The Next Generation of Austrian Economics: Essays in Honor of Joseph T. Salerno

Economists* beyond a certain age will recall a simple mnemonic when listing money’s main functions: “Money is a matter of functions four, a medium, a measure, a standard, a store.” The four functions of the categorization of money are known today as the, (1) medium of account, (2) measure (or unit) of value, (3) standard of deferred payments, and (4) store of value. The rhyme alludes to the fact that economists thought that money served a somewhat broader role once upon a time than it does today.

The mnemonic also makes clear that money has several well-defined uses, unlike other economic concepts, like “goods” which have innumerable uses subjectively determined by their users, or a “price” which is the unique objective embodiment of these uses. In this way, money is special.

Due to good luck endued in him by his parents, Joe Salerno is of the age necessary to be included in the group of economists who cut their teeth in monetary economics by learning this rhyme. Unfortunately, he may well be old enough to have forgotten it, as well as where he left his glasses, his wife’s birthday, their anniversary, and all sorts of other things important to his life!1

In this chapter I will revisit the use of this simple mnemonic to underscore what money is. I will then use these insights to augment Salerno’s (1987) work on the “true money supply.”

Money is as Money Does

In an unsettling way, the old adage that “money is as money does” has a ring of truth to it. When defined, as it commonly is in introductory economics textbooks, as “the generally accepted medium of exchange,” money can be a variety of goods, provided they meet three criteria: (1) that the good is used to settle exchanges, (2) that the good is the final means of settlement, i.e., not credit, and (3) that the economic community generally accepts such a good to settle exchanges. Economists then move on to a discussion of whether a “good” is a candidate for inclusion in the definition of the money supply when it satisfies all three of these conditions. The result is any of the common “M” measures of money.

While it is trivially true that money is as money does, there must be a better way to approach the problem. The old trusty mnemonic hints at how we can proceed.

In the common story of the origin and evolution of money, one central aspect is the reduction of transaction costs (i.e., Menger 1871, chap. 8, 1892). In a moneyless world there is a double-coincidence of wants problem, as elaborated by Jevons (1875, p. 3). As the scope of trades is limited and the costs associated with setting an agreeable price once trading partners do meet is high, there is an incentive for traders to use specific goods that are widely demanded to settle their transactions. As more individuals use these few specific goods to settle their exchanges, they gain a value for exchange purposes in addition to the value they possess for direct use. The process ends when one (or very few) goods begin to be traded solely for exchange purposes, and their acceptance is due to the knowledge that they can be easily traded with, and accepted by, another individual. Money is the outcome of this process, and it is also clear that whatever good is functioning as money will also be the generally accepted medium of exchange as a result.

Money’s use during its evolutionary process is clearly for exchange purposes but there is also an additional role of great importance. Mises (1949, pp. 244–51) sheds light on this by way of his equilibrium construct of the “evenly rotating economy” to demonstrate when money is not necessary. Only in a world of full certainty — one where all expenditures are known in advance, both in magnitude and timing — would money not be necessary. The reason comes from a simple opportunity cost analysis.2

Since money functions as the final means of settlement, it is also always and everywhere a present good. Indeed, money functions as the present good par excellence and as such yields no interest payment. Holding money will always force an individual to incur a cost in terms of the yield on whatever other best but foregone option is available to him. Rather than forego an opportunity by holding money, if the individual knew in advance what his monetary demands would be he would either lend his money at interest until it was needed, or would turn to the futures market to settle his future transactions at some discounted value in the present.

Depart from the perfectly certain world, however, and one runs into the intractable problem of how to best meet his future needs. As Mises (1949, pp. 14, 249) shows, money serves as a security hedge to guard against these uncertain situations. The key problem is that “[u]ncertain of what, when, where or the amount of future expenditures, individuals demand to hold an amount of money to safeguard against this uncertain future” (Bagus and Howden 2013, p. 236).

Of course, other highly liquid money substitutes can also serve this role to some degree. Rothbard (1962, p. 713) refers to these as goods as a type of “quasi money,” but to the extent that they are not perfectly liquid assets or the final means of settlement, they cannot function as “money.”

Thus, while a highly liquid very short-term bond may substitute for money in some ways, the fact that it is never the final means of settlement and is itself open to some degree (however small) of default risk forever trap it in the category of quasi moneys and stop it from claiming a monetary status. Chief among these quasi moneys in today’s economy are money market mutual funds (currently amounting to about $2.7 trillion) and liquid assets used as collateral by the shadow banking industry.3

In this brief discussion of the evolution and use of money there are several roles taking place concurrently. The most obvious one is the medium of exchange — a unit to transfer in settlement of pecuniary obligations. There is also the role of money in mitigating our felt uncertainty, however. In order to function accordingly, we must identify what the relevant uncertainties are that the individual will face.

Having already commented on the unknowledge of what, how much or when we will need purchasing power in the future, we can now comment on why money is held as a hedge against these expectations. After all, most individuals can and do hold a variety of liquid non-money financial assets to assist them with their future expenses, e.g., equities, short-term bonds or certificates of deposit. All of these non-money financial assets have a risk inherent in them which the money holder must overcome.

It is useful to think about financial assets in terms of two characteristics — when are they available, and what value they will have at that moment when they are used. The first criterion can be divided into two categories. A good is either a present good, i.e., it can be used at any time, or it is a future good, i.e., its value cannot be realized until some point in the future. The values in question also come in two distinct forms. A financial asset either trades at par or market value, with the latter fluctuating as per supply-demand conditions in the market. All financial assets can be classified according to these characteristics, as in Figure 1.

In the scope of financial assets, money is unique. It is the only good that is available at a moment’s notice and at par value. The par value nature of a financial asset comes from the fact that its payout is defined in terms of itself. One dollar held as currency or on deposit equals one dollar of purchasing power. Likewise, bonds are denominated in terms of money units (e.g., dollars), such that the purchaser receives a set nominal amount of said currency units upon maturity. In contrast, financial assets that trade at market value are purchased in terms of “shares” (or a claim to shares in the case of a future), with each share deriving its value from an underlying asset, whether it exists in the present or the future. When an individual buys a share in a company, the value is defined as a percentage of the company’s future earnings stream, discounted to the present at an appropriate discount rate.

Equities and money are both present goods in the sense that their respective values, or purchasing powers, are unleashed at a moment’s notice. The owner of equity is forever unsure of the value he will receive for the sale of his shares, however, as it is dependent on market conditions at the time of sale. The owner of a bond is assured the value of his asset, but only if he waits until maturity to sell it. (He can, of course, sell at any moment though the value he receives will be dependent on supply-demand conditions at the time, i.e., he will receive the market value at that moment in time, effectively making the bond an equity investment ex post.)

In a superficial sense, money is demanded because it is highly liquid. Yet this cannot be the sole reason money is demanded, as other financial assets such as equities and heavily traded debt securities are also highly liquid. Money is also demanded because its nominal purchasing power is guaranteed, as it is with bonds if we abstract from default risk. Thus, in some ways money exhibits features of equity securities (e.g., high liquidity) and other features more common in debt (e.g., par value redemption).

More to the point, money is demanded because of its uniqueness. Money is the only asset that is able to combine both features — par value and on demand availability — into one package. It is this combination that makes money such an exceptional, and also essential, part of a portfolio of financial assets.

Money as Medium of Exchange and Unit of Account, Present and Future

Thus far I have been able to establish some characteristics of money without making reference to its specific functions. Actually, the causality runs the other way ‘round. There are some specific roles needed to be filled in the economy, and money (broadly defined for the moment) is the good that emerges to serve these roles. To understand why, consider two of the common functions of money in our introductory mnemonic. To jog the younger reader’s mind (as well as Joe’s): “Money is a matter of functions four: a medium, a unit, a standard, a store.”

The obvious two functions that correspond to what any introductory economics course teaches us are those of the unit of account and medium of exchange. In one very important way, these two roles share a common link. They both perform their role in the present. Money serving as a numéraire to express prices allows for value comparisons in the here and now, and when we exchange money we settle our transactional obligations instantly. Thus, the unit of account and medium of exchange are both present functions of money.

Although we commonly think of money in terms of these present functions, is it also possible for money to have future functions? Again, returning to our mnemonic we see that the other two roles — the store of value and standard of deferred payments — are important roles that money is expected to perform at some future date. Whether money will prove itself to be a useful store of value will not be known until the future is revealed. Long-dated contracts can be defined in terms different than the common unit of account by the standard of deferred payments.4

Each of money’s four roles has a temporal dimension, but they also have a common connection by the general category of use that they are satisfying. Generally speaking money is either used to price a good for sale (if one is the seller) or exchange for the good to complete the transaction (if one is the buyer). Figure 2 shows how money’s four roles dovetail with the two criteria defining their demand. Money, by serving in any of these four functions, is demanded to set prices or exchange for goods, either now or in the future.

As previously alluded to, one monetary good need not serve all of these roles simultaneously. Historically, many goods have served as pricing units without also being exchanged to settle transactions. Although gold and other precious metals have commonly served as pricing units in recent history, accounts abound of other, less common goods, performing the same role. Cigarettes in POW camps (Radford 1945), large circular Rai stones on the South Pacific islands of Palau and Yap (Bryan 2004) and even slave women (cumal) in Early Medieval Ireland (Nolan 1926) are well-known (and well-used) examples provided by economists.

Likewise media of exchange are varied over history, though much less so than with the units of account. The reason for this is straightforward. As per Menger’s theory of the evolution of money, for money to achieve the status of the “generally accepted medium of exchange,” it must be broadly demanded throughout the economy. Together with some of the objective properties of precious metals (e.g., divisibility, durability, difficulty to counterfeit, etc.), metallic goods were used because of the assuredness that the recipient would accept them.

Pricing units need not be chosen mindful of this constraint. Instead they have been selected for criteria that include general knowledge of their value, constancy of value of time (or, at least, a non-volatility of value compared to the values of other goods), and ease of recognition. Divisibility has never been an issue for pricing units, as fractions of any unit can express value as well as any whole number. Fractions of women were used to define fines in ancient Ireland, though these prices were not paid with the aid of a steady-handed surgeon. Instead they were settled with another good functioning as a medium of exchange, at the going exchange rate of that good for women.5

Money’s four roles are a direct outgrowth of the fact that what we call “money” is actually the combination of several functions commonly embodied in one good. Denominating the prices of all goods in terms of one good brings great computational ease when comparing the opportunity costs of alternatives. Not only is the calculation provided by money prices “a device for lowering transaction costs relevant to deliberate search,” it is also the embodiment of a social arrangement allowing for spontaneous learners to easily recognize overlooked opportunities (Kirzner 1979, p. 150).

As an example, a simple economy consisting of ten goods to exchange against each other would have 45 “prices” if there was not a single good used to express their value with a common denominator.6 Using one of these ten goods to express all other prices results in only nine prices (with the price of the good in terms of itself, one, making an additional tenth “price”). In the modern economy, the number of goods is many orders of magnitude greater than this example. The average car, to take one small component of the vast number of goods produced in the American economy, has upwards of 15,000 separate parts. If these individual parts were transacted without a common pricing unit, there would be over 112 million separate exchange ratios! Since the automotive industry is less than 2.5 percent of the whole American economy, I leave it to the reader to consider the number of “prices” that could exist across the United States lacking a common denominator through the unit of account. Needless to say it is doubtful that such computational complexity resulting from direct exchange ratios would allow for anything more than a simplistic, nearly autarkic, economy.7

Money may be a present good, but the people who use it are always future oriented. Thus there will be a necessary forward-looking perspective on each of money’s two roles, in addition to their demands in the present.

The store of value, being the future extension of the medium of exchange role, is probably the simplest future-oriented function to understand. Money is demanded in the present to settle current debt and transactional obligations. However, due to the uncertainty inherent in the future, there will need to be a medium of exchange demanded today to fulfill requirements in the future. The exact dates and magnitudes of these expenses are as yet unknown, but the money saved today must retain its value, or purchasing power, until that unknown future date.

Thus, the store of value function is the other side of the medium of exchange coin. Economists often couch their discussion of the store of value function as if it was a way to transmit wealth to the future. Such an understanding of the role obfuscates the issue. Money is not demanded to transmit wealth into the future, although it can certainly perform this role. Almost no one holds a sum of money today because he is preserving his “wealth” for the future. After all, there is an opportunity cost to using money for this role given its lack of interest return. In its place, investment vehicles commonly perform this task.

Money serving as a store of value is more correctly thought of as the property whereby money will only be demanded today based on its expected purchasing power in the future. This future purchasing power will be determined by how well the medium of exchange preserves its value, i.e., functions as a store of value. Note that this is quite different from more typical discussions of storing wealth for the future in the general sense, something which is not unique to the monetary asset. We are here concerned with money’s ability to preserve its value to be used in the future for monetary needs, which are, incidentally, the same category of needs that money is demanded for in the present as a medium of exchange.

The standard of deferred payments functions as the reverse side of the unit of account coin. It is the ability of a good to express the value of other goods, but over a longer time horizon than the standard unit of account. As an example of this distinction today, despite having lost 98 percent of its purchasing power over the last 100 years, the U.S. dollar has managed to do so with constancy. Each year prices increase by around 3 percent on average, notwithstanding some outlying periods. On a year-to-year basis the U.S. dollar performs well as a unit of account, and, e.g., a clothing shop, can take comfort in knowing the price tag made in one year will suffice for the following year as well; menu costs are minimal. Over longer periods the dollar has performed terribly and lacking an alternative good to use as the standard of deferred payments, Americans have had to suffer the costs of hedging their bets on long-term contracts denominated in dollars.

When using the term “money,” what economists have in mind is actually any of the four specific roles performed by money. In this way, one reason that monetary economics has become so confused is that the very adjective in its title is ill-defined. Furthermore, with the exception of select works in the now well-aged “New Monetary Economics” literature (Black 1970; Hall 1982a, b; Greenfield and Yeager 1983), very few serious attempts have been made to look at money’s individual roles in isolation of their shared embodiment in a single good. General equilibrium models are at a loss to incorporate money since they have no scope for a medium of exchange. It has been difficult to integrate money into basic utility analysis since money confers no direct utility, unlike other goods. (And since utility analysis forms the bedrock of microeconomics, the economics profession has long grappled unsuccessfully at providing “microfoundations” for monetary economics.) In short, much has been lost by using one word — money — to describe four different functions.

Multiple or a Unique “Monetary” Good?

The source of the muddled state of present monetary economics stems, at least in part, from the simple fact that for the better part of a century, one good has served all four monetary roles. This is understandable given that the enforcement of legal tender laws effectively forces one good (i.e., the legal tender) to serve all roles simultaneously. Before the passage of such laws in the mid-nineteenth century, an American could purchase a home with a mortgage denominated in ounces of gold and furnish it with goods priced in U.S. dollars. Neither dollars nor gold would be needed to pay for either transaction, as silver could be exchanged at the market rate. With the advent of legal tender laws, prices could still be struck in any good, but the payer would always be able to use U.S. dollars in settlement. As a result, U.S. dollars became the dominant pricing unit, both for current and long-dated contracts.

Yet there is still another reason why one good would assume all roles concurrently. Consider the origin of the demand for money. Mise’s use of the evenly rotating economy illustrates that it is only the existence of uncertainty that makes money a necessity. Money need not exist as a medium of exchange, not in any abstract sense anyhow, since any contract can be settled with a future if its magnitude and timing are known in advance (or an option if not even the timing is known).

Money is held to mitigate the holder from the uncertainty concerning his future transactions needs. In this way, one may get the impression that money’s key role is the store of value —the ability for it to unleash purchasing power in the future. Such thinking is also erroneous, as there are several assets that can provide more-or-less good stores of value over time. (It is often recollected that one ounce of gold has purchased a good men’s suit for hundreds, if not thousands, of years.)

The way that money insures the holder from uncertainty stems from its unique properties as a financial asset, as in Figure 1. It is the unique good that is redeemable at par value at a moment’s notice. From this simple fact we can derive three important insights about what money is.

The first is that a good only functions as “money” when its two general functions coincide. Specifically, if a good is used as the pricing unit and is also exchanged to settle transactions, it will by necessity trade at par value. At the same time, since money is the generally accepted medium of exchange it will also be available on demand since the timing of future transactions cannot be estimated, evenly probabilistically, in the present. This is important to the extent that we can see why money takes on its specific role in the schema of financial assets, a position attributable to the specific monetary demands by individuals.

The second insight is that we can better explain what is not money. In short, any asset not trading at par value and available on demand cannot be so categorized. The reason is that it would negate the original reason why money is held — to mitigate uncertainty. Holding an asset as “money” even though it is not available on demand (e.g., a future or a bond) entails a degree of risk since there is no guarantee that the purchasing power will be available at that moment when the holder demands it. What good is a 30-year bond to the holder as money if he requires funds in ten years’ time?

On the other hand, holding a good that trades at market value (e.g., equities) will give the holder no assurance that its value will be retained, either in whole or in part, at that moment when the holder needs it. Holding Enron shares may have seemed to satisfy an individual’s demand for money superficially, but when it turned out that his shares were worthless, he moved on to satisfy this monetary role by means of another good.

Thus only goods available on demand and at par value can survive as money, and these two criteria are only fulfilled when a good is used as a pricing unit and as a medium of exchange simultaneously.

Finally, we gain some insight into better defining what the money supply is. Currency obviously fits the bill, but what of bank accounts? To the extent that they are guaranteed to be paid on demand and at par value, demand deposits also comprise an important component of the money supply. Herein lays two important caveats. Fractional-reserve banks do not necessarily come with either of these assurances. As recent events in Cyprus have made clear, fractional-reserve deposits are effectively equity holdings masquerading as money. When bank assets lost sufficient value to render them illiquid, depositors were paid out a corresponding fraction of their account’s value, an event akin to receiving the market value of a number of shares. Alternatively, some fractional-reserve banks honor the par value redemption of their deposits, but only after the depositor incurs a waiting period to receive his funds. Such a condition is imposed in nearly all banking systems on redemption requests above a certain amount.

Historically, a similar condition was used liberally on fractional-reserve deposit accounts under the guise of the “option clause.”8 This has since been heralded as a stabilizing force of free-banking systems lacking a guarantor such as a central bank to function as a lender of last resort (White 1984, pp. 28–29; Selgin 1988, pp. 161–62; Selgin and White 1994, pp. 17–26). Such advocacy gets the problem of stabilizing the monetary system exactly backwards. Solving the problem of banking instability by removing the on demand criterion, even if for only a short while, removes one-half of the key features making money so unique. It also removes one-half of the reasons why money is demanded.

Thus, deposits held in fractional-reserve bank deposits are a tenuous component of the money supply. Provided that the issuing bank can maintain on demand and par value redemption, there is no significant problem. Changing either of these aspects effectively removes the asset from the upper-left quadrant in Figure 1, and relegates the former “money” to some other financial role.

(Re)defining the Money Supply

Defining the money supply is tricky business. This is so not least because of what criteria define monetary assets, but also because some of those assets are not capable of performing their jobs without serious caveats. I will close with some brief and sundry comments on Salerno’s (1987) definition of the “true money supply.”

In writing this pithy article, Salerno builds from the theoretical framework of Rothbard (1963, pp. 83–86; 1978; 1983, pp. 265–62) used to accurately define the money supply. In doing so Salerno diverges from Rothbard by excluding life insurance net policy reserves, owing to the fact that very few, if anyone, considers them to be part of the money supply. Since the supply in question is concerned with the “generally accepted” medium of exchange, Salerno excludes this component due the lack of perception that it is money on the part of money holders.

While this exclusion is warranted if one is concerned with money as the “generally accepted medium of exchange,” it is unwarranted if one defines “money” under a different set of criteria. As money is demonstrated herein to be defined as “the unique financial asset that is available at par value, on demand,” the inclusion of life insurance policy reserves is not only warranted, but necessary. Indeed, some works, e.g., Nash (2009), Lara and Murphy (2010), point to the use of life insurance policies as a bank account, and thus implicitly include these reserves in the money supply.

Salerno also excludes money market mutual funds (MMMF) because they are not instantly redeemable, nor are they par value claims to cash. While they may look like this at first glance, a MMMF is an equity claim to a managed investment portfolio of short-term, high-grade financial assets. Cases where these funds have “broke the buck,” i.e., the net asset value of the underlying portfolio drops below the value of MMMF claims to the assets, have historically resulted in either the owners receiving less than the par value of their holdings, or a capital infusion from the fund’s sponsors. Likewise, Salerno excludes short-term time deposits on the grounds that they are not available on demand.

More common attempts to define the money supply have suffered from an ad hoc approach, as is the case with the common “M” measures.9 Austrian economists have made great strides by realizing that the money supply can be defined by the two main reasons that money is demanded, whether to facilitate payments or to provide an uncertainty hedge. Most notably this approach follows Rothbard (1962, pp. 756–62) in defining the reservation demand to hold money separately from its exchange demand (Howden 2013, p. 21).

Ultimately, definitions of the money supply are tricky because they grapple with four problems at once. These four problems allude to money’s four roles, as listed in the opening mnemonic. I will end this chapter with one approach to measure money, and draw one implication.

In one way, money defines prices that will need to be paid for with the medium of exchange. The stock of exchange media available to settle these prices is one “money supply.” For simplicity I suggest we call this “exchange supply of money,” Mx.

Money as used to price goods comes with one complication. At any given time there is a set of obligations priced in terms of the money unit that require the medium of exchange to settle (e.g., debts coming due). To this set we can include those goods desired (but not obliged) to be purchased, which are priced in the money unit and which the medium of exchange will be required to settle (e.g., consumers and producers goods). The sum of these prices, or units of exchange, comprises what we can call the “pricing supply of money,” Mp. There is also a known amount of units of account that will arise at a future date, due to existing debt contracts yet to be fulfilled. The standard of deferred payments, thus, can also be defined with some degree of certainty in the present and we can call this the “future pricing supply of money,” Mp´.

This approach to defining the money supply gives rise to several distinct quantities, only one of which has any bearing to the more commonly given measures. While the Mx supply is easily understood, both Mp and Mp´ are determined not by any monetary factor, but instead by the demand of individuals to purchase goods and services (whether on the current spot market or on some futures market in the past). Readers will see an affinity between this approach and Salerno (2006), whereby prices are not the result of the demand for money per se (as is commonly extrapolated from the quantity theory of money), but are rather the result of the demands for goods and services which in turn create the pricing money supplies, Mp and Mp´.

One implication of, and benefit from, using several “money” supplies is that it allows for an alternative method to look at how the purchasing power of the medium of exchange fluctuates over time. If, e.g., Mx < Mp, the value of the medium of exchange must rise to clear the market. Since some of the prices that comprise the supply of pricing units of money, Mp, are fixed at a pre-defined value (e.g., those resulting from a previous debt contract), either the prices of goods contained in Mp will fall, or the real value of the supply of the medium of exchange, Mx, will rise. Of course, these implications are just two sides of the same coin.

References

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——. 1983b. “Explorations in the Gold Standard and Related Policies for Stabilizing the Dollar.” In Robert E. Hall, ed., Inflation: Causes and Effects, pp. 111–22. Chicago: University of Chicago Press.

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• *David Howden is professor of economics and chair of the Department of Business and Economics at St. Louis University, at their Madrid campus, Madrid Spain.
• 1Amongst other things important to his life, I will take the liberty to include the first time Joe met me. By my “young” mind’s recollection, this was at a dinner at a taco house in Auburn, Alabama, some balmy early June evening in 2008. This was the first of two summers I would spend at the Ludwig von Mises Institute as a summer fellow under the guidance of Joe. Thank you, Joe, for your intellectual encouragement, mentoring and, of course, friendship, over these past six years.
• 2Confusions suffered while interpreting the results of Mises’ evenly rotating economy commonly center on misunderstandings of what role money is embodying within it. Specifically, it is not necessary for money to circulate as a medium of exchange but it is of importance that it exists to denominate prices (Howden 2009, 8 n.8).
• 3Notoriously difficult to define or measure, some estimates place the size of the shadow banking system in the United States at $19 trillion as at year-end 2011 (Singh 2012). By way of comparison, the True Money Supply figure, defined in Salerno (1987) and elaborated on below, was substantially smaller at the end of 2011 — $7.3 trillion.
• 4A weight of gold served this purpose for most of history, even when a different currency unit was used in exchange for more short-term oriented pricing. This changed in the United States starting with the Legal Tender Act of 1862 (which, despite a tumultuous start was finally ruled constitutional in the 1884 case of Juilliard v. Greenman, 110 U.S. 421). Despite contracting for settlement in a different good than was commonly used as the medium of exchange, legal tender laws effectively make the standard of deferred payments (as well as the other monetary functions) the same as the preferred money of the state. Since payment must be accepted if rendered in the legal tender, even a pre-agreed alternative cannot be upheld in a court of law.
• 5Although using fractions of women to pay fines could lead to more accurate convictions and judicious verdicts, as with King Solomon’s ruling to “split the baby,” as recounted in 1 Kings 3: 16–28.
• 6An economy with n goods will result in (1/2)(n-1)(n) direct exchange ratios.
• 7Confusions around the origin and emergence of money commonly treat the unit and account and medium of exchange interchangeably. David Graeber (2011) is unconvinced by Menger’s evolutionary theory, relying on anthropological data that seems to suggest there was never a time when direct exchange existed, an important first step in the path to a money emerging as a form of indirect exchange. As proof, Graeber points to the lack of pricing boards showing prices expressed in terms of multiple goods. In this criticism, Graeber asks too much and too little. Too much because he extends what is really an example of a lack of multiple units of account as means to express prices to conclude that there was never a time with multiple goods functioning as media of exchange. On the other hand he asks too little by expecting there to be evidence of a primitive society expressing prices in terms of all, or many, other goods. Given the computational problems discussed above for a small economy not using a common unit of account, I would expect that this monetary function was eclipsed by one, or a very small number of, goods in anything more advanced than a very primitive society, thus explaining the lack of anthropological evidence from very early human developments.
• 8Checkland (1975, p. 85) describes the Scottish free-banking period as one of “continuous partial suspension of payments.”
• 9Alternative measures of the quantity of money run into similar difficulties. The “Divisia” monetary aggregates developed by Barnett (1980) use what are essentially the same types of money and money substitutes as in the more common M measures, though weighted by their expenditure share instead of evenly.