting a consensus evaluation of the average opinion, with the time series of price changes conveying information on the dynamics. With every improvement in technology, the stock market as a clearing device becomes less expensive to operate.

In contrast there are always at least two and possibly several parties face to face in an essentially quasi-cooperative game involved in the financing of a non-self-financed innovation, where evaluation is of the essence and transaction costs are, of necessity, high. The distinction is not unlike that between a marketable derivative where all the boilerplate has been standardized and all units agreed on and the hand-tailored derivatives that are personalized contracts with little or no marketability.

## 10.3.3 Financing and two-way causality

The availability of a perceived-to-be-worthwhile new process to be developed may bring forth a demand for extra credit or money; however, the financing of innovation may also be generated by the availability of extra money or credit (p.408) looking for an opportunity to sponsor a desired innovation; thus causality may go in both directions. The history of innovation during wartime and the bubble behavior in Silicon Valley provide examples. Consider margarine, aircraft, radar, the atomic bomb, the computer.

## 10.3.4 Bankruptcy as the delimiter of risk in a loosely coupled system

In general, in any loosely coupled economy we have already noted that bankruptcy laws are a logical necessity needed to account for the possibility of failure. If innovation fails and individuals are bankrupted, their remaining resources may be redistributed to cover fully or in part their contractual obligations.

As has been observed elsewhere [356], bankruptcy settlements by the very nature of their role are neither a pure market phenomenon nor are they unique. They are a joint product of their societies and polities as well as their economies; but they are even far more. They are a key factor in the dynamic ecology of an ongoing socioeconomy, as is indicated immediately below.

## 10.3.5 Bankruptcy and the money supply as public goods controlling mutation

As soon as exogenous uncertainty is present in an economy, there is a confounding of the phenomenon of strategic bankruptcy with misfortune.

The concept of an optimal bankruptcy code under exogenous uncertainty must contain within it a consideration of the willingness of a society as a whole to absorb the losses caused by what ex post turned out to be a misallocation of resources. In essence, given uncertainty the severity of the bankruptcy penalties influence the willingness of individuals to take risk; thus it is a control factor of the intensity of economic mutation. From the viewpoint of society as a whole, the bankruptcy laws are a public good.

In general, optimal bankruptcy laws will not be unique, as has been noted in chapter 12 of [356]. The pressures of the political and social structure in any specific society may favor the debtors or the creditors as a matter of social and political choice.

## 10.3.6 Failure involves the destruction of credit, not government money

In many uses in everyday life, the distinction between bank money and fiat or government money comes only at the level of details affecting the individual (p.409) such as portability, divisibility, cognizability, anonymity, speed of transfer, and other aspects of a transactions technology that may be of considerable importance in some contexts but are often not of high conscious import in everyday life.

Especially in times of politicoeconomic uncertainty, the possibility of default becomes nontrivial. A key distinction can be made between what happens to credit instruments and to government money under (nonsovereign) bankruptcy. In a default it is only credit instruments that are destroyed. Neither real goods nor government money are destroyed; they get redistributed. The distinction between bank money and government money becomes painfully clear.

It is in extremis under hyperinflation or revolution that the context changes to the point that fiat money may be wiped out and the virtues of gold reappear.

## 10.3.7 The locus of innovation finance may be public or private

Necessity is the mother of invention.

—Origin unknown

Historically both private and public resources have been involved in innovation. Items such as global exploration, then space exploration, were heavily government enterprises to start with, and the private sector followed. This is also true for items such as the Internet.

Although it may fly against the sensibilities of many, war appears to provide a considerable impetus to invention. In the United States, though the cotton gin is held up as an example of great individual enterprise, it appears to be one of the earliest candidates for government subsidy. Another important innovation emerging from the Civil War was the standardization of manufactured parts so that it became considerably easier to repair items such as damaged rifles [188]. Later in the United States the roles of the Office of Naval Research (ONR) and the Advanced Research Projects Agency (ARPA) were considerable. Over the years basic research has been sponsored by emperors and governments. In modern times in parts of Europe and the United States, development and implementation are claimed to be primarily the domain of private industry. However, while the individual inventor may tinker in his garage, the financing of innovation basic research, especially in times of war, involves government sponsorship; and as indicated by the work of Richard Day, Gunnar Eliasson, and Clas Wihlborg, a government may play the role of both the initial direct sponsor and the architect of the privatization of the industry [73].

# (p.410) 10.4 Increasing Returns and Innovation

Our prime concern is with the financing of innovation, not with the specific details of innovation itself. But innovation is closely interlinked with both increasing returns and disequilibrium. This brief section merely notes a few of the developments involving increasing returns. Marshall describes what may be considered as increasing returns via scope [247]: as the infrastructure builds up, so do districts with many competitors in the same trade. For the treatment of corporate scale and scope see Panzar andWillig [283, 284] and Chandler [54]. Arrow [11] describes a different form of increasing returns from learning. The elementary textbooks from at least the 1940s came complete with graphs of U-shaped average cost curves that essentially signaled the presence of set-up costs that were spread over increasing production.

The Phelps [290] and Solow [389] growth models utilizing a production function of the form axα‎y1-α‎ for multistage macroeconomic models added an exogenous growth term kt to reflect the increasing productivity of labor.

The work of Brian Arthur [14] treats stochastic increasing returns and the possibility of path dependence as characteristic of an innovating economy. In oligopolistic competition that characterizes much of mass production, stochastic increasing returns of the variety indicated by Arthur appear to be highly relevant.

With a random event occurring each period, the turbulence may be large, and the characterization of even the simplest market with innovation with a random element in each period will lead to a path-dependent nonsymmetric distribution of firm size.

More recently Paul Krugman [288] has considered trade and geography and offered a view of trade theory blending a macroeconomic theory of an intertwined industrial and occupational distribution characterized by economies of scale in production and a preference for diversity in consumption. Paul Romer [307] offers a long-run competitive-growth model where the driver of innovation is the endogenous growth of intellectual capital stock in a multiplicative manner.

These models appear to assume implicitly that the financing of development is more or less a minor side issue to economic growth. We believe that in context, all of the work noted briefly above represents different relevant contributions to understanding increasing returns; but in all instances an understanding is needed of the battle for the allocation of funds, both private and public. It is (p.411) key to the appreciation of the locus of the sources for control, perception, and evaluation that critically affect innovation.

# 10.5 Unpacking the Commercial and Investment Banks: Context and Control

The devil is in the details.

—Origin unclear

In chapter 9 many functions of three banking institutions are packed into one: these are the central banks, the commercial banks, and the investment banks.12

## 10.5.1 A sketch of an approach

In the packing together of functions in chapter 9 there was only one means of payment, the “blue chips” of the central bank. We now add the “red chips” of the commercial banks as a means of payment.13 , 14

The understanding of institutional detail in financial structure is critical in application but only merits explicit mathematical modeling with the appropriate detail if there is a specific important question that cannot be answered adequately otherwise. The speed of change in institutions and instruments is such that form is ephemeral,15 but basic functions remain, and as complexity increases, new functions are added. Here we discuss some of the basic questions about the relationship between central and commercial banking as well as commenting on investment banking, and we discuss the building blocks for a formal model for illustration.

We advocate treating different financial instruments as though they are different colors of poker chips in order to give them a simple physical reality. The red chips and the white chips are created together in pairs. The blue chips are “paper gold” mined, issued, or hoarded in central banks and treasuries in many different institutional ways blessed by the various laws of the nations. In treating different monies and credit this way and encountering the difficulties in trying to do so, it becomes easier to see what is left out in dealing with the proliferation of credit in a complex economy.

By splitting banking into two pieces, the central bank and the commercial banking system, we are able to describe in a fairly natural way the earnings from lending and the various control mechanisms between the commercial (p.412) banks and the central bank that provide flexibility in the money supply in return for being able to earn commercial bank profits. This is in contrast to an alternative of a monolithic central bank with owned outlets and the attendant bureaucratic costs.

Among the functions handled by a commercial banking system are the provision of consumer transactions and producer working capital needs, information gathering, and evaluation services over an area on which to base lending decisions as well as providing the host of bookkeeping and managerial services that accompany these activities.16 The system provides an alternative to having a centralized central banking system’s branches provide the services.

Given the changes in transactions and clearance technology and law, the delivery of the functions associated with commercial banks is in a state of flux.

The commercial banking system poses many ad hoc problems in mechanism design. The control of variation in money supply alone is sufficient to illustrate why competition in the commercial banking system is not a simple problem in enterprise economics such as competition among restaurants or shoe stores or even supermarkets.

## 10.5.2 National debt and taxes

We note below in section 10.8 that in modern biology much consideration is given to the concepts of modularity, flexibility, and robustness in an uncertain environment. These have their analogues in the financial control system.

In chapter 9 a minimal model of government influence on the money supply was sketched in the construction of a playable game. Throughout this volume our approach has tended to introduce new features one item at a time and to consider increasing complexity.

For this sketch of a system with commercial banks we introduce several new instruments and institutions in order not only to consider the variation of the money supply but to illustrate the links between monetary and fiscal problems and to illustrate that from the viewpoint of mechanism design the additional complexity in adding fiscal instruments may make the monetary control problem considerably easier.

The presence of both taxation and a national debt provide a mechanism to construct a capacitance in a monetary flow system of any size, as taxes provide a flow of money from the private or essentially nongovernment sector to the government while the payments on the national debt provide a flow in the opposite direction. Adjustments of net flows change the money supply. In his (p.413) advocacy for a central bank, Alexander Hamilton [255, pp. 40–44] understood the control aspects of both the bank and a national debt.

In actuality the time structure of a national debt provides flexibility in adjusting a whole profile of maturity-dependent interest rates, thus increasing flexibility in the fine tuning of time-dependent rates while also imposing new inflexibility in creating a need for retirement or refinancing of bonds due for repayment. For simplicity in analysis or the construction of a game, we may suppose the national debt to be in perpetuities with a single interest rate based on a perpetuity’s face value. All have the opportunity buy or sell the perpetuities that constitute the national debt.

At the level of detail required to fully define a playable game we have a modeling choice: Are bonds bought and sold for blue chips, red chips, or both, or are there special conditions that the central bank rules may apply? As one of the roles of the central bank here is to enable the banking system to adjust the money supply smoothly, a natural policy for the central bank is to permit the purchase and sale of the national debt in blue or red chips, using the mix of its payments as a factor in the control over the reserve money.

Let:

• $x t α$ = bid for consols by consumers;

• $x t K$ = bid for consols by banks;

• $x t CB$ = bid for consols by the central bank.

Let:

• $y t α$ = offer of consols by consumers;

• $y t K$ = offer of consols by banks;

• $y t CB$ = offer of consols by the central bank.

The price of consols will be

$Display mathematics$

Moving the price of consols moves their effective yield to

$Display mathematics$

The ability to move this interest rate depends on the relative size of government purchases and sales in comparison to those of the other agents which individually may be small.

### (p.414) 10.5.2.1 A reprise on a continuum of agents

We have used the technical term “a continuum of agents” to remind us that from the viewpoint of strictly formal modeling if we wish to prove that the agents are small enough to become (posted, previous) price takers, we require that each agent be of measure zero. At this level of modeling this level of precision is usually not required. There are many ways in which one can consider white noise, or many other market imperfections, such that for all intents and purposes the assumption that all agents are price takers is reasonable without a discourse on measure theory. In much experimental gaming the presence of around 10 to 20 agents appears to be adequate for the players to ignore their individual influence on price.

If measures are used, it is probably desirable to note that the relative measures of the different agents are considerably different. In the United States currently there is only 1 central bank; 5, 000–6, 000 commercial banks; around 340, 000 manufacturing establishments; and a population of around 318 million. The sizes of the banks and manufacturing establishments are heavily skewed, as are the incomes of individuals.

## 10.5.3 Why commercial banks?

In any process model where consumers have no direct utility for money but are given both a per-period and terminal boundary condition penalizing any individual for default and there is a final settlement at t = T + 1, the terminal conditions will determine a range on a price of money at t = T + 1. Any point in the range will provide a basis for a backward induction that together with the per-period default conditions suffice to determine the ratios of price to marginal utility of consumption u'(c) across periods. In a competitive equilibrium the path of the dynamics is interior; it presses neither the bounding conditions of default nor the money supply in any period. In disequilibrium the money supply and the courts provide the (porous)17 barriers that permit the value of money to fluctuate.

The importance of the boundary conditions is signaled in their shadow prices, and two vital roles of the commercial banks are to sense the pressures and act to relieve them.

Consider a structure with a single central bank and many (say k) commercial banks. We introduce two kinds of money. One kind of money (the “blue chips”) is exchanged only between the central bank and the commercial banks.18 This is “heavy money,” and we think of it as the central bank’s currency. Neither (p.415) commercial banks nor firms and consumers can either create or destroy it. The central bank is an outside bank with respect to this model but with a larger set of instruments comprising its given strategy than in the models of section 9.8.4. These include the existence of taxes and a national debt.

A second kind of money (the “red chips”) is exchanged between the commercial banks and the firms and consumers. We think of this as the commercial banks’ money. For additional simplicity we may assume that only red chips circulate outside the banks. In this analogy we may consider that in the game the banks all issue their own banknotes that circulate. Immediately we are faced with operational and historical detail. In the United States in the nineteenth century many banks issued their own notes, and, depending on the distance from the point of circulation and the evaluation of the reputation of the specific bank, an array of discounts appeared. With the growth of the use of checks the pattern of payments changed considerably. With better interbank communication and accounting, more and more of bank money becomes a virtual money existing only as a set of ciphers in a network of bank accounts moved electronically.

In a game stressing the physical existence of bank money, given that all banks are required to have blue chip reserves we may assume that all individually issued red chips are identical in value; but if a red chip is identified with and can only be destroyed by the bank that issued it, there are k different bank monies. These can only be regarded as one money if there is a set of rules and an enforcement mechanism over the commercial banking system that enforces fungibility among all red chips. This requires both bank failure and consumer insurance laws. Suppose that one of the many ways of selecting this structure were in place. Our achievement over the models in chapter 9 has been to separate out the consumer transactions and producer short-term circulating capital functions, assigning them to the commercial banks. The central bank may retain its role as an investment bank. In order to separate out private invesment bankers, yet another complication would be required.

The commercial banks may be considered to be owned by the consumers in equal shares, and they distribute their profits to the consumer-owners in red chips.

### 10.5.3.1 A sketch of model structure and behavior

The boundary conditions and the terminal settlement condition lead to a shadow price and extraction of all money (both blue and red chips) from the economy at a definite time t = T + 1.

(p.416) In essence the terminal conditions are exogenous. The rational-expectations assumption provides a behavioral assertion that apparently endogenizes them and links (in a not necessarily unique manner) initial and terminal conditions for a stationary state, but even this “proof by assumption” is not sufficient to provide equations of motion that lead to an equilibrium.

The model employs a separation of ownership from control. Commercial banks are profit-maximizing institutions that flow profits back to their owners much as firms do. The banks are controlled by the central bank’s rules on reserve requirements and other constraints specified below.

Consumers and firms optimize their purchases subject to no-default conditions within each period. The shadow price of default therefore creates a flexible relation between price levels and marginal utilities of consumption u'(c), leading to price dynamics like those created by a threshold utility of money in section 9.8.4.

Commercial banks do not break the circular flow of funds in response to innovation or other shocks. Borrowing for innovation requires a separate entity willing to lend long. This could be an investment bank or a development bank. For simplicity here we may consider a development bank that is part of government.

### 10.5.3.2 The structure of a class of models

The main features of a class of models, and some variables associated with each, are the following:

1. 1. Time is discrete with periods t = 0, 1, , T. A terminal period t = T + 1 is used to provide a modified “bite-your-tail” boundary condition where all initial monetary endowments must be returned.

2. 2. Each commercial bank maintains a quantity of blue chips r* with the central bank which are required reserves. If it holds less than this amount the bank is not permitted to function. The reserves held at the beginning of period t are denoted $r t K .$. Reserves held with the central bank neither earn nor pay interest.19 A commercial bank may have paid in capital of r** ≥ r*.

3. 3. At the beginning of any period, a commercial bank may deposit in or borrow blue chips from the central bank to increase its reserves, or it may draw down any reserves above its required minimum reserves; it may return capital or buy government bonds. Central bank loans accrue interest at a rate ρ‎CB, which is time-independent. We denote by $d t K$ the quantity of blue chips borrowed by a commercial bank at the beginning of period $t( d t K <0 )$ (p.417) is a deposit in the central bank). The bank’s reserves entering period t are then $r t + d t K ,$ which are required to be at least r*. The reserve ratio determined by the central bank is ϕ‎, permitting a commercial bank to issue ϕ‎ units of red chips for 1 unit of blue chips held in reserve.

4. 4. All red chips available for payments at the beginning of each period are held by consumers and the central bank. We denote their quantities by $n t α$ and $n t CB .$.

5. 5. The interest on red chip loans between the commercial banks and the firms and consumers, which we denote by $p t K ,$, is dynamically determined. We establish an interest rate by introducing a buy-sell trading post between red chips and firms’ or consumers’ IOU notes in the morning. Either commercial banks or consumers may offer red chips, and banks, firms, and consumers may bid in IOU notes payable in red or blue chips, but denominated in blue chips at the end of the period. The trading post clears using the standard quantity price formation rule. (Notation is provided below.)

6. 6. Consumers may carry red chips from one period to the next, but firms (which deliver all their remaining red chips as profits to the consumer-owners at the end of each period) must borrow red chips in order to purchase inputs to production. Once the morning trading post for red chips has cleared, firms and consumers bid for the firms’ previous-period output of consumable goods f (it-1) in a sell-all trading post as in section 9.8.4. Firms purchase inputs to production denoted it in period t, and consumers purchase quantities ct of goods for consumption.

7. 7. After the goods market has cleared, firms pay their debts of IOU notes (in red chips) to the commercial banks, and then distribute their profits to the consumer-owners. Firms are pure pass-through entities, meaning that any unpaid IOU notes are also passed to consumer-owners.

8. 8. Once manufacturing firms’ and banks’ profits have been distributed, consumers pay their debts of IOU notes (in red chips, including any unpaid IOU notes from the firms) to the commercial banks. A default penalty is imposed for any IOU notes in excess of the chips they have to pay.

9. 9. At the start of next period, there is trade in national debt and the natural persons pay an income tax. No tax is paid by the firms or banks.

10. 10. At settlement day the commercial banks are liquidated. r* must be returned and an addition to or subtraction from the final payoff is based on the amount rT+1. -r*. (p.418)

Figure 10.1 Structure of exchanges within a single period of the central/commercial banking system model. Flows of blue and red chips are indicated with dashed and dark gray arrows, respectively. IOU notes (all of which are bids) are in black. Consumable goods flows are in light gray. Each box indicates the clearing of one market. Quantities indicated where repayment is required are those that involve no default (to simplify notation) in type-symmetric noncooperative equilibria. The arrow on blue chip flows indicates the direction if dK > 0, but deposits with dK < 0 and flow in the opposite sense are also possible.

A diagram with the structure of the trading day for this model is shown in figure 10.1.

### 10.5.3.3 The trading post for red chips and IOUs

We note that by utilizing unlimited liability this model rules out both bankruptcy of the firms and bank failure and hence is not suitable for considering panic or runs as was done in the model in chapter 8.

The following list defines the bid and offer variables, and which agents control them:

$b t α$ = the bid for bank money by a consumer α‎;

$b t ϕ$ = the offer of bank money by a bank ϕ‎.

$q t K$ = the offer of bank money by a bank K.

The interest rate ρ‎t for red chip loans in period t is then formed as

$Display mathematics$

In a type-symmetric solution, the quantities of red chips received by each group in the beginning of the period are:20

$b t d ( 1+ ρ t )$ by the firms;

$b t g ( 1+ ρ t )− q t g$ by the consumers.

(p.419) The quantities of red chips paid out by each type of agent at the period’s end is21

$b t K − q t K ( 1+ ρ t )$ by the commercial bank;

$b t d$ by the firms;

$b t g − q t g ( 1+ ρ t )$ by the consumers.

10.5.3.4 Initial and terminal conditions As initial conditions, we provide each firm with a quantity i0 of goods in production, and nothing else. Each consumer begins with a quantity $m 0 α$ of red chips, and equal ownership claims to the firms and banks held in a mutual fund that flows through all profits. Each commercial bank begins with a quantity $r 0 K = r ** ≥ r *$ of blue chips held as its capital.

The only terminal condition is the default penalty for $r T+1 K <0.$ Commercial banks are defined to maximize discounted profits, which they can do by increasing the size of loans or buying government bonds. Therefore they have an incentive to increase their reserves by borrowing from the central bank, or to draw down their reserves to avoid paying interest on borrowings. A nonzero shadow price therefore forms at t D T + 1, setting $r T+1 K =0.$

### 10.5.3.5 Commercial bank profits and changing the money supply

In this model, commercial banks choose their bids or offers in the red chip markets to maximize discounted profits. The three quantities that control profit maximization under reserve ratio restrictions are the amount of reserves held, given by

$Display mathematics$

the net quantity of red chips in circulation in the period, given by

$Display mathematics$

and the net income at period’s end, if no agents default, given by

$Display mathematics$

Commercial banks either pay or accrue interest if they borrow or deposit blue chips at the central bank, so their reserves between periods update as

$Display mathematics$

(p.420) One needs to specify whether the central bank will permit a commercial bank to pay the interest due to the central bank on its borrowing of reserves using only blue chips, or will also accept earned profits in red chips. If the former, then by conservation the banks may eventually run out of blue chips unless borrowing is unbounded. It is details such as these that make the full definition of a closed complete model hardly worth doing unless the model is to be used as an experimental game or as a representation of an explicit empirical system. An economic historian might argue with much justification that custom and the opaque aspects of the law overrule trying to incorporate this level of microdetail into a general model.

### 10.5.3.6 Properties of solutions

If all agents other than the central bank are optimizers, then no-arbitrage conditions require that

$Display mathematics$

The central bank interest rate and reserve ratio are control parameters, and the other two rates are determined in part by competition. By the device of having the national debt in position, the central bank has an easy way to flood the economy with commercial bank credit by buying some of its debt. Again more microdetail is required. The central bank’s loan facility, by the rules of the game, permits the commercial banks to borrow to increase their reserves. They cannot borrow to buy bonds. If this were not so, at least temporarily a widow’s cruise would be opened. The central bank could permit, at least for some period, the commercial banks to purchase bonds with red chips, thereby immediately giving them an instant profit of

$Display mathematics$

per unit of bond sold. The pressures would be for the interest rates to eventually equalize; however, if the central bank/treasury is also issuing bonds at the same time, it controls both an input and output variable and can thereby have considerable influence on the adjustment speeds of the interest rates. Furthermore if the level of income taxes can be changed, another opportunity is provided for control of profit levels.

• Distribution of profits: As the profits of the banking system are flowed through, this device for a speedy injection of purchasing power per se createsno (p.421) questions of equity. In the models sketched above, all consumers were lumped into a symmetric ownership of all sources of income. The question of equity might arise via a skewed ownership structure.

• Exogenous uncertainty and wealth shares: Ignoring obvious differences in talent and specialization among the population, the presence of uninsured, not fully correlated uncertainty, is sufficient to produce a considerable skewing of wealth [199]. The income distribution feature is obliterated in a representative-agent model unless there are many representative agents.

• The development bank: The class of models sketched above need a specification as to who lends long in a situation involving risk. Once more there are several different institutions that are sufficient to perform the necessary task. An easy-to-select and historically justified institution is the development bank; another is the independent investment banker. In either instance the determination of the price of the loan depends on the perception and assessment of the risk interest rate and the structure of the market, which appears to be both oligopolistic in structure and possibly subject to increasing returns to scale. A potential for instability exists in the use of leveraged short-term borrowing instruments such as repos, as has been noted in section 8.4.1.1.

• Other behavior: It cannot be overstressed that all through this volume we have utilized a variant of noncooperative equilibrium behavior not because we believe in it, but because it provides a useful connection to much of the generally accepted literature. It gains some appeal when the role of many small agents is made clear; but even then many open questions remain. From our point of view there are many highly different solution concepts all of which, in the appropriate context, are able to complete the equations of motion for specialized models. We do not believe that one behavioral solution concept fits all contexts. Much investigation remains to be done in comparing different solution concepts on several test beds reflecting different contexts.

## 10.5.4 Investment banks

Critical to innovation are the investment banks, but these unlike the commercial banks are consumers and distributors, not producers,22 of the means of payment. They may create new instruments such as a whole cascade of common and preferred stock and other mezzanine financial instruments; thus (p.422) their various methods of financing may influence liquidity and in the United States may add briefly (and sometimes violently) to the M2 money supply (for example the repo). Even so, to some extent the nomenclature of “investment bank” rather than a term such as “investment house” is misleading.

Although we do not develop formal models of investment banking here, we note that investment banks are critical to the control aspects of innovation, and they along with direct government actions provide much of the direct control of the forces of innovation.

Public mythology and the understanding of causal factors in innovation are only loosely connected. The symbolism of Silicon Valley with gunslinger entrepreneurs, Wild West individualists, and garage inventors is far more congenial to the ethos of a country such as the United States than are its beliefs in ONR, ARPA, and Los Alamos, let alone the sponsorship of invention under empires and dictatorships and the universal stimulus of war.

# 10.6 A Comment on Monied Individuals: Retirees or Active Capitalists?

In section 9.7.1 we considered a class of individuals whose only asset was money. Because the solution supported the fiat as both a means of payment and a store of value, these individuals were able live off their money. In our example in section 9.8.4, looking only at central bank financing we omitted them for simplicity.

The introduction of a class of agents living off money provides for a basic reconsideration of the role of finance in the economy. In particular their interest in influencing a government-set rate of interest may be diametrically opposed to the desires of the producers.

Is a retired surgeon with $10,000,000 the economic equivalent of a professional money lender or investment banker or hedge fund operator with$10,000,000? Almost always the answer is no. Information, evaluation, and expertise and specialization of the financial functions are in essence an evolutionary aspect of the overall body economic. The essential difference between a merely rich amateur investor and a professional is perception, expertise, knowledge, and a network of professional connections. The professional investor is part of the perception and general sensory system of the economy, dealing in the perception and evaluation of risk in an economy in motion. The rich retiree is better off investing indirectly though a professional investor, be it a bank, (p.423) investment bank, or other financial professional, unless she has a network of connections of her own that enable her to invest directly in a family’s or friend’s business.

The remarks above imply that at least we should split the savers into two parts, passive savers and active financiers. The first deposit only in the commercial banks, pension funds, or mutual funds, while the second are involved in evaluation and deal directly with the firms and the markets for firms and their stocks.

Finance is micro-microeconomics. It deals with information, perception, and evaluation as well as the retail and wholesale aspects of the transactions, saving, and investment technologies. The level of aggregation of institutional structure employed in formal models depends heavily on the basic questions being answered. Aggregations such as monied individuals or a banking system cover many functions. In our models the stress is on breaking out some of the basic functions attributed to the institution.

A natural model that we do not develop here but that merits noting, at least, would involve both investment bankers and the savers in our society: in particular the retirees and pension funds whose fiduciaries supply the funds to the investment bankers as part of the needed division of labor in the perceptual and due diligence part of the investment process in a complex economy.

# 10.7 A Comment on Monetary and Fiscal Policy

It has been customary in applied macroeconomics to make a distinction between monetary and fiscal policy. Tobin [400], Okun [277], Nordhaus [276], and many others have observed that both are a part of the policy of the same player. From the purely economic viewpoint this is clear, and policy coordination is called for, but the distinction between them may be justified by the history of political and bureaucratic happenstance. In the context of day-by-day political and bureaucratic behavior, the boundary constraints on the various governmental policy weapons are such that they do not offer independent choice.

The long debate on the level of political freedom that should be bestowed on a central bank represents a concern as to how to design a powerful bureaucracy with the strategic freedom to function under less political pressure on a far longer time horizon than those of fiscal policymakers answerable to their (p.424) political masters on a day-by-day basis. The answers to the problems posed here are given in the process of an ongoing political-legal-societal-economic debate that is somewhat institutionally different in various societies. Pure economic methodology provides no direct answers to sociopolitical questions; at best it can give economic advice to all the constituencies. This provides some boundary conditions, but little more.

## 10.7.1 Money as a flexible measure

In the earlier parts of this book we have stressed the relationship between some of the methods of physics and economics. Here, as we stress aspects of innovation and a complex financial control structure, we appear to be veering toward connections with biology. Whereas physics employs a standard meter that for most purposes is a fixed measure, all participants in the economy know that their central measure—money—is in motion relative to preferences, though hopefully by “not too much.” It is designed to provide measurement in a loosely coupled system where virtually any construction links money to preferences via ever-moving prices and more slowly shifting default laws and depreciating assets.

The miracle, in our estimation, is how well, given the complexity of the system, it appears to have worked. Bewley [30, p. 284] terms the constant marginal utility of money the formalization of the “permanent income hypothesis” of Friedman.

The breaking of the circular flow calls for violation of the constant utility of money for a transient of indefinite length; and with intermittent innovation the system has to be in perpetual irregular motion. This sets the context for a central bank’s attempt to keep a purchasing power or marginal value for its money within bounds.

## 10.7.2 Many monies and the weakening of control

In spite of the difficulties and complexity, we have suggested that, at least in principle, it is possible to specify a full mathematical model of the control problem of a government in a simplified economy containing only one source of government money and one source of credit; but with the advances in communication and computation the monetary system becomes ever more porous, and the clear control mechanisms of yesterday become museum specimens of today. The era of the powerful national central bank is over, and the economic guidance and control mechanisms are undergoing a sea change.

# (p.425) 10.8 Fluctuation, Uncertainty, and Robustness

In the remainder of this chapter we sketch some analogical connections among biology, ecology, and economics. The more one views the economic system as a dynamic evolving entity, the more the biological analogy appears relevant to the proliferation of forms designed to cope with viability in an uncertain environment. A reader skipping this section will not lose the continuity of the overall work, but will miss some of the signposts concerning future interdisciplinary developments.

We have shown in chapter 9 how deterministic models can suffer large structural instabilities when even single instances of innovation are introduced as new elements that the economy must absorb. A simple extrapolation of this result might suggest that economies undergoing constant innovation would be structurally chaotic, or that our models would produce such chaos even when we do not see it in actual economies most of the time.

There are two reasons, learned from experience in evolutionary biology, to believe that real instability in economies will not be continuous but a matter of occasional punctuation [169], and that at least in principle we understand the origin of this phenomenon and have some tools with which to model it. First, selection for robustness will often produce modular and buffered systems that concentrate change within rare large events against backgrounds of quiescence. Second, the presence of noise, which provides a constant signal on which selection for robustness can act, may produce systems whose buffering also lends stability against the disrupting effect of innovations.

## 10.8.1 Fluctuations, modularity, robustness, and canalization

The economy, like the polity, society, and biosphere within which it occupies a nested hierarchy, is a loosely coupled system of components, each experiencing continual stochastic shocks and disturbances. The response of a multicomponent system to stochastic perturbation may be either unstable or stable, depending on details of the component interactions (which may not be apparent). However, if the system is to function reliably, we expect that only architectures that remain stable enough of the time will emerge from filters that select for reliability.23 Modeling the process of selection for robustness, and characterizing robust architectures, is still a frontier of theory in evolutionary dynamics, and will likely remain technically challenging for economics as well. However, a number of general principles relating robust architecture to perturbations and selection are widely used by evolutionary theorists.

(p.426) Herbert Simon, who studied robust organization in a range of economic, social, biological, and engineered systems, put forth a well-known argument [372, 373] that hierarchical, complex organizations may only be robust if their architecture is modular.24 Modular architectures are those in which components or processes are partitioned into subsystems (the “modules”), with dense or strong linkage among components within each module, and less dense or weaker linkage among components in different modules. The dynamics within modules is largely autonomous, and in a stochastic setting is responsible for identifying and eliminating many errors without reliance on signals from the environment. The weaker coupling between modules limits propagation of errors, but for the same reason limits the flow of controlling information, requiring autonomous stability of most intramodular processes. Conventional examples in Simon’s writing include the assembly of complex multicomponent instruments such as (old-fashioned mechanical) wristwatches or the Alexandrian empire.

Modularity may be a “found” property of the material or social substrate, along which an evolving system naturally aligns because this makes its error correction problem easiest, as has been argued for metabolism [43]. However, modularity may also be actively evolved through selection both for robustness and (perhaps surprisingly) for adaptability. A theory in biology known as facilitated variation [158, 159] asserts that biological systems often show modular architecture, in which the weak links across module boundaries have evolved to become standardized interfaces for control or coordination. Thus, not only do they erect barriers against error propagation, but they provide predictable signaling systems which may be used to change intermodular interactions without disrupting intramodular stability and functions. In systems showing facilitated variation, modular stability enhances robustness, at the same time as standardized interfaces support adaptation. Interface standardization may also ease the prediction problem for systems that depend on internal models for their regulatory functions [60], because viable evolutionary change is concentrated at the few links on module boundaries. Examples of deliberate engineering for modularity, in the spirit of facilitated variation, are widespread in computer science, and include the separation of hardware from operating-system layers, the transfer control protocol/internet protocol (TCP/IP), and the widespread shift from procedural to object-oriented programming languages.25

A particular evolutionary process recognized by biologists, in which external cues become anticipated and incorporated into internal regulatory systems, is known as canalization [412]. Canalization is one process by which systems (p.427) can become more modular and less sensitive to their environments, though canalization produces a form of robustness that does not necessarily serve greater adaptability unless specific sensors are added at the interface to the environment.

A system that has evolved robustness, whether through canalization or by exploiting some other (preexisting or actively evolved) form of modularity, becomes a capacitor for shocks [213, 214]. Because it can absorb more error than a system not similarly selected for robustness, it can also fail to express changes in function which might otherwise provide feedback enabling selection to eliminate the errors.26 Therefore such systems may show long-term steady-state behavior punctuated by rare but large transitions, not necessarily triggered by outsized causes. Such punctuated intervals need not be equilibria in either the mechanical physicists’ or the neoclassical economists’ sense; they may be internally active dynamical steady states.

## 10.8.2 Evolution designs using the robust components

When we observe evolved natural systems, whether molecular, organismal, social, or institutional, we may fall into the illusion of a collection of inherently rigid mechanical components assembled into a Newtonian clockwork. This illusion is harmless as long as we can take for granted that both the natural system and our designed interventions draw from a common stock of devices already filtered by selection for robustness.

The risk in using deterministic models to describe evolved natural systems is that the model interactions may not respect the actual structure of perturbations or the selection that has happened in response to them, making it difficult to distinguish model instabilities that reflect inappropriate model choice from those that predict instabilities in real systems.

In molecular biology, some progress has been made toward showing the explicit role of stochasticity in selecting system components. In some cases stochasticity is a negative effect, away from which selection directs the system, as in the case of “kinetic funnels” or chaperones27 in protein folding [201, 278]. In other cases, stochasticity may be actively employed as part of system function. Examples include stochastic resonance (first proposed as a mechanism for sensitivity enhancement in auditory systems) [28, 197], or the employment of large spaces of correlated fluctuations to increase discriminatory resolution and reliability (proposed for optimal molecular recognition) [323, 324].

## (p.428) 10.8.3 Robustness evolved to absorb fluctuations may also absorb innovations

The same mechanisms that may insulate the components of a system evolved for robustness from random shocks may also enable them to absorb effects of innovation without structural instability—up to a point. Examples in biology include developmental regulatory networks apparently evolved for robustness against environmental noise, which secondarily produce phenotypes that are robust against many mutations causing large changes in the coupling parameters between the regulatory components themselves [407].

Ultimately, sufficient change in system components (whether through shocks or through innovation) must change system function. In systems buffered as a result of selection for robustness, these changes appear as destabilizing transitions or tipping points [318]. As for noise-induced structural changes, instabilities triggered by innovation may not indicate that the triggering events are especially large. They may simply reflect watershed events that result from saturation of underlying buffers.

A pattern that is widely recognized in both engineered and natural systems [47] is the tuning of buffers to actively compensate for certain classes of shocks, in which the active compensation renders them more sensitive to shocks for which they are not designed.28 It has been argued that the resulting robust yet fragile system performance reflects a principle that the absolute capacity of a system’s components to absorb external change is fixed; only the distribution of that capacity over the spectrum of events may be altered by design or natural selection.

The concept of a fixed capacity to respond to variation has been quantified for some classes of combinatorial search and optimization problems in a set of “no free lunch” theorems [422, 423]. These theorems apply to discrete problems such as search for Boolean variable assignments simultaneously satisfying complex networks of constraints, in which the problem instances are related by elements within some permutation group. A solution algorithm, which must be defined for all instances in the problem set, may be viewed as an active system designed to identify and remove the permutation degrees of freedom by which instances differ, as it reduces each problem instance to a standard solution form such as a satisfying variable assignment. The no-free-lunch theorems show that, under a uniform probability measure to sample problem instances over the permutation group, no algorithm can have performance better than the average on all problem instances. That is, the best that can be achieved is to match the properties of the solution method to a known class of problem instances, at the cost that the method will perform worse than the average on instances outside the class.

## (p.429) 10.8.4 Liquidity as an example

Liquidity may furnish an example in the economy of a property adopted to handle uncertainty but also capable of enabling innovation. We derived in chapter 9 an example of Schumpeter’s problem of “breaking the circular flow of funds” created by the introduction of new methods in production. In an optimal deterministic system, all money is fully utilized, and the adoption of new production methods creates a transient problem of reallocating money (or providing new money) to new sectors whose solution is undefined within the equilibrium paradigm. As Keynes suggested, in a monetary economy there may be both precautionary and speculative reasons for holding money. As is shown in inventory theory [32, 317], agents may keep stocks of money untouched to cope with ordinary uncertainties such as clearing or unforeseen demand shocks, and they may also hold stocks of money to spend on targets of opportunity in the form of new products or methods of production. To the extent that we model liquidity as a deliberate underutilization of money, we explicitly acknowledge that economic process falls outside the paradigm of equilibrium under perfect knowledge and complete contracts. (A system with complete contracts would by assumption contain correctly priced insurance to enable transactions under all states of the world.) It may not be surprising, then, that attempts to characterize liquidity within equilibrium demand models such as Hicks’s IS/LM model [185] fail to capture dissimilarities between liquidity and ordinary goods or services, at the same time as noncooperative equilibrium models with incomplete markets may show instability under innovation that would be absorbed in nonequilibrium models requiring liquidity as a buffer.

### 10.8.4.1 A note on mark-to-market

The characterization of liquidity as a buffer for market “noise” is only one approach to formalization or operationalization that we might pursue. The adoption of mark-to-market rules to define collateral value creates a new functional role for liquidity as the concept applies to market clearing. A practical measure of the liquidity of a market (which may be contingent on the degree of leverage of the associated securities) is that ordinary fluctuations in demand for securities do not lead to price fluctuations large enough to feed back through the collateral valuation to create self-fulfilling price spirals.

# 10.9 How Many Derived Layers Will a Production and Exchange Economy Support?

Innovation in finance, as in production, is a perpetual feature of capitalist economies, and a pressure toward it appears to be a constant in human society, (p.430) at least in the industrial era. Commentators such as Minsky have argued [263] that financial innovation is inherently destabilizing, and it certainly gives the appearance in current society of generating an evolutionary arms race between bankers and regulators. We are therefore led to ask whether there is a natural limit to the number of layers of derivative complexity, or of regulatory complexity, that may evolve on top of a given production and exchange economy. We do not propose that we (or anyone else) can provide a definitive answer to this question for economies, but we may find precedents for it in the evolution of biological complexity.

## 10.9.1 Metabolic primary production as an analogue to production and exchange

The rough analogue to production and exchange in the economy is metabolism in biology. Like the extraction of consumer’s surplus from aggregate production technologies and scarce resources, metabolic primary production is the aggregate output of a network of processes balanced both within organisms and among organisms within ecosystems. A remarkable fact is that innovations in the core process of primary production—carbon fixation—appear to have occurred entirely within the first 1.5 billion years of life, before the rise of biologically produced molecular oxygen [42, 43, 381]. Over this entire interval, life was not only unicellular but composed exclusively of bacteria and archaea—that is, even the composite eukaryotic cell architecture shared by one-celled protists and all plants and animals had not yet evolved. The most complex aggregates under the control of single genotypes were colonies of unicells, and the most complex ecosystems were microbial communities. The history of innovation in carbon fixation therefore played out entirely within an era of comparatively low, and slowly changing, regulation.

## 10.9.2 The major transitions in evolution and the distinctive separation of productive from regulatory innovation

The second-largest transition in evolution, after the emergence of cellular life, came with the saturation of the earth’s chemical buffers with biotically produced oxygen [216]. In rapid succession, eukaryotic cells and then multicellular organisms emerged, land was colonized by colonial unicells, animals, and plants, and major cycles of carbon, water, and continental weathering were altered. It is difficult to make precise estimates of the change in primary production through this period [254, 293], but the estimated increase in power density of cells enabled by molecular oxygen is at least tenfold. The change (p.431) enabled by this increase in power density [216] was reflected in innovations in both organism and ecosystem architecture, but more fundamentally it introduced an era of innovation in regulation, which continues into the present.

We are careful to emphasize that innovations in regulation—manifested as developmental complexity and diversification in organisms [71, 113–116] and network complexity in trophic ecosystems [106]—were largely driven by increases in the magnitude of primary production. Indeed, a strong argument can be made [117] that the best-known elaboration of regulatory systems—the early-Cambrian radiation of taxonomic groups—was tightly coupled to increases in available energy, as the oxidation state of the ocean and benthic muds shifted rapidly through a period of disequilibrium. However, these changes in magnitude were not due to innovations in mechanisms of core processes such as carbon fixation.29 Rather, the rise of oxygen seems to have marked (more likely, to have actively created) a boundary, dividing an earlier period of innovation in the most fundamental mechanisms of primary production from a later period where increases in production rate generated more complex regulatory systems within organisms, and more complex life cycles, predations, digestive, fermentative, and respiratory metabolisms, symbioses, and other protocols that coordinate the interactions between organisms within ecosystems.

Thus, in at least one realized example, innovations in both the extent and mechanisms of regulation did not require parallel innovations in the diversification of primary production, though they almost certainly required increases in its rate.

### 10.9.3 The importance of friction in setting limits of complexity

The completion of the first-round human genome project [61] and other related projects brought several surprises—the protein-coding parts of human and chimp genomes (the “gene” parts of the genomes) are roughly 99 percent identical [330];30 several vegetables as well as some mollusks have more genes than humans (human est. 23,000; rice est. 28,236; tomato est. 31,760 [62]; maize est. 32,000 [322]; sea urchin est. 23,300; pufferfish est. 27,918); and similar violations of expectations. It is now widely appreciated that the manifest differences in organisms long characterized as “genetic” are largely differences in developmental regulation [87]. As is apparent for human and chimp, these regulatory changes appear to depend on no absolute increase in metabolic power.

(p.432) At the level of ecosystems a similar observation may be made. It is difficult to compare net primary productivity (NPP) for ancient and modern systems, but for some isolated systems such as reefs attempts have been made [110, 282]. Whereas the species inhabitants of paleo-reefs may differ widely from the current inhabitants, NPP values for the two are estimated to be broadly similar.

Two further figures bearing on the relation between primary production and regulation may be worth noting. First, in general the genomes of bacteria and archaea consist mostly of sequences coding for proteins, the directly functional machinery of the cell. Some of these proteins are regulatory in nature, but the amount of genetic material used for regulation at the expense of protein synthesis remains small across the range of bacterial genome sizes. With eukaryotes—the protists, animals, plants, and fungi that emerged following the rise of oxygen—this basic relation changes. Genome size increases in direct proportion to cell size, while the part used for protein coding increases much more slowly.31 For reference, in humans roughly 1.5 percent of the genome codes for protein [61]. How much of the remainder will eventually be found to participate either directly or indirectly in regulation is currently unknown, but many diverse and extensively used classes of regulatory domains within the noncoding regions are already recognized [87]. Second, among the protein-coding part of the genome, estimates are that a fully self-sufficient metabolism could be supported by about 700 genes [162]. The smallest free-living self-sufficient bacteria possess about 1,500 genes [80]. Moreover, if we kept only those genes within an ecosystem that contribute to the core reactions of primary production, they would be largely the same gene set. For comparison, the common intestinal bacterium E. coli has about 5,000 genes, and a human has about 23,000.32 Essentially all of this excess, and the great majority of the gene inventory in the biosphere, contributes to development, complex physiology, specializations or plasticity of organism phenotype that enable coupling to ecological neighbors, life cycle complexity, or direct active regulation. A further allotment of genetic material to regulatory functions arises through control loci or the production of RNA outside the protein-coding regions [87]. By any measure, the vast majority of genomes and genetic activity in the biosphere serve some form of developmental complexity or regulation not directly within the chemical pathways of primary production.

Thus, while structurally major changes to very low-level developmental and physiological regulatory networks appear to have required increases in power density, many of the differences in regulation that have been the focus of (p.433) evolutionary biologists from Darwin into the early twentieth century appear to have been energetically nearly “free of additional cost.” If such an observation generalizes to the economy, it would suggest that incremental limits to economic complexity may come from dynamic instability in the arms race between financial innovation and regulatory control, but that the underlying production mechanisms impose no obvious limits to complexity as long as the costs of regulatory mechanisms can be kept sufficiently small.

At the same time, a word of caution is in order. Whether before the rise of oxygen, in the early Cambrian, or in the present, the biosphere has never contained all carbon on earth. Even in the modern age of photosynthesis, natural systems only alter the conversion rate of energy from sunlight to heat by about 0.1 percent of the planetary ambient rate. Some problem of balancing growth against decay appears to limit NPP across all these periods, and while this limit has not strongly constrained the innovation of regulatory strategies, it also has not been much shifted by them, at least since the Cambrian and the subsequent colonization of continents. Therefore, while the fraction of biological activity devoted to regulation can apparently exceed the fraction in primary production by a large factor, it does not follow that the total magnitude of either system can expand without limit. Since the economy falls within the biosphere on a finite planet, it seems that such limits are inevitable.

It appears that in the economy the presence of transaction costs and other frictions are at least as severe as in biology.

# 10.10 Body Economic or Ecology Economic?

The participants in an economy are heterogeneous, partly autonomous but also coordinated, limited in the flexibility of their roles, and constantly subject to constraints from both institutional rules and the collective effects of behavior by other participants. While we conventionally model economic action with severely simplified games involving a few categories of agents and one or a few atomic players representing firms or the government, a richer description could attempt to posit an extensive-form game involving anywhere from tens to hundreds of millions of agents, with complex information conditions and a mix of noncooperative and coalitional-form solution concepts. The play of such a game at many points is hierarchically ordered with tight constraints on player strategies, and suggests a coarse-graining into large aggregates subsuming many individuals’ autonomy.

(p.434) The temptation is considerable to digress even further into the opening vistas in biology and ecology, but we limit ourselves to noting briefly a few further germane items:

• Professions of economic actors may resemble cell types in a multicellular organism in the sense that both are specialized for a range of functions. The body versions include:

1. 1. Perception and evaluation: These include sense organs, the somatosensory nervous system, the brain and central nervous system. The human brain accounts for about 2 percent of body mass, but consumes 20 percent of whole-body O2.

2. 2. Maintenance of the internal chemical environment: The highest energy demand comes from the liver. It is comparable to metabolic demand from the brain in humans, and two or more times larger than the brain in other mammals. (In other mammals, the brain is smaller in proportion to body size, whereas the liver is comparable.)

3. 3. Transport: This includes blood circulation, breathing, peristalsis in the gut, etc. The heart accounts for about 10 percent of whole-body O2 consumption.

4. 4. Motion and mechanical action on the environment: In humans, this comes primarily from skeletal muscles, which collectively account for about 20 percent of whole-body O2 consumption.

There is probably considerable freedom and ambiguity in assigning function to a particular tissue type as we go further down the list.

• Cells in an organism are, for the most part, subject to tighter control than most agents in an economy. The very limited “autonomy” that many cells have as their developmental programs become set defines one sense in which the organism provides a less apt analogy for the economy than would an ecological community.

• Importantly, most cells in an organism (the “soma”) do not reproduce beyond a certain stage in development, and therefore are not directly subject to Darwinian selection as a population. Because mathematically selection is equivalent to Bayesian updating [331], one might say that these cell populations do not “learn” over generational time, in the same parallel sense that populations of organisms do “learn” (as a synonym for adaptation) when all individuals have the opportunity to reproduce.33

• (p.435) The Darwinian character of competition among agents in an economy has been heavily emphasized (for instance by Friedman)34 and may act either on the agents as repositories of information or skills or on their portfolios which are effectively a different class of entities within the economy. To the extent that economies as wholes are made up of competing agents, but are not themselves vertically oriented entities undergoing competitive selection and replication, economies resemble ecosystems more than they resemble organisms. Firms are perhaps better analogues to organisms, in the sense that their status as entities is legally defined, they may be formed, may divest branches, or may close at discrete events, and their internal vertical integration through lines of command and control is (at least in stylized accounts) put up as an alternative to the negotiated-contract interaction protocols of markets.

• The way that selection can act at multiple levels to produce both stability and adaptedness has sometimes led to blurring of distinctions between organisms and ecosystems. Ecosystems, like organisms, can sometimes actively maintain homeostasis against external perturbations, functioning analogously to the way the body acts to maintain a stable internal state, though not necessarily employing analogous regulatory architectures to do so. Observations of this kind have led to characterizations of ecosystems as “super-organisms,” in efforts to capture their status as elementary entities [230]. We regard this as an error, though one that must be stated carefully. The fundamental distinction between ecosystems and organisms is that organisms instantiate forms of individuality in their architecture and dynamics, whereas ecosystems employ less hierarchical and more parallel threads of coevolutionary and community dynamics. Although individuality is a complex concept instantiated in multiple forms and possibly at multiple levels within a single system [183], it is nonetheless a distinctive shift in regulatory architecture from that of a community. The wish to emphasize the status of ecosystems as primitive entities in their own right is not to be criticized in the Gaia approach. It should be properly addressed by a shift in thinking in evolutionary biology that would take individuality less for granted and acknowledge its complexity as a constructed mode of organization, and at the same time recognize the fundamental and integrated status of other levels of organization such as ecosystems as well. An interesting case in which the distinction between organism and ecosystem may genuinely blur concepts is the case of eusocial insects, in which colonies possess many but not all features of organism-level organization [227].

• (p.436) The in-principle formalization of economies as 108–1010-player games allows us to make contact with both organism and ecosystem organization at two points. Gathered together in [380] are a variety of standard observations that general fitness functions for evolutionary dynamics can be expanded in hierarchies of k-player normal-form games, for k 2 1, ,1. It can further be argued that the general framework provided by this game expansion should be understood as formalizing development in its most general sense (thus including processes such as niche construction) [380]. The use of games to describe the way the fitness function is generated, both for selection within organismal development and among organisms in a population, is fairly common, and can provide a disciplined way to think about social evolution [139]. The further refinement from normal-form to extensive-form games gives a process underpinning to the way the fitness function is constructed from more elementary moves [65, 380], including such functions as message passing to coordinate multistage developmental processes. The refinement from normal-form to extensive-form games provides an important general mechanism to characterize lateral or oblique transmission (in parallel with the “vertical” transmission by descent).

The use of extensive-form games to characterize the interplay of development and ecological interactions with reproduction and selection dynamics begins to capture the complexity of serious evolutionary thinking, and the diversity of cases that are worth distinguishing. It demands explicit descriptions of processes, either the unfolding of events and interactions that take place between events of reproduction, or the processes of matching and change in population composition that change the information content between generations. The ambiguity in what concept an “agent” or “player” represents, which admits interpretations both as an individual within an ecosystem and as a component such as a chromosome within an individual, and the ambiguity that the extensive-form game admits, between processes that occur within ontogeny and complex interactions that take place in populations, are valid reflections of the reuse of mechanisms in real systems, which tend to cross-cut categories and sharpen the needs for conceptual clarity in their use.

• Many of the themes that we briefly note in this section, when developed in depth, lead to a reconceptualization of the nature of the living state in a much broader range of terms than has traditionally been used. While all of the operative concepts are resident in extant biological, chemical, or physical (p.437) sciences, the need to conceptually integrate them is compelled particularly in efforts to understand the emergence of life on Earth from an earlier lifeless planetary state. A fuller treatment of the problem of the origin of life, and its dependence on a theory of the nature of the living state, is pursued in [382].

Among the most important revisions argued there is the need for a comprehensive theory of stability and total, asymptotic error correction in systems which develop complex, multilevel order that is inherently an order of processes. Total error correction is a concept formalized in communication theory [333] and optimal control theory [18], and also in statistical physics [165] (though only sometimes in this language). In the context of biology it leads to a distinction between such processes as Darwinian selection on populations as mechanisms supporting error correction, and the closure of error correction itself. It is argued that a theory of total biological error correction must also account for the context of population processes originating in scales ranging from chemistry to ecology, which determine the “paths of least resistance” along which the optimal control problem of evolution possesses solutions.

## 10.10.1 Envoi

In the near-poetic area around ecology, biology, economics, and organization theory which we have here briefly explored, much is in a high state of flux, definitions are incomplete, taxonomies are shaky, and analogies and metaphors abound. We considered styling the representative of a human as “a portrait of the artist as a 242-person game,” with the actors being the human cells and the organs institutions; but decided to provide a somewhat more sober overview indicating that the time is drawing close when these highly diverse disciplines will have much to contribute to a joint understanding.35

Three widely recognized contexts in which selection grants significant autonomy to cell populations within a single organism include the function of the adaptive immune system, the perfusion and pruning of neuronal synapses in brain development, and the pathological proliferation of cells in cancers. Here the behavior of cell populations retains more of the manifest character of autonomy usually associated with organisms in ecological contexts.

The number of people on earth is under 1010 and the number of ants is possibly 1015. The number of stars in the Milky Way may be as high as 4 x 1011, with the universe holding around 1013 or 1014 galaxies. The number of atoms in the galaxy may be around 1068 or 1069. In contrast the number of firms in the US in 1992 was 23 x 106 of which 5.7 x 106 had a payroll. An oligopolistic industry has around 2–20 firms.

## Notes:

(1) Including the specification of initial conditions.

(2) Even with the poor, social custom clashes with utilitarian economics. Among the nearly destitute, weddings and funerals provide an opportunity for conspicuous consumption that the individuals can ill afford from the viewpoint of mere economics.

(3) There are some special consumption sinks for the centimillionaire or billionaire such as high-end art collection or running one’s own space program, buying a major sports team, or becoming a philanthropist. Buying political office or satisfying one’s need for revenge in the style of the Count of Monte Cristo can be sinks for conspicuous consumption.

(p.438) (4) As von Neumann himself stressed, axioms such as this must have their basis in observations of the physical world, hence they should be testable. Although intuitively attractive, the whole concept of the existence of an individual utility function is fraught with difficulties and has not yielded much in the way of satisfactory experimental results.

(5) A completely different way to approach measurable utility was proposed by Lloyd Shapley. The measure is developed utilizing axioms describing individual ability to perceive preference differences among pairs of objects. An individual can state that her preference for item a over b is greater than, less than, or equal to her preference for c over d. The two scales are clearly different and require a further axiom in order to match that is, in all probability, empirically false [297].

(6) The bound may well be loose in the sense of some decision rule such as “Stay within 10 percent of last year’s budget”; but unless the question being asked of the theory requires that details of consumption be relevant to investment, there is no need to provide them to consider investment.

(7) Although it requires considerable legal consideration to define the operational meaning of the ownership of government, the religious bodies, educational institutions, and other social institutions.

(8) Chapter 20 of [359] was devoted to considering this possibility.

(9) The tension between physical production economics and financial and ownership economics is illustrated in the different uses of the word “capital.”

(10) Other than the possibly real joys of looking at an undeveloped uninhabited landscape.

(11) Leaving out Man Friday.

(12) In chapters 8 and 9 of [359] a long list of functions of these institutions was given. The set of functions reinforce each other, yet a central minimal function of two of these institutions is the variation of the money supply. In the ideal world of complete markets run by the perfect clearinghouse this disappears. How close to this ideal a modern economy can approach is not evident. But even the slightest friction makes the limit unattainable.

(13) We could further divide a commercial bank’s money into banknotes and checks and pure ciphers, but at this point we stay with “red chips.”

(14) This could include the signed, legalized IOU notes of the borrowers as “white chips” that may serve as a local or global money depending on the size of the acceptance network.

(15) Although names for highly changed institutions may remain the same, such as “bank.”

(16) Any good modern text on financial institutions such as Ang [9] or Elton et al. [111] provides a listing. A discussion is also given in [359], ch. 8, p. 217.

(17) We use the adjective “porous” to indicate that depending on the timescale the boundary conditions may change as part of “the games within the game,” where the rules for financial motion are set by political control and that, in turn, may be subjected to social pressure.

(18) This provides a considerable simplification that was also utilized in chapter 3 of volume 1 of Schumpeter’s discussion of business cycles [326].

(19) These are societal rules and there is no logical reason to rule out interest payments.

(20) We rule out wash selling by consumers as it can be shown that with a continuum of agents it will not occur. Examples were derived in chapter 4.

(21) Some entries in these lists can of course be negative. The entries indicated are gross “receipts” or “payments” when they are positive. If they are negative, then the converse.

(22) Even here the clash between law, custom, and reputation appears. If an individual’s IOU is accepted endorsed to others at face value, she has, for practical purposes, created a near money.

(23) Selection for robustness, of course, may co-occur with selection for other properties such as adaptability, and the two forces may or may not be aligned. We discuss the particular interaction between robustness and adaptability further below.

(p.439) (24) In a somewhat different way, Marvin Minsky’s The Society of Mind [264] can be interpreted as stressing modularity.

(25) The first high-level languages in wide industrial use were all procedural. These included FOR-TRAN and C. Procedural languages act directly on memory stores in the form of variables with assigned values, in a way that offers only limited protection against interference by the procedures in one section of code with structures of data or even assigned values that other sections of code depend on having preserved. In object-oriented languages (of which almost all heavily used modern programming languages are instances), both data and procedures are encapsulated into structures termed objects, which provide defined input/output services through defined interfaces. An object’s internal mechanism for providing these services is permitted to change freely, and as long as it supports the defined function through defined interfaces, its interaction with other objects in higher-level architectures is undisturbed. For an introduction to concepts and applications, see [36].

(26) Whether buffering or amplifying the exposure of errors is an advantage can depend on population size. Krakauer and Plotkin [214] show in models that either behavior can itself be selected, and they argue, for a range of mechanisms observed in biology, that those actively provide either buffering or amplification.

(27) The folding of a polypeptide chain into a three-dimensional functional protein is a complex process of packing in space subject to a network of interlocking constraints of molecular affinity both within the chain and with molecules (water or lipids) in the embedding environment. The search for a most-stable fold is a combinatorially hard optimization problem, and the fast and reliable folding of polypeptides is not a generic property. One method of fast and reliable folding starts with collapse of local regions into three-dimensional structures that will remain in the final folded state, and subsequent accretion of other parts of the sequence onto these kernels. Such folding avoids traps of locally stable but globally unstable (termed metastable) folds, so that the free energy landscape on which the polypeptide passes from the unfolded state to its final state resembles a funnel with mostly smooth walls, rather than a jagged surface with many local minima in which the folding process can lodge in a nonfunctional state. Some proteins that do not fold in such kinetic funnels may be aided by so-called “chaperones.” These are helper proteins that sense signatures of misfolding (such as amino acids at the surface of a fold that are incompatible with the solvent), and either unfold the misfolded chain or in some other manner help guide it to the stable functional final state.

(28) The paradigmatic examples of this phenomenon are active, negative-feedback control loops in amplifier design. Characteristics such as the response time or amplitude range in the setpoint of a controller create frequency bands of shocks that it can actively compensate. Outside this band, the active response of the controller can amplify rather than suppress shocks, leading to control loop failure. The “swing angle” (phase) in AC electric power distribution systems is such a variable controlled by phase adjustments among power plants driving a transmission line system. Failure of the swing angle control system can lead some power plants to drain the transmission line while others drive it, a situation that requires system shutdown to avoid catastrophic overload and destruction of the system components.

(29) We mention carbon fixation because its innovations involve the most complex network changes and continued to arise for the longest time. For some other equally fundamental processes in primary production, the same assertion is true in even simpler form. The two primary mechanisms to produce energetic phosphates were likely in place by the formation of the first cells [74, 248, 289]. Nitrogen fixation appears to have evolved a single time, deep in the preoxygenic period [41, 303], and to have retained its core mechanisms for the remainder of history.

(30) This comparison refers to the estimate of 1.06 percent of fixed differences in single-nucleotide polymorphisms (SNPs), for which such a numerical comparison may readily be made. Other changes include insertions, deletions, and chromosomal rearrangements, but these do not qualitatively alter the degree of similarity claimed from SNPs.

(p.440) (31) An existing estimate from Woodruff et al. is that the protein-coding footprint continues to scale as the 1/4-power of cell size found for whole-genome scaling in bacteria [368]. However, these data still are not published, and we do not know how much current work by Brown et al. may alter the claims.

(32) The tiny numbers and overall universality of core genes that are metabolically essential to create a self-sufficient living ecosystem contrast with the enormous number and variability of gene variants and regulatory strategies used in ecosystems. Shotgun sequencing of genes from the Sargasso sea by Venter et al. [405] was interpreted as identifying more than 1.2 million previously unidentified genes.

(33) The role played by selection in development as well as in population evolution is carefully discussed in developmental biology [45, 183]. Selection does not cease to function within development, but the emergence of organism-level organization changes the mechanisms that generate variation [158] and the selective context, thereby subsuming the “learning” aspect of selective dynamics within cell differentiation in the frame of single generations. Aligning the consequences of selection on cell populations within an organism’s lifetime with the population-level selective forces that make the organism fit in its ecological context is one of the major problems that development solves, in ways that researchers still actively seek to understand.

(34) We find Friedman’s characterization here, like much of “social Darwinism,” to leave much to be desired. R. A. Fisher famously opened The Genetical Theory of Natural Selection [131] with the statement “Natural selection is not evolution.” Serious evolutionary studies [158, 169] are sensitive throughout to the structure in the mechanisms that generate variation, the units and levels of development and selection, the requirements for stability that limit viable developmental programs, and the coevolutionary dynamics in ecosystems that determine which ways of life can survive together. Darwin was, in the best of his tradition of natural history, a student of relations and system dynamics [70]. It can be cogent to argue that agents need not be rational in strategizing and planning if ex post selection can filter populations for strategies so that the survivors function “as if” they had chosen rationally. However, characterizing established power structures as “fit” simply by virtue of their prevalence is at best a statistical tautology if the assumptions underlying Fisherian fitness as a summary statistic are met [140], and at worst an analogy with no formal status if Fisherian fitness is not defined for the class of actors or strategies being described. Some analyses of recent banking failures [167, 168, 393] seem to us good examples of the kind of economic “ecological” depth that could support a serious application of evolutionary ideas.

(35) It is worth noting that quantitative differences often are linked with qualitative differences in understanding the nature of the dynamics. A few frivolous orders of magnitude are observed here.