Chapter 2 COMPARATIVE STATICS

The purpose of this chapter is to offer a formal interpretation of the most detailed verbal treatment of free banking extant: George Selgin’s explanation of such a system structured around a specie-convertible currency (1988a, 1988b, 1990). The key points in Selgin’s argument, as well as the relevant features of the present work, will be identified. A mathematical model will be constructed from which comparative static equilibrium conclusions will be drawn. Also, graphical illustrations of the various parametric effects will be offered. It is hoped that this effort will both capture the essential elements of Selgin’s model and facilitate the classroom presentation of same.

THE MEANING OF MONEY

First of all, one must make clear what Selgin (and the present study) means by the term “money.” His focus is on the classic medium of exchange function. Thus, he takes money to be the sum of currency held by the public plus checkable deposits, that is, the total of “inside money”—the aggregate demand liabilities of commercial banks. Selgin deals rather little with “outside money” (circulating specie coins), since he believes that “in a mature free banking system . . . commodity money seldom if ever appears in circulation” (1988a, 31). Moreover, he notes that his primary concern will be with the issuing of private currency (banknotes), since that is “a relatively unfamiliar and unexplored possibility, and one that most economists dismiss” (1988a, 5). Besides, the topic of bank competition for checkable deposits has “been extensively dealt with elsewhere” (1988a, 4).

KEY CHARACTERISTICS OF FREE BANKING

There are at least three dimensions along which free banks differ significantly from commercial banks in a central banking system. First of all, reserve ratios are not set by law; free banks may hold whatever specie reserves they deem prudent. Thus, perhaps the most common mechanism by which the nominal supply of money varies is not an exogenous change in the monetary base, but an endogenous change in the so-called money multiplier. Indeed, Selgin explicitly allows for the possibility of a constant monetary base (1988a, 167–69).¹ Second, since there would be no legal tender laws, free banks must expend real resources in order to expand the circulation of their currencies. This implies that free banks face rising marginal costs. Finally, free banking exhibits a unique relationship with credit markets. Because nontrivial amounts of real resources are needed for a free bank to increase its liabilities, if that is to occur, it is necessary for the public to refrain voluntarily from some degree of present consumption; that is, savings must rise. In contrast to central banking, it is unlikely that free banking could create an excess of credit.

Optimal Reserve Ratios

Perhaps the single most important theoretical contribution that Selgin makes is his exhumation and elucidation of a principle largely buried and forgotten by a world of economists accustomed to central banks and legally imposed reserve requirements: the realization that, under competitive conditions, changes in the income velocity of money bring about changes in banks’ demand for reserves in the same direction (1988a, 70–80). Citing discussions of this principle that date as far back as F. Y. Edgeworth in 1888, Selgin argues that a bank’s demand for reserves depends not only on the total volume of transactions, but also on the frequency of those transactions (1988a, 74). One must understand that in Selgin’s proposed system, reserves are in the form of gold coin, and they are needed in order to (1) redeem notes and/or demand deposits held by customers and (2) settle interbank clearing debts.

Item (1) above is the concept of “reflux” utilized by Lawrence White (1984a, 14–18). Item (2) is the closely related concept of “adverse clearings.” Both function as automatic corrective devices, and both arise from attempts by a single bank to overissue its currency or deposit accounts. However, adverse clearings exhibit an additional feature. They are, under most conditions, positively related to both the volume and frequency of monetary transactions in the geographical area under consideration, but what if all banks in an area experienced “equal and simultaneous changes” in the demand for their respective liabilities (Selgin 1988a, 73)? Selgin concedes that in that special case (an unlikely one), all banks would be affected equiproportionally and the component of their total demand for reserves, which reflects their relative positions (“average net reserve demand”), would not change. Nevertheless, a second component of total demand for reserves would still be affected. This is the “precautionary reserve demand,” and it stems not from the average expected level of adverse clearings, but from the probability of random fluctuations around that expected level (Selgin 1988a, 72–74). It is interesting to observe that Don Patinkin presents the same argument, although he couches the principle in terms of a consumer’s demand for cash balances to meet personal liabilities (1965, 82–88). The principle applies equally well in both cases.

Thus, for example, a decline in velocity (an increase in its reciprocal, the Cambridge cash balance equation’s “k”) reduces banks’ need for reserves. This brings about a decline in their preferred (or optimal) reserve ratios, the money multiplier rises, and the money supply increases so as to maintain monetary equilibrium. Free banks “passively adjust the supply of inside money to changes in the demand for it. They are credit transferers or intermediaries, and not credit creators” (Selgin 1988a, 82). In other words, in the typical Keynesian scenario of a depression in which a significant “hoarding” of cash balances occurs (k rises), free banks would tend to respond automatically by increasing the money supply so that nominal incomes might be maintained.

It would be reasonable at this point to wonder whether such a mechanism would exhibit sufficiently powerful effects to achieve the kind of countercyclical results Selgin envisions. In short, by how much will banks’ reserve holdings change because of a change in the frequency of transactions? Patinkin, among others, supplies an answer: An entity’s optimal liquid holdings will change by a factor equal to the square root of the factor by which transaction frequency changes (1965, 87).

One might experiment with a hypothetical example. Assume that at time t_o, total bank reserves equal $1 billion, the supply of inside money equals $3 billion, and the simple money multiplier, therefore, equals 3. Suppose further that at time t_o, the frequency of transactions is 20/period, but that at t₁, this falls to 15/period. Thus, frequency changes by a factor of .75. Since the square root of that is .866, the optimal reserves of banks will fall to $.866 billion, creating excess reserves of $.134 billion. The new money multiplier is the reciprocal of the new optimal reserve ratio, or 3.464. Thus, the increase in the money supply should equal excess reserves multiplied by 3.464, or $.464 billion. In proportional terms, a 25 percent decrease in frequency leads to a 15.5 percent increase in the nominal money supply, and this, it must be remembered, is merely the effect of the decline in the frequency of transactions on reserves and the money supply. It is likely that the volume of transactions would also decline and, thereby, amplify such results. Furthermore, Ernst Baltensperger has argued that the effect on reserve holdings of a change in frequency will be larger than the square root rule suggests. He states that “the elasticity of demand for precautionary reserves with respect to scale can be quite different from one-half (the value implied by the standard square root result) and may well be in the neighborhood of one” (1974, 210).² It would seem that the magnitude of this effect is sufficient to act in the fashion Selgin suggests.

Marginal Costs

Of considerable importance to the perspective adopted in this book is the argument that, in contrast to central banking, the short-run marginal costs to free banks of producing, issuing, and—most significant of all—maintaining in circulation their notes are positive and rising. Central banks are usually described as facing marginal costs of production and circulation, given the presumptions of irredeemable paper currency and legal tender laws, that are constant and approximately zero (Meyer 1982, 41). In other words, the short-run costs of central banks are almost exclusively fixed costs. This is quite plausible. Such central banks, being legal monopolists, need not (1) redeem their liabilities on demand in terms of some commodity, (2) clear any interbank debts arising from a note-exchange system, or (3) compete for customers with other domestic currency suppliers.

The situation is very different for free banks of the sort modeled in this chapter. Free banks emphatically do have to redeem their liabilities in specie on demand, clear their interbank debts, and compete for customers. In order to redeem notes and clear debts with other banks, a free bank must hold some specie reserves. This fact, if taken alone, might seem to imply that such a bank’s short-run marginal costs are definitely positive but constant, since, for any given income velocity of money, the same fractional reserves are held as backing for each additional unit of currency in circulation. However, it is likely that the unit cost of acquiring specie rises with the demand for it.³ Therefore, an increased demand for specie as backing for a bank’s expanded circulation of currency would entail rising marginal (liquidity) costs.

Moreover, it is also true that free banks, if they are to increase the quantity of their notes in circulation, must compete with one another for customers. That is, they must attract additional business by offering new or better services and/or by having longer operating hours. That necessitates either the hiring of new employees or the more intensive utilization of their present employees. As David Glasner has remarked: “Aside from holding non-interest-bearing reserves, what other costs does a bank incur? Primarily wages. Banking is a labor-using activity” (1989, 17). If one accepts the validity of the law of diminishing marginal returns, it is then necessarily true that a free bank’s incremental labor costs rise as its note circulation increases in the short run.

Last, but not least, to attract additional deposits, a free bank (like present-day banks) must offer a higher interest rate on said deposits. Thus, interest expenditures rise at the margin.

The import of all the foregoing seems clear. For a given optimal reserve ratio, a given reputation for redemption,⁴ given plant and equipment, and given technology, the short-run marginal costs of a free bank increase as it issues more notes. Needless to say, similar costs also apply to a bank’s expansion of its deposit liabilities. In short, a free bank’s short-run marginal cost schedule must be positively sloped: (d²C/dM²) > Ø, where C is total cost and M is the nominal quantity of money.

This conclusion is one commonly drawn by free-banking theorists. White refers to “the rising marginal costs associated with a growing volume of banknotes outstanding” and “the rising marginal costs of expanding the bank’s deposit business” (1984a, 6). Selgin (1988a, 96), Kevin Dowd (1989, 45–46), and Glasner (1989, 18–20) all make similar references to the cost structure of a free bank that issues specie-convertible liabilities.

Given that the marginal cost schedule is positively sloped and that the marginal revenue schedule is either horizontal (perfect competition) or negatively sloped (oligopoly or monopolistic competition), then profit-maximizing free banks would not, contrary to conventional belief, flood the market with unlimited quantities of inside money. To argue otherwise is to assume that free banks would systematically fail to act in their own self-interest. Moreover, it assumes that consumers are willing to hold money balances whose per-unit purchasing power is rapidly declining.

Money and Loanable Funds

A third distinctive feature of free banking deals with the relationship between a competitively issued money supply and the market for loanable funds. Specifically, the question is whether or not the preservation of monetary equilibrium, by means of changes in the supply of loanable funds, is consistent with voluntary savings. Selgin argues that it is, since the “aggregate demand to hold balances of inside money is a reflection of the public’s willingness to supply loanable funds through the banks whose liabilities are held. To hold inside money is to engage in voluntary saving” (1988a, 54). This is true because to hold the liabilities of free banks is to choose to refrain from purchasing goods and services. In effect, as long as the supply of inside money keeps pace with changes in the demand for inside money, free banks loan out only that which has been willingly saved. They are “simply intermediaries of loanable funds” (Selgin 1988a, 55).

This relationship further implies that a well-functioning free-banking system would maintain the market rate of interest on loanable funds at the level Knut Wicksell called “a certain rate of interest on loans which is neutral in respect to commodity prices, and tends neither to raise nor to lower them . . . the natural rate of interest on capital” (1936, 102). Since a number of economists have argued that departures of the market rate from the natural rate constitute the primary source of business cycles—or “intertemporal discoordination” as Friedrich Hayek puts it (1935, 85–100)—it would appear that free banking would minimize such cyclical fluctuations. Real shocks would still occur, but cycles merely resulting from disequilibria in the money and credit markets would be more or less eliminated.

If one recalls the earlier discussion of the countercyclical effects of a change in the income velocity of money on free banks’ optimal reserve ratios and, therefore, on the money supply, such a suggestion becomes plausible. The details of the relationship between banking and business cycles alone would constitute a complete work, so they will not be presented here. To pursue the issue, one might consult Gerald O’Driscoll (1977), Hayek (1933, 1935, 1941), Ludwig von Mises (1971, 349–66), Milton Friedman (1968), or David Laidler (1981). However, Chapter 3 is devoted to a limited discussion of some of the more important aspects of the question.

In mechanistic terms, one may describe the markets for (1) money and (2) loanable funds under a free-banking structure as follows: The demand for money and the supply of loanable funds are positively related. Thus, “an increase in the demand for money warrants an increase in bank loans and investments. A decrease in the demand for money warrants a reduction in bank loans and investments” (Selgin 1988a, 55). This makes interest rate signals redundant for free banks. That is, what is more immediate and more telling in effect is a change in the demand for money that reveals itself by way of a change in the level of adverse interbank clearings and, thereby, in the optimal reserve ratio. If, for example, the demand for money and its purchasing power per unit rise (the price level falls), then the quantity of money supplied and the supply of loanable funds will also rise, bringing about a lower market interest rate. If the demand for money and its purchasing power fall (the price level rises), the quantity of money supplied as well as the supply of loanable funds will fall, leading to a higher rate of interest. One may take note from the foregoing that free banking should be consistent with the long-observed positive relation between the price level and market interest rates, a phenomenon dubbed the “Gibson paradox” by John Maynard Keynes (1930, 198–208).

A FORMAL MODEL

Rather little has been done in the way of formalizing free-banking theory. This is understandable in light of the fact that economists of the Austrian School have been in the vanguard of such work. The Austrian critique of and aversion to mathematical modeling is well known.⁵

Nevertheless, White offers an insightful, but brief, Lagrangian analysis of free banks (1984a, 3–12), although Selgin’s early work is entirely verbal except for bits of algebra regarding money multipliers and the precautionary demand for reserves (1988a, 75–76, 124–25). Bart Taub (1985) provides an analysis of banks that issue inconvertible paper currencies along the lines of Hayek’s proposal. However, the works by Hayek (1978), Dowd (1988, 1989), Robert King (1983), Robert Greenfield and Leland Yeager (1983), Glasner (1989), Donald Wells and Leslie Scruggs (1983, 1984, 1986a, 1986b), and Selgin and White (1987) are verbal in method. More recently, mathematical treatments have been offered by Carl Christ (1989), Larry Sechrest (1990, 24–65), and Selgin (1991).⁶

In the following pages, this writer presents a simple comparative statics model of free banking that utilizes elementary differential calculus, matrix algebra, and graphs. These have become—for good or ill—some of the standard tools of the economics profession. Moreover, the methods used should be familiar to all graduate students as well as to many advanced undergraduate students of economics. The intent is to supply a model that can readily be used in a classroom context to explain the essential features of free banking.

One is here reminded of the formalization of Keynes’ ideas provided by John Hicks (1937). Without that boost, the so-called “Keynesian revolution” might have been stillborn. No claim is being made that the present work will prove as influential as that of Hicks. Nevertheless, this effort bears the same relation to that of Selgin (and, to a lesser extent, to that of White) that Hicks’ essay bears to The General Theory of Employment, Interest, and Money.

Some will question the need for a formal model. In defense of such, one may argue that a mathematical approach forces one to “check his premises,” that is, to (1) identify those factors that are the variables and the parameters of the function at hand and (2) ascertain how such factors affect said function. In the process of doing so, anomalies, contradictions, and hidden assumptions may be revealed. As for graphs, one need only point out that they have proven themselves to be excellent expository and pedagogical devices over a considerable span of time.⁷

Others may find the model insufficiently exotic. No cognizance is taken of informational asymmetries, transaction costs, moral hazard, externalities, adverse selection, rational expectations, or game theory, to name a few of the possible approaches that could be taken. The reason is straightforward. None of the above is necessary in order to capture the basics of free banking.

As Dowd has said, “Money and the industry that provides it, the banking system, can be understood using the same kinds of analytical tools which we apply to other commodities and the industries that produce them . . . there is nothing fundamentally different about money at all” (1989, vii). Selgin seems to concur when he states that “nothing about free banking requires it to be approached with technical sophistication beyond what might be found in a graduate money and banking textbook” (1988a, 5). Regarding his initial interest in free banking, Glasner adds that “the notion that the analysis of the supply of money should be carried out within the same framework that we use to analyze the supply of other goods was a compelling one” (1989, xiv). In short, if supply and demand suffice to explain the market for televisions or corporate bonds or housing, then supply and demand will suffice to explain free banking.

Furthermore, the suggestion that standard price theory is applicable to money and banking is not unique to advocates of free banking. There exist a number of such applications in the literature. For example, Jurg Niehans (1978, 166–99) develops a detailed theory of profit-maximizing bank behavior that focuses on rates of interest paid on deposits and charged on loans. Graphically and mathematically, Niehans’ effort clearly represents a price-theory approach to banking. A different treatment using the same methodological tools is that of Lyle Gramley and Samuel Chase (1965), in which they describe the interactions in a world of four assets (currency and reserve deposit credits issued by a central bank, demand deposits, time deposits, and private securities) and three sectors (a central bank, commercial banks, and the public). Other examples one might mention are Raymond Lombra and Herbert Kaufman (1984), Bruce Dalgaard (1987, 337–39), John Gurley and Edward Shaw (1960), James Tobin (1963), and Boris Pesek and Thomas Saving (1967, 79–126; 1968, 144–63). Particularly striking are the statements by Pesek and Saving that “commercial banks are producers and sellers of money” (1967, 79), that “the standard analysis learned in principles of economics is just as applicable to a bank as to any other firm in the economy” (1968, 163), and that “the equilibrium quantity and price of any good, including money, depend on both demand and supply” (emphasis added) (1968, 50). Furthermore, one must not overlook the fact that both Selgin (1988a, 95–96) and White (1984a, 5–7) explicitly argue that the first-order condition for profit maximization, that is, production at a level where marginal cost equals marginal revenue, is as relevant to a free bank as it is to any other firm.

Finally, it may be observed that some renowned economists have in the past insisted that money is as subject to supply and demand conditions as is any other economic good. Arthur C. Pigou stated that the exchange value of money “is governed, like the value of everything else, by the general conditions of demand and supply” (1917, 39). Similarly, Jean-Baptiste Say asserted that money “is a commodity, whose value is determined by the same general laws, as that of all other commodities; that is to say, rises and falls in proportion to the relative demand and supply” (1971, 226).⁸ John Stuart Mill argued at length along such lines. Mill saw that

the value or purchasing power of money depends, in the first instance, on demand and supply. But demand and supply, in relation to money, present themselves in a somewhat different shape from the demand and supply of other things . . . whoever sells corn, or tallow, or cotton, buys money. Whoever buys bread, or wine, or clothes, sells money. (1923, 490)

That is precisely the perspective adopted here.

As indicated earlier, an attempt will be made to apply neoclassical price theory to free-banking firms, a free-banking industry, and the relations between the industry and the economy as a whole. In all graphical illustrations, the axes depicted will represent Walrasian price/quantity space, where price is assumed to be the independent and quantity the dependent variable.

The time period involved is assumed to be the Marshallian short run as opposed to the “market period” or the “long run” (Marshall 1949, 330, 378–79). The very short run, or market period, is rejected, since it is too short to permit an analysis of how free banks might react to changing conditions. The long run is similarly rejected, because it allows no differentiation of free banking from central banking. Given enough time for all adjustments to be made, there will be neither excess quantity of money supplied nor excess quantity of money demanded at the existing level of prices, regardless of the banking regime. The critical question to be examined is how free banks react to changes in economic conditions in the short run. Finally, the following simplifying assumptions will be made: (1) all banks face identical costs, (2) because of the absence of any legal barriers to entry (or exit), the market structure is one of perfect competition,⁹ and (3) the society being modeled is a large, closed economy. Therefore, the purchasing power of money is an endogenous variable.

The Variables

Given that there exist sufficient justification and precedent for a price-theoretical approach to free banking, one must next identify the variables, changes in which bring about movement along either the demand schedule or the supply schedule. That is, what do the independent variable “price” and the dependent variable “quantity” represent?

Here the term “quantity” refers to the number of units of inside money (currency plus demand deposits) held by the public during any given time period. The unit of measure is assumed to be the “dollar.” ¹⁰ The objection might be raised at this point that to use the dollar as a unit is quite arbitrary and that, therefore, the price of money is indeterminate, being dependent on the definition of the quantity measure. By that sort of reasoning, however, the price of almost everything would become indeterminate, since most commodities are traded in terms of units just as arbitrary as the dollar. For example, why sell gasoline by the gallon instead of by the liter or potatoes by the pound instead of by the kilogram? All such units are arbitrary in a sense. Nevertheless, being reinforced by convenience or custom, they are meaningful to both buyer and seller. Here the dollar will be taken to be the meaningful unit of money.

What then of price? What, indeed, should one understand the price of money to be? Most scholarly articles and most textbooks—see Campbell McConnell (1987, 345–47) and Lawrence Ritter and William Silber (1989, 314–23), for example—assume without hesitation that the price of money is some interest rate, this assumption being based on the idea that forgone interest on some alternative financial asset is the opportunity cost of holding money and, thus, money’s price. If the interest rate¹¹ is the price of money, then there is a problem. It is unavoidable that the interest rate is the price of credit, or loanable funds, but how can the interest rate be the price of both money and credit? Surely to suggest such a thing is erroneously to posit that money and credit are identical. This is very common, but nonetheless false.

As Friedman has stated, “The confusion of money and credit has been a primary source of difficulty in monetary policy. And recent experience indicates this is still so” (1969, 263). Moreover, “the interest rate is not the price of money. The interest rate is the price of credit . . . the inverse of the price level is the price of money” (Friedman 1972, 201). Robert Greenfield and Leland Yeager arrive at a similar conclusion while discussing a different topic. They suggest that “to suppose the interest rate to be the ‘price of money,’ determined so as to ensure that each existing unit of money is a unit demanded in cash balances as well—is to blur two analytically distinguishable concepts, money and credit” (1986, 371). The pervasiveness of this error may be seen in the fact that Gurley and Shaw (1960), Tobin (1963), Lyle Gramley and Samuel Chase (1965), Niehans (1978), Lombra and Kaufman (1984), Dalgaard (1987), and even White (1984a), Benjamin Klein (1974), and Taub (1985) all speak of the interest rate as the price of money.

Is Friedman alone in his belief that the price of money is its purchasing power per unit, that is, the reciprocal of the price level? By no means. Don Patinkin explains with his usual lucidity that although the “absolute price level” is the price of real money balances, the “reciprocal of the price level 1/P can be considered as the ‘real’ or ‘relative’ price of the good nominal money holdings. Accordingly, we can conceive of a curve which describes the demand for these holdings as a function of this relative price” (1965, 28). Pesek and Saving refer to “the realization that the general price level is the reciprocal of the average relative price of money” (1967, 58). Richard Timberlake and Edward Selby offer a graphical illustration much like that of Patinkin in which the nominal demand for money is plotted as a function of the “inversion of a price index” (1972, 83).

As with the works just cited, this book will take the price of nominal money holdings to be their purchasing power per unit (PPM).¹² It is further assumed that such purchasing power can be measured (at least approximately) by the reciprocal of the price level (1/P), with that price level represented by the appropriate price index.¹³

Insofar as the application of price theory to free banking is concerned, one must be careful to reason in a fashion that is parallel to, but the inverse of the ordinary process. That is, individual consumer demand schedules do exist, and the horizontal summation of such constitutes the market demand schedule (since money is not a public good). However, such schedules represent, ceteris paribus, not the quantities of some good or service that consumers will purchase at various money prices, but rather the quantities of nominal inside money consumers choose to acquire by exchanging various amounts of goods or services for them. The demand schedules are negatively sloped since, ceteris paribus, as the purchasing power of each dollar falls, consumers must hold more dollars if they are to maintain the same total purchasing power, that is, command over the same real goods (Patinkin 1965, 28–31).

On the supply side, one finds that each firm experiences short-run costs that rise at the margin and that the horizontal summation of such marginal cost curves produces a market supply schedule. The marginal cost schedule facing each firm represents the manner in which its total costs vary as the quantity supplied changes. In this instance, however, cost is measured not in monetary terms, but in terms of actual goods or services needed to produce and (more importantly) maintain in circulation various quantities of money. Thus, the positively sloped market supply schedule reveals the quantities of money banks will offer for goods and services at various rates of exchange.

It has been suggested that the methodological heart of neoclassical theory consists of (1) the identification of certain key concepts (exemplars) and (2) the consistent application of those concepts to disparate topics so as to form matrices (paradigms) that reveal both gaps in the theory and its essential parallelism (Holland 1987). The present analysis—idiosyncratic though it may appear—does not violate such parallelism. Specifically, what does a firm give up and receive when it produces and sells its product? For the typical firm, the answers are, respectively, marginal cost and marginal revenue, with both couched in monetary terms since goods trade against money. For a “money producer” (a free bank), however, the firm’s product trades against goods and services, not money. Thus, for such firms, marginal cost and marginal revenue must be measured in terms of goods and services rather than in money terms. If the price of money is its purchasing power, it cannot be otherwise.

At this point, some readers might voice a concern about a particular aspect of the sort of supply and demand analysis described above. They might question whether it is appropriate to use supply and demand schedules at the market level, or marginal cost and marginal revenue schedules at the level of the firm, to portray a stock, such as money balances, since such schedules are conventionally taken to represent flows. This is not an insurmountable problem.

Pesek and Saving state in a straightforward fashion that “the supply of money at a point in time will consist of (1) the stock existing in the previous period and (2) any net additions . . . that occur during the period in question. If the additions to the stock exceed the reductions in the stock, then the stock of money will be increasing, and if the additions are less than the reductions, it will be decreasing” (1968, 50). Furthermore, “because the current output of money is a small part of the existing stock of money, the increases in revenue from producing an additional unit of the money commodity will equal its price” (Pesek and Saving 1968, 51). Finally, “the equilibrium stock of money will occur where the demand for money function intersects the supply of money function” (Pesek and Saving 1968, 52). Obviously, those two economists find nothing incongruous about the application of supply and demand concepts to money. Still, they fail to provide any explicit justification for the combination of stocks and flows—of money or any other traded good—in the same diagram.

For such a justification, one may turn to Patinkin (1965, 516–21), who points out that if one has a flow (F), a discount rate (r) per time period, and a number (h) of such time periods per payment interval, then the related stock (S₀) can be expressed as: S₀ = F/rh. It is important to realize that if the definition of the time period changes (from, say, a week to a day), the values of S₀ and F remain unchanged. All that would occur is that h would rise by a factor of seven and r would fall to one-seventh of its former value. Yet if h changes while the time unit remains constant, then F changes proportionally, leaving S₀ unchanged. It is in this sense that stocks are “time-dimensionless,” whereas flows are not.

Patinkin notes that, properly understood, a flow should not be thought of as some quantity per unit of time, but rather as “a quantity whose magnitude is directly proportionate to h,” whereas a stock is not a quantity measured at some instant in time, but “a quantity whose magnitude is independent of h. Clearly, such ‘stocks’ and ‘flows’ can be added together” (1965, 521). If stocks and flows can be added together, they must be of the same dimensions. Thus, one is not remiss in viewing money in a supply and demand context.

The Parameters

In the previous section, the issues of money’s price (PPM) and quantity were discussed. Briefly, it was seen that an increase (decrease) in the level of goods’ prices, that is, a decrease (increase) in the purchasing power of money, led to an increase (decrease) in the quantity of money demanded and to a decrease (increase) in the quantity of money supplied. In short, typical positively sloped supply curves and negatively sloped demand curves are involved. Thus, changes in the price level elicit movements along existing nominal money supply (MS) or nominal money demand (MD) curves.

What, however, are the parameters of MS and MD? That is, what factors will bring about shifts of the MS or MD schedule? Mirroring Selgin’s treatment, five suggest themselves: (1) the ratio of money desired as a fraction of income (k), (2) changes in real income (y) that result from an increase in productivity, (3) changes in the specie reserves (S) that form the monetary base of free banking, (4) changes in the composition of currency demand, that is, changes in the public’s desired ratio of inside to outside money (k_i/k_o), and (5) the real unit cost of specie (P_s) (Selgin 1988a, 96, 98–102, 113, 129–33; 1990; 1991). These five will be utilized in a simultaneous equation system. Another issue, the effects of a change in the composition of the public’s demand for money, that is, a change in the desired ratio of currency to demand deposits (C/DD), will be examined separately.

The direction of the effect of k, y, S, and P_s on MS or MD is assumed to be as follows. An increase in k—which is initially taken to mean the ratio of desired nominal inside money holdings to nominal income, since specie “seldom if ever appears in circulation” (Selgin 1988a, 31) in a mature free-banking system—increases both the demand for money and the supply of it. The impact on demand follows from the Cambridge cash balance equation (M = kPy), whereas the effect on supply is derived from the fact that a free bank’s demand for specie reserves is inversely related to k. This latter fact, which was explained in some detail in an earlier section of this chapter, implies that as k rises, the money supply will also rise, ceteris paribus.

When real output/income rises because of productivity gains, then y rises. Such an increase in y increases the demand for money (Cambridge cash balance equation again), but decreases the supply of money. This latter may appear paradoxical, but it is not. If either the supplies of inputs increase or technological improvements occur, then such gains will generally bring about lower money costs of producing nonmonetary goods and services. Thinking inversely again, this means that the costs in terms of real goods and services of producing money and maintaining it in circulation have risen. Therefore, the marginal cost curves of individual banks and the market supply curve shift up and to the left.

An increase in S should have no effect on the demand for money, but it will increase the supply of money. Such a conclusion follows from the simple fact that, under such a free-banking system, specie represents the monetary base. Furthermore, just as with a central banking structure, an increase in the monetary base should, ceteris paribus, increase the money supply.

An increase in P_s, the real cost of specie, increases the marginal liquidity costs of free banks. That is, if P_s rises, their costs in terms of real goods and services—for any given optimal reserve ratio—of each additional dollar of money in circulation must rise. So an increase in P_s brings about a leftward shift in each of the marginal cost curves for each bank and the market supply curve.

As a succinct summary of the foregoing, the following relationships are herein assumed:

A Quantity Theory Approach

Regarding model selection, two considerations were of paramount importance: (1) to utilize the simplest model that produced useful conclusions and (2) to reflect, as closely as possible, Selgin’s presentation.¹⁴ Therefore, a quantity theory approach was chosen. Here the demand for money is a function only of k, P, and y; interest rates play no role.¹⁵ Both the prices of goods and the prices of inputs respond to market considerations, that is, they are “flexible” (though not necessarily instantaneously so) rather than “fixed.” Aggregate demand and, therefore, nominal income are affected by nominal money holdings, but real income is determined exogenously.

Two items common to many macromodels are missing from this one: a “real-balance effect” and a bond market. The real-balance effect refers to the idea that, for given aggregate nominal money holdings, as the price level falls, real money balances increase and, as a result, consumer expenditures rise as well. In the system Selgin describes, however, the real-balance effect on expenditures will be small or even nonexistent.

The controversy over whether there will be such an effect in an all-inside-money regime dates back to the late 1960s. At first it was thought that if there were no outside money in circulation, then there would be no real-balance effect (Patinkin 1965, 297). Later it was demonstrated that the inside-outside contrast was not the determining factor. What was crucial was whether the money represented net wealth, and, as David Laidler has pointed out, “regardless of whose liability it is, any money which bears interest at a market rate is not net wealth on the margin, and any money which does not bear such interest is net wealth” (1990, 33). In all modern industrial economies, the money supply consists primarily of deposits, not banknotes or coins. There is no reason to think matters would be appreciably different under free banking. Since competition would compel banks to pay interest on deposits,¹⁶ only a fraction of the money supply could constitute net wealth. Furthermore, it is even conceivable, though unlikely, that interest might be paid on banknotes.¹⁷ Therefore, free banking will exhibit a small, or no, real-balance effect.

The bond (or credit) market is ignored (for now), because it is superfluous. If certain comparative statics properties emerge from a system “when analyzed from the viewpoint of the commodity and bond markets, then it must also be stable—or have these properties—when analyzed from the viewpoint of the commodity and money markets. Every set of assumptions in the former framework has its exact counterpart in the latter” (Patinkin 1965, 377). Here the focus is on the commodity and money markets.

The specification of the model takes the following forms.

Implicitly,

MD = MD (P; k, y)

MS = MS (P; S, k, Ps, y)

Y = Y (P; y)

Explicitly,

MD = aP + by + ck(1)

MS = eS + fk − gPs − hP − jy(2)

Y = Py(3)

where MD, MS, S, k, y, and P_s are as defined previously. P is the price level, and Y is nominal national income. Furthermore, a>, b>, c>, e>, f>, g>, h>, j>, l>k>.

Assuming that MD = MS = M and that M, P, and Y are the endogenous variables of the system, this becomes:

M − aP = by + ck(1a)

M + hP = eS + fk − gPs − jy(2a)

Y − Py = (3a)

Setting this up in the matrix form Ax = d, one has the following:

Solving for the determinant |A| = (h + a) > . Thus, there exists a unique and nontrivial solution to the system. Utilizing Cramer’s Rule, one can solve for M, P, and Y, the equilibrium values of M, P, and Y.

To determine the effects of parametric changes, one may take the partial derivative of each M, P, and Y with respect to k, y, S, and P_s. Please note that only the basic results are presented here. The details may be found in the Appendix.

A Change in k. If the fraction (k) of income that consumers desire to hold as money changes, then,

To maintain equilibrium,

or c=f. Therefore,

To summarize,

This scenario is illustrated in Figures 1 and 2. The demand for nominal money balances rises as k rises, but the increase in k also reduces the marginal liquidity costs of free banks, since less specie is needed to cover adverse interbank clearings, the volume and frequency of transactions having declined. This increases the money multiplier and, thus, the money supply. In macroterms, the increased demand for money reduces aggregate demand (AD), but aggregate demand rises again as the supply of money increases. The net result is that neither the price level nor income changes. However, nominal (and real) money balances are greater than before. Such an increase in money balances is in accord with the increase in k that was the premise of the case. In short, “free banks maintain constant the supply of inside money multiplied by its income velocity of circulation” (Selgin 1988a, 102). That is to say, free banking tends to maintain nominal national income in the face of a change in k. This result, as noted by Selgin (1988a, 56), may be termed a “neutral money policy” and has been advocated by economists such as Hayek (1935), William Hutt (1979), Dennis Robertson (1926), Pigou (1933), Gottfried Haberler (1931), and J. E. Meade (1933).

Figure 1
Microeffects of an Increase in k

Figure 2
Macroeffects of an Increase in k

A Change in y. Turning to the effects of a change in real output/income brought about by an increase in productivity,

To maintain equilibrium in the market for money,

and

Substituting,

Following Selgin (1988a, 98–101; 1990, 272), who assumes that aggregate demand is unit elastic, then

and since

then

Of course, if aggregate demand were elastic then ∂Y/∂y >. Furthermore, if aggregate demand were inelastic, then ∂Y/∂y<. Selgin suggests that if “the supply of labor is inelastic with respect to changes in productivity, then . . . changes in the price level should be fully proportionate to opposite changes in output” (1990, 272). That is the case assumed here. Thus,

To summarize,

These results are portrayed in Figures 3 and 4. The general improvement in productivity increases aggregate supply (AS) and real income, lowers goods’ production costs, and exerts downward pressure on the price level. The increase in real income elicits an increase in the demand for money as well as a decrease in the supply of money. The net effects are a general decline in prices, no change in nominal income, and an increase in real money balances. This last is necessary given that real income rises while k is constant. The reduction in goods’ money prices raises the marginal costs of banks and, therefore, reduces the money supply. One may recall that this follows from the observation that free banks should perceive their marginal costs in real terms, that is, the goods and services required to produce an additional dollar and maintain it in circulation.

Figure 3
Microeffects of a Decrease in Goods’ Production Costs

Figure 4
Macroeffects of a Decrease in Goods’ Production Costs

Selgin quite appropriately emphasizes at this point that “a ‘neutral’ monetary policy, one that maintains monetary equilibrium, is not likely to keep any price index stable. What is needed is a policy that prevents price changes due to changes in the demand for money relative to income without preventing price changes due to changes in productive efficiency” (1988a, 101). This free banking tends to do.

Two related problems appear in Selgin’s treatment of the above sequence of events. First of all, as noted earlier, it is unlikely that this would include a real-balance effect of any consequence. Yet Selgin makes reference to such an effect (1988a, 101–2). Second, he is certainly correct to conclude that the nominal supply of money must contract in the face of a general productivity gain. However, he offers no sound explanation of why this would occur—unlike the present work. The explanation he offers is that “the nominal supply of inside money will adjust only in response to any change in spending associated with some real-balance effect” (1988a, 102). That is, if the rate of spending rises as an expression of a real-balance effect (k falls), then the money supply will fall, but this comes to nought as an explanation given that the real-balance effect will be small, if not nonexistent, under free banking.

A Change in S. To continue with the comparative statics analysis, one also must look at the effects of a change in the quantity of specie that forms the monetary base:

There is nothing unusual here. An increase in specie—if it is held by banks as reserves—tends, ceteris paribus, to increase the money supply, the price level, and nominal income. The increased inside money supply results from the decrease in marginal liquidity costs implied by the greater specie reserves. This is shown in Figures 5 and 6. Admittedly, to the extent that such a sequence of events occurs, free banking might justifiably be termed “unstable.”

However, there is a distinction to be made that is of some importance. Selgin explains that a commodity-backed monetary system will be unstable because of short-run changes in the production of that commodity only if such bursts in production constitute exogenous supply shocks that are not merely reactions to a change in demand for the monetary commodity (1988a, 130). Furthermore, a review of the history of gold production suggests that “discoveries and improvements in extraction techniques are best understood as responses to increased demand for gold rather than as supply shocks” (Selgin 1988a, 131).

Redemption Runs. The destabilizing events described above and revealed in Figures 5 and 6 are the result of exogenous supply shocks. If Selgin’s research is to be believed, it is far more likely that an increase in the supply of specie would follow a shift in consumer preferences away from inside money and toward outside money, that is, gold coin. Michael Bordo (1984, 201), for example, seems to concur with this appraisal of the essential stability of gold production. In other words, an increase in specie would probably be preceded by a decline in k_i, k_i being the fraction of income one wishes to hold in the form of inside money, whereas the fraction of income one wishes to hold in the form of outside money might be termed k_o, with k_i + k_o = k. The fall in k_i decreases the demand for inside money and, at the same time, also decreases its supply by virtue of raising the marginal costs of banks.

Figure 5
Microeffects of an Increase in Specie Reserves

Figure 6
Macroeffects of an Increase in Specie Reserves

Two points require clarification. Earlier it was assumed that k represented a money/income relation that referred only to inside money. Now one encounters k_i and k_o, one for inside money and one for outside money. The reason for the change is quite simple. Emulating Selgin, it was earlier assumed that no outside money was in circulation, it all being held by banks as reserves, that is, previously k_o = . The present case is merely one in which outside money demand grows at the expense of inside money demand. Thus, k_o>. It is, furthermore, important to recognize this as a classic “redemption run” on banks.¹⁸. That is, consumers liquidate part of their holdings of banknotes and/or checkable deposits and demand payment in specie. The conventional textbook explanation of redemption runs under central banking is that an increase in the demand for outside money reduces the total reserves of the banking system, which, in turn, brings about a multiplicative decline in the total money supply and a destabilizing deflation in the economy (Jaffee 1989, 341–42).

The increase in free banks’ marginal liquidity costs resulting from a preference shift toward outside money is, of course, due both to the higher real unit cost of specie and to the higher optimal reserve ratio, that is, the higher ratio of specie held per dollar of inside money in circulation, necessitated by the decline in k_i. Together these changes suggest a large increase in marginal costs and a large decrease in the inside money supply. When the supply of specie subsequently increases—as a result of either improvements in extraction techniques or new discoveries, per Selgin—the marginal costs of inside money fall and the supply of that inside money rises. However, since by assumption k_i and k_o do not change further, the decline in marginal costs should be smaller than its earlier increase. That is, marginal costs will fall only because of the lower real unit cost of specie; the optimal reserve ratio will not also be lower.

Recall that it was earlier assumed that no outside money was in circulation. In such a case, k_o = and k_i = k. Mathematically, then, the effects of a change in k_i are such that

Furthermore, for changes in the real cost of specie (P_s),

A decrease in k_i that is accompanied by an increase in both k_o and the price of specie P_s must, as a first effect, lead to a smaller nominal inside money supply. As long as the optimal reserve ratio remains less than 1, that is, as long as free banks hold fractional reserves, it must also be true that the decline in the inside money supply must exceed the increase in outside money—each change in specie reserves having a multiplicative impact on the inside money supply. In short, the total money supply, the price level, and nominal income must fall.

Such a scenario is depicted in Figures 7 and 8. There one sees the preference shift away from inside money and toward outside money. Outside money demand (OMD) rises as inside money demand (IMD) falls. Higher liquidity costs and higher reserve ratios combine greatly to reduce the inside money supply (IMS). The total money supply falls as does the price level and nominal income. When, after some time lag, the supply of outside money (OMS) increases, liquidity costs fall back, and the inside money supply, the total money supply, the price level, and nominal income all rise again. As seen earlier,

Figure 7
Microeffects of an Increase in k_o/Decrease in k_i

Figure 8
Macroeffects of an Increase in k_o/Decrease in k_i

and

As conveyed by Figures 7 and 8, although the redemption run is indeed deflationary initially, the supply-side gains in the production of specie lead to an increase in the inside as well as the outside money supply. This tends to bring the price level back toward its original state. It therefore appears that free banking, once again, is self-correcting.

The obvious question arises, however, as to how long it will take for the specie production gains to take effect. Selgin seems inconsistent in his treatment of this time element. On the one hand, he makes reference to “short-run” changes in the gold supply (1988a, 129), whereas on the other hand he ascribes these changes to “discoveries and improvements in extraction techniques” (1988a, 131). The latter appear to belong more nearly within the domain of the economic long run than in the short run.

Why must one wait, however, for the long run to bring forth increased supplies of specie? Could not free banks simply—and quickly—purchase additional monetary gold from abroad? This is certainly White’s position. He states that “as the public desires to hold a greater share of its currency in the form of specie rather than in notes . . . there will arise a short-run equilibrating tendency for specie to flow in from outside the region” (1984a, 12). Thus, the self-correction discussed above is likely to be short-run rather than long-run in nature.

Finally, one cannot help but be mystified by Selgin’s assertion that “only exogenous changes in output, which imply a shift in the supply schedule of gold (rather than mere movement along the supply schedule) support the conclusion that gold output has been unstable” (1988a, 130). As seen earlier, it is precisely the movement along the supply curve of monetary gold that leads to a destabilizing deflation, and it is the supply curve shift that tends to bring prices back up to their earlier level. The distinction may not be crucial, but Selgin seems to have things backward.

Currency Runs. The ramifications of a redemption run have just been explored in some detail. Yet there remains a similar—but subtly distinct—issue that must be discussed: the effects of a “currency run.” This is a shift of consumer preferences away from deposit account credits and toward currency. That is, consumers liquidate part (or all) of their demand deposits so as to acquire cash instead.

Currency runs reveal a dramatic inherent advantage that free banking possesses over central banking. Under central banking, the liabilities of the central bank, for example, Federal Reserve notes, are held both by the public as the sole legal currency and by commercial banks as a part of their reserves. Therefore, any change in the composition of the demand for money (the ratio of currency to deposits) will result in a multiplicative change in the money supply in the opposite direction (Mishkin 1989, 317–18). Under free banking, however, currency is not a reserve asset of the bank but a liability—at least if one refers to inside currency. Thus, for a free bank to satisfy its customers’ desire for relatively greater currency holdings and relatively smaller deposit holdings, it only needs to substitute one liability (its own notes) for another liability (deposit credits). There need not occur any decrease in reserves or any decrease in the total money supply.

It is simple to convey this contrast in formal terms. Under a central banking structure, the money supply (MS) may be defined, quite conventionally, as the sum of currency held by the public (C) plus demand deposits (DD), whereas the monetary base (MB) equals the sum of currency held by the public plus reserves held by banks (R). That is, MS = C + DD and MB = C + R. If the statutory reserve ratio is RR, with RR < 1, then RR = R/DD or DD = R/RR. Therefore, substituting the expression for DD back into the earlier expression for MS,

This last is clearly negative as long as RR < 1, that is, as long as there is fractional reserve banking. For example, if the legal reserve ratio is 0.1 and consumers exchange $1 million in deposit credits for $1 million in currency, for any given monetary base, the net effect on the money supply will be a decrease of $9 million. One should be cognizant of the essential problem facing a central banking system in this context: All currency runs necessarily are also (deflationary) redemption runs. This is a serious flaw in central banking that is ineradicable as long as competition in the supply of currency is forbidden.

The absence of such a problem under free banking may be formalized in the following equally simple way. Assuming, as initially, that no outside money is in circulation, then the money supply (MS) is the sum of private banknotes (N) held by the public plus demand deposits (DD), and the monetary base is the stock of specie (S) held by banks. Thus, MS = N + DD and MB = S. If OR_N is the optimal reserve ratio for notes, OR_DD is the optimal ratio for demand deposits, S_N the specie reserves for notes, and S_DD the specie reserves for deposits, then

or

If one assumes that all free banks exhibit the same optimal reserve ratios for all deposits and notes, then OR_N = OR_DD = OR. Keeping in mind that specie reserves can be used to redeem either notes or deposits, the above expression for the money supply may be transformed such that

Thus,

That is, an increased demand for currency (banknotes) has no net effect whatever on the money supply. Currency runs pose no threat to free banks and do not imply deflation for the economy,¹⁹ unlike the case of central banking.

The contrasts between central banking and free banking in the context of a currency run are seen in Figures 9, 10, and 11. The first two of these figures are adapted from Pesek and Saving (1968, 193). In Figure 9, under central banking, an equilibrium position is achieved at a point where the desired currency/demand deposit ratio for consumers equals the currency/demand deposit ratio for banks, that latter ratio being equal to the statutory reserve requirement (RR). Assuming that both the legal reserve ratio and the total quantity of currency in the economy (CC) remain constant, one sees that an increased relative demand for currency on the part of the public brings about a large decrease in total demand deposits and a proportionally smaller increase in currency held by the public. Thus, the net effect is a decrease in the total money supply. Figure 10, on the other hand, reveals that under a free-banking structure, firms can supply the desired additional currency to consumers without depleting their reserves and, therefore, without causing a net decrease in the overall money supply. The decrease in demand deposits may be matched by an increase in currency so as to avoid any net change. This ability of free banks derives from (1) their legal right to print their own currencies and (2) the absence of statutory reserve requirements. Figure 11 simply contrasts the likely deflationary effect of a net decline in the money supply brought about by a currency run (central banking) with the absence of such an effect (free banking).

Figure 9
Effects of an Increase in the Relative Demand for Currency (Central Banking)

Source: Reprinted with the permission of Macmillan Publishing Company from The Foundation of Money and Banking by Boris P. Pesek. Copyright © 1968 by Macmillan Publishing Company.

Figure 10
Effects of an Increase in the Relative Demand for Currency (Free Banking)

Source: Reprinted with the permission of Macmillan Publishing Company from The Foundation of Money and Banking by Boris P. Pesek. Copyright © 1968 by Macmillan Publishing Company.

Figure 11
Price Effects of an Increase in Relative Currency Demand

SUMMARY

The purpose of this chapter has been to translate the White-Selgin approach to free banking into a formal model that, it is hoped, can be used both to illuminate the essence of that approach and to convey its characteristics to students of economics.

The conclusions that emerged from the comparative statics analysis were as follows. If the Cambridge cash balance k increases, then the money supply as well as the demand for money increases so that equilibrium money holdings increase (which is consistent with the rise in k), but neither the price level, nominal income, nor real income changes. If there are productivity improvements such that real output/income increases, then the demand for money increases while the supply of money decreases. Equilibrium nominal money holdings are unchanged, while real money balances rise. The price level falls, but nominal income remains unchanged (assuming aggregate demand is unit elastic). If there is a sudden increase in monetary gold production that results in larger specie holdings by banks, then the money supply rises, as do the price level and nominal income, while real income remains constant. If—as Selgin argues is much more likely to occur than the preceding—specie productivity gains follow a shift in consumer preferences toward outside money at the expense of inside money (a redemption run), then the total money stock, the price level, and nominal income all first fall and then rise again back toward the original equilibrium conditions. Finally, if consumer preferences shift toward currency at the expense of demand deposits (a currency run), then under free banking, there is no net change in the money supply, the price level, or nominal income, whereas under central banking, the money supply, the price level, and nominal income all decline.

In short, free banking appears to be self-correcting in the important sense that, under several different scenarios, profit-maximizing action on the part of banks will, even in the short run, tend to maintain nominal national income. The one clear exception, an unprovoked and unanticipated gold supply shock, seems seldom if ever actually to occur. In other words, the “invisible hand” of Adam Smith is revealed when banking is made truly competitive.

The question remains as to how actual episodes of free banking would perform. Regrettably, there are no historical cases of a “true” or “pure” free-banking regime from which one might draw unambiguous conclusions. However, there have been several experiments involving multiple issuers of banknotes, from which one can glean some provocative material for review and debate. The best documented of these are (1) Scotland (1765–1845) and (2) the United States (1837–1863). Chapters 5 and 6 are devoted to examinations of these cases.

First, however, there are certain additional theoretical issues to be addressed. Chapter 3 discusses Say’s Law, business cycles, and the role of free banking in reconciling some well-known cycle theories. Chapter 4 argues that central banks face insurmountable problems that prevent them from maintaining stable economic conditions.

NOTES

1. The case Selgin discusses is that of freezing the quantity of Federal Reserve notes. Basing a free-banking system on such a fiat currency appears to be, as he admits, very much removed from the specie-based system he examines throughout most of his book. Nevertheless, Selgin insists that the differences are not large.

2. In an earlier article, J. H. G. Olivera demonstrated that the numerical value of such elasticity must lie between 0.5 and 1.0 (1971).

3. See the discussion of parametric effects later in the chapter. Also, it is difficult to imagine that the supply of specie would ever be perfectly elastic.

4. A bank’s reputation for redemption is here taken to be an asset of the firm (part of its “brand name capital”) that is developed over the long run and that, therefore, is a given in the short run. Many economists would, no doubt, argue that “reputation” is an ephemeral thing that can vaporize in an instant during a bank “panic.” They err in reasoning from what is true in central banking to what (they think) would be true of free banking. Contagion effects, as they are called, are much less likely to occur under free banking. For evidence on the absence of contagion in American free banking, see Arthur Rolnick and Warren Weber (1986).

5. For examples of the Austrian position, one should consult Murray Rothbard (1970, 277–78), O’Driscoll and Mario Rizzo (1985, 121), and Mises (1966, 350–57).

6. The reader should not assume that all the economists mentioned in this paragraph would categorize themselves as Austrians.

7. The author, although in agreement with their policy prescriptions and very sympathetic to their methodological stance, does not accept the categorical dismissal of all math and statistics espoused by many Austrians. It is ironic that some Austrians condemn any mathematical, graphical, or statistical work undertaken by non-Austrians, but indulge in it themselves on occasion. See Rothbard (1970; 1975) and Roger Garrison (1978) for examples of the insightful use of graphs and/or statistics by well-known Austrians.

8. Say took “money” to mean only specie, that is, only outside money.

9. Alternatively, one may think of banking as a “contestable” market (Baumol 1982).

10. In this system, the medium of exchange and unit of account are coextensive. See Chapter 7 for a discussion of versions of free banking in which they are divorced from one another.

11. In reality, of course, there is not a single interest rate, but an array of interest rates.

12. Some economists argue that money has neither a market nor a price of its own (Yeager 1986, 377). Their conclusion stems from the observation that, since money trades against goods and services in a multitude of markets, the price of money (its purchasing power) does not instantaneously adjust to changes in the supply of or demand for money. One need not challenge the accuracy of that observation in order to maintain that (conceptually) money has a market and a price. This is especially true if one thinks of the price level as the array of goods’ relative prices rather than as their weighted average.

13. This is not meant to deny that there are problems inherent in the use of any price index. All that is being suggested is that the concept “price level” is useful pedagogically.

14. There are, however, some departures from Selgin, as will be seen.

15. They are not ignored altogether, however. Chapter 3 discusses the interest rate effects of the parametric changes dealt with here.

16. Legal constraints (the Banking Act of 1933, also known as the Glass-Steagall Act) are the only reason for the long-standing absence of interest-bearing demand deposits in the United States.

17. An obvious possibility would be the issuance of notes subject to an option clause.

18. Since free banks would have a profit incentive to maintain redeemability and to nurture consumer confidence in that redeemability, it seems unlikely that redemption runs would occur with any frequency in a free-banking regime.

19. This is certainly true as long as the currency run does not degenerate into a redemption run. Even then, as discussed earlier, it is likely that free banking would prove to be self-correcting.