[Introduction - Animated Graphics of Global Currencies and the Federal Reserve]
Voiceover: "Contrary to common misconceptions, there is indeed a well-agreed-upon definition of money in economics. The Federal Reserve of the United States, which issues the US dollar—the most globally recognized and used currency—explicitly defines money on its website. According to the Federal Reserve, money consistently fulfills three key roles across all economies: as a unit of account, a medium of exchange, and a store of value."
[Transition to Historical Economic Theories]
Voiceover: "The Arrow-Debreu model, a cornerstone of mainstream economic thought, shapes our understanding of money primarily as a unit of account, which is different from viewing money as a medium of exchange, reflecting deep-rooted traditions in economic theory that date back to the late 19th century."
[Discussion of Axioms and Modern Challenges]
Voiceover: "However, axioms such as those concerning the nature of money are hypotheses introduced without empirical proof, and could therefore always turn out to be inaccurate. This reality fuels ongoing debates about the monetary status of traditional assets like gold and emerging ones such as Bitcoin."
[Introduction of Harmonized Monetary Theories]
Voiceover: "Despite these ongoing debates and scientific challenges, there is a universal consensus among economists about the three essential functions of money that remain uncontested and empirically observed by institutions like the Federal Reserve."
[Analysis of Money's Roles]
Voiceover: "We begin our exploration with money's role as a medium of exchange, as initially described by classical economists. This extends to its use as a unit of account in modern economies, effectively capturing the total spendable money supply, akin to the M2 money supply estimated by the Federal Reserve."
[Historical and Current Analogies]
Voiceover: "This concept of M2 money supply can be likened to the quantity of gold coins in ancient economies, where the total amount of minted gold reflected both a medium of exchange and a store of value."
[Exclusive Dual-Use Principle of Money]
Voiceover: "Money functions either as a store of value or as a medium of exchange at any given time, not both. This exclusive dual-use principle is pivotal in understanding how money retains its purchasing power and facilitates economic transactions in both tangible and abstract forms."
[Transition to Mathematical Discussion]
Voiceover: "With these foundations, we can define money mathematically as U=S+E, representing its roles as a unit of account, store of value, and medium of exchange. This framework helps demystify how money operates within different economic systems and transitions smoothly between its various roles."
[Closing Remarks]
Voiceover: "Understanding the comprehensive function of money within the economic system, from classical theories to modern applications, reveals its indispensable role in shaping global trade and individual financial stability."
[End with Call to Action]
Voiceover: "What do you think defines real money today? How do you see these economic principles playing out in your daily transactions? Share your thoughts in the comments below!"
What is Money?
By Joseph Mark Haykov
May 3, 2024
Abstract
In economics, money is primarily viewed as a medium of exchange, specifically designed to address the 'double coincidence of wants' problem, as described by notable 19th-century economists Jevons, Menger, and Walras. Within a modified Arrow-Debreu framework that incorporates monetary elements, money is recognized as essential for its role as a unit of account, providing a standard for quoting and measuring prices. To reconcile these theoretical perspectives, we introduce the equation U = S + E, which relates these fundamental roles of money. This equation asserts that the total spendable money supply in an economy, exemplified by the U.S. M2 money supply, functions as the unit of account (U), aligning with the principles of the Arrow-Debreu model. M2, comprising cash and balances in checking, savings, and money market accounts, is utilized not only for transactions (E) but also acts as a store of value (S) when not actively facilitating payments—a phenomenon Keynes identified as a liquidity trap. The U = S + E model of money not only transforms the traditional quantity theory of money (MV = PY) into an accounting identity (EV = PY) but also clarifies the relationship between the exchange value and the use value of currencies. Within this framework, the value of a currency in a free market is determined by its effectiveness as a unit of account (U), a medium of exchange (E), and a store of value (S).
Introduction
Contrary to the general misconception often propagated by mainstream media, there is indeed a well-agreed-upon definition of money in economics. The Federal Reserve of the United States, the issuer of the US dollar—the most widely recognized and used currency globally—explicitly defines money on its website. According to the Federal Reserve, money consistently fulfills three key roles across all economies, both historically and presently: as a unit of account, a medium of exchange, and a store of value (Federal Reserve Education). This is universally acknowledged and uncontested.
The Arrow-Debreu model of mathematical economics, foundational to mainstream economic thought and utilized by institutions such as the Federal Reserve to set interest rates, identifies money primarily as a unit of account. This paper1 clarifies that the current debate about the nature of money traces back to the seminal work of early mathematical economists, specifically Jevons, Menger, and Walras. In the late 19th century, they hypothesized that money primarily serves as a medium of exchange, a solution necessary to address the double coincidence of wants problem inherent in direct barter.
Over time, this perspective has evolved into what is now often treated as an assumption-dependent axiom in mathematical economics: that money is inherently a medium of exchange. However, accepting this conjecture uncritically is precarious—as any axiom, including the Euclidean postulate that the shortest distance between two points is a straight line, is merely a hypothesis introduced into discourse without empirical proof. It is crucial to recognize that such axioms can, and often do, prove to be fallacious. For instance, the 'straight line' axiom fails in non-Euclidean geometries, such as those used by GPS systems, which adjust for the curvature of space-time. These systems employ Riemannian geometry, based on axioms that more accurately represent the curvature of space as described by Einstein.
Not very often, but frequently enough, assumption-dependent axioms that appear self-evidently true turn out to be false. Consider the axiom of pairing in ZF set theory, which posits that any set consisting of two elements can be separated into two subsets, each containing one of the elements—an axiom that seems obviously true. However, this axiom encounters issues as evidenced by the empirical disproval of Bell’s Inequality, which is logically deduced using the axiom of pairing. The 2022 Nobel Prize in Physics highlighted this, awarding discoveries related to the behavior of entangled quantum particles like electrons and photons, which do not adhere to traditional set theory predictions. When such particles are the set elements, the axiom of pairing is violated, much like the Euclidean axiom that the shortest distance between two points is a straight line. This inconsistency has led some to suggest that theoretical physicists should work on developing a better set theory, though funding and focus in this area remain limited. The point here is that any axiom could prove false under specific circumstances, and this potential for error fuels intense debates, particularly regarding whether assets like gold, used by central banks as reserve assets but not as a medium of exchange, should be considered 'real' money. Despite such debates, there is no controversy surrounding the following established facts:
There is no debate that money has taken many forms throughout history, from cattle and tobacco leaves to cowrie shells, and from gold and silver coins to the present day's diverse currencies. These various currencies—considered units of account in mathematical economics, or simply ‘money-units’—actively facilitate global trade. This diversity is exemplified by the approximately 30 different currencies actively traded on the Forex market. Each of these money units, such as the Euro (EUR), is recognized as a valid fiat currency within its respective country or regional economy.
Moreover, there is a universal consensus on the three essential functions that any form of money must fulfill within the economies that utilize it. According to the St. Louis Federal Reserve2, money historically and presently serves as a unit of account ("U"), a store of value ("S"), and a medium of exchange ("E"). These roles, encapsulated under the mnemonic "USE," provide not only a practical framework for this discussion but also anchor our analysis. We posit as an axiom that the more effectively a currency performs these three U·S·E functions, the greater its utility or use-value as money. Consequently, under this axiom, it logically follows as a theorem that in a competitive market, this increased use value will result in a higher exchange value against all other goods and services in the economy, including all competing currencies.
Axiomatic Definition of Money:
Within the Arrow-Debreu framework, money is a unit of account, encapsulating the entire spendable money supply within an economy. In the context of the US dollar, this spendable money supply is identified as the M2 money supply, which is estimated by the Federal Reserve Bank. M2 includes all immediately spendable on-demand funds, such as cash, balances in checking and savings accounts, and money market funds—all denominated in US dollars and available for immediate expenditure. By defining "U" as the spendable supply, such as M2, we can distinctly analyze its usage in two functional roles: as a medium of exchange and as a store of value.
Formula Representation:
In our framework, the total money supply within an economy, denoted as U, is conceptualized as the sum of money used as a store of value (S) and as a medium of exchange (E). This relationship is succinctly expressed by the formula: U=S+E
This formula serves as the cornerstone of our analysis, illustrating how the spendable money supply is distributed between its primary functions. It quantitatively captures the dual roles of money, facilitating a deeper understanding of its operational dynamics within the economy.
Definitions:
U represents the total money supply and serves as the unit of account. It encapsulates the complete scope of monetary assets within an economy, aligning with the Arrow-Debreu conceptualization of money: as a unit of account in which prices are determined. This conceptual framework is detailed in the referenced Harvard paper on a Walrasian theory of money.
S denotes the segment of the money supply held as a store of value. This includes assets not utilized in immediate transactions but reserved for future use or savings. Examples include gold coins stored in a vault or funds maintained in savings accounts that are not invested in bonds—a situation John Maynard Keynes identified as a liquidity trap in 1934. These funds (S) serve to store purchasing power, contrasting with more liquid uses like spending or investments in bonds. This definition highlights the role of S in providing financial security and stability by retaining value over time.
E is the portion of the money supply actively utilized as a medium of exchange. This includes the money you receive as wages and subsequently spend on essentials like rent, groceries, or services. It encompasses all money that circulates within the economy, facilitating transactions and payments for goods and services. This definition aligns with the historical understanding of money by Jevons, Menger, and Walras, who recognized it as a crucial medium to solve the double coincidence of wants problem inherent in direct barter.
Explanation:
The equation U=S+E provides a structured way to view the total money supply by distinguishing its distinct uses: E for transactional purposes and S for savings or deferred spending. This formula effectively underscores the dual functionality of money, separating the active components from the inactive within the total monetary assets, denoted as U. Analyzing these roles offers deeper insights into the dynamics of money and their implications for economic policy and analysis. This approach not only harmonizes economic theory with practical monetary applications but also furnishes a clear, formulaic expression that elucidates the multifunctional nature of money.
What we are stating here is, in fact, quite straightforward: you can either save or spend your money, but you cannot do both at the same time—much like you can’t have your cake and eat it too. This 'exclusive dual-use' principle posits that money operates either as a store of value or as a medium of exchange on demand, but not simultaneously, except in cases such as bounced checks or other forms of counterfeiting or fraud. The function of money as a unit of account is intricately linked to these exclusive dual-use roles (expressed as E xor S).
Money, as a unit of account, thus serves not only to measure purchasing power (or wealth/value, terms that are synonymous in this context) as a store of value, but also to quantify the prices of goods and services during its use as a medium of exchange. The formula U = S + E encapsulates this relationship, aligning with empirical data from the Federal Reserve as well as the theories of Arrow, Debreu, Jevons, Menger, Walras, and others. Typically, this would be the juncture at which we would proceed to the next section. However, for you, dear reader, this paper includes a little 'extra'.
As we aim to deepen the academic rigor of this paper suitable for a scholarly journal, we now introduce a more mathematical perspective. This section is particularly designed to illustrate how our definition of money aligns with the first welfare theorem of mathematical economics. For those with less interest or background in mathematical formulations, it's important to note that the understanding of this next section is not crucial for the remainder of the paper. Its inclusion is intended primarily for theoretical substantiation. If you prefer, you may skip this technical exposition and proceed directly to the subsequent section, entitled "What Makes Money ‘USE’-able?"
The Arrow-Debreu Model: Exploring its Foundations and Implications in Economic Theory
The Arrow-Debreu model stands as a cornerstone of mainstream economic thought, significantly influencing various sectors, including policy-making. Institutions like the Federal Reserve rely on its principles to guide key decisions, such as setting interest rates. The widespread adoption of the model is supported by its rigorous mathematical formalism, which provides a definitive mathematical proof of what Adam Smith posited in 'The Wealth of Nations' in 1776—namely, that labor specialization enhances productivity.
Similar to the still unproven Riemann Hypothesis, the Adam Smith hypothesis remained theoretical until Arrow and Debreu mathematically substantiated it in 1954, showing that labor specialization, under perfect market conditions, leads to optimal welfare outcomes. Through independently verifiable logical deductions, the Arrow-Debreu model rigorously validates this principle, cementing its role as a critical component of both economic theory and practice.
Paramount in its foundational significance, the first welfare theorem of mathematical economics, pivotal to the Arrow-Debreu model, asserts that under ideal market conditions—characterized by free trade and symmetric information—a Pareto efficient outcome is inevitable. In such an environment, devoid of externalities and monopolistic influences, all goods become freely tradable. This setting compels participants, who function simultaneously as consumer-producers, to inherently pursue the maximization of their individual welfare. Each transaction in this ideal market naturally aligns with their self-interest, collectively guiding the economy towards an optimal distribution of resources where no individual can be made better off without making someone else worse off.
Within this idealized market framework, free trade is inherently mutually beneficial or Pareto-improving, guiding the economy toward a state of Pareto efficiency. In this optimal state, no individual can enhance their welfare without consequently diminishing another's. Key conditions, such as the diminishing marginal utility of consumption, are crucial as they ensure that the objective function remains convex, facilitating the optimization process. However, optimizing the convex sum of everyone's collective subjective utilities presents a significant challenge, due to their inherently unmeasurable nature by third parties, and often, even by the consumers themselves. Quantifying the subjective benefit of experiences in absolute terms—such as measuring the relief of stepping into an air-conditioned room on a hot day in hypothetical 'utils'—is practically impossible, even subjectively by the consumer. This predicament highlights the role of money as a unit of account in mathematical economics, which aids in translating these subjective utilities into quantifiable terms, thus enabling economic analysis of decision-making that encompasses a broader range of human experiences.
In the Arrow-Debreu model, money plays a pivotal role as a unit of account by quantifying subjective utilities in monetary terms, thereby facilitating the optimization of collective welfare through the maximization of these monetary rankings. In this framework, consumer-producers engage in mutually beneficial trade by exchanging the fruits of their labor—measured in wages or other forms of income—for goods and services produced by others. In this model, money serves a dual function: it facilitates transactions as a medium of exchange and quantifies the subjective expected benefits (or utility) of purchases against the subjective costs, which are predominantly determined by the time invested in labor. Additionally, in scenarios where money is not actively used for immediate payments, it seamlessly transitions to serving as a store of value, thus fulfilling its universally recognized roles: unit of account, medium of exchange, and store of value.
The mechanism enabling the gradient descent optimization of welfare in a perfect market is the mutual benefit derived from unfettered and symmetrically informed trade. This ensures that each participant—whether acting as a consumer or a producer—experiences a benefit from their transactions. This principle requires that all parties involved in a trade derive ‘surplus’, which is crucial for achieving a Pareto-improving outcome. Such outcomes lead to Pareto efficiency, where the economic condition of one party cannot be improved without worsening the condition of another.
Producer surplus is relatively straightforward to measure—it represents the difference between the price at which goods are sold and their total, all-encompassing or "economic" cost of production. This cost includes not only direct expenses like materials and labor but also all opportunity costs associated with the production process. For instance, in the context of real estate, the opportunity costs might include expenses for advertising an apartment, the time spent by the owner or managers in collecting rent, performing repairs, and managing tenant relations, including the eviction of non-paying tenants. Each of these elements represents an investment of resources that could have been used elsewhere, and their inclusion is crucial for accurately assessing the economic profitability of property management.
Unlike producer surplus, consumer surplus cannot be directly quantified because it is inherently based on the subjective perceptions of benefit and cost to the consumer. This is precisely why money is essential for defining consumer surplus, which is calculated as the difference between the maximum price a consumer is willing to pay for an item and the market price at which the item is actually purchased. For example, the consumer surplus on an iPhone would be the difference between what a consumer is prepared to pay for it, based on their personal valuation, and what they actually pay at the store.
Money plays a pivotal role in this context as a unit of account, aiding in the quantification of the subjective cost of an item. This cost is often measured in terms of the time required to earn the income necessary for the purchase, typically calculated in wages. This measurement captures not only the financial expense but also the effort and time investment that the consumer perceives as equivalent to the value of the product. Therefore, consumer surplus offers a valuable insight into how much more value consumers subjectively receive from their purchases compared to the labor they expend to earn the necessary income. This illustrates the personal economic benefit derived from market transactions.
Indeed, while consumer surplus is inherently subjective, it is intrinsically linked to monetary units because the amount a consumer is willing to pay for a product reflects their perceived benefit from the purchase. Although we cannot conclusively determine that a consumer derives twice the subjective benefit from buying Product A (Bentley) compared to Product B (Ford) simply because the price of A is twice that of B, we can assert that the consumer perceives a greater benefit from Product A, as evidenced by their willingness to pay more. This willingness to pay provides a quantifiable measure, not of the perceived benefit itself, but of its relative value compared to other choices.
Measuring subjective utility directly is inherently challenging. However, an approximation can be achieved by observing the rate at which goods and services are consumed over time. This rate of consumption can be mathematically expressed in monetary units as equal to rank(dU/dT), or E=R(dU/dT), where dU/dT represents the rate of change in subjective utility with respect to time. Money plays a pivotal role here, not only quantifying this rate but also serving as a critical unit of account and a measure of purchasing power. Its dual function is intertwined with its capacity as a store of wealth, effectively modulating consumption rates. This highlights the essential function of money as a unit of account: it quantifies and ranks subjective utilities over time and provides a practical framework for economic analysis and decision-making. By moderating consumption according to financial resources, money fulfills its role as a store of value, preserving purchasing power over time, thereby stabilizing economic interactions and promoting a sustainable economic environment.
An added benefit of the U=S+E framework is that local nonsatiation is no longer merely an assumption—it logically emerges from our axiomatic framework, which leverages a fundamental principle of biology: evolution necessitates selection. In humans, this selection often manifests through female choice, with females typically favoring partners who display traits perceived as desirable. Although these traits vary across different times and cultures, a common binding constraint for most males is the availability of purchasing power when signaling their relative social ranking. This dynamic inherently guarantees local nonsatiation when measured in units of money—which not only serves as a unit of account, measuring purchasing power but also functions as a store of wealth due to its acceptance as a medium of exchange. To reiterate, individual males are inherently motivated to enhance their relative status to attract the most desirable partners. In this pursuit, the capacity to store and accumulate wealth becomes a crucial factor. Money, in its role as a store of wealth, acts indirectly as a consumption constraint that males strive to minimize relative to other competing males, thereby maximizing their reproductive success with females.
This willingness to pay more effectively translates subjective utilities into quantifiable monetary units. This translation enables us to assert with certainty that higher trading volumes in terms of dollars signify increased overall welfare, provided these trades are genuinely mutually beneficial. This conclusion is analogous to how the Pythagorean theorem follows from Euclidean axioms in geometry, which assume the shortest distance between two points is a straight line. By quantifying these utilities, we gain valuable insights into consumer preferences and economic dynamics, thereby enhancing our understanding of market efficiency and consumer behavior.
Recalling our middle school mathematics, we understand that the accuracy of logical proofs is guaranteed because they are independently verifiable. Many, even those as young as fifth graders who are capable of mathematical reasoning, have proved the Pythagorean Theorem. However, the truths established through such proofs are conditional rather than absolute.
This is because if the foundational Euclidean axioms were incorrect, then the Pythagorean theorem would not hold. For instance, Einstein’s adoption of Riemannian geometry to describe curved space-time underpins a more accurate model of the universe, challenging traditional Euclidean views. This concept is practically applied in technologies like GPS, which must account for time dilation effects due to the differing speeds of clocks on satellites compared to those on Earth. Consequently, in our objective reality, where GPS technology is indispensable, the shortest distance between two points is not necessarily a straight line.
Similarly, the Arrow-Debreu model, despite its rigorous mathematical structure, faces limitations due to its often unrealistic assumptions about real-world economies. When fundamental assumptions, such as unfettered trade, are not met, the model’s predictions fail to capture the complexity of actual market dynamics. This shortcoming is exemplified by George Akerlof's study in the market for 'lemons', where asymmetric information leads to suboptimal outcomes. A more striking illustration is the stark disparity in per capita GDP between Haiti and the Dominican Republic, attributable to the prevalence of involuntary exchanges in Haiti. Such conditions contravene the unfettered trade assumption posited by the first welfare theorem of mathematical economics and by Arrow-Debreu, underscoring the critical importance of adhering to these theoretical prerequisites for achieving efficient market conditions. This discrepancy highlights the inherent limitations of applying theoretical economic models without considering the variability and unpredictability of real-world economic environments.
As a quick side note, violations of two specific Arrow-Debreu conditions—voluntary exchange and symmetric information—are particularly detrimental to economic efficiency, both theoretically and practically. Notably, Jensen and Meckling have highlighted the inefficiencies, termed 'agency costs,' that arise from asymmetric information in their seminal work, 'The Theory of the Firm3.' However, violations of voluntary trade assumptions can be even more detrimental to economic efficiency than information asymmetries. This is starkly evident in former Soviet Union republics, where despite abundant natural resources and a well-educated population, real GDP growth has been severely hampered by numerous instances of involuntary exchanges, similar to those observed in Haiti.
In these former Soviet Union countries, involuntary exchanges do not manifest as robbery or theft due to general lawlessness, as seen in Haiti, but rather primarily through bribes and the expropriation of assets by politically well-connected individuals, such as FSB colonels. These activities are tolerated by the governing coalitions as a means to generate what effectively amounts to bribes or other wealth transfers to those in charge of law enforcement. This arrangement secures the loyalty of law enforcement officials to the ruling government by allowing them to engage in corruption as compensation for their support. This leads to a sub-optimal form of a stable Nash equilibrium—akin to the sub-optimal outcome in the Prisoner’s Dilemma where accomplices betray each other instead of cooperating for an optimal outcome. This type of equilibrium, defined by corruption, persists across all former Soviet Union republics, from Ukraine to Russia. The widespread persistence of involuntary exchanges starkly contradicts the Arrow-Debreu model’s assumption of unhindered trade, naturally leading to inefficiencies—from Haiti to former Soviet Union countries and beyond.
In this discussion, the term ‘involuntary exchange’ specifically refers to violations of the unfettered trade condition posited by the Arrow-Debreu model of mathematical economics, which is essential for achieving Pareto efficiency. This condition asserts that all trade should be voluntarily entered into by both parties, without duress, entirely of their own free will, and unhindered. Acts like robbery and theft are clear examples of involuntary exchange — unambiguous crimes punishable by prison terms in a proper legal system. However, the situation with taxes is more nuanced. In a competitive, free-market economy, taxes do not inherently constitute involuntary exchange, although they can. The crucial distinction lies in whether such taxes lead to market failures—defined by transactions that are not mutually beneficial. Taxes that result in involuntary exchange ultimately reduce welfare and productivity efficiency, as they prevent trades from being Pareto improving due to their non-mutual benefits, thereby tending to diminish rather than increase overall individual welfare.
From an economics perspective, a citizen owning property in a country like France is fundamentally no different from any other fractional ownership of property, such as you owning a condominium. Just as your condominium association collects fees necessary to maintain the property and its common areas—such as gyms, restaurants, and front desks, all staffed by employees whose salaries must be paid—so too does a government collect taxes. When taxes are utilized to provide services that are needed and benefit everyone, such as police departments, the military, the legal system, and even welfare payments aimed at minimizing police budgets, they are generally considered mutually beneficial exchanges. Similarly, paying condominium fees or rent is not an involuntary exchange but rather compensation for services rendered, and therefore such taxes do not fall under the classification of involuntary exchanges.
However, as those familiar with condominium associations can attest, barring rare exceptions, there is a propensity for corruption among condominium boards. This often manifests as management pilfering fees for personal benefit, a scenario that aligns with the concept of agency costs described by Jensen and Meckling. Moreover, this situation parallels public choice theory and rent-seeking behaviors, particularly in the context of government tax pilfering. Although Gordon Tullock contributed significantly to these theories, it was James Buchanan who was awarded the Nobel Prize for his work in this field. This comparison sheds light on similar challenges in both private and public sectors regarding the management and allocation of collected funds. The imposition of taxes and regulations through rent-seeking—such as the prohibition of the sale of raw milk, while allowing the sale of raw oysters and eggs—illustrates examples of involuntary exchange that may lead to market failures.
It is fascinating how even those not formally trained in economics often intuitively recognize market failures in situations where individuals seek to gain wealth without making a reciprocal contribution to productivity — effectively what Gordon Tullock defined as economic rents. This concept aligns notably with Lenin's idea of 'from each according to his ability, to each according to his contribution,' where economic parasites are those who consume goods and services produced by others without participating in their production — a characterization often attributed to the capitalist class. This principle of 'from each according to his ability, to each according to his contribution' is effectively realized within the Arrow model in a perfectly competitive market, as it aligns the marginal revenue of labor with its marginal cost, thus avoiding the pitfalls of policies based on involuntary exchange. Achieving efficiency, as measured by real per capita GDP, without unfettered trade is not impossible. However, it requires significant measures to mitigate agency costs and rent-seeking behaviors. Historically, such measures have included the use of extensive surveillance ('stukachi') and punitive systems like the gulag under Stalin’s regime, underscoring the severe trade-offs required.
This discussion serves to align the existing theory of mathematical economics, particularly the Arrow-Debreu model, with our USE definition of money within this paper. It holds no other significance within this context, although its relevance may extend to broader contexts. To recapitulate formally: in a perfect market, mutually beneficial trade not only enhances Pareto efficiency but also represents a real-world application of gradient descent optimization. Such trade reaches an optimality condition where the gradient of the objective function is zero, defining a state of Pareto efficiency where no individual can improve their welfare without diminishing someone else's. This trade necessitates the use of money not merely as a medium of exchange, as initially proposed in the mid-1870s, but also as a unit of account and a store of value. This scenario underscores a fundamental economic principle: under ideal conditions, free trade utilizing money in its U=S+E roles maximizes overall welfare without disadvantaging any participants. Consequently, it logically follows as a theorem that in a competitive free market, the effectiveness of currency in fulfilling its three essential roles—unit of account, medium of exchange, and store of value—directly enhances the ability of consumer-producer representative agents to maximize collective welfare. Thus, a well-functioning currency in a competitive, free-market economy is crucial for optimal economic outcomes.
What Makes Money ‘USE’-able?
Having established that the roles of money are intricately entangled, as encapsulated by the U = S + E equation, where money serves not only as a unit of account (U) and a medium of exchange (E) but also transitions into a store of value (S) when not utilized for exchange, it is crucial to examine what enables a currency to fulfill these functions effectively. For instance, for money to function efficiently as a medium of exchange, its smallest denomination, such as a penny, must be sufficiently small to facilitate convenient transactions. It turns out that to perform effectively in all three roles—unit of account, medium of exchange, and store of value—specific dual requirements are essential. These requirements, necessary for each role to be adequately fulfilled, are outlined below, with a detailed discussion to follow.
Unit of Account (U):
This role necessitates not only a stable supply—akin to the constant length of a ruler—but also divisibility—similar to a ruler marked in increments of 1/8th of an inch, reminiscent of the era when stocks on the NYSE traded in 1/8th of a dollar increments before the shift to decimalization, which introduced a minimum price variation of one penny
Store of Value (S):
For money to serve as an effective store of value, it must be both secure and accessible. It should be difficult to steal, which underscores the importance of a stable money supply and illustrates the interconnectedness of the U (unit of account) and S (store of value) roles. Furthermore, the money must be readily accessible; for example, gold buried on a deserted island does not serve as an effective store of value due to its inaccessibility
Medium of Exchange (E):
To effectively serve as a medium of exchange, money must be easy to transfer and simple to authenticate. Cash and gold coins are exemplary in this regard; they are readily used for payments and their authenticity can be relatively easily verified, thus minimizing the risk of counterfeit transactions
In summary, by evaluating any currency from this 'USE' perspective, we can gauge how well it functions as money and how this effectiveness as a monetary unit correlates with its exchange rate relative to competing currencies. Let us start with gold coins as our first example.
Title: What Makes Money ‘USE’-able?
[Scene 1: Introduction]
Narrator: "Hello, everyone! Today we're going to talk about money! Not just any money, but what makes money really useful. We use a special formula called U = S + E to understand this better. Let’s dive in!"
[Scene 2: Unit of Account]
Narrator: "First up is U, which stands for Unit of Account. Imagine if you had a ruler that changed size every day. It would be really hard to measure anything correctly, right? Money needs to be like a good ruler—always the same length so everyone knows what it’s worth. Just like a ruler with marks that help us measure things, money needs to be divided into smaller parts, like dollars and cents, so we can use it easily."
Character (Kid with a ruler): "So, having money divided into dollars and cents makes it a great tool for measuring how much things are worth!"
Narrator: "Exactly! But that’s not all. The amount of money available, what we call the money supply, also needs to be stable. If it changes too quickly, it can lead to inflation or deflation, which are like our ruler suddenly stretching or shrinking. That would make it tough to know the real value of things, wouldn't it?"
Character (Kid with a ruler): "Totally! Just like the length of a ruler needs to stay the same, the amount of money out there should be steady too, so it can be good at telling us how much things really cost!"
[Scene 3: Store of Value]
Narrator: "Next is S, which means Store of Value. Money should be safe and easy to keep until you need it. If you buried your toy in a forest and couldn’t find it, that wouldn’t be very useful, right?"
Character (Kid with a treasure chest): "I keep my money in a piggy bank so I know it’s safe and I can get it when I want to buy something special!"
[Scene 4: Medium of Exchange]
Narrator: "Last is E for Medium of Exchange. This means you can easily give it to someone else when you buy things. Money should be easy to carry, and it’s important that everyone can tell it's real, not fake."
Character (Kid with toy cash register): "That’s why I like using money to buy ice cream. It's simple to hand over, and everyone accepts it! Plus, I know how to spot if someone tries to give me a fake coin—it looks and feels different from the real thing."
Narrator: "Exactly! Money being easy to recognize and accept means you can buy things quickly without any fuss. Whether it's toys, books, or even a delicious ice cream, money helps make the exchange smooth and simple."
[Scene 5: Conclusion]
Narrator: "So, when we look at money with our U = S + E glasses, we can see if it’s doing a good job as a unit of account, a store of value, and a medium of exchange. Let’s start with gold coins. They're shiny and valuable, but are they good at all these things? Let’s find out in our next episode!"
Character (Kid looking curious): "Can’t wait to learn more about gold coins!"
Narrator: "Thanks for joining us today! Remember, money is amazing because it helps us buy things we need and want. But it has to be good at being U, S, and E to be super useful. See you next time!"
This is the screwed up version — need to fix the script and re-do the video:
What Makes for Good Money: Some Case Studies
Let us begin this section by summarizing our discussion so far. Money serves three primary functions, denoted as U (Unit of Account), E (Medium of Exchange), and S (Store of Value). To be an effective unit of account—a term interchangeable with 'unit of measure' in the context of monetary units—a currency must be both divisible and have a stable total supply. As a store of value, it must be easily retrievable by the owner, yet as difficult as possible for anyone else but the legitimate owner to access. Lastly, to function optimally as a medium of exchange, a currency must be easy to transfer and difficult to counterfeit, akin to cash or gold coins.
With these criteria established, let's delve into some historical use cases, starting with one of the earliest forms of money: cattle. Before we do, however, let's consider a provocative question. Why, in a country like the United States, which offers unprecedented freedoms in terms of property ownership and is considered one of the best places on Earth to live, is carrying large amounts of cash often treated with suspicion, sometimes even equated with money laundering or seized under asset forfeiture laws without the same protections afforded to other forms of personal property like jewelry or vehicles?
This peculiar scenario underscores the competitive dynamics between different forms of money and payment systems. Cash, being a direct, low-cost way to make payments, poses a competitive threat to more traceable and profitable payment methods promoted by financial institutions, which lobby for regulations that discourage cash usage.
At TNT-bank, we've recognized this challenge and developed a solution. Our system allows any issuer to independently verify the identity of both the spender and the recipient of each payment, enabling any government-licensed bank, no matter how small, to use TNT-bank money as their general ledger while remaining fully compliant with all laws.
Consider the differences between making a credit card payment versus a cash payment. When you pay a merchant with cash, the $20 bill you hand over remains exactly $20 in the merchant’s possession. In contrast, when you use a credit card, the $20 you charge is subject to a fee, usually around 3%, which the merchant must pay to the credit card company. Thus, of the $20 you spend, the merchant receives slightly less, losing out on about 60 cents due to processing fees. This wealth transfer, though seemingly small per transaction, accumulates significant costs for end users—both consumers and merchants—benefiting the credit card processor instead. This underscores why cash remains the most cost-effective payment option, aside from TNT-bank funds, which we will discuss later. But first, let’s return to our historical exploration with cattle as one of the earliest forms of money.
As a unit of account, cattle can serve effectively, provided that the number of cattle remains constant and a single cow represents a sufficiently small unit of price variation. Indeed, cattle, to a considerable extent, make for a reasonable currency. As a store of value, cattle are notably difficult to steal and relatively easy to transfer, qualities that also make them a good medium of exchange. Moreover, the authenticity and quality of a cow are relatively simple to verify, making transactions straightforward. Of course, the stability of this 'money supply' can be threatened by factors like mad cow disease, but then again, managing a currency system is seldom straightforward.
Throughout history, various forms of currency have been utilized, each meeting the outlined criteria to varying degrees. However, gold and silver emerged as dominant currencies for many centuries, particularly under the bimetallic standard. Dating back to the Middle Ages, gold and silver coins were widely circulated. Notably, the exchange rate between gold and silver coins remained remarkably stable at 15-1, with one gold coin consistently valued at 15 silver coins. This stability endured despite fluctuations in the available supply of gold and silver. The enduring stability of this price ratio can be attributed to the fact that both metals derived much of their 'use-value' from being utilized to mint circulating money.
Here, we employ the term 'use-value,' introduced by Aristotle, to distinguish an object's utility to an individual consumer from its exchange value, represented by its monetary price. Despite Marx's use of Aristotle's terminology in his writings, we adopt Aristotle's language for clarity, undeterred by its association with Marx.
The advantages of using gold and silver coins as units of measure are clear. As units of account, their stable supply ensures that the length of the 'ruler' remains constant, enabling precise measurements of the relative prices of goods and services. Additionally, the malleability of these metals allows for the production of coins in various denominations, facilitating transactions of different sizes. Moreover, when adjustments to the Minimum Price Variation (MPV) are necessary, as demonstrated when the New York Stock Exchange transitioned from pricing stocks in fractions (1/8ths and 1/16ths) to pennies, similar modifications can be implemented by altering the gold and silver content of minted coins. Although such practices had predictably adverse consequences during periods like the Roman Empire, due to the expansion of the spendable money supply, they underscore the adaptability of gold and silver coins as units of account. This adaptability, distinct yet closely related to their role as a medium of exchange, will be the focus of our next discussion.
As mediums of exchange, gold and silver coins function effectively for direct transactions. However, they fall short in scenarios requiring remote payments, such as placing a deposit on a Ferrari that will be manufactured in Italy while you are in New York. In such cases, the physical delivery of gold and silver coins as a deposit presents a logistical challenge. Except for such situations, transferring a gold or silver coin directly to another person is straightforward and incurs no additional cost. When it comes to high-value transactions like purchasing a Ferrari, alternatives such as cash on delivery are typically available, circumventing the need for international wire transfers. Thus, while gold and silver coins are generally reliable as mediums of exchange, they are less suited for complex, international financial transactions. But this is not the only reason why banks are needed.
The role of money as a store of value is where both gold and silver coins, and commodity money in general, fall short. Commodity money is inherently easy to lose due to its physical nature. It can be pilfered, stolen, or otherwise lost in numerous real-world scenarios. Examples range from routine theft and household pilferage to government confiscation, such as the 1933 incident in the United States when President Roosevelt mandated the handover of all gold used as money. These vulnerabilities stem from the tangible and portable nature of physical coins, making them susceptible to various forms of loss.
It is precisely to diversify the risk of physical loss associated with commodity money that bank money emerged as a solution. In the United States, up until 1933, bank money represented fractional ownership of gold stored in the banks' vaults. However, the issuance of excessive fractional ownership certificates—represented by bank money such as cash, checking, and savings account balances (collectively known as M2)—was backed by insufficient gold reserves. This imbalance contributed to the Great Depression, but that's a discussion for another time. Essentially, while bank money reduces the risk associated with the physical possession of commodity money, it introduces counterparty risk from the issuer itself. This risk can lead to an expanded money supply, devaluing the currency and undermining its effectiveness as a unit of measure. This is why fiat currencies, which have been known about since as early as 800 years ago in ancient China, were historically avoided—they presented excessive issuer counterparty risk.
This issuer counterparty risk, stemming from asymmetric information regarding the timing and magnitude of expansions in the US dollar M2 money supply, remains a significant concern. To mitigate this risk, central banks maintain gold as a reserve asset, capitalizing on its enduring value and stability. Today, all major central banks hold substantial gold reserves as part of their strategies to stabilize their currencies. Additionally, central banks in countries like China and Russia, which face higher counterparty risks with US dollar reserves, have been actively increasing their gold holdings. This sustained use of gold, effectively as a reserve currency, alongside its widespread role as a means to store and preserve purchasing power outside of central banks, has significantly impacted the precious metals market. Specifically, the price ratio of gold to silver has escalated to over 80:1, largely because silver ceased to be used as money after the 19th century. Thus, the market price (or exchange value) of gold is determined primarily by its use value as money, rather than as a commodity. In contrast, silver, which lacks a monetary use value due to being demonetized between 1850 and 1890 by all major economies of that era, is primarily valued as a commodity.
This strategy of using gold as reserves serves not only as a hedge against known risks of currency devaluation but also as a safeguard against the unknown, particularly the uncertainties associated with relying on foreign reserve currencies, which are ultimately backed only by the issuing government's promise to meet its tax obligations—a key principle emphasized by Modern Monetary Theory (MMT). Indeed, this promise, combined with central bank gold holdings, forms the foundational support for the value of all fiat currencies. Additionally, the use of government authority to enforce the adoption of its fiat currency for transactions can influence currency value, though as the case of the Venezuelan Bolivar demonstrates, this does not inherently confer value. Over the long term, the spendable money supply of any fiat currency, such as the US dollar—which is currently considered the most stable fiat currency—will likely grow at a rate significantly higher than the supply of gold. This growing disparity is reflected in the relative prices of gold and the US dollar. The broader implications of this disparity, however, warrant further exploration in a separate discussion. This viewpoint is supported by a consensus presented in a referenced Harvard paper, which affirms that the instability of the fiat money supply is inevitable — as politicians are unlikely to raise taxes when they can simply print more money. Even if King Solomon, guided by divine wisdom, were to manage the Fed, instability in the spendable money supply would still occur due to rent-seeking behaviors.
It is precisely for these reasons that cryptocurrencies are perceived as highly valuable in the marketplace. They approach the ideal of what money could be—decentralized, stable, and not bound by the whims of policy changes. Curious to learn exactly how? Discover the potential of cryptocurrencies and how they compare to traditional forms of money by visiting us at tnt.money! However, our exploration doesn't end here. While this paper has already exceeded its intended length, we conclude it by showing that replacing MV with EV transforms the equation MV = PY from a theoretical model into a comprehensive accounting identity. Fear not; there is still plenty more to explore in future discussions. These will include the intriguing realms of 'mathecon game theory black papers' (distinct from white papers) and subjective logical claim rings — an abstract algebraic structure designed to formally and mathematically model cognitive biases without resorting to labeling individuals as irrational.
Practical Example of the U=S+E Formula
Let's explore the quantity theory of money and the concept of the money supply using the U=S+E formula. Consider the M2 money supply in the US, which currently stands at approximately $21 trillion. This amount represents the unit of account (U)—the total money supply in the economy that is available for spending or saving. In this example, we assume that $15 trillion of the total money supply is actively used to facilitate transactions, denoted as E (exchange). The remaining $6 trillion, represented as S (savings), indicates the portion of the M2 money supply that is held as a store of value or savings.
The M2 money supply, also referred to as the spendable money supply, is designed to reflect the concept akin to the number of minted gold coins in a bank-less monetary system. It represents the portion of the money supply that is available for use as a medium of exchange. Classified by the Federal Reserve Bank, the M2 includes all money units that are readily accessible for transactions. This encompasses cash, checking account balances, as well as savings accounts and money market funds. These are considered liquid assets due to their ability to be quickly mobilized for transactions through various methods such as wire transfers, check writing, or electronic transfers, thus all equally and effectively serving as viable mediums of exchange.
People often utilize bank accounts, a component of the M2 money supply, to store funds when short-term liquidity is necessary. This could involve covering margin calls or unforeseen medical expenses, showcasing a key use of money as the most liquid asset: a store of value. In environments characterized by low interest rates and minimal inflation, savings accounts often become preferable to bonds. This preference arises from their greater liquidity and lower risk. Unlike bonds, where prices can decline if yields rise, the balance in a savings account remains stable. Consequently, using M2 components like bank accounts as savings vehicles becomes particularly appealing during periods of low interest rates, as cash assures that yields cannot turn negative and drop, though yields can always increase, as they did.
The Stock Market as a Metaphor for Money's Accounting Identity
Contrary to common perception, the quantity theory of money is actually an accounting identity and not a theory, because it can be expressed as a tautology based on arithmetic laws. This concept finds a parallel in the financial realm, specifically in Bill Sharpe's 1991 paper titled "The Arithmetic of Active Management." Sharpe shows that, when considered collectively, active investors cannot outperform the market. This is because, collectively, these investors own the market—or more precisely, the segment of the market portfolio not held by passive investors. Sharpe’s findings underscore a reality governed by accounting principles rather than theoretical speculation.
Similarly, the quantity theory of money establishing a straightforward arithmetic relationship (an accounting equality) between inflation and nominal GDP. Nominal GDP, defined as the total market value of all final goods and services produced and consumed within an economy by end users, is distinct from gross output. Gross output includes all production activities, not just the final products that contribute to GDP but also intermediate goods consumed during production, such as the lumber used in making furniture.
The quantity theory of money posits as an axiom the following equation: MV=PY, which, when each variable is precisely defined within the realm of mathematical economics, emerges as a straightforward accounting identity. Let's delve into what each variable stands for in this particular equation:
'P' represents the Price Level, a core concept in macroeconomics that serves as a formal indicator of inflation. Inflation is typically gauged by the Consumer Price Index (CPI), which tracks the general price level of a diverse basket of goods and services. This basket is carefully selected to mirror the composition of the broader GDP, acting as a barometer for average price movements over time. Thus, 'P' is crucial for understanding the cost of living, as it reflects the financial outlay required to purchase this representative basket of goods and services. The CPI is calculated by averaging the price changes of these goods and services, weighted by their significance or share in the typical spending patterns of households. For example, if households, on average, allocate forty percent of their income to housing, the change in housing prices will carry a weight of 0.4 in the CPI calculation. This method ensures that the CPI accurately reflects how price changes affect the average consumer, offering a realistic picture of inflation and its impact on daily life.
'Y' represents the 'Volume of Final Goods and Services,' or real Gross Domestic Product (GDP). This metric quantifies the total amount of goods and services produced and consumed within an economy, focusing on the physical output without the distortions due to price changes. In essence, 'Y' measures the economy's overall productive capacity and output in real terms, providing a snapshot of economic activity and health.
By combining 'P', the Price Level, with 'Y', the Volume of Final Goods and Services, we arrive at nominal GDP. This measurement, as defined in economics, encapsulates the total of all transactions within a year. It's calculated by multiplying the quantity of items purchased by their price, thus determining the overall value of trading activity during a fiscal year in an economy. A crucial detail of this calculation is the exclusion of intermediary consumption, aligning with the strict definition of nominal GDP in economics. Essentially, nominal GDP offers a thorough overview of the economy's output in dollar terms, reflecting total spending on final goods and services without adjusting for price fluctuations.
Using the stock market as an analogy can help illuminate the concepts of real and nominal GDP. Real GDP is akin to the share trading volume of the S&P 500 index, representing the quantity of transactions. In contrast, nominal GDP parallels the dollar trading volume, reflecting the total value of these transactions.
Expanding on this comparison, think about how the return on a market index, like the S&P 500, is determined. It's typically calculated as the weighted average of the returns on individual stocks, with the weights based on their market capitalization. In a similar vein, calculating CPI inflation resembles computing the return on the S&P 500, but with a twist: instead of using market capitalization as the weight, it uses the past year's dollar trading volume for each stock. This approach is analogous to how CPI inflation is calculated by weighting the price changes of goods and services according to their share of total spending. This method prioritizes the impact of price changes on the average consumer, focusing on their spending habits rather than the absolute economic size or significance of the goods and services.
By understanding 'PY' as Nominal GDP—or, in our stock market analogy, the dollar trading volume of the S&P 500—we can delve deeper into the mechanics of the economy. If we take this dollar trading volume and divide it by the portion of the money supply that actively participates in these transactions (referred to as 'E' in the context of the equation 'U = S + E', rather than the entire spendable money supply, or 'M2', which is 'U'), we uncover an accounting identity. This identity illustrates how Nominal GDP, or the total economic activity in dollar terms, can be viewed through the lens of transactions facilitated by money serving as the medium of exchange.
This method enhances our understanding of economic dynamics by centering on the money that's actively facilitating transactions, rather than the entire pool of money that's potentially available for spending. It highlights the pivotal role of active, circulating money in propelling economic activities, reinforcing the idea that it's not the money lying idle but the money in motion that energizes the economy.
The 'MV' part of the equation sheds light on why some view MV=PY as theoretical rather than an accounting identity; this perspective often stems from misconceptions about what 'M' (money supply) and 'V' (velocity of money) represent. In the formula U=S+E, 'U' represents the total M2 money supply when we’re looking at the broader picture of available money.
However, in the discussion surrounding the MV=PY equation, 'M' aligns specifically with 'E', not 'U'. In this sense, the real quantity theory of money posits that EV=PY as the accounting identity, where 'E' denotes the segment of money that is actively engaging in economic activities, distinct from 'S', which indicates saved money. Importantly, 'S' includes funds in savings accounts that are counted within the M2 money supply but excludes investments like government bonds (part of M3) or any other assets not considered immediately spendable or on-demand within M2. Thus, 'S', while part of M2, is viewed as money taken out of the immediate circulation that fuels transactions and broader economic interactions.
This distinction is crucial for understanding the intricacies of money's role in the economy and its impact on overall economic activity. It underscores that the significance of money isn't solely determined by its quantity but also by its velocity—the rate at which it circulates and fuels economic transactions. Drawing an analogy to the S&P 500, where share trading volume velocity reflects the speed at which stocks change hands, highlights this point.
However, unlike the stock market, the volume of transactions in an economy tends to remain remarkably stable over time. Money used as a medium of exchange ('E') is primarily earned as income (typically wages) and spent on purchasing goods and services, contributing to nominal GDP. The repetitive nature of consumption spending—on essentials like clothes, food, rent, and haircuts—reflects our inherent consumer behavior, resulting in a frequency of transactions that remains relatively constant. In essence, unlike share volume in the stock market, the share volume of GDP remains largely consistent.
Therefore, inaccurately calculating 'V' by dividing Nominal GDP by the total M2 money supply (instead of 'E') leads to misconceptions. Any observed changes in 'V' are better understood as shifts in the balance between 'E' (money designated for spending) and 'S' (money saved or invested) within the overall money supply ('U'). This adjustment in perspective shifts the focus from the speed of money's circulation to how the balance between its active and inactive segments evolves over time. It suggests that variations in 'V' reflect changes in the distribution and utilization of money within the economy, rather than simply the rate of its movement. This approach underscores that it's the dynamics of money's distribution and its engagement in economic activities that truly shape economic conditions, rather than just the speed at which it changes hands.
This perspective serves to demystify intricate economic indicators, offering insight into how the quantity theory of money provides a framework for understanding the interplay between money supply, velocity of money, price levels, and economic output. By likening these dynamics to familiar stock market transactions, we can better comprehend how these foundational economic principles manifest in practical scenarios, rendering abstract concepts more tangible and understandable. Additionally, examining the historical correlation between nominal GDP and M2 money supply underscores the significant risks associated with relying solely on the fiat dollar money unit or dollar-denominated fixed-income securities to preserve purchasing power.
This understanding is pivotal for appreciating the multifaceted roles of money within the economy, highlighting the strategic utilization of money to align with financial objectives and prevailing economic conditions. Furthermore, it elucidates how the inherent instability of the fiat money system prompts broader adoption and subsequent price increases of alternative monetary units to fiat currencies, such as gold and cryptocurrencies.
1https://scholar.harvard.edu/files/maskin/files/a_walrasian_theory_of_money_and_barter.pdf
2https://www.stlouisfed.org/education/economic-lowdown-podcast-series/episode-9-functions-of-money
3Jensen's later work, particularly his seminal paper "Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers" (1986), explores how agency conflicts between managers and shareholders can influence corporate decision-making, including dividend policy. In this paper, Jensen argues that managers may have incentives to retain earnings rather than pay them out as dividends, particularly when they have discretion over investment decisions. This aligns with the notion that asymmetric information between managers and shareholders can affect dividend policy in a way that disadvantages the shareholders.