What is Money?
By Joseph Mark Haykov, with Nathan and Phillip as interns
May 30, 2024
Abstract
In the nineteenth century, economists William Stanley Jevons, Carl Menger, and Léon Walras noticed that money had a central role to play as a medium of exchange, necessary to overcome the double coincidence of wants problem inherent in direct barter systems. The Arrow-Debreu model—the foundation of modern mathematical economics—does not deal with money directly, but introduces it only as an afterthought: as a unit of account in which prices are measured in a theoretical Pareto-efficient equilibrium.
The equation U=S+E integrates these perspectives by highlighting that the immediately available money supply, such as M2 in the U.S., is mathematically equivalent both in theory and in reality to the total number of minted gold coins in a bank-less economy such as ancient Rome. This readily available currency functions not only as a unit of account (U), but also as a store of value (S) and a medium of exchange (E). This framework refines the traditional quantity theory of money (M·V = P·Y) into a more precise accounting identity (E·V = P·Y), where E specifically denotes the portion of the M2 money supply that is actively used in transactions, excluding funds that lie dormant in savings accounts for extended periods.
Furthermore, the equation U=S+E illuminates how the exchange value—or the purchasing power—of a currency is determined by its utility. For instance, Bitcoin’s current exchange value of approximately $1.3 trillion is determined by its utility, or its 'U = S + E' value, reflecting its effectiveness in fulfilling money’s three functional roles: E as a medium of exchange, S as a store of value, and U as a unit of account. In its role as a unit of account (U), money not only measures the relative prices of competing products, such as cars, but also relates these prices to wages and the time required to earn them, thus representing the true opportunity cost for individuals who act as both consumers and producers within the Arrow-Debreu model.
Keywords: Money as a Medium of Exchange, Arrow-Debreu Model, Quantity Theory of Money, Utility Value of Currency, Market Capitalization, Bitcoin, Mathematical Economics
JEL Codes: E40, E41, E42, C02
Introduction
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 website1. According to the Federal Reserve, money consistently fulfills three key roles across all economies, both historically and currently: as a unit of account, a medium of exchange, and a store of value. This definition is universally acknowledged and uncontested.
The Arrow-Debreu model, a cornerstone of mainstream economic thought and the basis for general equilibrium models used by institutions like the Federal Reserve to set interest rates, does not inherently necessitate money. In the context of the first welfare theorem of mathematical economics, money is simply a unit of account in which prices are expressed in an equilibrium. "A Walrasian Theory of Money and Barter," freely available from Harvard2, is cited for its succinct summary of the ongoing debate about the nature of money, a discussion that can be traced back to the seminal contributions of early mathematical economists, namely Jevons, Menger, and Walras. In the late 19th century, these economists correctly identified a key function of money as a necessary medium of exchange—to solve the double coincidence of wants problem inherent in direct barter.
Over time, the characterization of money as a medium of exchange has crystallized into what is best described as dogma—an assumption-dependent axiom within mainstream mathematical economics. However, accepting such conjectures uncritically is precarious. We would be wise to remember that any axiom, even the most obvious Euclidean postulate that the shortest distance between two points is a straight line, is by definition merely a hypothesis introduced without empirical proof. It is important to recognize that such axioms can, and sometimes do, prove to be erroneous. For instance, the 'straight line' axiom does not hold in non-Euclidean geometries, such as those employed by GPS systems that adjust for the curvature of space-time. These systems utilize Riemannian geometry, which is based on axioms that more accurately represent the curvature of space as described by Einstein.
All axioms, by their nature, are assumptions—essentially educated guesses that are often deemed 'self-evidently true' by those who formulated them, sometimes centuries ago. Over time, these axioms can become conflated with facts, effectively turning into dogma. This becomes particularly problematic when such assumptions are not universally applicable, as many prove to be false under specific circumstances. For example, the axiom of pairing in Zermelo-Fraenkel (ZF) set theory posits that any set consisting of two elements can be separated into two subsets, each containing one of the elements in the original set. This axiom seems intuitively self-evident. However, it is self-evidently logically false when applied to entangled elementary particles such as electrons or photons, revealing the limitations of traditional axiomatic approaches in the face of quantum mechanics. The application of this axiom becomes problematic in real-world scenarios, as evidenced by the empirical falsification of Bell’s Inequality3.
Despite ongoing debates—particularly regarding whether assets like gold, which central banks use as reserve assets but not as mediums of exchange, should be considered 'real' money—the fundamental facts remain uncontroversial: Money has assumed various forms throughout history. These have ranged from cattle and tobacco leaves to cowrie shells, and from gold and silver coins to today's diverse fiat currencies. Within the Arrow-Debreu framework, all these forms of money are categorized as units of account or simply ‘money-units,’ and have actively facilitated global trade. This diversity is exemplified by the approximately 30 different currencies actively traded on the Forex market, each recognized as a valid fiat currency within its respective country or regional economy, such as the Euro (EUR).
Drawing insights from Bertrand Russell’s 1959 interview4 on the legacy of future generations, we see a clear imperative to transcend existing dogmas and focus on factual evidence. This approach reveals that the views expressed not only by Jevons, Menger, and Walras, but also by Arrow and Debreu, are not in conflict with each other, nor with the empirically observed roles and functions of money as detailed by the Federal Reserve Bank of the United States. In theory and in fact, there is agreement on the three indispensable functions that any currency must serve within its economy: acting as a unit of account (U), a store of value (S), and a medium of exchange (E).
The Three Roles of Money Equality: U = S + E
We initiate our discussion by examining money's role as a medium of exchange ('E'), a concept extensively explored by Jevons, Menger, and Walras. The proverb "measure twice, cut once" aptly applies to monetary transactions, encapsulating the essence of using money as a medium of exchange to pay for things. Before making a purchase, rational economic agents engage in comparative price evaluations—whether assessing different car models or other comparable goods and services—considering both price and its proportionality to their financial status. In this sense, as money is used as a medium of exchange, it also measures the exchange rates between all the goods and services that are traded. This defines money’s 'U + E' (Unit of Account + Exchange Medium) role. The use of money as a unit of account, in which the exchange rates of goods and services are measured, such as the relative costs of different consumption options, or the price of an apartment relative to your monthly wages, employs money as both a unit of account ('U') ex-ante and a medium of exchange ('E') at the point of purchase, enabling a thorough appraisal of purchasing options within one’s economic means.
While the Arrow-Debreu model primarily focuses on general equilibrium without explicitly integrating money, it implicitly necessitates money as a unit of account to articulate equilibrium prices. This requirement underscores the importance of the total spendable money supply in facilitating complex economic calculations and enhancing market operations. In today’s real-world economy, the U.S. dollar's total spendable supply, as gauged by the M2 money supply estimated by the Federal Reserve, encompasses all readily available funds—including cash, balances in checking and savings accounts, and money market funds—all denominated in U.S. dollars. This concept mirrors ancient economies such as Rome, where the total quantity of minted aureus gold coins represented a comparable measure of spendable wealth.
Defining 'U' as units of money that are concurrently available to be used as payment illustrates the dual functionality of money as both a medium of exchange and a store of value. Unspent money is, by definition, a store of value ('S'), as exemplified by gold coins stored in a vault or bank funds saved rather than invested. This delineation resonates with Keynes's liquidity trap concept from his 1936 seminal work, The General Theory of Employment, Interest, and Money, depicting money also as 'U + S' (Unit of Account + Store of Value)—a metric for more abstract, generalized purchasing power.
We assert a principle of exclusive dual-use, stating that money can either be saved or spent, but not both simultaneously—similar to the adage, "you cannot have your cake and eat it too." Thus, money functions exclusively as a store of value or a medium of exchange at any given time. By combining 'S' and 'E,' we get the spendable money supply. This integral view, denoted as 'U,' merges the roles of 'U + E' and 'U + S,' crucially linking overall purchasing power with specific and relative good and service prices. Therefore, money’s dual role, transitioning smoothly between a unit of account and a medium of exchange, and into a store of value when not used as payment, encapsulates its comprehensive function within the economic system.
In conclusion, money is mathematically defined by its usage, represented as U = S + E. This foundation prepares us to delve deeper into the mathematical underpinnings of our money definition, aligning it with the first welfare theorem of mathematical economics. The upcoming technical sections aim to bolster this discourse. Readers less inclined towards mathematical detail may skip this segment and proceed to "What Makes Money 'USE'-able?", focusing on the practical aspects of money's utility.
The Mechanism of Welfare Optimization in Perfect Markets: Exploring Mutual Benefit and Pareto Efficiency
The Arrow-Debreu model mathematically proves that a Pareto-efficient equilibrium, defined by maximum overall welfare, inevitably results under a set of strict assumptions. These include local nonsatiation and marginal diminishing utility of consumption, which ensure that a maximum exists and is sought. Additional assumptions, such as the absence of externalities and the presence of competitive markets (meaning no monopolies), are necessary to ensure that the maximum overall welfare is indeed the global maximum. This represents the maximum theoretical happiness achievable under existing production constraints. Yet, as George Orwell famously wrote, “All animals are equal, but some are more equal than others.” In this context, the key assumptions that ensure at least a local, if not global, maximum welfare are the dual requirements of unfettered and symmetrically informed exchange.
Unfettered exchange means fully voluntary transactions by each counterparty, excluding theft and robbery. Symmetrically informed exchange means that each counterparty has equal knowledge about the goods and services being exchanged, precluding the possibility of fraud. Together, these conditions ensure the generation of both producer and consumer surplus.
Fraud facilitated by asymmetric information is an extensively studied topic in mathematical economics. This type of fraud manifests as the difference between ex-ante consumer surplus (represented by the expected use value of purchased eggs, thought to be fresh) and ex-post consumer surplus (defined, for example, by the lack of use value upon realizing the eggs are rotten).
The first welfare theorem of mathematical economics asserts that unfettered and symmetrically informed exchange is guaranteed to be mutually beneficial. The reason is simple: no rational individual, under any definition of rationality, would willingly engage in an arm's length transaction unless they perceived a net benefit beforehand, thereby guaranteeing ex-ante surplus.
This guarantee of ex-ante surplus translates, under the condition of symmetric information, into a realized ex-post surplus, barring acts of God, such as dropping purchased eggs on the way home from the supermarket. Both counterparties to the trade being equally well-informed about the goods and services being traded ensures mutual benefits in reality under the condition of unfettered trade. For example, when someone buys a bottle of Coca-Cola from Walmart, the seller knows exactly how much money they are receiving, and the buyer knows exactly what they are buying.
Because such unfettered, symmetrically informed trade is guaranteed to be mutually beneficial, in the context of this theorem, it is referred to as Pareto-improving, and represents real-world gradient descent optimization. Mutual benefits incrementally drive the economy towards a state of Pareto-efficiency, where the gradient of the objective function becomes zero in a theoretical equilibrium. Vilfredo Pareto elegantly described this as a situation where no one can be made better off without making someone else worse off.
To mathematically represent consumer and producer surplus, the Arrow-Debreu model introduces the concept of money as a unit of account in which prices are measured. Prices are used to define consumer surplus as the difference between the maximum price a consumer is willing to pay and the actual market price. Similarly, a producer's surplus is the difference between the sale price and the total costs of production, including opportunity costs. However, all these costs and benefits are measured in money.
Moreover, the maximum price a consumer is willing to pay is dually defined by the opportunity cost as a producer, specifically the time necessary to spend working to earn enough wages to purchase the desired goods and services. Wages, also measured in money, make money a crucial unit of measure within the Arrow-Debreu framework. It is used not only to compare the prices of competing goods and services, such as different cars we might consider purchasing, but also to relate these prices to our income. This allows us to compare the subjective costs and benefits of consuming goods and services versus producing the necessary wages to engage in further consumption.
This comparison motivates us to improve labor productivity in a free market. In effect, this proves mathematically that at least a local maximum (though perhaps not a global one) in labor productivity results from “honest” trade. This naturally motivates us to engage in labor specialization to maximize productivity, exactly as Adam Smith posited in The Wealth of Nations.
Assuming no robbery, theft, cheating, or fraud facilitated by asymmetric information about the goods and services being traded, the Arrow-Debreu framework provides a comprehensive system to measure and optimize economic welfare. And the U = S + E equation makes the role of money clear.
Quantifying the subjective benefits of experiences poses a significant challenge due to their inherently unmeasurable nature. Within this economic framework, money plays a crucial role as a unit of account, facilitating trade and optimizing collective welfare by converting subjective utilities into monetary terms. Consumers and producers engage in mutually beneficial trade, exchanging the fruits of their labor, quantified as monetary wages, for goods and services similarly priced in monetary terms. Thus, money serves a dual function: firstly, as a medium of exchange that enables transactions; and secondly, as a unit of account, quantifying the subjective expected benefits of purchases against their subjective costs, often assessed in terms of the time required to earn the necessary funds. Many individuals may evaluate the subjective cost of an apartment based on the time it takes to earn the income necessary to cover the rent. Additionally, in scenarios where money is not immediately utilized for payments, it seamlessly transitions into its defined dual role as a store of value, thereby encapsulating its universally recognized functions as a unit of account, medium of exchange, and store of value.
Unraveling the Optimization of Welfare in Perfect Markets: A Comprehensive Analysis
In a perfect market, welfare maximization results from assured mutual gains from trade, operating without restrictions and based on symmetric information. This principle ensures that every participant, whether consumer or producer, benefits from their transactions. Effectively, the Arrow-Debreu model conceptualizes welfare maximization as a real-world gradient descent optimization, where mutual benefits drive the system toward a global maximum. Here, maximum welfare is achieved when the gradient of this objective function approaches zero—a condition characterized by Pareto efficiency. This state, where no further mutually beneficial trades are possible because improving one party's welfare would necessitate diminishing another's, is eloquently defined by Vilfredo Pareto. He described it as a situation where "no one can be made better off without making someone else worse off," saying that "the gradient of the objective function becomes zero" in more intuitive language for describing economic equilibria.
To ensure mutual benefit, buyers must achieve a consumer surplus, which represents the difference between the maximum amount they are willing to pay and the actual price they pay. Similarly, sellers must realize a producer surplus, defined as the difference between the price they receive and their cost of production. These surpluses are essential for defining Pareto-improving outcomes, where the welfare of one participant can be enhanced only alongside the benefit of another, ensuring a situation where everyone wins.
Such outcomes inevitably lead to Pareto efficiency, a state in which it is impossible to improve the economic welfare of one party without reducing the welfare of another. This state marks the culmination of optimal resource distribution and maximum welfare under perfect market conditions.
Producer surplus is defined as the difference between the price at which goods are sold and their total economic cost of production. Measuring this surplus is relatively straightforward, encompassing not only direct expenses such as materials and labor but also the opportunity costs associated with the production process. In mathematical economics, opportunity costs are considered the value of the next best alternative that is forgone when a decision is made. For example, in the real estate industry, opportunity costs might include expenses related to advertising an apartment, the time spent by owners 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 allocated elsewhere. Accurately accounting for these costs is crucial for assessing the economic profitability of property management comprehensively. It provides a more detailed view of the economic sacrifices made in the pursuit of business activities, highlighting the real costs involved in maintaining and enhancing the value of real estate properties.
Unlike producer surplus, consumer surplus cannot be directly quantified due to its reliance on the subjective perceptions of benefit and cost to the individual. This is precisely why money plays a crucial role in defining consumer surplus in mathematical economics. Consumer surplus is defined as the difference between the maximum price a consumer is willing to pay for an item—based on their personal valuation—and the market price at which the item is actually purchased. Money, in its role as a medium of exchange, naturally becomes a unit of account in which the exchange rates of all goods and services in the economy are measured, including the exchange rate between our wages and the goods and services we purchase and consume. Money transforms such subjective valuations into quantifiable terms. This allows individuals to compare their willingness to pay with actual market prices and to assess the surplus they derive from transactions. For instance, the consumer surplus on an iPhone would be the difference between what a consumer is prepared to pay for it, reflecting their personal valuation of its features and utility, and the price they actually pay at the store. This surplus represents the perceived value gained by purchasing the product at a lower price than what was internally deemed acceptable.
Quantifying Consumer Surplus: The Role of Money in Valuing Subjective Benefits
Money plays a pivotal role in quantifying the subjective costs of items to individuals, serving as a unit of account for the ‘true’ opportunity cost in economic transactions. Individuals, in their dual roles as both producers and consumers, typically measure the subjective cost of an item in terms of the time required to earn the income necessary for its purchase, often calculated in wages. This measurement captures not only the financial expense but also the effort and time invested, which individuals equate with the value of the product. Thus, consumer surplus provides valuable insights into the additional value individuals derive from their purchases relative to the labor they expend to earn the necessary income. This concept is fundamental in the context of mathematical economics, highlighting the intricate relationship between subjective valuations and economic decision-making.
Although consumer surplus is subjective, it can be quantified in monetary units because the amount a consumer is willing to pay for a product reflects their perceived benefit from the purchase. It is impossible for a third-party observer to determine whether an individual consumer derives twice the subjective benefit from buying Product A (e.g., a Bentley) as from Product B (e.g., a Ford) simply because the price of A is twice that of B. However, we can assert with absolute certainty that the consumer perceives a relatively greater benefit from Product A than from Product B, as evidenced by their willingness to pay a higher price for it. This willingness to pay more provides a 'rank-order' measure of utility. Money does not measure subjective benefit directly, but it is 100% rank-order correlated with subjective utility to the consumer, as more money is guaranteed to provide more utility by imposing fewer constraints on what the consumer is able to consume. Thus, money serves as a unit of account for the rank-order value of subjective utility.
Direct measurement of subjective utility is challenging due to its dual nature: expected subjective utility of a product (ex-ante, or before the purchase) can drastically differ from the realized utility (ex-post, or after the purchase), as illustrated by George Akerlof in the market for “Lemons.” For example, the expected utility of eggs might be high before purchase, but this can change significantly if the eggs turn out to be rotten. Measuring subjective utility is inherently difficult due to its abstract nature. 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 ‘subjective-rank-order(dU/dT),’ where dU/dT represents the rate of change in subjective utility with respect to time.
In this formulation, money plays a crucial role not only in quantifying consumption rates but also as a critical unit of account and a measure of purchasing power. It is continuously used to compare the costs of different potential purchase options to the hourly wages, serving as a unit of measure before being utilized as a medium of exchange to facilitate trade. Furthermore, its function as a unit of account is intertwined with its capacity as a store of wealth, effectively modulating consumption rates. This underscores the essential function of money as a unit of account: it quantifies and ranks subjective utilities over time before making purchases, providing a practical framework for economic analysis and decision-making. By moderating consumption according to financial resources, money fulfills its dual role as both a measure of value and a store of value, helping preserve purchasing power over time, stabilize economic interactions, and promote a sustainable economic environment.
The U=S+E Framework: Integrating Economics with Evolutionary Biology
The U=S+E framework provides an additional benefit: local nonsatiation is not merely an assumption but a logical outcome of our axiomatic framework, integrating a fundamental principle of biology—evolution through natural selection. In humans, this manifests through female choice, where females typically favor partners who exhibit traits perceived as desirable. Although these traits vary across cultures and epochs, a common constraint for most males is demonstrating purchasing power as a signal of their social ranking.
This dynamic inherently ensures local nonsatiation when measured in monetary units. Money serves multiple roles in this context: it acts as a unit of account by measuring purchasing power and as a store of wealth due to its acceptance as a medium of exchange. Individuals are inherently motivated to enhance their status to attract desirable partners. In this pursuit, the ability to store and accumulate wealth becomes a crucial factor. Consequently, money, in its role as a store of wealth, acts indirectly as a consumption constraint that individuals strive to minimize relative to their competitors, aiming to maximize their reproductive success.
In non-traditional relationships, such as those involving two or more biological males and/or females of the same species, regardless of subsequent medical interventions or alterations, one partner always assumes the dominant role of a money provider, often perceived as the de-facto ‘provider’ role traditionally associated with males. Competition for better partners exists everywhere, even in places like prison, where males segregate themselves into groups where “providers” compete for attractive younger males forced into homosexuality—a well-known empirical fact, as per game theory axioms.
This willingness to pay more effectively translates subjective utilities into quantifiable monetary units. This translation allows us to assert with certainty that higher trading volumes, expressed in dollars, indicate an increase in overall welfare, assuming these trades are genuinely mutually beneficial. This conclusion is analogous to how the Pythagorean theorem derives from the Euclidean axioms in geometry, which assert that the shortest distance between two points is a straight line. By order-ranking these utilities, we gain valuable insights into consumer preferences and economic dynamics, thereby enhancing our understanding of market efficiency and consumer behavior.
The Arrow-Debreu Model and Its Real-World Limitations
Recalling our middle school mathematics, we appreciate that the accuracy of logical proofs is fully guaranteed because they are independently verifiable. Many individuals, including those as young as fifth graders capable of mathematical reasoning, have proven the Pythagorean Theorem individually, for themselves. However, it's important to note that the “absolute” truths established through such proofs are conditional rather than absolute.
All such mathematical proof does is establish logical equivalence between the axioms and the theorems, which are absolutely guaranteed to hold true as long as the axioms hold true, both in theory and in reality. For example, the Pythagorean Theorem is absolutely certain, due to independent verification, to hold true under the foundational Euclidean axioms. Yet, Einstein’s adoption of Riemannian geometry to describe curved space-time provides a more accurate model of the universe, challenging traditional Euclidean perspectives. This concept has practical applications 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. Indeed, in our objective reality, where GPS technology is indispensable, the shortest distance between two points is not necessarily a straight line—not just in theory, but also in fact.
Similarly, the Arrow-Debreu model, known for its rigorous mathematical framework, encounters significant limitations due to its often unrealistic assumptions about real-world economies. The model assumes conditions such as unrestricted and symmetrically informed trade. However, when these foundational assumptions are not met, as is frequently the case, outcomes like theft, robbery, and fraud facilitated by asymmetrical information invariably occur. This is exemplified by the selling of a “lemon”—a defective car misrepresented as fully operational. Without robust law enforcement and free-market mechanisms to address these market failures, the model’s predictions fall short of capturing the complexity of actual market dynamics.
Limitations of the Arrow-Debreu Model: Rational Utility Maximization and Real-World Application
The Arrow-Debreu model accurately describes real-world human behavior using a praxeological method rooted in ancient Greece, where praxeology posited as an axiom that human action was not random, but goal-driven. This goal, both in mathematical economics and game theory, has been identified as ‘winning’. At the core of this model is the axiom of the 'rational utility maximizer representative agent'. This axiom posits that individuals—or players in a game—are rational, utility-maximizing actors. These actors behave in ways that maximize their welfare within the constraints of the game’s rules, employing strategies that yield the highest possible payoff.
This characterization logically implies that a representative agent in the economy aims to maximize utility not only by maximizing labor productivity but also by minimizing prices/costs, even if it means resorting to unethical behaviors when they prove profitable. For instance, in San Francisco, the policy decision not to prosecute thefts under $950 as criminal offenses has led to predictable outcomes. The minimal enforcement of this threshold has spurred such a high rate of theft that many stores have been forced to close or relocate. This situation illustrates a significant deviation from theoretical economic models, highlighting a stark contrast when foundational assumptions—such as effective legal deterrence—are not met in practice.
Another notable deviation from the Arrow-Debreu conditions is highlighted by George Akerlof’s study on the market for "lemons," where asymmetric information—not direct theft like in San Francisco—leads to suboptimal outcomes. An even more striking example of the violation of assumptions is observed in the stark disparity in per capita GDP between Haiti and the Dominican Republic, attributable to widespread involuntary exchanges in Haiti. These conditions violate the unfettered trade assumption posited by the first welfare theorem of mathematical economics and the Arrow-Debreu model, underscoring the critical importance of adhering to these theoretical prerequisites for achieving efficient market conditions. Such discrepancies between axiomatic assumptions and reality emphasize the inherent limitations of applying theoretical economic models without accommodating the variability and unpredictability of real-world economic environments.
The Impact of Asymmetric Information on Economic Efficiency
Violations of the two key Arrow-Debreu conditions—voluntary exchange and symmetric information—always undermine economic efficiency, both in theoretical models and real-world scenarios. The reason is obvious: such violations prevent the achievement of even a local, let alone a global, maximum. George Akerlof, along with Michael Jensen and William Meckling, has profoundly enhanced our understanding of how asymmetric information can lead to market inefficiencies. In their seminal work "The Theory of the Firm," Jensen and Meckling introduce the concept of "agency costs," which arise from information asymmetry between agents and principals.
Expanding on this dynamic, Jensen's influential 1986 paper "Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers," discusses the agency conflicts between managers and shareholders that influence corporate decisions, such as dividend policies. Jensen argues that managers might prefer to retain earnings rather than distribute them as dividends, particularly when they control investment decisions. This preference can disadvantage shareholders by restricting their potential gains from dividends, thus illustrating the practical implications of asymmetric information on dividend policy. This discussion also highlights the broader consequences of information gaps on corporate governance and shareholder value, demonstrating the extensive reach of asymmetric information in affecting economic outcomes.
Mitigating Market Inefficiencies: The Role of Money in Reducing Asymmetric Information and Arbitrage
As we delve into the concept of asymmetric information, it becomes clear how this phenomenon not only facilitates fraud—characterized by exchanges that are not mutually beneficial—but also underscores the crucial role of money as a unit of account in preventing arbitrage. Arbitrage involves the simultaneous purchase and sale of the same asset in different markets and is a clear indicator of market inefficiency. Within the Arrow-Debreu model, market inefficiency, or failure, is defined as the ability to earn 'economic rents.' These can be metaphorically likened to goods pilfered by rodents or other vermin in a warehouse, who consume without producing—aligning with Gordon Tullock’s definition of rent-seeking, which describes the pursuit of wealth without a reciprocal contribution to productivity.
The prevalent issue of real-world arbitrage is particularly troubling as it allows arbitrageurs to gain purchasing power—represented by money—without enhancing productivity. This scenario critically undermines market efficiency, emphasizing the importance of money in maintaining economic stability and fairness.
Information asymmetry exists not in space, but in time; it manifests ex-post when the true value of goods and services obtained in a trade becomes apparent. This realization often does not align with the ex-ante expectations of utility or use value that the buyer had before purchasing items like rotten eggs or a "lemon" car. This temporal discrepancy between expected use value ex-ante and actual use value ex-post leads to dissatisfaction or perceptions of unfairness in the exchange value paid or received.
Arbitrage opportunities are often facilitated by temporal asymmetric information between buyers and sellers about prices, a concept vividly illustrated by Michael Lewis in Flash Boys: A Wall Street Revolt (Lewis, 2014). The absence of real-time knowledge regarding all active pending bids and offers allows high-frequency trading (HFT) firms, such as Citadel and Virtu Financial, to amass substantial profits through straightforward arbitrage strategies. These firms exploit the information gap by accessing data on different prices for the same asset more quickly than others. In an environment devoid of such information asymmetry, transactions that these intermediaries facilitate would instead occur directly between buyers and sellers across markets. In scenarios where information asymmetry is eliminated, all parties would have complete visibility and understanding of market conditions and prices, thereby rendering the arbitrageur's role obsolete. This ideal situation underscores the significant impact of timely and transparent information in ensuring market efficiency. The profits that arbitrageurs derive from these informational gaps underscore the necessity for mechanisms that can bridge these asymmetries.
No-Arbitrage Constraint on 𝐸: The Transpose of Its Own Hadamard Inverse
Our discussion begins with an analysis of the Forex market. In the real-world FX market, approximately (n=30) of the most actively traded currencies are exchanged, and their exchange rates can be mathematically represented as an exchange rate matrix, denoted as E. In this matrix, the value in row i and column j represents the exchange rate from currency i to currency j. This matrix serves as a model for understanding how exchange rates between not only currencies but also between all goods and services that can be either bought or sold in an arm's length commercial transaction in an economy are structured to prevent arbitrage.
Arbitrage, by its very nature, is not possible if a uniform price is maintained for an asset in different markets. Specifically, in the foreign exchange market, if the exchange rate of currency A to B is set, then it must be the reciprocal of the exchange rate of B to A. For example, if $1 buys £0.50, then £1 should buy $2. This reciprocal relationship is crucial to eliminating arbitrage opportunities arising from exchange rate discrepancies. Let the matrix E represent a set of exchange rates, such as those observed between the 30 or so currencies in the FX market, where n, the number of rows and columns, would be 30. The no-arbitrage condition dictates that E must be equal to its own transpose once the Hadamard inverse is applied. Mathematically, the exchange rate matrix is constrained as follows: . This condition, where the matrix becomes the reciprocal of its own transpose under the E=ET “no-arb” constraint, is very similar to the property of a matrix being involutory, where an involutory matrix is its own inverse, A=A-1. Let us formally refer to such matrices as ‘evolutory’, rather than involutory. An evolutory matrix E, is equal to its own reciprocal transpose, ET constrained such that ei,j=1÷ej,i. The reason for the distinction is that while A·A-1=I (the identity matrix), 𝐸⋅𝐸𝑇=E2=𝑛⋅𝐸.
As we can see, the evolutory matrix, when multiplied by its-own reciprocal transpose, results not in the identity matrix but rather a scalar multiple of E scaled by its row count, n effectively becoming E2. The reason for this is that the constrained matrix E=ET has a single eigenvalue, which is also its trace, and is invariably equal to n, due to the fact that the exchange rate of a currency with itself is, by definition, always 1.
By imposing the E=ET condition, the matrix E simplifies, having only a single eigenvalue, n, and reducing to a vector-like structure. This simplification occurs because each row or column of E can define the entire matrix, dramatically reducing the dimensionality of the information required to quote exchange rates. For example, the entire matrix E is equal to the outer product of its first column and its first row, which also happens to be the reciprocal of the first column, producing the full matrix. Consequently, each row or column of E is proportional to the others, meaning that all rows or columns are scalar multiples of one another. This characteristic renders E a rank-1 matrix, indicating that all of its information can be captured by a single vector.
What is interesting here is that in theory, an unbounded matrix raised to the fourth power should have four roots, but in reality, because of the E=ET constraint, the matrix E has only two such fourth roots, E and ET because E4=E·E·E·E=(ET·ET·ET·ET)T.
We believe it is worthwhile to highlight what might be an obvious connection. In the context of Einstein's equation E=mc2, if E is a bounded E=ET matrix, we see that . As we can see, mass is simply the fourth root of energy. However, whereas E theoretically has four roots, in reality, only two roots exist due to the E = ET evolutory constraint imposed on E via quantum entanglement. Thus, under this evolutory constraint on E, .
While this remains purely conjectural, it intriguingly aligns not only with the principle of supersymmetry in theoretical physics but also, surprisingly, with the ancient Hermetic axiom 'as above, so below.' This concept also echoes the geometry of the Egyptian pyramids and is reminiscent of the notion that '42' is the 'answer' to the ultimate question of life, the universe, and everything, as humorously proposed in The Hitchhiker's Guide to the Galaxy. Although this reference is not directly related to quantum physics, it touches on probability.
At this point, we must caution that our expertise in theoretical physics is limited to interactions with physicist colleagues during our tenure managing the stat-arb book at RBC on Wall Street. Therefore, please treat our comments about physics with considerable skepticism, particularly the ideas about quantum set theory outlined below, which are purely speculative. This may assist a physicist who is not on Wall Street, unlike those making real money at hedge funds such as Renaissance, founded by the late Jim Simons.
In a matrix that simplifies to a vector-like structure, the entirety of the matrix can be described by any of its rows or columns. Here’s what happens in such a scenario:
Instead of needing to know all elements of a matrix (which in a full matrix would be 𝑛×𝑚 values), you only need to know the elements of a single vector (either 𝑛 or 𝑚 values, depending on whether it's a row or a column vector). This drastically reduces the dimensionality of the information required.
This vector represents a form of data compression, where instead of storing or processing multiple independent pieces of information, one vector informs the entire structure. This simplification could improve the efficiency of computations and analyses involving 𝐸.
Extending this idea to a theoretical framework, especially in contexts like quantum mechanics, can lead to intriguing possibilities:
In quantum mechanics, states can be superposed and entangled. A matrix that simplifies to a vector-like structure might analogously suggest a system where states are not independently variable but are intrinsically linked—a form of quantum entanglement at a mathematical level.
A new set theory that models such matrices could consider sets where elements are fundamentally interconnected. Traditional set theory deals with distinct, separate elements, but this new theory could focus on sets where elements are vector-like projections of one another.
Such a theory could be useful in fields like quantum computing or quantum information, where understanding entangled states in a compressed, simplified form could lead to more efficient algorithms and a better understanding of quantum systems.
By utilizing a matrix that reduces to a vector-like structure as a basic element, we could potentially model a system where traditional notions of independence between elements are replaced by a more interconnected, entangled state representation. This could open new avenues in both theoretical and applied physics, especially in handling complex systems where interdependencies are crucial.
We note in passing, as illustrated here in this video from MIT online lectures5, the axiom of pairing from ZF set theory is used to derive Bell’s Inequality. At approximately the 1 hour and 15 minute mark, the lecturer uses the axiom of pairing, for example, to split up the set 𝑁(𝑈,¬𝐵) into 𝑁(𝑈,¬𝐵,¬𝑀) and 𝑁(𝑈,¬𝐵,𝑀) In this particular case, when set elements are pairs of entangled particles, the axiom of pairing does not work, simply because such a set cannot be split up into two separate subsets. However, if we replace set elements with vectors that are all entangled on account of being constrained by 𝐸=𝐸𝑇, we may—with hard work that no one in their right mind would do for free—develop a better set theory that will more accurately model quantum entanglement, akin to the way Riemannian geometry was derived from a set of axioms that more accurately reflect the reality of how space-time operates.
If you want to find out more, please visit us at tnt.money, as we may have a way to properly motivate people to do such research using one-true money!
The Role of Linear Algebra in Market Efficiency
As mathematical economists, we find that the linear algebra formulation captures the essential idea that in an arbitrage-free market, the reciprocal relationships between exchange rates of different currencies, as well as all goods and services, must be consistent. An arbitrage-free exchange rate matrix E such that ET=E (since it is equal to its reciprocal transpose) imposes constraints on exchange rates, eliminating opportunities for arbitrage by simply transposing and reciprocating the exchange rate matrix. In this framework, prices represent the exchange rates of all goods and services relative to a single specific row or column in the full exchange rate matrix E, chosen as the unit of account. This framework supports the theories of Arrow and Debreu and is even, surprisingly, consistent with the ideas of Marx. Indeed, the key role of money is to regulate markets by preventing arbitrage.
This is vividly illustrated by the real-world practice of quoting all currencies in the foreign exchange (FX) market against a single standard currency, currently the U.S. dollar, which plays a pivotal role in reducing the scope for arbitrage, thereby nudging the market towards an ideal no-arbitrage condition. By standardizing currency pairs relative to the dollar, there is greater predictability and consistency in exchange rates. This systemic approach effectively minimizes the discrepancies and gaps that arbitrageurs typically exploit, leading to a more stable and equitable trading environment.
While the application of linear algebra might often seem excessive in financial contexts, its use in this scenario is particularly warranted. Viewing the prices of goods and services through an exchange rate matrix effectively underscores money’s role strictly as a unit of account. In the real-world FX market, where all currencies are traded in pairs, cross rates for pairs such as EUR/GBP or EUR/JPY are determined using the U.S. dollar solely as a unit of account. This approach not only emphasizes the functional use of money exclusively as a unit of account but also highlights the practical utility of quoting all prices relative to a single standard asset. Adopting this methodological choice significantly enhances market efficiency by increasing information symmetry among participants and reducing arbitrage opportunities, thereby establishing consistent prices for each asset across all markets.
Measuring Pareto-Efficiency
Introducing the E=ET constraint offers significant benefits, as it facilitates the computation of Pareto efficiency in an economy by examining the prices at which trades for specific goods or services occur. It becomes evident that the more “inefficient” the market is, the more E will diverge from ET. This concept is mathematically analogous to simple arbitrage, where an arbitrageur, X, buys a stock from counterparty A in market 1 and sells it to counterparty B in market 2, generating a profit from asymmetric information. This profit, known as “economic rents,” diminishes productivity because it allows a non-producing arbitrageur, X, to consume goods and services produced by others without contributing to their production.
Note: X is able to earn money by facilitating a trade between A and B that should have occurred directly between them in a more efficient market if both had symmetric information. The fact that both parties had placed open orders to buy and sell, which did not cross due to X's speed, highlights this inefficiency. We posit that losing half the bid-ask spread is not worth having your trade executed 2 milliseconds earlier for 99.99999% of the public.
Consider two scenarios, with the only difference between them being the presence of arbitrageur X, who acts as an unwanted intermediary preventing A and B from trading directly with each other. In the absence of X, all trades will occur at the mid-quote. However, if X is present, some trades will occur at the bid and others at the offer. In other words, the difference between E and ET becomes greater in the presence of X—by definition—as this bid-ask bounce volatility represents the “alpha” that X earns.
What we are highlighting here is that the root cause of market inefficiency, as defined by arbitrage in terms of prices, is the existence of multiple prices for the same asset. This is exemplified by the ability to buy at the offer and sell at the bid, instead of consistently trading at the mid-quote. Within the framework of the exchange rate matrix E, this inefficiency can be quantified as the difference between E (ask or bid) and ET (mid-quote) multiplied by the trading volume. In this specific scenario, the calculation equals the profits earned by the arbitrageur (half bid-ask spread), down to the penny.
Of course, not every trade in reality is facilitated by an arbitrageur. However, we can approximate ET by the Volume Weighted Average Price (VWAP) for the time period we are examining, subtracting it from the price of each executed trade, using the fill price as E (ask or bid). What we are effectively doing in this case is “collapsing the wave function”—taking all the different E matrices over time and averaging them out, thereby producing an estimate of the value of ET. When we measure Pareto-efficiency this way, it becomes clear that the more volatile the prices, the greater the difference between E and ET, and the less Pareto-efficient the market.
What we are doing here is simply debugging Karl Marx's old source code, which correctly notes that corporate profits measure Pareto-efficiency. However, the “bug” he introduced is incorrectly guessing that corporate profits represent ‘economic rents’—an utterly ridiculous idea. Both in theory and in fact, in order to extract added value from any counterparty in unfettered trade (which means no involuntary exchanges, as exemplified by slavery, robbery, and theft), including selling labor for wages, the employer must possess asymmetric information about the labor being provided to defraud the worker and extract economic rents from them, as Marx posited. In reality, any such ‘surplus’—which in this context means ‘unearned or fraudulent’ value extraction—can only run the other way—from employer to employee—as exemplified by agency costs. This is due to the fact that the employee is always better informed about the labor they produce than the employer.
However, if we set aside the bug that equates corporate profits with rent seeking, we immediately see that corporate profits actually measure the relative Pareto-efficiency of an economy, given the existing production constraints. In this sense, the higher the profits, the less Pareto-efficient the economy. While the bid-ask bounce for most commodities is fairly low, this is not the case for labor. In that sense, the difference between the price at which you sell your wages to your employer and the price at which your employer effectively re-sells your wages to the end user (consumer) is measured by the economic profits the employer earns, adjusted for all opportunity costs, naturally. In this case, E−ET for labor measures the bid-ask spread on wages and is rank order correlated with corporate profits.
Also, if you just think about it for a second, it becomes clear even without any math. Why do you think we still use the imperial system of units in the U.S., even though the metric system is much easier to use, given that we use a base 10 system for math and the scales between the two are much better aligned than in the imperial system? The reason is obvious: once we get used to a system of imperial units as a unit of account, it becomes uniquely difficult to switch to metric. Can you imagine how inconvenient and difficult it becomes to measure exchange rates with a ruler whose length is effectively constantly changing, as the spendable money supply, like M2, keeps going up (or down, as is the case currently), as if you were switching from metric to imperial, and back to metric every other day? Not to mention the fact that some prices, like wages, tend to be stickier than others, like prices of gasoline at the pump, further destabilizing relative, as opposed to absolute, prices during inflationary or deflationary periods, for example. It is important to point out that money, in its role as a unit of account, measures not only absolute prices but also, and even more importantly, relative prices. When the money supply becomes not only prone to inflation but also unpredictable, bad things can always happen, as money becomes a poor unit of account. No wonder price volatility is bad for market efficiency. This is why all central banks fear deflation worse than death and vigorously fight inflation at the same time, aiming to keep prices stable—we are not saying anything new here.
This, by the way, shows exactly why price volatility, as measured by inflation and deflation, is bad for the economy—an obvious fact that is now mathematically proven, as opposed to being merely a hypothesis. This is also why Bitcoin is worth over a trillion dollars, another fact.
Involuntary Exchanges and Their Economic Consequences
Violations of the voluntary trade assumption can have severe implications for economic efficiency, often more significant than those caused by information asymmetries. This phenomenon is vividly illustrated in the former Soviet Union republics, where real GDP growth has been notably hindered by numerous instances of involuntary exchanges, similar to those observed in Haiti. In these countries, involuntary exchanges often occur not primarily as acts of robbery or theft due to general lawlessness—as seen in Haiti—but rather through mechanisms such as bribes and asset expropriation by politically connected individuals, including FSB colonels.
These activities are frequently tolerated by governing coalitions as a means to generate wealth transfers or bribes to those in charge of law enforcement. This arrangement ensures the loyalty of law enforcement officials to the ruling government, allowing them to engage in corruption as a form of compensation for their support. The result is a sub-optimal form of a stable Nash equilibrium—reminiscent of the sub-optimal outcomes in the Prisoner’s Dilemma, where accomplices betray each other instead of cooperating.
This type of equilibrium, characterized by corruption, is prevalent 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, leading naturally to inefficiencies that affect regions from Haiti to the former Soviet Union and beyond.
The term 'involuntary exchange' used here specifically refers to violations of the unfettered trade condition posited by the Arrow-Debreu model of mathematical economics, which is crucial for achieving Pareto efficiency. According to this model, all trade should be voluntarily entered into by both parties, without duress, entirely of their own free will, and unhindered. Clear examples of involuntary exchange include acts like robbery and theft—unequivocal crimes punishable by prison terms under a proper legal system.
The Role of Taxes and Market Efficiency
The impact of taxes on market efficiency presents a nuanced scenario. In a competitive, free-market economy, taxes do not inherently constitute an involuntary exchange, although they can lead to such outcomes. The crucial distinction lies in whether taxes induce market failures—defined as transactions that are not mutually beneficial. Taxes that result in involuntary exchanges ultimately reduce welfare and productivity efficiency by preventing trades from being Pareto-improving, thereby diminishing overall welfare.
From an economic perspective, owning property in a country like France is fundamentally no different from other forms of fractional ownership, such as owning a condominium. Just as a condominium association collects fees necessary to maintain the property and its common areas—such as gyms, restaurants, and front desks, all staffed by employees—governments collect taxes to fund services that benefit everyone. These services include police departments, the military, the legal system, and welfare payments aimed at minimizing police budgets. When taxes are effectively used to provide such services, they are generally considered mutually beneficial exchanges, akin to paying condominium fees or rent, which are compensations for services rendered and thus not classified as involuntary exchanges.
However, anyone familiar with condominium associations knows that there is often a propensity for corruption among the boards, typically manifesting as management misappropriating fees for personal benefits. This scenario aligns with the concept of agency costs, as described by Jensen and Meckling, and parallels public choice theory and rent-seeking behaviors, particularly in the context of government tax mismanagement. Notably, Gordon Tullock contributed significantly to these theories, but it was James Buchanan Jr. who was awarded the 1986 Nobel Prize in Economics for his work in developing public choice theory, which identifies rent-seeking as a market failure. This is comparable to market failures induced by asymmetric information, as identified by George Akerlof, or the theft and robbery scenarios in Haiti.
Indeed, a simple example of the imposition of taxes and regulations through rent-seeking—such as the prohibition of raw milk sales while allowing the sale of raw oysters and eggs—vividly illustrates how such policies can prevent voluntary exchanges, thus qualifying as market failures. This comparison highlights the similar challenges faced in both the private and public sectors regarding the management and allocation of collected funds. These inconsistencies in regulatory practices not only disrupt market efficiency but also raise questions about the equitable treatment of different goods within the same regulatory framework.
Intuitive Recognition of Market Failures and Economic Ideologies
It is fascinating to observe how individuals, even those without formal training in mathematical economics or game theory, often intuitively recognize market failures—scenarios characterized by the pursuit of wealth without corresponding contributions to productivity. This phenomenon, identified by Gordon Tullock as economic rents, echoes Lenin's principle of 'from each according to his ability, to each according to his contribution.' Within this ideological framework, Lenin labels economic parasites—those who consume goods and services without contributing to their production—as members of the capitalist class, accusing them of living off savings and consuming without producing.
However, it's crucial to understand that merely living off savings, provided the wealth was acquired legitimately without fraud, theft, or dishonesty, does not inherently introduce inefficiencies into the economy, either theoretically or practically. The absence of deceptive practices in the accumulation of wealth ensures that such savings do not disrupt economic efficiency, thereby separating ethical considerations from economic outcomes.
Lenin's principle, akin to the concept of ‘fairness in trade,’ reflects the notion of ‘no economic rents being earned’ as understood in modern mathematical economics. This finds a practical echo in the Arrow-Debreu model within a perfectly competitive market, where the marginal revenue of labor aligns with its marginal cost. This alignment aims to avoid the pitfalls of ineffective economic policies rooted in involuntary exchange—an approach widely regarded as fundamentally flawed. Observing violations of Arrow-Debreu assumptions in reality is undoubtedly fascinating, yet often acutely painful for the countries subjected to policies enacted by the mathematically illiterate. And as we are about to show yet again, logical deduction does not lie.
Petr Chaadaev's critical view of Russia's historical role, as articulated in his 'Philosophical Letters,' serves as a cautionary tale, urging us to consider the outcomes of economic and political experiments that have led to significant human suffering and cost. These unfortunate outcomes illustrate that deviations from the Arrow-Debreu model's assumptions, such as unrestricted free trade, do not inherently result in inefficiency. However, achieving real GDP growth without these principles requires very costly interventions to address agency costs and combat rent-seeking behaviors that inevitably result when the product of one’s labor is involuntarily expropriated by the government, providing rational utility maximizers with all the incentive in the world to steal whatever they can from the government – which is only fair – given that the government steals pretty much most of their labor from them.
For instance, under Stalin, the establishment of a surveillance network known as 'stukachi' and a punitive gulag system were drastic measures aimed at mitigating endemic rent-seeking and agency costs, compensating for the absence of free-market mechanisms like the stock market. This example underscores the complexities of applying economic theories in varied political environments and highlights the deep understanding required to navigate these challenges effectively. Failing to grasp these economic principles can lead to severe consequences, the costs of which, in terms of human suffering and economic inefficiency, continue to impact us to this day.
Measuring Pareto-Efficiency
Of course, minimizing corporate profits in the absence of externalities, such as rent-seeking behavior, monopolies, pollution, and so on, is counterproductive. Such excess profits in a theoretically perfect market are derived from developing innovative patented technologies and benefit society collectively as a group. The key here is eradicating other inefficiencies, such as rent seeking, agency costs, theft, robbery, extortion, and, of course, asymmetric information, as it facilitates fraud by rational cost minimizers.
The question becomes, how is that surplus to be split between consumers and producers? A 50-50 split, naturally. If we switch the individuals' roles (as consumer-producers), under the principles of information symmetry and rational behavior, assuming you don’t know which side you will wind up on—buying or selling—how would you set the price? A 50/50 surplus split—right at the mid-quote—is precisely where the derived subjective utility is equal for both parties. Thus, the midpoint is the optimal point. This is where the economy operates with maximum Pareto-efficiency, minimizing unearned wealth procured by non-producing arbitrageurs—or economic parasites—according to Lenin.
You see, the end result is the same, regardless of whether arbitrage takes place in space or in time. This becomes evident by collapsing the wave function, comparing E to its reciprocal transpose ET, and seeing how much they differ. Whether ‘arb-profits’ are earned in space or in time, the end result is mathematically exactly the same. Therefore, true economic efficiency is measured by three parameters:
The difference between E and ET, multiplied by real GDP
The extent to which unfettered exchange is permitted
The extent to which symmetric information is available
That’s how you really measure market efficiency, at least in statistical arbitrage. And finally, to find out how theoretical physicists may be paid for doing research on quantum set theory by using one-true money backed by patents, please visit us at tnt.money. Just type “tnt.money” into your browser, and hit Enter. Oh, and by the way, Einstein was wrong. God does play dice with the universe, just loaded dice, loaded in a way such that God always wins in the end, on account of everything being entangled, and therefore Pareto-efficient and balanced in the long run—always. In this reality, no matter what, E always equals ET! Isn’t that what restated E=mc2 says: E4=ET⋅c2?
Conclusion
In a perfect market, mutually beneficial trade not only enhances Pareto efficiency but also serves as a real-world application of gradient descent optimization. This dynamic necessitates the use of money in its multifaceted roles to maximize overall welfare without disadvantaging any participants. Therefore, it logically follows that in a competitive free market, the effectiveness of a currency in fulfilling its essential functions—unit of account (U), medium of exchange (E), and store of value (S), collectively referred to as "U=S+E"—directly contributes to maximizing economic welfare.
This concludes our discussion, whose purpose was to formally integrate the first welfare theorem with our U=S+E definition of money, highlighting the essential roles of any currency in a competitive free market. These roles are crucial for enabling consumer-producer representative agents to maximize collective welfare, making a well-functioning currency indispensable for achieving optimal economic outcomes. Although this section is comprehensive, its length is justified. Moreover, as noted at the outset, it can be skipped by those who prefer to proceed directly to the subsequent discussion, which promises to be even more engaging and enlightening.
What Makes Money 'USE'-able?
Having established that the roles of money are intricately intertwined, as encapsulated by the U=S+E equation, it's crucial to understand what enables a currency to effectively fulfill these functions. 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 actively used in transactions. To function efficiently across all three roles, specific dual requirements are essential:
Unit of Account (U): For a currency to be an effective unit of account, it requires a stable supply—akin to the constant length of a ruler—and divisibility—similar to a ruler marked in increments. This divisibility allows prices to reflect a minimum price variation (MPV), such as one penny, which defines the precision with which values can be measured. Historically, stocks on the NYSE traded in increments of 1/8th of a dollar. However, the transition to decimalization, introducing a minimum price variation of one penny, not only streamlined trading but also enhanced the precision of price measurements. These improvements are crucial for ensuring that a currency reliably serves as a unit of account.
Store of Value (S): For money to effectively serve as a store of value, it must be safe to store and readily accessible when needed for exchanges. The risk of losing purchasing power through currency debasement underscores the importance of maintaining a stable money supply, highlighting the interplay between the roles of a unit of account and a store of value. Money must be difficult to steal, whether physically or virtually (via debasement), and should be immediately accessible when required. For example, gold buried on a deserted island, while secure, fails 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 difficult to counterfeit. This requires that recipients be able to quickly verify the authenticity of incoming payments, thus necessitating the ability to exclude counterfeit transactions, including bounced checks. Cash and gold coins, for instance, are simple to use for payments and their authenticity can be relatively easily verified, minimizing the risk of fraudulent transactions.
By evaluating any currency from the comprehensive perspective of serving as a unit of account (U), a store of value (S), and a medium of exchange (E), we can assess its use-value as money. In a free, competitive market, the efficiency with which a currency fulfills all six of the dual requirements listed above will impact its exchange value relative to all other goods and services in the economy, thereby making it the preferred alternative selected to be used as money among all competing potential currencies. Next, we will explore practical examples, such as gold coins, to illustrate these principles in action.
What Makes for Good Money: Some Case Studies
As we delve into this section, let's recap our discussion thus far. Money fulfills three primary functions: it serves as a Unit of Account (U), a Medium of Exchange (E), and a Store of Value (S). To effectively serve as a unit of account—a term synonymous with 'unit of measure' in monetary contexts—a currency must be both divisible and have a stable total supply. As a store of value, it should be readily accessible to the owner, yet secure against unauthorized access. Lastly, for optimal functionality as a medium of exchange, a currency must be easy to transfer and difficult to counterfeit, traits exemplified by cash or gold coins. Furthermore, for efficient operation as a medium of exchange, the cost of processing payments must be low, and the transaction speed should be high, as is the case when handing someone a $20 bill. However, this is not always the case with bitcoin payments, international wire transfers, paper checks, and especially credit card transactions—which, while fast, are particularly expensive.
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, typically around 3%, which the merchant must pay to the credit card company. As a result, the merchant receives slightly less, losing out on about 60 cents due to processing fees. While this wealth transfer may seem minor per transaction, it accumulates significant costs for both consumers and merchants, ultimately benefiting the credit card processor the most.
This scenario underscores why cash remains the most cost-effective payment option, aside from TNT-bank funds, which offer an innovative alternative. TNT-bank has addressed the inherent challenges of both traditional and digital payment systems with a robust, patent-pending, open-source solution. Our system replaces the traditional proof-of-work with a superior consensus algorithm, allowing anyone to monitor TNT-bank money for suspicious activities and prevent illegal transfers by refusing credits. This capability is enabled by our dual-approval private key system, specifically designed to authorize credits, not debits. In TNT, transactions must be dually digitally signed by both the spender and the recipient of funds in order to be deemed valid and recognized, and any transaction without both signatures is deemed invalid and does not impact account balances of either wallet.
Soon, this innovative feature will be available in our patented open-source, peer-to-peer distributed software, similar in deployment to Bitcoin software where all nodes run it. This enables any government-licensed bank, regardless of size, to adopt TNT-bank money as their general ledger. It ensures full compliance with all relevant financial regulations, offering a versatile and secure option for financial institutions eager to innovate and enhance their payment systems.
The Intersection of Mathematical Literacy and Cultural Icons: The Case of Mr. T
To underscore the practical implications of mathematical literacy and economic theory for our readers who have navigated through our discussions on the Arrow-Debreu model and the concept of rent-seeking, we present a compelling example involving a cultural icon. Mr. T, born Laurence Tureaud, emerged as a cultural phenomenon in the 1980s, most famously for his role as B.A. Baracus in the television series "The A-Team." Known for his rugged demeanor, mechanical prowess, and distinctive fear of flying, his character was often seen adorned with a full set of gold chains, which also became emblematic of Mr. T's persona both on and off the screen. His catchphrase, "I pity the fool!" and his unique style have cemented his place in pop culture as one of the most recognizable figures from the 1980s.
Today, imagine Mr. T walking into any New York airport, his neck draped with his iconic gold chains, flying off to California without a hitch. Contrast this with him carrying an equivalent value in gold coins or, especially, cash. In the latter scenario, he might face arrest under suspicion of money laundering, with his assets possibly being confiscated under current asset forfeiture laws. This stark difference in treatment illustrates not only the societal norms and legal stipulations around different forms of carrying value but also highlights the broader economic and regulatory implications.
The strict regulation of cash and the leniency towards other forms of wealth like gold jewelry can be viewed through the lens of rent-seeking. This economic concept, described by economists Gordon Tullock and James Buchanan, involves entities attempting to increase their share of existing wealth without creating new wealth, thus imposing a cost on society. Such dynamics are vividly demonstrated by the practices of payment processors that levy a 3% fee on credit card transactions, benefiting from the regulation and societal norms without contributing additional value to the economy.
This exercise in connecting theoretical economic concepts with tangible real-world scenarios, like that of Mr. T's experiences, not only enriches our understanding but also brings to light the subtleties of economic policies and their impact on everyday life. By marrying cultural references with economic theory, we aim to illustrate the pervasive influence of mathematical literacy in decoding complex, everyday phenomena.
Part I: From Cattle to Gold and Silver
Cattle have historically served as an effective unit of account, especially when their population remains stable, allowing a single cow to represent a sufficiently small unit of price variation. Indeed, cattle have functioned reasonably well as a currency in many aspects. As a store of value, cattle are notably difficult to steal due to their size and the specific conditions required for their upkeep, and they are relatively easy to transfer ownership, qualities that also make them a good medium of exchange. Furthermore, the authenticity and quality of a cow are relatively simple to verify, simplifying transactions.
However, the stability of this 'money supply' can be threatened by factors such as diseases like mad cow disease, illustrating that managing a currency system, even one based on livestock, is seldom straightforward.
Throughout history, various forms of currency have been utilized, each meeting the established criteria for effective money to varying degrees. Gold and silver, however, emerged as the dominant currencies for many centuries, especially under the bimetallic standard. Dating back to the Middle Ages, gold and silver coins were widely circulated. Notably, the exchange rate between these two metals remained remarkably stable at 15:1 for centuries, with one gold coin consistently valued at 15 silver coins. This stability persisted despite fluctuations in the available supplies of both metals. The enduring stability of this price ratio can largely be attributed to the fact that both gold and silver derived much of their 'use-value' from their application in minting circulating money.
Indeed, gold and silver coins have historically served as effective units of account due to their stable supply, which ensures a consistent measurement of relative prices. Their malleability allows for the production of coins in various denominations, facilitating transactions of differing sizes. Similar to adjustments in Minimum Price Variation (MPV) seen in stock exchanges' transitions from fractions to pennies, the metal content of minted coins can be altered to implement similar adjustments. However, historical periods like the Roman Empire witnessed adverse consequences due to increases in the money supply from lowering the gold content in coins. Despite these challenges, the adaptability of gold and silver coins as units of account is well-documented, underscoring their enduring utility in economic systems.
Part II: Why Commodity Money Leads to the Use of Bank-Money
As a medium of exchange, gold and silver coins are effective for in-person transactions but become impractical for remote payments, such as making a down payment on a Ferrari manufactured in Italy by a buyer in New York. Shipping gold to Italy presents logistical challenges and risks. While for most transactions, transferring coins directly incurs no additional cost, for high-value transactions like purchasing a luxury car, simpler methods like cash on delivery (COD) may prove inadequate. This scenario underscores the necessity for international wire transfers, which offer a more practical solution for handling significant monetary exchanges across distances.
While gold and silver coins are reliable for everyday exchanges, they are less suitable for complex international financial transactions, underscoring the necessity of banks in modern economies. Beyond facilitating long-distance payments, the role of banks is also critical due to the inherent limitations of commodity money, such as gold coins, as a store of value. These shortcomings, including vulnerability to theft, degradation, and the practical challenges of safe storage and transportation, highlight the essential functions of banks in safeguarding physical commodity money.
Commodity money presents significant drawbacks as a store of value. It is inherently easy to lose due to its physical nature, susceptible to theft, pilferage, or confiscation. Examples range from routine theft and household burglaries to government seizures, such as the 1933 incident in the United States when President Roosevelt ordered the surrender of all gold used as money. These vulnerabilities arise from the tangible and portable nature of physical coins, making them a risky option for long-term wealth preservation.
Part III: Bank Money-Units Introduce Issuer Counterparty Risk
The advent of bank money was intended to diversify the risks of physical loss inherent in commodity money. In the United States, until 1933, bank money represented fractional ownership of gold held in bank vaults. However, the issuance of excessive fractional ownership certificates, in forms such as cash and balances in checking and savings accounts (collectively known as M2), often exceeded the actual gold reserves. This imbalance contributed significantly to the Great Depression, although a detailed discussion of this historical event is beyond the scope of our current discourse.
While bank money was initially intended to mitigate the risks associated with the physical possession of commodity money, it introduced a new set of risks associated with the issuer itself, known as counterparty risk. This risk can lead to an expansion of the money supply, resulting in currency devaluation and undermining its effectiveness as a unit of measure. Historically, fiat currencies, which were invented and utilized as early as 800 years ago in ancient China, were generally avoided precisely because of their inherent excessive issuer counterparty risk.
Today, 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, facing 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 monetary use value due to being demonetized between 1850 and 1890 by all major economies of that era, is primarily valued as a commodity.
Part IV: Mitigating Issuer Counterparty Risk
Using gold as a reserve asset serves not only as a hedge against the known risks of future currency debasement, particularly in relation to the dynamics of the M2 money supply in the US, but also as a safeguard against the uncertainties associated with relying on fiat currencies as an asset class. In reality, fiat currencies derive their value primarily from the issuing government's promise to honor its fiscal obligations. This includes paying interest on bonds and accepting the currency for tax liabilities—a foundational principle of Modern Monetary Theory (MMT). Indeed, this governmental promise, when bolstered by central bank gold holdings, provides crucial support for the value of all fiat currencies, reinforcing their stability in the global financial system. By backing fiat currencies with gold, central banks offer a tangible assurance of their currency’s value, thus enhancing investor and public confidence even during periods of economic uncertainty.
The alternative to this promise-based system involves the direct enforcement of paper money usage through government authority, compelling its acceptance in transactions, as seen in places like the Soviet Union under Stalin and North Korea. Yet, as evidenced by the devaluation of currencies like the Venezuelan bolivar and the Argentine peso, such enforcement does not in and of itself secure substantial value relative to competing monetary units. These examples illuminate the inherent weaknesses in fiat currencies and underscore the enduring importance of gold as a stable and reliable reserve asset, essential for maintaining confidence in the monetary system.
The spendable money supply of any fiat currency, such as the US dollar—which is currently considered the most stable fiat currency—is almost certain to grow at a rate significantly higher than the supply of gold. This trend has been observable since the dollar was fully removed from the gold standard in August 1971 under President Nixon, and it is especially evident when looking at the dollar gold price after 1974, once Ford again allowed people to own monetary gold, having its price de-pegged from the dollar. Why or how people look at the dollar price of gold prior to 1974, when the dollar represented fractional ownership of gold, as evidenced by De Gaulle’s repatriation of dollars into gold as per prior agreements in the late 1960s, is beyond us!
While the broader implications of the disparity between the growth rate of fiat currency money supply and the supply of gold warrant further exploration, one inevitable result is the instability of the money supply, supported by a consensus from academic sources. This includes insights from the referenced Walrasian theory paper, which also asserts that instability in the fiat money supply is inevitable. This perspective highlights the inherent challenges in managing fiat currencies within modern economic frameworks.
This instability is a product of the rational utility maximization axiom, as no politician acting rationally within this framework will opt to raise taxes when they can simply increase the money supply by default. Thus, to introduce a rare biblical reference in an academic discussion, even if King Solomon himself, endowed with divine wisdom, were appointed head of the Federal Reserve, he would likely decline the position. However, hypothetically assuming he accepted, the instability in the M2 money supply would still inevitably ensue as a simple consequence of unfunded spending.
It is precisely for these reasons that cryptocurrencies have gained substantial value in the marketplace. They epitomize the ideal of what money could be: decentralized, stable, and unaffected by the whims of political changes. Interested in learning more about how cryptocurrencies achieve these attributes? Explore their potential and compare them to traditional forms of money by visiting us at tnt.money!
While this article has extended beyond its intended length, we fulfill our promise by demonstrating how replacing M⋅V (Money Velocity) with E⋅V (Medium of Exchange Velocity) transforms MV=PY into a comprehensive accounting identity: EV=PY. This adaptation provides a clearer understanding of how money circulates within an economy, reflecting the direct impact of the medium of exchange on overall economic activity.
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 figure represents the unit of account (U)—the total money available in the economy 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.
The M2 money supply, also referred to as the spendable money supply, mirrors the number of minted gold coins in a bank-less monetary system. It includes all money units readily accessible for transactions, encompassing cash, checking account balances, savings accounts, and money market funds. Classified by the Federal Reserve Bank, these components 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 serving effectively as mediums of exchange.
Bank accounts, a key component of the M2 money supply, are often used to store funds when short-term liquidity is necessary, much like gold coins used to be stored in a vault in case purchasing power was needed—gold (and money in general) being the most widely accepted payment medium. This could be for covering margin calls, unforeseen expenses, or temporary job losses, showcasing money’s role as the most liquid asset—a store of value characterized by purchasing power.
Particularly in environments marked by low interest rates and minimal inflation, savings accounts often become preferable to bonds due to their greater liquidity and lower risk. Unlike bonds, where prices can decline if yields rise, the balance in a savings account remains stable. This makes using components like bank accounts as savings vehicles particularly appealing during periods of low interest rates, as cash assures stability of value. While there is no upside to holding bonds given that yields cannot turn negative and drop because cash exists, yields can always increase, as they have historically. This introduces an additional price risk to holding bonds, absent in bank accounts classified as M2, yet both having roughly comparable yields. This exemplifies how a part of the M2 money supply can be used as S (Store of Value).
Understanding the Quantity Theory of Money
Contrary to common perception, the quantity theory of money is not merely a theoretical construct but an accounting identity, expressed as a tautology based on arithmetic laws. This principle is paralleled in the financial realm, as demonstrated in Bill Sharpe's 1991 paper, "The Arithmetic of Active Management." Sharpe illustrates that active investors, when considered collectively, cannot outperform the market because they collectively own the market—or more precisely, the segment of the market portfolio not held by passive investors. Sharpe’s findings emphasize a reality governed by accounting principles rather than theoretical speculation.
Similarly, the quantity theory of money establishes a straightforward accounting equality between inflation and nominal GDP. Nominal GDP is defined as the total market value of all final goods and services produced and consumed within an economy by end users. This contrasts with gross output, which includes all production activities, accounting not only for final products that contribute to GDP but also for intermediate goods consumed during production, such as the sand used in making semiconductors.
The quantity theory, often described as an identity or equality in monetary economics, asserts that MV=PY. This equation becomes a straightforward accounting identity when each variable is precisely defined within the realm of mathematical economics. Let's define what we mean by variables P and Y.
'P' - Price Level: P represents the price level, a core concept in macroeconomics and a formal indicator of inflation. Inflation is typically measured by the Consumer Price Index (CPI), which tracks the general price level of a diverse basket of goods and services. This basket is selected to reflect the composition of the broader GDP, serving as a barometer for average price movements over time. The CPI is calculated by averaging the price changes of these goods and services, weighted by their significance or share in typical household spending patterns.
'Y' - Volume of Final Goods and Services (Real GDP): Y denotes 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 exclusively on physical output and thus eliminating distortions due to price changes. Y measures the economy's overall productive capacity and output in real terms, offering a snapshot of economic activity and health.
By combining P, the price level, with Y, the volume of final goods and services, we calculate nominal GDP. This metric encapsulates the total value of all transactions within a year, obtained by multiplying the quantity of items purchased by their prices. Nominal GDP reflects the total spending on final goods and services, excluding intermediary consumption like the lumber used in furniture making, without any adjustment for price fluctuations. It thus provides a comprehensive overview of the economy's output in dollar terms, summing up the market value of all final goods and services consumers paid for in a year.
Exploring Economic Concepts Through the Stock Market Analogy
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. If we extend this analogy, the S&P 500 would be analogous to the final goods and services, while non-S&P stocks would represent intermediate consumption. In this context, nominal GDP is similar to the dollar trading volume, reflecting the total value of these transactions. This comparison helps distinguish between the physical volume of economic activities (real GDP = share trading volume of the S&P 500 index) and their total monetary value (nominal GDP = dollar trading volume of the S&P 500 index).
Expanding on this comparison, consider 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, where the weights are based on their market capitalization. Similarly, calculating CPI inflation mirrors this approach but with a crucial modification: instead of using market capitalization as the weight, it uses the past year’s dollar trading volume for each stock. This method is analogous to how CPI inflation is calculated by weighting the price changes of goods and services according to their share of total consumer spending. By adopting this approach, the calculation emphasizes the impact of price changes on the average consumer, focusing on their spending habits.
Using the U=S+E Formula to Clarify that 'M=E' in MV=PY
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. When this dollar trading volume is divided by the portion of the money supply actively participating in transactions (referred to as 'E' in the equation U=S+E, rather than the entire spendable money supply or 'M2', which is 'U'), we reveal an accounting identity. This identity illustrates how Nominal GDP, or the total economic activity in dollar terms, is facilitated by transactions using money as a medium of exchange.
The 'MV' part of the equation often leads to discussions about whether MV=PY is theoretical rather than an accounting identity. This perspective typically stems from misconceptions about what 'M' (money supply) and 'V' (velocity of money) represent. In the U=S+E formula, 'U' represents the total M2 money supply when considering the broader spectrum of available money.
In the context of the MV=PY equation, it is crucial to recognize that 'M' specifically aligns with 'E', not 'U'. This distinction redefines the traditional interpretation of the quantity theory of money, positing E⋅V=PY as the accounting identity. Here, 'E' represents the portion of the money supply that is actively engaged in economic activities, distinct from 'S', which denotes saved or non-circulating money.
Importantly, 'S' includes funds held in savings accounts, which are part of the M2 money supply, but it excludes investments like government bonds (typically categorized under M3) or other assets that are not considered immediately spendable or on-demand within M2. Therefore, while 'S' is included in M2, it is viewed as money that is removed from immediate circulation, not contributing directly to the transactions and broader economic interactions that drive nominal GDP.
This clarification allows for a deeper understanding of how money circulates within the economy and the dynamics between circulating and non-circulating funds, emphasizing the active role of 'E' in influencing economic output as measured by nominal GDP.
Exploring the Dynamics of Money: Is It V or the E/S Balance in the U=S+E Equality?
The distinction between 'E' (money designated for spending) and 'S' (money saved or invested) in the use of the M2 US dollar money supply is key for understanding the intricacies of money's role in the economy and its impact on overall economic activity. This distinction underscores that the significance of money is not determined solely 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 the velocity of share trading volume reflects the speed at which stocks change hands, further emphasizes this point.
However, unlike the stock market, the volume of transactions in an economy tends to be remarkably stable over time. Money used as a medium of exchange ("M", properly redefined as 'E' in the U=S+E equation) is primarily earned as income (typically wages) and spent to purchase goods and services, contributing to nominal GDP. The repetitive nature of consumer spending—on necessities such as clothing, food, rent, and haircuts—reflects our inherent consumer behavior, resulting in a frequency of transactions that remains relatively constant. Unlike the volume of shares in the stock market, the transaction volume of GDP remains super-consistent.
Therefore, when we estimate 'V' by dividing Nominal GDP by the total M2 money supply (instead of by 'E'), the result can lead to misconceptions. Any observed changes in 'V' are better understood as shifts in the balance between 'E' (money actively participating in economic transactions) and 'S' (money held out of the active circulation) 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', when computed using M2 instead of 'E', reflect changes in the distribution and utilization of money within the economy, rather than merely the rate at which it moves. This approach underscores that it is the dynamics of money's distribution and its engagement in economic activities that truly shape economic conditions, not just the speed at which it changes hands.
Understanding Monetary Dynamics with the U=S+E Framework
When we examine the velocity of money, V, the picture isn't very clear from M2 Velocity6 alone. However, analyzing the relationship between the M2 Money Stock7 and Nominal GDP8, both indexed9, significantly clarifies the situation. The implementation of Quantitative Easing (QE), which pushed bond yields and inflation rates down to nearly zero, led to a noticeable shift in the utilization of M2 assets from E (exchange) to S (store of value), as evidenced in the M2-GDP indexed graph post-2010. This trend is now reversing due to visible monetary inflation. Moreover, the precariousness of the current situation is significantly exacerbated by the fact that the $27 trillion in publicly held Federal debt10—interest payments on which are added to M2—exceeds the $21 trillion M2 money supply. This ensures that, regardless of the interest rate level, real interest rates remain negative.
At TNT-bank, we believe this perspective provides a clear understanding of complex economic indicators by elucidating how the quantity theory of money serves as a framework for comprehending the dynamics between money supply, velocity of money, price levels, and economic output. Drawing parallels to familiar stock market transactions helps make these concepts more tangible and accessible, demonstrating how foundational economic principles manifest in practical scenarios.
Moreover, examining the relationship between nominal GDP and the M2 money supply, given the reality of the existing welfare system and significant personal savings, the actual count of real-world transactions facilitated using money as payment does not change very much. This highlights the risks associated with relying on fiat currency or dollar-denominated fixed-income securities to preserve purchasing power. This distinction underscores the importance of understanding not just the quantity of currency in circulation but also its velocity and the broader economic context in which it operates.
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.
Conclusion
We invite you to explore further insights at tnt.money, where you will find valuable information at absolutely no obligation or cost. Our goal is to ensure symmetric information about the products we offer. We want you to know what you buy as a client, which is why everything we sell is fully open source. At TNT-bank, we embody the True-NO-Trust principle, represented by our commitment to Transparent Network Technologies, ensuring free and open access to all information on our site. Our innovative approach to TNT-bank money, which can represent fractional ownership backed by real or intellectual property assets, including copyrights and patents, caters to a growing preference for alternatives that may mitigate the risks of volatility and devaluation inherent in traditional fiat currencies.
Our discussion does not conclude here. Additional essays that delve into the intricate realms of 'mathecon game theory black papers' and subjective logical claim rings—an abstract algebraic framework designed to mathematically model cognitive biases—are available at tnt.money. We are committed to avoiding derogatory labels and unjust accusations of irrationality simply because someone is influenced by prevailing dogmas or affected by cognitive biases such as theory-induced blindness. Attentive readers will recognize that such blindness often stems from a dogmatic belief in the implicit assumptions underlying faulty, assumption-dependent axioms, rather than from the logical conclusions of the theories themselves. This phenomenon is akin to how the Pythagorean theorem inevitably results from the Euclidean axioms, a concept understandable even to a diligent fifth grader. Remember, 'garbage in, garbage out’!
In closing, we propose a novel approach to bolstering economic systems: consider backing money with patents. This approach could synchronize currency with innovation, fostering a culture of continuous technological advancement and replacing the negative externalities of traditional mining with the positive externalities of mining intellectual capital. Imagine a world where every new invention not only advances society but also strengthens the economy. This straightforward yet revolutionary idea could be the key to a more dynamic and sustainable economic future.
We urge the academic community, policymakers, and innovators to explore and adopt these ideas, advancing our scientific and technological capabilities to create a more equitable and prosperous world. Let us work together to harness the power of intellectual capital, transforming it into a cornerstone of our economic systems, and thereby driving sustainable growth and development.
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1https://www.stlouisfed.org/education/economic-lowdown-podcast-series/episode-9-functions-of-money
2https://scholar.harvard.edu/files/maskin/files/a_walrasian_theory_of_money_and_barter.pdf
3https://www.quantamagazine.org/pioneering-quantum-physicists-win-nobel-prize-in-physics-20221004/
6https://fred.stlouisfed.org/series/M2V
7https://fred.stlouisfed.org/series/M2SL
8https://fred.stlouisfed.org/series/GDP
9https://fred.stlouisfed.org/graph/fredgraph.pdf?hires=1&type=application/pdf&bgcolor=%23e1e9f0&chart_type=line&drp=0&fo=open%20sans&graph_bgcolor=%23ffffff&height=450&mode=fred&recession_bars=on&txtcolor=%23444444&ts=12&tts=12&width=1318&nt=0&thu=0&trc=0&show_legend=yes&show_axis_titles=yes&show_tooltip=yes&id=M2SL,GDP&scale=left,left&cosd=1959-01-01,1947-01-01&coed=2024-03-01,2024-01-01&line_color=%234572a7,%23aa4643&link_values=false,false&line_style=solid,solid&mark_type=none,none&mw=3,3&lw=2,2&ost=-99999,-99999&oet=99999,99999&mma=0,0&fml=a,a&fq=Quarterly,Quarterly&fam=eop,avg&fgst=lin,lin&fgsnd=2020-02-01,2020-02-01&line_index=1,2&transformation=nbd,nbd&vintage_date=2024-05-06,2024-05-06&revision_date=2024-05-06,2024-05-06&nd=1959-01-01,1959-01-01
10https://fiscaldata.treasury.gov/datasets/debt-to-the-penny/debt-to-the-penny