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Money in some form has been around for at least five thousand years, with the earliest evidence of its use in the Fertile Crescent in Mesopotamia. In contrast even after three hundred years a theory of money has scarcely been developed.
There are several basic reasons why a theory of money has been long in coming. The number of properties that ideal money needs to possess is so large that it is easy for any author to develop a theory omitting several functions. Thus we have seen the development of many partially correct theories, each one emphasizing different properties relevant to the context of the times. The blending of history, context, and institutional understanding with abstraction and analysis is one that is rarely congenial to either institutionally or mathematically oriented scholars. Furthermore, because money and financial institutions are at the center of practical affairs, theory and practice, advocacy and understanding, have been dangerously mixed.
Although Plato noted in passing the use of money as a means of exchange, possibly the first person known to have considered seriously the meaning of money was Aristotle. He identified the uses of money as a means of exchange, a store of value and a numeraire. However, considerable damage persists even today from Aristotle’s misunderstanding of the subtlety of the basic properties of economic systems utilizing money. Utilizing an unfortunate and simplistic analogy between the fecundity of the living and the sterility of inanimate objects, Aristotle’s comments helped to lay the philosophical foundation for opposition to the charging of any rate of interest whatsoever on loans by the Catholic Church and by the Moslems.
The Romans had an advanced business economy and legal system that included the development of the corporation, but there is little evidence of an interest in economic theory. Nor is there any clear evidence of it in Chinese thought or elsewhere. Possibly the next glimmerings on theorizing about money and interest were the Catholic scholastic doctors as exemplified by Saint Thomas Aquinas (1225–1274).
Key themes developed from Jean Bodin (1530–1596) and Richard Cantillon (1680?–1734) onward have been the quantity theory of money and the credit or “bills only” view of financing. Another basic division in the development of monetary theory has been the development of microeconomic theory, where the control role of government is hardly alluded to, as contrasted with the macroeconomic approaches, where government and the control aspects of the economy are central. The work of John Maynard Keynes (1883–1946), his followers James Tobin (1918–2002) and Don Patinkin (1922–1995), and competitors such as Milton Friedman (1912–2006) exemplify a joining of theoretical studies and advocacy of policy.
Prior to the great work of Keynes, the early twentieth century produced significant works by Ludwig Edler von Mises (1881–1973), Joseph A. Schumpeter (1883–1950), and Knut Wicksell (1851–1926) that set the stage for the developments to come. In a class of its own, but of considerable importance to those who wish to appreciate the subtlety of money and financial institutions, is the work of Georg Simmel (1858–1918) dealing with the philosophy of money.
In the debate on macroeconomic control of the economy, Friedman and his followers, in contrast with Keynes and his intellectual successors, have stressed the importance of the quantity of money as key to control of the economy. Simon Newcomb (1835–1909) first wrote down the explicit equation to describe the quantity theory as MV = PT, where P is the average price level, M is the amount of money in the system, V is the velocity of circulation, and T is the number of transactions in the economy. Irving Fisher (1867–1947) provided the more sophisticated analysis. In its simplest form it is assumed that V and T are constants, thereby giving an equation where a change in the money supply directly changes the price level.
The observations by William Stanley Jevons (1835–1882) concerning the failure of the double coincidence of wants may be regarded as a precursor to much formal mathematical work on the microeconomic theory of money. The failure of the double coincidence of wants can be illustrated by three individuals trading in three commodities where no pair can improve directly by trade but all can benefit from monetary intermediation that enables pairs to trade.
The work of John Hicks (1904–1989) straddled general equilibrium theory and the macroeconomic theory of money. He also introduced the idea of calculating adjustments in multistage general equilibrium models with sticky or fixed prices. This was taken up by Jean-Michel Grandmont (1983) and Jean-Pascal Bénassy (1982).
Work on the microeconomic theory of money has grown considerably since 1960, perhaps given impulse by Gerard Debreu’s Theory of Value; An Axiomatic Analysis of Economic Equilibrium (1959). This work, which established the general mathematical conditions for the existence of efficient market prices, was presented as an extension of the work of Léon Walras (1834–1910). Yet paradoxically it does not involve money except in the sense that the mathematical observation that prices are homogeneous of order zero implies the classical dichotomy that a homogeneous increase of money merely changes the price level.
Search and sequential binary trade models have been utilized as mathematical economic anthropology models to consider pre-market mechanisms of exchange that might lead to the emergence of markets and money. This includes the works of Ross M. Starr, Ariel Rubinstein, Douglas Gale, and others.
Frank H. Hahn raised the basic question of what supports the value of a paper money in any economy with a finite existence. Because all know the paper will be worthless at the end, by backward induction it can be shown that no one will take it at the start. How can this backward argument be avoided? It turns out that there are many different solutions to this problem depending on institutional and technical detail, such as terminal conditions, transactions costs, costs of producing money, policing trade, handling default, and enforcing contract.
Hahn, Mordecai Kurz, Duncan Foley, and several others have considered transactions costs. Seignorage and cost of production have been considered by Martin Shubik and Dimitri Tsomocos. Nobuhiro Kiyotaki and Randall Wright offered a formal model of three individuals producing and trading three commodities where the failure of the double coincidence of wants is overcome endogenously at equilibrium by consistent expectations that support intrinsically worthless money. Per Bak, Simon Norrelykke, and Shubik utilized a somewhat related model to consider the dynamics of adjustment.
David Cass and Karl Shell note that the presence of outside or exogenous uncertainties which would appear to have nothing to do with the functioning of a monetary economy can have a correlating influence on behavior generating what they term “sunspot equilibrium.” In a monetary economy with many different independent agents the obtaining of coordination is critical for efficient behavior.
Maurice Allais (1946) and Paul A. Samuelson (1958) recognized the importance of the overlapping generation aspects of a human economy. Real property and financial assets are transferred across the generations as individuals are born and die. Samuelson showed the important role played by money acting as a store of value in this process.
A game theoretic approach to the theory of money and financial institutions has been developed by Martin Shubik (1999) and others. In particular the set of models known as Strategic Market Games (see Lloyd Shapley and Shubik , Pradeep Dubey and Shubik, , and Sylvain Sorin ) make it possible to devise full process models that can be studied for their noncooperative equilibriums. A noncooperative equilibrium is an outcome that satisfies mutually consistent expectations; if all individuals expect that all others are going to take certain actions, there are some actions for which everyone’s expectations will turn out to be correct. These expectations are also known as rational expectations.
The key stress is on the game theory and the experimental gaming concept of a playable game as a device to make sure that a full process model is constructed. There are so many institutional possibilities in constructing process models that a concept of minimal institution is called for.
Parallel stochastic dynamic programs to study monetary phenomena was first introduced by Robert Lucas (1972); Lucas and colleagues have laid out a considerable program linking primarily representative agent, cash-inadvance microeconomic optimizing models to macroeconomic models utilizing solutions with rational expectations. They have utilized these models to address several of the major problems in macroeconomics. Some believe that it is premature to try to draw policy conclusions from models at this level of aggregation and low dimension.
In contrast Ioannis Karatzas, Shubik, and William Sudderth (1994) primarily have considered the behavior of individual agents. These models lead to the existence of equilibriums showing nonsymmetric income and wealth distributions caused by the random elements.
Debate on The Neutrality or Non-Neutrality of Money
Although new methods of parallel dynamic programming have been introduced and the mathematical models of process have evolved considerably since the writings of David Hume (1711–1776), the debate on the neutrality or non-neutrality of money is still present among economists in the early twenty-first century, although in a form somewhat different from the debate of the previous 250 years. Basically the argument has been that if money is of no intrinsic value, a doubling or halving of its supply will merely influence the price level and not the distribution of real resources. But if it does not influence the distribution of real resources it can be said to be neutral in its effect. This is a virtual tautology when comparing equilibrium states. However, when issue or withdrawal of money by the government is considered as a potential dynamic control variable, what may be a tautology in equilibrium may be false in a dynamic process.
Friedman offers a thought experiment in which a helicopter drops banknotes on a city. How do the prices and distribution of money change during this exercise? Patinkin discusses the classical separation of the monetary sector from the real economy. All of these writings deal with the same empirical problem. The key question is exactly how much the monetary and financial control mechanism actually controls the real economy. The followers of Schumpeter who are concerned with this equilibrium and uncertainty would say a great deal. The Keynesians, neo-Keynesians, Friedmanites, and neoFriedmanites all perceive the same question but differ in the answer.
The microeconomists viewing the economy from the assumptions of general equilibrium theory can prove rigorously that the price system is homogeneous of order zero. This means, in plain English, that a doubling or halving of prices makes no difference to the real economy. The mathematics is rigorous, but the model is incomplete for the problem at hand. Modifications such as Hicks’s temporary equilibrium studied by individuals such as Grandmont arrive at different conclusions. Other microeconomic theorists such as Pradeep Dubey, John Geanakoplos, Shubik, Charles Wilson, and William R. Zame introduce bankruptcy. The bankruptcy penalty links the value of paper money to the utility function, and if there are any limits to the supply of money and its velocity this implies that money is no longer neutral. Prices are defined on a finite closed interval.
The difficulties in defining and measuring near monies or other money substitutes and the empirical problems in measuring velocity make the forceful statements of Hume and the attractive simple price quantity equation of Newcombe and Fisher no longer generally tenable. We can say, “Given the assumptions of general equilibrium theory and its macroeconomic equivalents, in equilibrium, money is neutral in the economy.” It is a matter of the appropriate modeling. In reality, with incomplete markets and time lags in reaction, money is not neutral in disequilibrium. It influences the distribution of real goods. How heavily non-neutral it is and how useful it is as a control mechanism over the economy is a matter of judgment concerning detailed economic observations and measurements. No matter what the economist’s persuasion, the consensus in the early twenty-first century appears to be that the control mechanism of money over the economy is weakened by the growth of modern communications and the proliferation of money substitutes.
In spite of the considerable developments since the early twentieth century, many problems, especially those concerning the measurement of velocity and the understanding of how it changes, remain to be dealt with. A satisfactory theory of money must deal with financial institutions and with the nature and the relationship of government fiscal and monetary control. Much of the mathematical analysis of the theory of money leaves out innovation, expertise, and heterogeneous expectations. The straitjacket of the dynamic programming format together with representative agents with rational expectations forces a fixed velocity on most models. In contrast, the nonmathematical models of Keynes, Schumpeter, and Hyman Minsky present a world with innovation and differentiation in both expertise and expectations. This gives room for a dynamics of control based not on the smooth noncooperative equilibrium of the dynamic programming approach but one with the government, banks, and financiers directing parts of the money supply selectively across the economy.
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