Money and Commerce under the one-truth postulate
By Joseph M. Haykov
Under the existing dictionary definition of the adjective “objective”, an objective definition must be factually accurate, which is to say an objective definition may not contradict any known facts. Currently, no such definition of money exists in economics. As clearly demonstrated by the fact that under whatever definition of money they use, most mainstream economists claim with absolute certainty and total conviction that gold has not been money for decades. However, this claim is clearly contradicted by the fact that under the 1999 Central Bank Gold Agreement (CBGA), central banks continue to maintain a huge hoard of gold. Moreover, the FOURTH CBGA agreement signed in 2014, explicitly states: “gold remains an important element of global monetary reserve”. So how can we objectively define money? Only recursively, in terms of commerce. And though money is thousands of years old, recursive definitions are a far more recent concept than money, and for this reason are essentially non-existent. We feel this is an oversight because recursive definitions allow us to model subjective perception.
Preface
The title of this paper is “Money and Commerce under the one-truth postulate”. Let us therefore first-define the one-truth postulate as:
The one-truth postulate states that EVERYTHING recursively defined under the one-truth postulate is true under the definition of itself BUT ONLY under the following two CONDITIONS:
1. one-truth ASSUMPTION: only one single unique objective truth exists which is that something is objectively either true or it isn’t.
2. NOTHING defined under this postulate contradicts itself.
OK, so what is the first “one-truth” postulate? What is its purpose? This postulate represents a formal logical/mathematical framework under which science can be done with mathematically provable precision, that is OBJECTIVELY, which is to say mathematically measured by maximum likelihood, resulting in NO theory induced blindness. Also, the one truth postulate is a PARTIAL solution to the Hilbert program, but ONLY under itself. That is because everything stated under the one truth postulate is by induction true under the existing rules of mathematics. Which is to say that everything currently known in/about mathematics is true under the one truth postulate.
This is explained in the attached Appendix A, also available online here
and here
Now, let us be careful right from the get go. There may be other PARTIAL solutions to the Hilbert program, such as the one truth postulate, or even FULL solutions, that we may not yet be aware of, and for THIS REASON!!! I am calling it not THE truth postulate, but only the FIRST truth postulate, which is to say the first “truth postulate” as first-defined by Haykov. For the simple reason that in this context “ONE” and “FIRST” are the same, but we should all be aware that other, additional postulates that PARTLY or FULLY solve the Hilbert program may eventually be found. So ONE and FIRST truth postulate can be used interchangeably, as synonyms, as they represent the same thing ONLY FOR NOW!
Under this postulate and also under Occam’s Razor, this paper describes Money and Commerce as re-discovered by Joseph Haykov based on facts as subjectively perceived by not only Joseph Haykov, but also Walter Block, in the winter of 2023.
Commerce
When people engage in commerce using money, what do they pay attention to first and foremost? It is of course the price. Which makes money, first and foremost, a unit in which prices are quoted and measured. OK, but what exactly do prices represent in the real world? The exchange rate of money to a particular product. Which makes money the exchange rate of itself to all goods and services traded using this money.
Such circular definitions, when things are inherently defined in terms of themselves, are called recursive in math and computer science. For example, the famous René Descartes quote “I think therefore I am” is recursive. The Fibonacci sequence in mathematics is recursively defined in terms of itself. In computer science, entire programming languages are defined recursively. For example, in a programming language called scheme, the ‘eval’ function is defined in terms of the ‘apply’ function, and the ‘apply’ function is defined in terms of the ‘eval’ function. And the entire scheme language is specified as an infinitely recursive apply/eval loop. So we end up with a recursive definition of money in terms of commerce conducted using money. So what? We know how to think recursively. Ask any scheme programmer. Indeed, all axioms, which is to say definitions in mathematics are either recursive or make assumptions or both, as already explained.
In fact, we are not saying ANYTHING new, as it pertains to money. It is already well known that money and trade are inexorably linked. There is no money without trade in which it is used as means of exchange. The German deutschemark was one of the most widely and actively used currencies in Europe for decades, up until the switch to the euro. However, now that it is no longer used in trade, the deutschemark today is just a piece of paper, only valuable as an old relic. And trade without money is by definition barter.
Barter
Of course we always try to barter, to the extent we can. That is exactly what kids do in school when they swap lunches or Pokemon or bubble gum cards. But as we all know, the double coincidence of wants problem makes barter, which is to say trade without money, VERY difficult. But HOW EXACTLY DOES money solve the double coincidence of wants problem that grinds down almost entirely to a halt the real world use of barter as a means of exchange? It has always been assumed that money is required to solve the double coincidence of wants problem. However, this is simply not true. Technically, there a way to use barter as a means of exchange, without using any money!
Imagine a central exchange, like the NYSE, where all those interested in barter could come to participate. And the exchange would offer everyone a chance to barter things, by placing limit and market orders. All matching orders would be filled at the closing auction, just like the one currently being conducted on the NYSE at 4 pm daily, except weekends and holidays. In this way, people could barter anything they would be willing to produce, in exchange for anything they planned on consuming. So a chicken farmer might place a limit order, “produce a dozen eggs in exchange for 2 quarts of milk”. Or he might place a market order, “produce a dozen eggs in exchange for the most milk I can get for my eggs”. And then the barter exchange would fill ALL matching orders at the closing auction, exactly as NYSE does every day currently, at 4 PM, except weekends and holidays.
And this may, and perhaps even not entirely theoretically, result in trade with no money changing hands. But wait a second! That is exactly what is happening right now. This is what the vast majority of people in the real world do with money. They trade their wages for what they consume. And their wages represent what they produce. So what is the purpose of money in all this? The answer lies in how money itself is exchanged!
Prices
Of course money itself is exchanged in the FX market. For example, suppose you are raising cows in Argentina, and shipping them to a restaurant in Dubai, which pays you in United Arab Emirates dirham. And you want to trade the dirham for Argentine pesos, as you live in Argentina. But there are roughly 30 currencies people are exchanging. IN THEORY, the alternative to having a single exchange rate to US dollars for all currencies would be to maintain a 30-by-30 matrix of exchange rates. But IN REALITY, this is not the case, because under the condition of no available arbitrage, the 30-by-30 matrix of exchange rates becomes equal to the reciprocal of its transpose, which makes it involutory.
What we are saying is that if there is no available arbitrage, then the exchange rate of dollars to euros must be equal to the reciprocal of the exchange rate of euros to dollars. More formally, if no arbitrage is available then for any two currencies as represented by a subset {X, Y}, the following condition must hold:
[exchange rate of X to Y] = 1 ÷ [exchange rate of Y to X]
Mathematically, this makes the exchange rate matrix, as represented by [exchange rate of X to Y] = the reciprocal of its transpose, as represented by 1 ÷ [exchange rate of Y to X]. Which of course by definition makes the exchange rate matrix involutory.
As we may remember from basic linear algebra, an involutory matrix is a matrix that is equal to its own inverse, which means that its eigenvalues must be either 1 or -1. Of course if ALL elements of a matrix are positive, as they are in this case, then ALL its eigenvalues must also be nonnegative, because the determinant of this matrix is positive and the sum of the eigenvalues of any matrix is equal to its trace, and the trace of any exchange rate matrix, by definition will be its size, because the diagonal elements of ANY exchange rate matrix represent the exchange rate of a currency to itself, and are therefore all equal to 1, by definition. Thus, the rank of any such matrix is 1, because it has only 1 non-zero eigenvalue. And ANY involutory matrix of rank 1 is fully defined by any one of its rows or columns, by definition, under the existing rules of matrix multiplication. And it is precisely the dollar row or column, doesn’t matter in the least, that represents the single exchange rate of all currencies to the USD under the condition of no arbitrage. To reiterate, the full 30-by-30 exchange rate matrix under the condition of no available arbitrage becomes fully defined by ANY ONE of its rows or columns of length 30, because more than 30 different exchange rates mathematically represents an arbitrage opportunity under free trade!
But there is no need to bring linear algebra into this, as the exact same thing can be just as easily explained in plain English. Under the condition of no available arbitrage, to the extent that it exists in the real world under free trade, currencies will automatically wind up having one exchange rate into a single numeraire, which today happens to be the US dollar. For the simple reason that adding another numeraire, such as the euro, not only adds no value, but also makes things far more inconvenient, because an arbitrage opportunity opens up any time the ratio of the price of any currency in euros to the price of the same currency in dollars differs from the exchange rate of euros to dollars. This means that in the real world, relative prices of all currencies as measured in euros, and as measured in dollars, and by induction, as measured in any of the other currencies, will be identical under the condition of no available arbitrage. Which is to say that the exchange rates between all currencies will, in the real FX market, to the extent that in the real world under free trade there is no available arbitrage, converge to a single set of arbitrage free relative prices, as represented mathematically by the fact that ANY single row or column fully defines the entire set of all possible exchange when there is no available arbitrage.
Of course supply and demand is what will ultimately determine the exchange rates, but if no arbitrage is available then exchange rates will converge to one unique set of arbitrage free relative prices, ultimately determined by supply and demand. And money units are whatever is elected to measure prices by the active market participants collectively, as a group, to ensure no availability of arbitrage under free trade. The “whatever is elected” in today’s forex market happens to be the dollar. But it just as easily could have been gold, or any other money. So long as there is a single exchange rate into some money that ensures no easily available arbitrage under free trade, which we call price. Let us first-define the terms no-arbitrage, or equivalently arbitrage-free, to refer to the condition of NO easily available arbitrage in the real world under fully free trade. Indeed, we can recursively define price as the exchange rate of money and goods and services whose prices are quoted and measured in this particular money. And while this all sounds good in theory, the truly important question is: how does USD forex money actually work, in the real world?
In the real world, currencies are traded in pairs. The US dollar is the most actively traded currency, as the most common pairs are the USD versus the euro, Japanese yen, British pound, and Australian dollar. So, if you were to actually exchange the dirham for the peso in the real world, you would most likely first exchange the dirham for the dollar, and then the dollar for the peso. In other words, you would wind up using the USD as a means of exchange. However, there are trading pairs that do not include the dollar. They are referred to as crosses. The most common crosses are the euro versus the pound and the euro versus the yen. So a different merchant, one that ships wine from France to Japan for example, is likely to wind up simply exchanging the yen for euros directly, without any dollars changing hands. In this case, US dollar would NOT be used as a means of exchange, but only as a unit of measure, because the USD-EUR and the USD-JPY currency pairs represent the dollar prices of euros and yen, which determine the EUR-JPY cross rate!
And the fact that money, as represented by the USD in this example, is not-always used as a means of exchange in forex trading, is what clearly demonstrates that the first-primary function of money is indeed that of a unit of measure, and only as a result of money inherently being a unit in which prices are measured does money also become an accepted form of payment, and therefore a means of exchange. Which is to say that money is not inherently a means-of-exchange, but only a recursively-induced-also means-of-exchange, whose first-primary purpose is to be a unit-of-measure in which prices are quoted and measured. For there can only be one price for any one given item, or else under free trade, an arbitrage opportunity opens up. And having one set of prices is what ensures no-arbitrage, precisely because without ONE set of arbitrage-free relative prices under which it can be conducted, ANY exchange becomes VERY inefficient, by definition, due to presence of arbitrage, which ALWAYS exists any time the number of exchange rates, as represented by the number of prices, is greater than the number of items being exchanged.
And now we can clearly see why the existing definition of money in economics does not work. In economics, money is defined as a generally accepted medium of exchange, which does not always define money! For example, stock options clearly fall under the definition of a generally accepted medium of exchange, because stock options represent a generally accepted form of payment by the CEOs of publicly traded companies. But stock options are clearly not money! Moreover, gold in the US under the Bretton Woods system clearly WAS money, as evidenced by the fact that in the mid 1960s, France was able to officially exchange dollars for gold, but otherwise, gold was NOT used a medium of exchange AT ALL! One could not even legally own gold money in the US from 1933 up until 1974.
What we are saying is that BEFORE ANY trade can be settled using money as payment, one must FIRST agree on the PRICE. This makes it impossible to define MONEY without first-defining PRICES! But under the proper definition of money as: SOMETHING that is used as a unit in which prices are quoted and measured, everything makes sense! Under this definition of money, stock options represent a formula that determines compensation as measured in dollars based on stock prices as also measured in dollars. And of course under the Bretton Woods system, gold WAS indeed money, but money that was used only as a price measure. Similarly to how the US dollar, in the real world FX market as it actually exists today, is sometimes used only a price measure that determines cross rates, such as the EUR-JPY rate, but is not otherwise used as a means of exchange.
Money
Consider the innumerable things that have been used as money throughout history. Salt, cigarettes, buckskins, pieces of paper, numerous metals such as gold and silver (typically in the physical form of coins and bars), sea shells, tally sticks (split tree branches), and all kinds of ledgers that used to be written down, but these days are mostly stored electronically, and this is just the tip of the iceberg. All of it of course makes sense because any money is better than no money at all, because without quoted prices as measured in something, we can only engage in terribly inefficient, prone to arbitrage barter.
Again, to reiterate, commercial free trade requires a set of arbitrage free relative prices, and therefore money, which is first-needed because prices have to first-exist BEFORE ANY ACTUAL EXCHANGE OCCURS, simply because prices need to be quoted and measured in SOMETHING that by definition must already exist, before trades are settled! And this SOMETHING is what we call money. Even if something we call money is local tree branches. Even if something elected to measure prices is salt. Or pieces of leather. Or sea shells. People in prison collectively, as a group in in the real world, often elect to measure prices in cigarettes or cans of meat. Today, as we write this, a large group of real people are voluntarily electing, collectively as a group to measure prices in an old paper currency that was issued by a country that no longer exists – the Yugoslav dinar, which was the currency of the former Socialist Federal Republic of Yugoslavia. The country dissolved in the 1990s, but the dinar is still used in some parts of the Balkans.
As all these examples clearly illustrate, it does not matter in the least as to what money is, so long as it can be used to quote and measure prices in the real world. This is exactly why so many different things have been used as money. Even things we consume have been used as money. But in terms of trade, money is a prerequisite. Without prices, free trade is prone to arbitrage and consequently becomes barter, that is so inefficient as to be of little practical significance as it pertains to the overall amount of real world exchange. In fact, barter, properly defined under the one-truth postulate IS: exchange without prices. And money is simply what most people choose to quote (hopefully) arbitrage free relative prices in a certain geographical location, over a certain period of time. That is all. The important thing is relative prices and commerce, which is to say voluntary exchange of goods and services that occurs over time under a given set of arbitrage-free relative prices.
Before we continue, we would like to point out that our definition of money in no way shape or form contradicts ANYTHING known about money. All we are saying is that the FIRST, which is to say the PRIMARY function of money is to serve as a unit in which prices are quoted and measured in the real world. And everything else is derived from that. In the real world, you have to actually pay for things you are buying with money, because trades have to ALSO be settled, which is precisely why money ALSO becomes a medium of exchange. So you can ALSO settle trades by exchanging money itself, and exchange of money itself sometimes occurs in surprisingly ingenious ways. For example, the Rai stone money on the isle of Yap is unmovable, so Rai stones are exchanged by a generally agreed upon consensus! In other words, the residents of the isle of Yap collectively, as a group come to a generally-agreed-upon-consensus as to who any particular Rai stone belongs to. As illustrated by the fact that the residents of the isle of Yap, TODAY as we write this, collectively as a group, know and agree as to exactly who owns each and every single one of the Rai stones, including those that have sunk to the bottom of the ocean years ago, and are now lost and non salvageable! And by the way, by a generally-agreed-upon-consensus to a very large extent, is also how the M2 money supply works in the US today. Your bank maintains a checking or a savings account that you are the designated owner of. But the tribe consensus can change, and the new designated owner of your bank account can become a winning counter-party in a lawsuit filed against you. And it does not matter in the least if you disagree with the consensus, the consensus does not need to be unanimous, but only generally agreed upon, which means generally, but not necessarily universally agreed upon by the tribe, collectively, as a group.
But regardless of exactly how money is exchanged, it is precisely because money is a medium-of-exchange under free trade that money-units become ALSO valuable, because you can ALSO exchange MONEY for ANYTHING that is-also exchanged in this money under free trade! So what else would you ALSO use to measure and store profits? So, yes. Money is-also a recursively-induced medium-of-exchange and store-of-wealth, but the first-primary function of money IS: a unit-of-measure in which (hopefully) arbitrage free prices are quoted and measured in the real world!
However, as Aristotle noted about 2,400 years ago, out of all the existing alternatives as of 350 b.c., gold was the best “something” that could measure the prices of a wide variety of goods and services, as a consequence of gold having the desirable physical attributes of being an accurate ruler with which prices could be measured given that money is-also a recursively-induced medium-of-exchange and store-of-wealth. Which is to say that the recursively-induced-also functions of money require real world attributes such as variable size, durability and others listed by Aristotle. For this reason, historically, gold was chosen as “the physical object” preponderantly used as money. However, plenty of other things were used as units with which prices were measured, which is to say money, throughout history. For example, under the bimetallic standard, gold and silver were both simultaneously used as money for CENTURIES! Yet, the demonetization of silver in the 1800s did not cause, or result in any perceptible economic problems. So why did silver demonetization go largely unnoticed? Precisely because a difference in relative prices represents an arbitrage opportunity, so commerce merrily continued along under the same set of relative prices as before, but quoted in just gold, rather than both gold and silver.
Commerce is how we actually exchange things. For example, in the real world today, with all sorts of electronic settlement options available, once stable exchange rates are established, what is the difference between NYSE-like barter exchange and monetary commerce, besides how trades may be best settled? To a typical end user, as represented in our NYSE-like barter exchange example by a chicken farmer, the only real world difference may be the location where the eggs are to be delivered, and the milk picked up from! Which is to say that to solve the double coincidence of wants problem, what we first-need isn’t money. What we first-need is an arbitrage-free set of relative prices under which to engage in commerce using money, where money first-primary represents the units in which these (hopefully) arbitrage free relative prices are measured. And so long as there exists a mechanism to transfer money between people when making payments, and there is a secure way of storing money, and of verifying the authenticity of money, it matters ASTONISHINGLY little as to what in fact represents money in the real world.
Consider what we are in fact using as money today. It is the M2 money supply, which in fact only exists as entries in electronic ledgers. Cash is so di-minimus relative to M2, as to have nearly no practical significance in paying for consumption, so long as electricity and connectivity to a bank is readily available. So, the M2-money we all use to make payments currently is, in fact, just a unit-of-measure already, today! Of course M2 is-also a recursively-induced means of exchange, and, astonishingly to anyone rational, a widely used store-of-wealth, but ONLY as a consequence of the fact that the US dollar money as represented by M2, inherently, by definition IS: a unit used to measure quoted prices, simply because that is the first-primary function of ANY money!
Why we trade
The sum total of all commerce that takes place in a country over a time period as measured in money is gross output, which consists of intermediate consumption and gross domestic product, better known by its abbreviation, GDP. This means that the efficiency of trade is of the paramount importance, as it determines real GDP.
But what is the real reason we trade? What is the end goal of trade? To voluntarily cooperate so as to produce more than each one can produce individually. For example, one of the ways in which this occurs in the real world is through specialization, which is to say division of labor that Adam Smith wrote about. I’m better at fishing, so let me fish. And you are better at catching rabbits, so catch rabbits. And then we can trade. This way, we can consume more than what we would be able to produce individually. However, please note that rabbits and fish in this example represent only the FINISHED products we collectively consume, which is to say real GDP. What we collectively produce is gross output that also includes intermediate consumption, which consists of things such as fishing nets and small game traps that represent tools used to catch fish and rabbits.
But what exactly ensures that we do not over work ourselves, relative to what we desire to consume, and that we divide up the production among ourselves in some fair way? The efficiency of trade that results from using money. Of course we have yet to define what the word efficiency means as it relates to trade. But to the extent that commerce occurs using money, the efficiency of the resulting trade will determine the overall efficiency of ALL exchange. Which is what makes commercial free-trade so important!
Method A
But for now, let us compare commerce to the alternative method of exchange. For people have been exchanging things for thousands of years. But how did we engage in exchange before money? And remember, before money, by definition, means before free trade, as trade without money in the real world does not exist, but for an utterly inconsequential amount of barter. So how does exchange without trade work? Just ask any anthropologist, and they will tell you exactly how such exchange works. The chief of the tribe takes some part of what was produced, and redistributes it, in whatever way he perceives best, according to his own subjective judgment as to who is most worthy of benefiting from consumption. Let us therefore define method A as any exchange that is not commerce. Because in the context of this paper, the terms trade, barter, voluntary trade, and free trade all mean the same thing, which is commerce. And we need to differentiate commerce from non-commerce. And now exchange method A is first-defined in the context of this paper, which is to say that from now on, the first-primary meaning of method A is any exchange that is not commerce.
Naturally, exchange under method A is not always voluntary, which is to say, method A often takes place through involuntary redistribution, such as robbery for example. Robber: Your money or your life, …, so what’s it gonna be? Jack Benny: I’m thinking, I’m thinking! Are we stretching the meaning of the word exchange by saying that under the condition of armed robbery or slavery, people are exchanging their money or labor for their life? Yes, but we have no other choice here, and neither does anyone else under the condition of armed robbery or slavery, but to either die or exchange their life for their money or their labor. And dead people, sad as this makes us, don’t impact gross output. What we are saying is that exchange under method A often occurs as a result of partly or fully involuntary redistribution of goods and services under what often in essence amounts to slavery, but using money, but the resulting monetary exchange becomes partly or fully voluntary! And the voluntary monetary exchange that occurs as a result of involuntary redistribution under slavery is sometimes VERY efficient in terms of real GDP growth. And we are not only talking about ancient history!
Consider the Soviet Union under Stalin. Of course, everybody had a job, and received wages. And everybody’s wages were paid in rubles. And you could buy stuff with rubles. But the amount of rubles you were paid for doing your job, which is to say your wages, were determined by Stalin, with the help of some kind of a central planning bureau, that determined everyone’s wages, resulting in INVOLUNTARY REDISTRIBUTION of consumption under voluntary MONETARY exchange, which is to say method A. Under the teachings of Marx and Lenin, Stalin in effect recreated the ancient, prehistoric system of redistribution/exchange where the chieftain of a tribe took away EVERYTHING everybody ever produced, barring personal possessions and such, and then decided how to allocate consumption in whatever way he subjectively perceived as being most beneficial.
Which, according to Lenin’s interpretation of Marx was: “from each according to ability, to each according to contribution”. And this is nothing to sneeze at. This is an optimality condition for maximizing real GDP. Because if you own the economy, to you a person’s ability represents how much he can produce for you, which is just his output as measured in money, or his revenue to you. And his contribution is what you pay him for generating this revenue, which are his wages as measured in money, or his cost to you. In other words, as measured in money, from each according to ability, to each according to contribution represents setting marginal revenue (ability) equal to marginal cost (contribution), which maximizes profits, and not only theoretically, but also in real-world profitable businesses!
And all evidence points to the fact that Stalin believed and agreed with Lenin. So, what happened? Well, “from each according to ability, to each according to contribution as perceived by Stalin” happened! Under Stalin, by design, rubles were used as a store of wealth by an utterly de-minimus number of people. This was attained by keeping the population, while perhaps not starving to death, generally poor enough so as to force everyone to spend virtually all their wages on consumption. For the simple reason that wealth results in UNKNOWABLE future consumption and all evidence points to the fact that Stalin deeply and truly believed in the idea of: to each according to contribution. As evidenced by the fact that his biological son Yakov was imprisoned by the Germans and died at the Sachsenhausen concentration camp in 1943 after his father refused to make a deal to secure his release. If this does not prove to you that Stalin firmly believed in: to each according to contribution, we do not know what would. The problem is, to each according to contribution does not work when there is wealth, because wealth represents UNKNOWABLE future consumption by any number of people that might not contribute much under ANY definition of contribution.
Of course if there is no wealth then consumption is measured by wages, and ends up being equal to contribution as perceived by whoever determines wages. As a direct result, people whose contribution Stalin perceived as positive, were extremely happy under Stalin, so long as he did not change his mind about their contribution. Everyone else, which is to say those that Stalin did not perceive as making a positive contribution, were not very happy at all. Thus, EVEN TODAY!, Stalin is still remembered with fondness by those people whose contribution Stalin valued more than the Czar, and absolute loathing by those whose contribution Stalin valued less that the Czar. But how did Stalin do when it came to not only estimating ability, but also forcing people who had ability, as subjectively perceived by Stalin, to actually WORK for Stalin, rather than shirk work?
Even an ancient, prehistoric system of exchange can be extremely efficient. As it was under a dictator named Stalin, who turned out to be not only brilliant at picking unbelievably able managers such as Lavrentiy Beria, but also totally merciless at controlling corruption and theft, that Beria, being the head of NKVD, was ALSO in charge of! For what the NKVD was IN REALITY in charge of was forcing people to WORK by severely punishing anyone shirking work demanded of them. People still talk about being sent away for years to labor camps as a result of being 15 minutes late to work. And academics who refused to engage in research for Stalin voluntarily, still talk about doing ground-breaking research in Sharashka prisons, INVOLUNTARILY, but actually DOING AMAZING RESEARCH!
Given how many people he killed, we can see how calling Stalin a genius may be offensive. Fine. Call him an evil genius if you will. But of the fact that Stalin was a genius there is no doubt, as evidenced by his famous 1935 saying: “кадры решают все”, which translates as “STAFF DECIDES ALL”. But how was STAFF subjectively perceived by genius Stalin? Clearly as MY STAFF which is to say those that work for me. And if you define MY STAFF as those MANAGERS that WORK FOR ME, which is to say you think of YOUR MANAGERS as “STAFF” then STAFF DECIDES ALL as subjectively perceived by genius Stalin meant: MY MANAGERS are the ones that will be making ALL the important DECISIONS, which is to say STAFF DECIDES ALL, thought Stalin, and then the GENIUS STALIN had an afterthought: and NOT necessarily in a way that I WOULD APPROVE OF!” Which is exactly, word-for-word what the Michael C. Jensen and William H. Meckling “Theory of the firm: Managerial behavior, agency costs and ownership structure” says! And this is not only the most quoted paper in corporate finance, this is actually how corporations are managed in the real world; by controlling agency costs, and the one thing that Stalin did well is control agency costs, and how!
By having a widespread system of paid informers, in addition to hand-picked high quality managers who informed not only on the managers to NKVD, but-also to the managers, on ANYONE who paid-informers thought was shirking work! And paid informers were only well-rewarded for their efforts if the person accused was in fact found guilty of shirking work! That is how the “justice system” worked under Stalin. Yes, a lot of innocent people were tortured and killed. We are describing slavery here, not the innocent until proven guilty justice system as envisioned by the US founding fathers. But, the hand picked managers and NKVD/informers recursively “paid-informed” everything important to Stalin, who then made the final decisions. If this is not genius, we don’t know what is.
Of course at the same time, the political system under Stalin was slavery, and as measured ONLY by the number of people tortured and killed as a percentage of the population, AND NOTHING ELSE!!!, a much less humane version of slavery than what exited in the US prior to the civil war! You could not legally reside anywhere for longer than your allotted vacation time by the state, other than your one and only official residence, as assigned to you by your local government official! And naturally, you could NOT leave the country. So if there is no wealth, and you can not leave, what are your options? Either you starve to death, or you get a job from Stalin, or you become a criminal, but the criminal economy under Stalin headed by thieves in law is outside the scope of this paper. So let us set aside the real GDP impact of the dual economy under Stalin, which is to say exchange method A as defined by: controlled criminality by thieves-in-law under Stalin.
The primary economy under Stalin WAS the slave economy as measured by real GDP growth under a genius-merciless as collectively perceived back then “GOD-FATHER” which is to say criminal-owner, as represented in the real world by sometimes/somewhat well-meaning, but criminal ex-bank-robber Stalin that effectively owned the economy. And the primary economy was very efficient, because there was almost no theft as measured by agency costs! And as also measured by the fact that back then everyone KNEW: NOBODY steals NOTHING from perhaps sometimes and somewhat well-meaning, but also INCREDIBLY scary all-powerful criminal ex-bank-robber Stalin! Just as nobody steals NOTHING, especially “the bag with all the envelopes and all the money” from a powerful criminal New York mafia member on his wedding day, as represented by Henry Hill in the famous “Goodfellas” wedding scene.
However, Stalin died, and the new guy, Khrushchev, while only slightly less merciless, was not very smart, for he killed Stalin’s genius manager Beria, but never got ANY genius manager as a replacement. And without a merciless-genius recursive-duality as represented by (genius/merciless)-boss-Stalin and-also (merciless/genius)-manager-Beria, it all went downhill. When everything you produce is taken from you anyway, and you feel underpaid, what do you do? Steal as much as you can of whatever it is you produce, what else? And with no Stalin in charge to select able managers AND Beria in charge to control theft and shirking, the whole system slowly but surely collapsed.
But when there is no theft, method A can work to everyone’s satisfaction, though not necessarily in an way that maximizes production. As it often does within a family, and used to within a Kibbutz. That is because Kibbutzes used to be relatively self-contained, and as a result, everyone collectively consumed pretty much what they produced. So within a Kibbutz, money used to represent consumption, not wealth, just as it did in the Soviet Union, under Stalin. Under the condition of no wealth, a good Kibbutz leader in a small community of people he knows and likes personally, can allocate consumption fairly, as perceived by other Kibbutz members. Until even non-dire poverty disappeared in Israel, which is why Kibbutzes no longer really work.
As time went on, and Israel became prosperous, money even in remote Kibbutzes recursively-induced-also slowly but surely became a store-of-wealth. Of course wealth, as we have already explained, by definition means consumption by those that may not contribute. And for this very reason, wealth allocation invariably results in fighting which often occurs when people see a chance to gain wealth without any reciprocal contribution of productivity. As evidenced by the fact that even close family members related by blood wind up battling each other over large inheritances on a regular basis.
To summarize, under method A=socialism, allocation of consumption=to each according to contribution, that only works efficiently when there is no theft and no wealth. With wealth, method A becomes communism, and under A=communism, allocation becomes to each according to need, but according to need by definition means NOT according to contribution, and ANY allocation NOT according to contribution IS rent seeking under the existing definition of economic rents which states: rent-seekers are those seeking to gain wealth without any reciprocal contribution of productivity. And of course, as we are all aware, rent seeking makes ANY economic system HORRIBLY inefficient, and not just theoretically! This why real-world Marxists are by definition either suckers or rent-seekers, not only under the one-truth postulate, but also under Occam’s RAZOR which IS maximum-likelihood under the one-truth postulate, as we will show in conclusion.
We use both
So we have two alternative methods of redistribution/exchange. A is “from each according to ability, to each according to contribution and/or need” or some variation thereof as perceived by those in charge. B is something called free trade. The closest thing to pure A in the real world would be a dictatorship, like North Korea. And the closest thing to pure B would be a completely free market, like the United States of America just after the Revolution, in the late 1780s and for a few decades after, apart of course from slavery. Slavery is method A, of the worst kind! Meaning that for whatever reason, in the real world, we invariably wind up with some combination of A and B. As little B as we may think exists in North Korea, North Koreans exchange many things among themselves voluntarily, however secretly, using any money they can get their hands on.
So today in the US, welfare (A) is combined with commerce (B). Yet the question remains, what is the benefit to trade, which is to ask in what way exactly is B better than A? Because “from each according to ability, to each according to contribution” under a smart and benevolent ruler, if GOD decided to exist for example, results in maximum production, as measured by real GDP. But who gets to consume the GDP that is produced?
Benefit of trade
In reality, we ONLY THINK we know precisely how money is used as a means of exchange. You have some chickens. They lay eggs. You want some milk. You go to the market. You exchange your eggs for money. You then exchange money for milk. And you go home. But how are RELATIVE PRICES determined? Because the extent to which the chicken farmer benefits from trade depends entirely on the ratio of the price of eggs to the price of milk. In other words, to any one person individually, in terms of trade, some price ratios are more beneficial than others. So how are relative prices, which is to say relative benefits determined? Hopefully, in the most beneficial way possible, for all those that trade using this money, collectively, as a group. But what does that mean?
In terms of trade, the only thing that money does is make it easier to exchange things; typically things we produce for things we consume. Now here, we need to be careful about using the word consumption, because consumption is defined as the using up of a resource. But what are you consuming, which is to say what resource are you using up when you watch TV? Consider the following two scenarios:
You are sitting on your couch, reading a book. And then you turn on your TV. You watch TV for an hour and a half. You then turn off the TV, and continue reading your book. Until 9 PM, when you go to sleep.
You are sitting on your couch, reading a book. And then you do nothing with your TV, and simply continue reading your book. Until 9 PM, when you go to sleep.
What is the marginal consumption of anything as it relates to watching TV in this example? On margin, you are not even consuming leisure, as your alternative to watching TV is also leisure, just a different kind of leisure, reading a book in this example. The only thing you are consuming on margin is the electricity it takes to run the TV when you watch TV, so you are not really consuming much of anything. What you are actually doing is subjectively benefiting from being entertained. In other words, you derive some subjective benefit from watching TV, and this is why you are paying for cable on a monthly basis, not because you consume any additional resources.
In economics, such subjective benefit is called utility. From now on, we will use the word utility to refer to the subjective benefit a person receives as a result of engaging in free trade, independent of resource consumption. In other words, we benefit by watching TV and eating steak, and it doesn’t matter which, as far as we are concerned, because in the real world, we are willing to pay money for both. And we use the word receives here because all trade, to the extent that it is voluntary, and there is no cheating involved, automatically, by definition, without making ANY prior assumptions about ANYTHING AT ALL, is always beneficial. As perceived, which is to say subjectively measured by whoever engages in trade, ex ante.
If trade is voluntary, why would we engage in it, unless we did not perceive it to benefit us in some way? In reality, the benefit we get from giving money to charity is subjectively feeling better about ourselves. Indeed, in terms of utility, there is a perceived benefit to every transaction. How could voluntary exchange result in a subjective cost? Subjective cost in the real world means you don’t want to do it, and voluntary, by definition means you don’t have to do anything you don’t want to.
Which makes all trade beneficial by definition, as it raises the subjective utility of both parties to the trade. Naturally, so long as trade is voluntary, and no cheating is involved. Of course in this paper, we are analyzing free trade under the condition of perfect information ONLY, with the full understanding that cheating WILL lower the efficiency of trade, as perfect information rarely, if ever, exists in the real world, though many transactions, such as buying a bottle of Coca Cola or an iPhone, come pretty close. Which is to say that under the condition of perfect information, everyone that participates in voluntary free trade benefits, collectively as a group. So there is a total benefit to trade that would not exist, but for money. Let us refer to this as the total utility of trade using money. Of course the total utility of monetary trade is completely subjective; it is the sum total of everyone’s utility, which is itself subjective. So, how do we measure the collective benefit of monetary trade, as subjectively perceived by all those that participate in such monetary trade, collectively, as a group?
Efficiency of trade
Voluntary exchange, by definition, can not make anyone worse off, which is precisely why the ex ante utility that results from each transaction is always positive. Moreover, money is an integer, the amount of money is finite, and the amount of goods and services for sale at any moment to any one of us is also finite, which makes the set of all possible trades a single individual can engage in at any given point in time using money finite, which makes the set of the subjective utilities associated with each possible such trade finite, and usually not even very large, as we will illustrate. And for ANY 3 members of ANY finite set of positive numbers as represented by subset {X, Y, Z} if X+Y>Z then rank(X)+rank(Y)>rank(Z) under ANY definition. Which means that subjective utility and its order rank will have the same ordering under addition under the definition of free trade that re-occurs under a given set of relative prices over time. This allows us to define an optimality condition for the subjective benefit of monetary trade as Pareto-efficiency of subjective ex ante utility that results from commerce that re-occurs under a given set of relative prices over time.
Let us tread very VERY!!! carefully here. Ex ante utility is only measurable subjectively, at the exact time of the trade, and even then only relative to money. Which makes subjectively perceived benefit, which is how we defined utility, objectively unmeasurable. But what allows us to add unmeasurable subjective benefit is that when exchange is voluntary it can not make anyone worse off, and if you can not make anyone worse off, subjective ex ante utility and its rank have the same ordering under addition. AND, TO BE PERFECTLY CLEAR, we are referring to subjective ex ante utility and subjective rank, as perceived by a single individual, SUBJECTIVELY at the exact moment of the trade, which is to say ex ante.
For those used to recursion, it becomes so secondhand, that one forgets that to those new to it, recursion can sometimes be VERY difficult to understand. Let us explain in detail precisely what all the TRIVIAL math about ranks above is REALLY saying, because trivial math under recursion is USUALLY saying quite a WHOLE LOT more than you think it is.
At any given point in time, a single individual has multiple options as they relate to monetary trade. For example, after you wake up in the morning and have had your coffee, as you are about to leave your house, you can walk to work, or take a bus, or a drive a Ford, or a Ferrari, or be driven by a chauffeur in a Rolls Royce. We all have some subjective utility, not ex ante utility mind you, but subjective benefit as it relates to using these alternatives in the foreseeable future which is unmeasurable, partly because it is extremely unstable. For example, the subjective utility of drinking water can, and does change drastically over time, depending on how thirsty you feel. But no matter how unstable your subjectively perceived benefit of drinking water, if you paid $4.20 for a glass of water, you valued it more highly than $4.20 worth of apples, or something else you could have bought, but did not. What this means is that at the exact time you engage in monetary trade, you RANK multiple options you can purchase with money. And this order RANK, as perceived subjectively by you is objectively measurable!
Say Bob likes to drive. For him subjectively, the ordinal ranking of utility on a Wednesday morning might be Ferrari=1, Ford=2, Rolls=3, Bus=4, Walk=5. And for Alice that does not like to drive, the perceived subjective utility ranking may be: Rolls=1, Bus=2, Ferrari=3, Ford=4, Walk=5. But each monetary transaction has two attributes, subjective utility AND cost measured in money, and under relative prices as they exist today, Bob would NEVER use the Rolls Royce, and Alice would NEVER EVEN CONSIDER driving ANYTHING. Take Bob for example. Why would Bob ever even think of being driven in a Rolls-Royce? For Bob, subjectively, Ford is not only BETTER, but ALSO CHEAPER! Of course if Bob never even considers using the Rolls Royce, it would by definition be excluded from being one of the options in his actual, real-world subjectively perceived order ranking of subjective utility as it pertains to monetary trade. So the ACTUAL real-world subjective ex ante utility ranking for Bob would be: Ferrari=1, Ford=2, Bus=3, Walk=4. And for Alice, it would be Rolls=1, Bus=2, Walk=3. And BOTH 100% SUBJECTIVE ranks ARE BOTH 100% correlated with relative prices as measured in recursively-induced-also medium-of-exchange MONEY! And we are talking about actual real-world ranks of subjective ex ante utility, not some idiocy about unmeasurable utils.
Let us be very careful here. What we are saying is that under some other alternative set of relative prices, these rankings may have been different. But under ANY set of arbitrage free relative prices and limited wealth, available consumption alternatives will be limited as determined by relative prices and wealth. And it is precisely this limit in consumption alternatives under a given set of relative prices and limited wealth, that mathematically represents itself in the real world by the fact that Bob would NEVER be driven in a Rolls Royce, because TO HIM SUBJECTIVELY the Ford is better AND CHEAPER! And this LIMIT TO CONSUMPTION ALTERNATIVES represents itself recursively-by-induction in the real-world by the fact that everyone’s INDIVIDUAL subjective RANK of utility of ANY monetary exchange is recursively-induced-also 100% correlated with money!
So for example, Bob’s subjective utility rankings on a Monday morning with a hangover may become the same as Alice’s. But it doesn’t matter in the least, because Alice’s order rank of ex ante subjective utility is-also 100% correlated with recursively-induced-also MONEY as represented in the real world by M2! AND SO IS EVERYONE ELSE’S! THAT IS WHAT USING RECURSION GETS YOU, MATHEMATICALLY!
And by defining efficiency as Pareto-optimality, we in effect define the objective function we are all collectively optimizing as the maximum of everybody’s subjective ranking of ex ante utility derived from past, and recursively-by-induction-also expected future commerce that takes place under a given set of relative prices! As measured in recursively-induced-also M2 medium-of-exchange money unit!
Let vector X denote Bob’s ex ante subjective utility associated with each transaction he engaged in over last month, and let Y denote the same for Alice. Rather than optimizing unmeasurable sum(X)+sum(Y), we are optimizing measurable max(sum(rank(X)), sum(rank(Y))). Which is to say that max(sum(rank(X)), sum(rank(Y))) is exactly the objective function we are all collectively, as a group maximizing in the real-world by engaging in voluntary trade that is Pareto-improving as a result of it being voluntary, under the existing definition of Pareto-optimality! So we are no longer acting like fools trying to model equilibrium that is never reachable. By using recursive definitions we are able to model DYNAMIC SYSTEMS MATHEMATICALLY. For the real-world is NEVER IN SOME EQUILIBRIUM, it is ALWAYS CHANGING DYNAMICALLY!
So what would represent Pareto-inefficiency in this case? The availability of arbitrage. Being able to purchase the same thing at different prices represents Pareto-inefficiency of ex ante subjective utility by its very definition, because no matter who else may or may not benefit, arbitrage makes the arbitrageur better off, without making anyone else worse off. Better off in terms of money of course, but again, just to drive this point home, the ordinal ranking of subjective ex ante benefit of trade is 100% correlated with, and consequently measurable by recursively-induced-also medium-of-exchange money! But other than subjectively benefiting the arbitrageur, does arbitrage improve economic efficiency? Of course it does, by allocating real resources to their best use. If the dairy farmer in a certain village is inefficient, then the price of his milk will be high, as he will not be able to produce enough milk to satisfy everyone’s demand. And everyone in his village will suffer as a result of having to pay a high relative price for milk. In which case some enterprising merchant, which is to say arbitrageur, will hopefully start buying milk from a neighboring village, and selling it in the village with an inefficient dairy farmer, at a more attractive price. Benefiting the merchant-arbitrageur, the efficient milk farmer, and the villagers that had to live with expensive milk.
So whom does arbitrage hurt? Not ex ante, but over time, in terms of total subjective utility, whose ordinal ranking is-also 100% correlated with, and consequently measurable by recursively-induced-also store-of-wealth money; simply because store-of-wealth money represents the expected value of subjective utility of future consumption, which is to say E[ordinal subjective utility ranking derived from E[future consumption under commerce]]! Mostly the guy bad at being a dairy farmer. Because the demand for his expensive milk will dry up. And the more efficient dairy farmer in the neighboring village will increase HIS capacity, to meet the excess demand from the people in the village that used to buy milk from a dairy farmer that was less efficient, in terms of milk production. This is how ARBITRAGE improves economic efficiency as measured by gross output: by allowing the lower cost, which is to say the more efficient producer to produce more, thereby benefiting everyone, particularly the arbitrageur while hurting the less efficient producer! As demonstrated in the real world by the fact that Dexter shoes went out of business due to new trade with low wage countries that caused a sharp drop in prices of shoes relative to prices of labor, factories, and raw materials in Maine. Of course efficiency as measured by gross output can be improved by things other than arbitrage. For example, innovation greatly improves economic efficiency. But this has nothing to do with Pareto-efficiency of exchange as it pertains to ARBITRAGE that is being discussed! How innovation improves economic efficiency is far outside the scope of this elementary introduction to economics. Here, we are talking about how ARBITRAGE improves efficiency, NOT innovation, or anything else!
Of course, in terms of Pareto-efficiency, the one parameter that clearly matters a great deal would be the ease with which one can engage in arbitrage. But before we delve into arbitrage, let us discuss what efficiency of exchange actually means in the real world as it pertains to the collectively perceived total subjective benefit, which is to say the total utility of trade using money, as measured by BOTH Pareto-efficiency AND of course actual consumption, which barring waste and stupidity, will be equal to real GDP portion of gross output as measured in money, which is to say nominal GDP.
Commerce, as it exists in the real world
Pareto-efficiency in the real world means that everyone is as happy as possible with free trade, which is to say exchange method B, collectively, as a group. Because under Pareto-optimality, everyone collectively benefits, to the extent possible, from using money in commerce. In other words, Pareto-efficiency corresponds to how effectively monetary commerce operates, as collectively perceived by the public. Meaning the more Pareto-efficient the commercial free trade, the better the economy. So what could possibly interfere with Pareto-efficiency of commerce? The government?
From an actual ruling elite’s point of view, whoever they may be, subject to the constraint of allowing themselves and their friends to engage in over-consumption, why make anyone else worse off in terms of overall satisfaction with how commerce operates? Which is to say, enjoy life as much as you want, but why needlessly upset everyone else for no reason? Meaning, it is in the ruling elite’s best interest to maximize Pareto-efficiency, as it relates to relative prices. Hence, barring extreme stupidity, such as imposing price controls, Pareto-inefficiency will not result from intentional malfeasance by the government, to the extent that it is controlled by the ruling elites. Unless of course the ruling elites desire to use only method A of redistribution, and don’t care about commerce at all, as is the case in North Korea, where just like under Stalin in Russia, officially money is used only under method A. And while the Pareto-efficiency of partly voluntary exchange under method A is a fascinating topic, it is outside the scope of this elementary introduction. Therefore, let us set aside outliers as represented by North Korea.
To the extent that exchange occurs under fully voluntary B, we would expect the government to do whatever it can to improve the Pareto-efficiency of commerce, within the limits of its knowledge and ability. Of course after ensuring necessary consumption, according to government’s own interests. Which among other things, includes ensuring that the ruling elite can consume whatever they deem appropriate, in peace and serenity. Welfare represents an example of government spending designed to ensure that the ruling elite can consume what they deem appropriate in peace and serenity, by repeatedly inducing the desperate poor to commit less street crime. Please note, we are no longer dealing with Pareto-efficiency. We have now switched to dealing with overall subjective unhappiness, beyond trade, by engaging in the ancient, hopefully benevolent dictator method of redistribution A.
Consider what welfare is designed to accomplish in theory, and to a limited extent in practice. It allows those most likely to subjectively benefit from additional consumption to consume more. The law of diminishing marginal utility of consumption as people consume more, by definition has a dual, which is the law of increasing marginal utility of consumption as people consume less. This is to say that those that consume the least as represented by the desperate poor, are the ones most likely to subjectively benefit the most from additional consumption, which represents the obvious, easy pickings as it pertains to the subjective ranking of the total benefit of consumption by the entire population, as measured not by max(everybody’s subjective rank), which is to say Pareto-optimality, but as measured by min(everybody’s subjective rank), which is to say Welfare.
And this is an example of both types of exchange happening at once; the US government engaging in redistribution method A by printing and spending money that is recursively-induced-also valuable as a result of being used to exchange goods and services under voluntarily exchange method B, which we call commerce/free-trade. Fiat money is first-primary valuable because it is used by fiat in method A, just as it was under Stalin in Russia; not only because ALL government spending is paid for in M2, but also because government accepts tax payments solely in M2, as per MMT. In other words, B makes fiat money ALSO valuable in A which makes fiat money ALSO valuable in B which makes fiat money ALSO valuable in A,….. and so on, under infinite recursion. This is what we meant by recursively-induced-also valuable. Which is not surprising, as money itself is inherently recursive, by definition.
But in general, people want Pareto-optimality of trade, and so do the rulers, as evidenced by the existence of Welfare, when the government pays good money for what Pareto-efficiency can accomplish for free. And of course Pareto-efficiency requires easy arbitrage, which means that when arbitrage is cheap, you get Pareto-efficiency, by definition. And what makes it less likely that people will engage in arbitrage? Besides idiocy like tariffs? Purely from a monetary point of view? Positive real rates, obviously. When you can earn real purchasing power risk-free, why bother with arbitrage? And the risk-premium.
The arbitrage risk premium
Why would that be; the risk-premium is just the investment return an asset is expected to yield in excess of the risk-free rate of return? Because the marginal cost of engaging in any kind of arbitrage will be the risk-premium associated with the revolving line of credit that is required to fund the arbitrage operation. After all, we are talking about arbitrage, and money needs to be paid for, too. And what determines the risk-premium of any revolving line of credit? Default risk, what else? So what is the default risk of trade? Uncertainty about the difference between the purchase and the sale price, which is to say, UNCERTAINTY ABOUT FUTURE RELATIVE PRICES! Because to arbitrage any price discrepancy, you first need to buy something, ship it somewhere, and only then sell it.
Of course there is always inherent default risk as it relates to unpredictable changes in relative prices that result from rare events, like oil price shocks, including but not limited to those that occurred circa 1973 and 1980. Covid is another example of such a rare event. After 2020, the cost of shipping containers tripled relative to prices of goods shipped inside the containers. But such unpredictable shifts in relative prices are in general VERY RARE and UNKNOWABLE. Of course relative prices can also change due to innovation, but to the extent that such relative price changes are predictable, they will not impact the arbitrage risk premium! In other words, in general, to the extent that relative prices remain predictable, default risk of arbitrage, in general, will not increase as a result of inflation or deflation. In this context, the words inflation and deflation are being used under their existing definition, which is that of a general increase or fall in prices.
However, relative prices can and often do become less predictable as a result of inflation or deflation. Given that money is just units, nominal GDP=real GDP part of gross output as measured in money in circulation, by definition of M2-money units being means-of-exchange in both A and B. So we can try to measure inflation as a percent change in GDP deflator. We can try to measure inflation as a percent change in the price of the CPI basket of goods and services, which under the condition that we collectively consume real GDP, should not and usually does not differ much from the GDP deflator measure of inflation. But at the end of the day, inflation BY DEFINITION is the difference in the rate at which gross output grows and the rate at which money supply in circulation grows, over some time period, such as last year. Where gross output consists of real intermediate consumption and real GDP.
And when money supply in circulation relative to output changes, it may not change for everyone equally, and there is no guarantee that people that wind up with more relative purchasing power will have the same consumption preferences as those that were in possession of this purchasing power previously. Which results in shifts in relative demand, and hence relative prices. And though such changes in relative prices may not be permanent, this fact has little to do with default risk. A bank MUST receive loan payments no matter what. Of course the official Fed monetary policy reflects this to the extent that it is designed to provide price stability IN THEORY. IN REALITY however, the only people that truly know what the Fed ACTUALLY does are the permanent staff at the Fed.
But let us stipulate away the Fed. Forget the Fed, before the Fed, under pure GOLD-COIN-ONLY money or whatever IDEAL money you can imagine, there exists a certain set of equilibrium, arbitrage-free relative prices that are determined by the overall supply and demand for various goods and services that we collectively produce and (hopefully) consume. And money is simply units in which these relative prices are measured. And the more volatile the price of money, as measured by inflation and deflation, the less accurately money measures “true/ideal” arbitrage-free relative prices. Because arbitrage-free relative prices require free, which is to say easy arbitrage, but arbitrage becomes VERY EXPENSIVE and DIFFICULT when relative prices become unpredictable. Think of money as a control variate in the sense that volatility relative to a control variate results in imprecise estimates. And precision is required to spot the difference between a genuine arbitrage opportunity and a less predictable estimate of equilibrium price due to money becoming an inaccurate ruler with which prices are measured. Which makes arbitrage more difficult. Which reduces the efficiency of commerce, because arbitrage is what ensures the Pareto-efficiency, and thus the overall efficiency of trade under B. And inefficient commerce causes inflation by reducing gross output and real GDP, both!
Hence, the inflationary business cycle recursive feedback loop: inflation → uncertainty/volatility → less predictable relative prices → less arbitrage → less efficiency → less output → inflation. But at some point in time, if the money supply in circulation doesn’t grow, inflation stops. And another business cycle may later re-occur.
Of course there is also a deflationary recursive business cycle, that under a fixed money supply is self-correcting: deflation → uncertainty/volatility → bad control variate → less arbitrage → less efficiency → lower output → inflation. But under fractional reserve banking, when the money supply in circulation can shrink faster than output, VERY bad things can happen in a deflationary business cycle, as we are about to explain. But first...
Limits to what Method B can do
Naturally, many outside factors can permanently change relative prices, that have nothing to do with Pareto-optimality that results from cheap arbitrage. By far the most important price ratio for the majority of the people is the ratio of their wages to the prices of what they consume, as approximated by the CPI. And changes in this price ratio for some people take a long time to adjust to. If you are displaced in your job as a coal miner, for any reason, how easy is it for you to find a new job at a comparable wage relative to the cost of living at your new job location? And you weren’t all that well off on a relative basis to begin with! Elementary selection bias tells you that those people that could make millions writing software for Google, that were born in Appalachia, do not become coal-miners, and ARE in realty most likely already making millions writing software for Google! So we see what we see in Appalachia. Such relative price changes are almost always bad, not necessarily for Pareto-optimality of relative prices as measured by economic output, but for the amount of consumption that those affected ARE ABLE TO derive from commerce, as a result of what may have been great innovation, very beneficial for real GDP growth, but not very beneficial to these particular people, subjectively. And it is precisely such desperate poor that to a limited extent benefit from welfare, which represents method of redistribution A, by a benevolent ruler IN-THEORY. IN-REALITY, the ONLY people that TRULY KNOW how welfare gets administered are those that actually administer and receive it.
But what we ALL should know is that CPI adjusted wages represent REAL compensation workers receive for their labor. And this is one of the most dangerous parameters to tinker with. Because wage inflation relative to CPI inflation represents the median change in subjective rank of utility as it relates to efficiency of commerce as measured directly, by the amount of actual real-world consumption of goods and services a person receives in exchange for their labor. This is precisely the reason why a sharp drop in median(subjective rank of utility), such as the one being experienced by out of work coal miners in Appalachia, usually means war, when a lot of GDP is not consumed, but wasted. Of course in a war, the enemy is blamed for the drop in consumption. But what happens if consumption drops without a war, due to free-trade becoming less Pareto-efficient?
Cost of arbitrage
Of course so long as inflation is stable, it doesn’t really matter what it is, in terms of its impact on costs of arbitrage. If inflation itself mattered, why would commerce work equally well, whether inflation is -3, -1, 0, 2, or 5 percent? Either outcome is perfectly acceptable, so long as relative prices remain predictable, and real rates stay reasonably close to zero. But what happens when this is not the case? What happened during the Great Depression? It started with random people’s savings being stolen as a result of bank failures that were caused partly by the 1929 stock market crash, but mostly by the inherent instability of ANY fractional reserve banking system that uses commodity money as a base currency, which is a fascinating topic in and of itself, but outside the scope this paper.
For the purposes of this discussion, we only need to state the obvious. The natural, free-market exchange rate of recursively-induced-also money, which is to say representative money such as cash, checking and savings accounts, and so forth, and first-primary gold dollars, which is to say commodity money is 1-to-1, and in ANY fractional reserve banking system that uses commodity money as the base currency, the higher this exchange rate, the more inherently unstable the system BY DEFINITION becomes. And the introduction of the Fed in 1913 resulted in a drastic increase in the ratio of recursively-induced-also dollars (representative money) to first-primary gold dollars (base currency) by the late 1920s. Inherently destabilizing the entire banking system. Unsurprisingly, as bad things invariably occur when people engage in rent-seeking, always under the guise of promoting some public good, like the Fed.
But there is absolutely no need for us to speculate on what triggered the banking crisis, or the creation of the Fed for that matter. For whatever reason, the banking system initially became destabilized after the 1929 stock market crash. Which is to say that runs on banks began to occur. And then they began to re-occur more and more frequently. Because as soon as you see your neighbors’ life savings wiped out as a result of a bank failure that resulted from a bank run, you are going to pull your-own gold commodity money out of your bank, and keep it at home or in a safety deposit box, so as not to loose your own life savings, thus causing the following recursive feedback loop:
Under fractional reserve banking, people keeping money in safety deposit boxes means less actual commodity gold reserves that protect all banks collectively as a group against runs. At the exact same time, any money people keep in their safety deposit boxes or at home is by definition NOT in circulation. And when the money supply in circulation drops, prices drop with it, leading to positive real rates of return on money itself! So who in their right mind would engage in any arbitrage? Especially considering the increased cost of engaging in arbitrage, as represented by the additional arbitrage risk-premium that resulted from immense uncertainty about the future. And without arbitrage, commerce can not function efficiently, which naturally results in people defaulting on more bank loans. Which, under fractional reserve banking, results in more bank failures, which results in more runs on banks, and more money being kept at home, and so on.
Until Roosevelt just decided to confiscate gold in 1933, and drastically increase redistribution under method of exchange A. But without a (merciless/genius)-(Stalin/Beria) duality, which is to say under Roosevelt, exchange method A’s efficiency BACK THEN is well represented in the real world TODAY by your local DMV or Post Office. However, method A does work in the military, under strict discipline and immediate merciless punishment for theft, just as A works under NKVD. So exchange method A under Roosevelt only became efficient in the United States after World War II started. Yet even then, method A only became efficient due to the inherent efficiency of commerce that resulted from using fiat-method-A-money to purchase weapons and other equipment needed for the war from private firms. No wonder people still remember this as the worst economic disaster in the entire history of the country.
And you can go through history, and look at any country, and any economic situation, and the Pareto-efficiency of commerce will determine the economic efficiency of voluntary exchange. Capitalism. Communism. Socialism. Fascism. Anarchism. Of course it matters in terms of subjective perception. Not many people today would want to live under Fascism in Germany, or under slavery in the US, or under Anarchy in Haiti, or under Stalin in Communist Russia, as represented today by North Korea. But in terms of economic efficiency of commerce as measured by Pareto-efficiency and as recursively-also measured by real GDP growth, it doesn’t matter in the least. What matters is the Pareto-efficiency of B, to the extent that free trade is being used as a method of exchange. And naturally, unsanctioned transfers of value as measured by things such as cheating, theft, agency costs, and rent-seeking. Such things must be controlled in order for ANY exchange to be efficient, as ANY transfers of value that are unsanctioned by those that use a particular money individually will recursively-induced-also have a negative impact on the overall efficiency of not only B, but also A. But that is a WHOLE other story that is way outside the scope of this trivial, basic, elementary introduction.
Recursive means BOTH subjective and objective at ONCE!
The purpose of this discussion is for us to fully and completely understand that money is fundamentally just units, same as feet, kilograms, or degrees Celsius, and these days it isn’t even anything physical. What is M2, in the real world? Just units. Electronic ledger entries. M2 doesn’t exist. It is a unit of measure, called the dollar, that is recorded somewhere next to your name. Which forces us to use recursion to define money by creating an objective definition of money we can all agree on, precisely because it is completely subjective.
Money to you, as perceived subjectively, by whoever YOU may be, is the units in which the relative prices of what YOU buy and sell are measured! And price is the exchange rate of what YOU buy and sell into money.
So we have an objective definition of money that everybody will subjectively agree with, because it is specific TO THEM. And what enables us to create objective definitions that ARE-ALSO subjective is recursion. Inherently recursive definitions are REQUIRED to mathematically model other people’s subjective perception.
How else could we model unmeasurable quantities, such as total utility of exchange, other than by defining the efficiency of free trade as Pareto optimality of ordinal rank of subjective ex ante utility of exchange that occurs over time? This was only possible because the subjectively perceived ordinal rank of otherwise unmeasurable subjective utility of exchange is 100% correlated with the ordinal rank of ex ante subjective utility of exchange as SUBJECTIVELY measured in means-of-exchange recursively-induced-also money-units, such as M2 as a result of money-units themselves being inherently recursive! Otherwise, we must make assumptions that can turn out to be wrong. And you can go ahead and re-read this paper as carefully as you want, now. And you will find one thing missing. Assumptions. There are NONE!
AND YOU WILL NOT FIND ANY, BY DEFINITION! BECAUSE USING RECURSIVE DEFINITIONS UNDER THE ONE TRUTH POSTULATE TURNS ANY SCIENTIFIC PAPER INTO A THEOREM! Where known facts become POSTULATES, and everything else is ABSOLUTELY MATHEMATICALLY PROVABLE! Your paper becomes a mathematical theorem AUTOMATICALLY when you use recursive definitions under the one truth postulate that everything is recursive as represented in the real world by the fact that everything has a cause and an effect.
And the fact that everything has a cause and also an effect is PRECISELY why we never understood money. We got the causality wrong. Money is not ONLY a medium-of-exchange. The original, first-primary money as defined in this paper under the first-one-truth postulate is: a unit in which RELATIVE prices are measured as subjectively perceived by SOME INDIVIDUAL, as represented by Bob and Alice! And only as a consequence of being a unit in which prices are SUBJECTIVELY measured, DOES MONEY recursively-induced-also BECOME medium-of-exchange ALSO-MONEY, we call the US dollar as represented in the real world by M2! Which is to say that:
M2 money-units that we refer to as the US dollar is not MONEY, but ALSO-MONEY, which is to say recursively-induced-also medium-of-exchange MONEY. Of course if we are just using money, it doesn’t matter in the least. But if we are trying to understand money fundamentally, we need to understand where it comes from; follow the logic mathematically from the beginning to the end, step by step, understanding both cause and effect. And what prevented us from doing so all these years of not being able to understand trivial things about economics, such as what money really is, is the fact that we thought money is means of exchange, whereas in reality, its first-primary function is a unit in which prices are SUBJECTIVELY measured.
Conclusion
In conclusion, as promised, we will show that under the one truth postulate, maximum-likelihood is-also Occam’s Razor. Maximum likelihood is a method used to determine the parameters of a statistical model that best fit the data. It involves finding the set of parameters that maximize the likelihood function, which is the probability of observing the data given the model and the parameters. Of course any set of axioms, which is to say a theory defined under the one truth postulate that includes assumptions is-also a statistical model because assumptions can always turn out to be inaccurate. But under the first-one-truth postulate, any axioms not based on assumptions are by definition recursive definitions such as maximum-likelihood itself. And any recursive definition, by definition of being recursive, MUST have a dual. And the dual likelihood function of maximum-likelihood itself is the probability of ALL axioms being true under a set of facts as they exist in the real-world, but there is only ONE truth. So what happens when we flip from primary to dual? The more axioms we add that make assumptions, the lower the likelihood of ALL such axioms being accurate under ONE set of real-world facts.
This is exactly why Occam's Razor requires us to remove unnecessary complexity as measured by the number of “assumption making” axioms. In other words, under the one truth postulate the dual of maximum-likelihood is now first-defined as the first-dual named Occam's Razor. Which is to say that first-dual is now first-defined, and first-defined ITSELF-recursively is now first-defined to mean first-defined under the one truth postulate. And now you can see that we’ve already first-defined terms such as first-primary, is-also, recursively-induced-also, and so on. So, as promised, maximum-likelihood under the ?first, as subjectively perceived by Haykov first, one-truth postulate that this particular paper is under, is-also its-own first-dual which has been now first-defined as Occam's Razor. So what is the first-dual of money? The first-dual of MONEY is: prices, as measured in money.
In other words, when we make a recursive definition, we simply define both the first-primary and-also the first-dual at once! Similar to how particles such as electrons have TWO properties that we can not measure at the same time, because they may be inherently recursive? Maybe economists can finally teach theoretical physicists something.