Economics
Extracted separately
Estimating Pareto-efficiency of Real-World Exchange
by Joseph Mark Haykov, with Nathan and Phillip as interns
May 23, 2024
Abstract
In the specific context of the first welfare theorem of mathematical economics, a foundational theorem that forms the basis of the broader Arrow-Debreu model, achieving even local, let alone global, Pareto-efficiency necessitates, at the very least, unfettered exchange under symmetric information. In this paper, we examine not only the precise mechanics of how violations of these assumptions result in real-world inefficiencies – such as low or negative per capita GDP growth – but also how these resulting inefficiencies can be more accurately estimated than is currently possible.
JEL Codes: D51, D82, G14, E31, C60, O47
Keywords: Pareto Efficiency, Arrow-Debreu Model, Symmetric Information, Unfettered Exchange, Consumer Surplus, Producer Surplus, Market Efficiency, Arbitrage, Exchange Rates, Real GDP, Labor Productivity, Statistical Arbitrage
Introduction
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 by setting the gradient of the objective function to zero in an equilibrium, the global maximum value of welfare is obtained. 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. Equal knowledge ensures mutual benefits in reality under the condition of unfettered trade. For example, consider someone buying a bottle of Coca-Cola from Walmart, where the producer knows exactly how much money they are receiving, and the consumer knows exactly what they are buying.
Mathematically, such guaranteed mutually beneficial trade, referred to as Pareto-improving, 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 the individual consumer faces in their dual role 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 account within the Arrow-Debreu framework, as this allows us to relate the “true” cost (opportunity cost) of the goods and services we consume to their subjective expected use value in our dual role as consumers. Money 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. The question then becomes: how do we actually measure the extent to which Pareto efficiency is obtained in the real-world economy, either using money or not? In other words, how can we tell if an economy is functioning efficiently? This is the question we address in this paper.
The Current Approach
The way we rank real-world economies, such as those of Canada vs. Ireland or the Dominican Republic vs. Haiti, by their efficiency (or Pareto-efficiency) is by evaluating metrics such as the level of unemployment and real per capita GDP, both level and growth. Essentially, an economy is considered better if it has a growing GDP and low unemployment – key indicators of efficiency. However, these metrics do not actually measure productivity efficiency.
Productivity is measured by real GDP, not per capita, but per labor force participation rate (or more precisely, per the total number of hours worked per annum). In this sense, increased productivity can paradoxically result in high unemployment but also high per capita GDP, if managed properly.
Before we learn to jump, let us first learn how to walk. How do we define market efficiency in a way that dually measures welfare correctly, not only in terms of benefits realized from additional consumption (as measured by real per capita GDP), but also benefits realized from additional leisure (as measured by lower labor force participation rate and sometimes high unemployment)? This is the challenge we must address to understand and improve economic efficiency comprehensively.
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.
For example, the Pythagorean Theorem holds true only 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. Consequently, 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 starts with an analysis of the Forex market, where approximately 30 of the most actively traded currencies are represented in a symmetrical 30-by-30 matrix, denoted as E. This matrix serves as a model for understanding how exchange rates between currencies are structured to prevent arbitrage.
Arbitrage, by its nature, is unfeasible when a uniform price is maintained for any asset across different markets. Specifically, in the foreign exchange market, if the exchange rate for currency A to B is set, then it must be the reciprocal of the exchange rate from B to A. For instance, if $1 buys £0.50, then £1 should buy $2. This reciprocal relationship is crucial to eliminating arbitrage possibilities stemming from rate discrepancies.
Let 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 both 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, this is expressed as: E=(E∘E−1)T where ∘ denotes the Hadamard product, and E−1 is the matrix formed by taking the reciprocal of each element in E. This expression ensures that E is symmetric in such a way that it mirrors the reciprocal nature of currency exchange rates. Mathematically, this is expressed as:
where eij represents the exchange rate from currency i to currency j, and ET denotes the reciprocal transpose of E.
This E=ET “no-arb” constraint is somewhat similar to the property of a matrix being involutory, where an involutory matrix is its own inverse, E=E-1. However, while E⋅E−1=I (the identity matrix), E⋅ET=n⋅E. As we can see, the resulting matrix is not the identity matrix but rather a scalar multiple of E scaled by its row count, n. 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. For any no-arbitrage E=ET matrix has one ET root:
𝐸⋅𝐸𝑇=𝐸𝑇⋅𝐸=𝐸⋅𝐸=𝐸𝑇⋅𝐸𝑇=𝐸2=𝑛⋅𝐸
This aligns with the principle that multiplication is associative. However, just as division is not associative, the product of 𝐸 with its transpose (𝐸⋅𝐸𝑇) is not the same as the product of its transpose with itself (𝐸𝑇⋅𝐸). Regardless of whether 𝐸 is pre-multiplied or post-multiplied by its transpose, the result, when squared, is always 𝐸4. Conceptually, the reciprocal operation of raising 𝐸 to the fourth power represents taking the fourth root of 𝐸, which generally results in four such roots of the 𝐸4 (or 𝑛2⋅𝐸) matrix: 𝐸 pre- and post-multiplied by its transpose, and the reciprocal Hadamard transpose. Since the two Hadamard roots are the same, there are three distinct roots. Both of the non-Hadamard roots, when raised to the fourth power, result in the same 𝑛2⋅𝐸 matrix.
(𝐸⋅𝐸𝑇)⋅(𝐸𝑇⋅𝐸)=𝐸⋅𝐸𝑇⋅𝐸𝑇⋅𝐸=𝐸⋅𝐸𝑇⋅𝐸𝑇⋅𝐸=𝐸4=𝑛⋅𝐸2=𝑛2⋅𝐸
(𝐸𝑇⋅𝐸)⋅(𝐸⋅𝐸𝑇)=𝐸𝑇⋅𝐸⋅𝐸⋅𝐸𝑇=𝐸𝑇⋅𝐸⋅𝐸⋅𝐸𝑇=𝐸4=𝑛⋅𝐸2=𝑛2⋅𝐸
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.
We believe it is worthwhile to highlight what might be an obvious connection. In the context of Einstein's equation E=mc2, if we represent the terms E and m as an E=ET matrix instead of a vector, we see that E4=m4c2, where the energy and mass “vectors” are inverse cross-products of each other. By taking the square root of both sides, we see not only that mass is the reciprocal of energy but also that both mass and energy have four square roots—computed by not only post-multiplying but also pre-multiplying the E matrix by not only its actual transpose, but also the transpose of the Hadamard inverse. Yet (E⋅ET)2 has just one root, namely E, because E=ET.
While this is all purely conjectural, it aligns not only with the supersymmetry principle in theoretical physics but also—shockingly—with the ancient Hermetic principle of "as above, so below." Additionally, the idea somehow mirrors the geometry of the Egyptian pyramids, though we can’t prove it. At this point, we should emphasize: because we are not theoretical physicists, you should take everything we say about physics with a big grain of salt. We only know a little bit of theoretical physics, having interacted with physicist colleagues during our time on Wall Street.
Therefore, these ideas about quantum set theory are purely speculative—just in case it helps a physicist who is not on Wall Street making real money working for hedge funds like Renaissance, started by the late Jim Simons1.
Condensation of Information
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:
Reduced Dimensionality: 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.
Data Compression: 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.
Basis for a New Set Theory
Extending this idea to a theoretical framework, especially in contexts like quantum mechanics, can lead to intriguing possibilities:
Modeling Quantum States: 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.
Set Theory and Quantum States: 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.
Applications: 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 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 lectures2, 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.
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The Role of Linear Algebra in Market Efficiency
As mathematical economists, we find that this linear algebra formulation captures the essential idea that in an arbitrage-free market, the reciprocal relationships between exchange rates across different currencies, as well as all goods and services, must be consistent. This consistency prevents opportunities for arbitrage by merely transposing and reciprocating the matrix of exchange rates. Within this framework, prices effectively represent the exchange rates of all goods and services relative to a single specific row or column in the full exchange rate matrix E, selected as the optimal unit of account. This framework supports the theories of Arrow and Debreu and even, astonishingly, aligns with the ideas posited by Marx. Indeed, the fundamental role of money is to regulate markets by preventing arbitrage.
In the real world, the practice of quoting all currencies in the foreign exchange (FX) market against a single standard currency, such as the U.S. dollar, 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, because 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 in any way.
Please 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.
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 relative prices with a ruler whose length is effectively constantly changing, as the spendable money supply, like M23, 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 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.
Conclusion
So, what is the optimal distribution of surpluses? 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, 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. In this reality, no matter what: E always equals ET in the end! As per that E=mc2 equation? No?
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3https://fred.stlouisfed.org/series/M2SL