Money and Commerce under the one-truth Postulate
FIRST STABLE VERSION
Money and Commerce under the one-truth postulate
By Joseph M. Haykov
There is no agreed upon definition of what money actually IS, as evidenced by the fact that many rational people, such as Charlie Munger are firmly convinced that Bitcoin is not money, while numerous other rational people, such as Michael J. Saylor are equally certain that it is. So how can we objectively define money, which is clearly perceived subjectively? Only recursively, in terms of commerce. And though we have been using money for thousands of years, 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 mathematically model DYNAMIC systems.
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.
What IS the one-truth postulate?
It represents a framework under which science can be done with ZERO theory induced blindness. Also, the one truth postulate is a PARTIAL solution to Hilbert’s program, but ONLY under itself. That is because EVERYTHING stated under the one truth postulate recursively is true under the rules of mathematics, so long as all the assumptions are true! Which is to say that everything currently known in/about mathematics IS true under the one truth postulate.
Now, let us be careful right from the get-go. There may be other PARTIAL solutions to Hilbert's 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 postulate?s that PARTLY or FULLY solve Hilbert's program may eventually be found. So ONE and FIRST truth postulate can be used interchangeably, as synonyms, as they represent the same thing FOR NOW ONLY!
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 Joseph Haykov with the help of Walter Block in January 2023.
Commerce
When people engage in commerce using money, what is the first thing they look at? The price. Which makes money, first and foremost, a unit in which prices are measured. And what are prices? The exchange rate of money to a particular product. Which is to say that money is 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. The eval function in scheme is recursively defined in terms of the apply function that calls, which is to say uses eval. 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 explained here
and also here
Just to be perfectly clear, we aren’t saying ANYTHING new. 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. Is a German Deutschemark money today? No. It is just a piece of paper. And there is no trade without money, as barter is very difficult to engage in, due to the double coincidence of wants problem.
Barter
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. Of course the double coincidence of wants makes trade without money difficult. However, money isn’t always needed to solve the double coincidence of wants problem as we can see from these schoolyard cases.
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 exchange would fill matching orders, by conducting the closing auction.
And this would, 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
Consider how the FX market works, in terms of exchange rates. 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. 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 under the condition of no available arbitrage, the exchange rate matrix becomes involutory, and since it is also symmetric, it becomes isomorphic, in which case involution diagonalizes into ONE unique signature matrix. And it is precisely the diagonal of the unique signature matrix that represents a single exchange rates to US dollars under the condition of no arbitrage. But why use scary math when the same thing can be BETTER explained in English?
Under the condition of free trade, currencies will always wind up having one exchange rate into a single numeraire, which today happens to be the US dollar. For a very simple reason. 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 anytime 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. Which means that in the real world, relative prices of currencies as measured in euros and dollars, and by induction ANY and ALL currencies, will be identical, assuming no available arbitrage. Which is to say that the exchange rates between all currencies will CONVERGE to one unique set of relative prices as represented mathematically by the diagonal signature of the isomorphic matrix of exchange rates under the absence of available arbitrage.
Consider what would happen if in addition to dollars, everyone started to quote currency prices in euros as well. We’d wind up with a single set of relative prices, but now measured in two different numeraire. Such an arrangement benefits no one, while creating the inconvenience of ALWAYS having to be on the look-out for an arbitrage opportunity we may be missing. But that is not all! As all of us that have used both the metric and imperial systems of units know, having two sets of units for anything is always inconvenient, just in general, due to human nature. Once we learn to think in centimeters, switching to inches is singularly difficult. And vice versa. People are so used to the imperial system, they continue using it despite the fact that changing scale under the decimal system, which we all use, is much more difficult with imperial units.
So money is simply whatever numeraire banks that actively participate in the Foreign Exchange Interbank Market collectively decide to quote relative prices for all currencies in. Which 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, which we call price. In fact, we can recursively define price as the exchange rate of money and goods and services whose relative prices are measured in this particular money.
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 which used to be written down, but these days are mostly stored electronically; and that is just the tip of the iceberg. All this of course makes sense, as any money is better than no money at all; without relative prices, we can only engage in barter.
Again, to reiterate, commercial trade requires a set of arbitrage-free relative prices, and therefore money, which is necessary first and foremost because relative prices are measured in money. Even if money is local tree branches, with some markings on them. Even if it is salt. Or pieces of leather. Or various colored pieces of paper. Even if it is old water bottles. Cans of meat. Even if it is some kind of old paper currency that was issued by a country that no longer exists, such as 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. Even if money is unmovable, like the Rai Stones on the Island of Yap. Unlike gold coins, unmovable stones can not be themselves exchanged, so the ONLY way they can be used as a medium of exchange is by acting as the units in which RELATIVE prices are measured! Which is to say that it does not matter what money is, so long as it can be used to quote relative 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 money, only barter is possible. And money is simply what most people choose to quote 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 exchange that takes place under a set of relative prices over time.
Before we continue, we would like to point out that our definition of money in no way shape or form contradicts any known facts 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 relative prices are 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. This is why money must ALSO be a medium of exchange. So you can exchange money itself. And money is ALSO valuable because you can ALSO exchange it for anything that is priced in this money. So what else would you ALSO use to measure things like profits? So, yes. Money is-also a recursively-induced medium-of-exchange and store-of-wealth, but the first-primary function of money is to be a unit-of-measure in which a set of relative prices is quoted 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 physical object that could perform the first-primary function of money in the real world, which is that of a unit-of-measure as a direct result of having the desirable physical attributes of being an accurate ruler with which prices could be measured under the constraint that money is-also a recursively-induced medium-of-exchange and a store-of-wealth. And of course it is these recursively-induced-also functions of money that 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, multiple other things have been 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. Until the demonetization of silver in the late 1800s that went largely unnoticed, 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. We just use money as something that enables us to engage in commerce, because commerce without quoted relative prices IS barter, and barter is so limited in the real world due to the double coincidence of wants problems, that we feel it would be prudent for us all to simply ignore the impact of barter on economics as a good first order approximation.
What we are saying is that in reality, to solve the double coincidence of wants problem, what we need isn’t money. What we need is a good, arbitrage-free set of relative prices to engage in commerce under, and money simply represents the units in which these relative prices are measured. And so long as there exists a mechanism to transfer money between people when making payments, and there exists a secure way of storing money, and of verifying the authenticity of money, it matters surprisingly little as to what represents the unit-of-measure that we refer to as money in the real world.
Consider what we are using as money today in the United States. It is the M2 money supply, which only exists as entries in electronic ledgers. Cash is so di-minimus relative to M2, as to be of virtually no significance in paying for consumption, so long as electricity is available. So, the M2-money we all use currently to make payments in REALITY IS just a unit-of-measure already, today! Of course M2 is-also a recursively-induced means of exchange, but ONLY as a consequence of the fact that the US dollar money as represented by M2, inherently, by definition IS the units in which relative prices are measured; that is its first-primary FUNCTION!
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 GDP. This means that the efficiency of exchange is of the paramount importance, as it determines real GDP. This renders trade very important, to the extent that exchange occurs through trade.
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 before money, by definition, means before trade, as trade without money in the real world does not exist, but for a very limited 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 voluntary trade. 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 necessarily voluntary, which is to say, method A often takes place through partly-or-fully involuntary redistribution, without using money. An example of fully involuntary redistribution would be robbery. Robber: Your money or your life, … long pause …, 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, you are exchanging your money or labor for your life? Yes we are, but we have no other choice here, and neither would you under the condition of armed robbery or slavery, but to either die or exchange your life for your money or your 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 by partly-or-fully involuntary redistribution of goods and services under what in essence amounts to slavery, but using money! And the partly-or-fully voluntary monetary EXCHANGE that occurs as a result of 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 only partly involuntary, but mostly 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 produced, and then decided how to properly allocate consumption among the population in whatever way he 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 indeed, 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, the concept of: to each according to contribution, does not have any coherent meaning as subjectively perceived by ANYONE rational if there is wealth, because wealth represents UNKNOWABLE future consumption by any number of people that might not contribute much under ANY objective 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 that 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 that refused to engage in research for Stalin voluntarily, still talk about doing ground-breaking research in Sharashka prisons, INVOLUNTARILY, but actually DOING AMAZING RESEARCH!
That Stalin was a genius is 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 most of the important DECISIONS, 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 AMAZINGLY well is control agency costs, and how!
By having a widespread system of paid informers, in addition to hand-picked high quality managers that informed not only on the managers to NKVD, but-also to the managers, on ANYONE that 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. So 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, perhaps a slightly more humane version of slavery than what exited in the US prior to the civil war, but slavery nonetheless. For you could not legally LIVE anywhere for longer than your allotted vacation time by the state, other than your ONE 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 first-dual economy under Stalin headed by thieves-in-law is WAY outside the scope of this paper. So let us set aside the real GDP impact of the first-dual economy under Stalin, which is to say exchange method A under controlled criminality under thieves-in-law.
The first-primary economy under Stalin WAS the slave economy as measured by real GDP growth under a genius-merciless OWNER duality, as represented by Stalin-Beria. And the first-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 Stalin, OR ELSE! Just as nobody steals “the bag with all the envelopes and all the money” from a US “thief-in-law” 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 a remote Kibbutzes recursively-induced-also BECAME a store-of-wealth!!!! You see the problem right away course; future to us is UNKNOWABLE, which makes it impossible to allocate wealth in ANY WAY that can in ANY WAY be objectively perceived as fair, regardless of how you choose to objectively define fair, precisely because wealth represents UNKNOWABLE future consumption. Which makes it impossible to allocate wealth in ANY way that COULD BE judged as fair by those living in a Kibbutz NOW under ANY OBJECTIVE definition of the word fair. For ANY definition to be considered OBJECTIVE everyone RATIONAL must agree with it. That is what OBJECTIVE means. If you are RATIONAL then you will agree with it, IF it is OBJECTIVE. Like any rational person will agree that 4+9=13. That is what we are saying. COMPLETELY OBJECTIVE. A definition that EVERYONE RATIONAL can agree with. Outside of math, an example of such an objective definition might be “you should mind your own business”. Something that everyone RATIONAL will agree with. And how can everyone RATIONAL agree on a fair allocation of wealth as represented in the real world by UNKNOWABLE future consumption?
To summarize, under method A=socialism, allocation of consumption=to each according to contribution, which 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 under the one-truth postulate, ANY allocation not according to contribution is unfair under ANY objective definition of the word fair. That is because under ANY OBJECTIVE definition of the word fair, fair MUST ALSO BE FAIR TO ALL, by definition of the word OBJECTIVE, which is to say something that ALL will agree with. This is to say that ANY allocation not according to contribution is CLEARLY unfair to ALL, by virtue of being unfair to those that contribute, under any objective definition of the word fair. This is why siblings fight over inheritance, even when their parents are billionaires. And this is also the reason why real-world Marxists in WEALTHY NATIONS are either idiots or rent-seekers, which is to say those seeking to gain wealth without any reciprocal contribution of productivity. Or some combination of the two, mathematically by definition under the one-truth postulate AND 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 real GDP that is produced?
Benefit of trade
Of course, we all 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? You are sitting on your couch, reading a book. And then you turn on your TV. What is the marginal consumption of anything? On margin, you are not even consuming leisure, as your alternative to watching TV is to just continue sitting on the couch and reading a book. 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. Of course so long as trade is voluntary, and no cheating is involved. WITH THE FULL UNDERSTANDING THAT: 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.
Under the condition of perfect information, everyone that participates in 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?
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 you can engage in ex ante 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 includes being 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 free-trade 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 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 SUBJECTIVELY perceived benefit as it relates to using these alternatives in the foreseeable future, which is not only unmeasurable objectively, but also extremely unstable. For example, your subjectively perceived benefit of drinking water can change drastically over time, depending on how thirsty you feel.
So for Bob that likes to drive, the ordinal ranking of UNMEASURABLE 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 UNMEASURABLE subjective 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 the relative prices as they exist today, Bob would NEVER use the Rolls, and Alice would NEVER drive ANYTHING. 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”. 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 ranking of ex ante subjective utility is-also 100% correlated with recursively-induced-also MONEY as represented in the real world by M2! 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 CUMULATIVE subjective ranking of ex ante utility derived from PAST and-also recursively-by-induction, which is to say recursively-induced utility of EXPECTED FUTURE monetary trade, which is to say commerce that takes place under a given set of relative prices! As measured in recursively-induced-also M2 medium-of-exchange money.
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 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! Which is to say 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-also the recursively-induced 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 recursively-induced store-of-wealth money; simply due to the fact that money represents future consumption, which is to say the expected value=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 represented by Dexter shoes going 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! 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 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 method A, and 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 WAY 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 as represented by Welfare. Welfare is government spending designed to ensure that the ruling elite can consume what they deem appropriate in peace and serenity, by repeatedly recursively-inducing the really desperate poor to commit less street crime. So we are NOT talking about Pareto-efficiency anymore. We are talking about overall subjective unhappiness, beyond trade. So we are NOW 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, has a first-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 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 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 the definition of money itself is inherently recursive.
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 CAN result from RARE EVENTS, like oil price shocks, including but not limited to those that occurred circa 1973 and 1980. The cost of shipping containers tripled relative to the price of goods shipped inside said containers due to a RARE EVENT called “Covid”. 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, to the extent that relative prices remain predictable, default risk in general will not increase as a result of inflation or deflation, which is to say 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 being used as 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, without 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 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, which may well be innovation by a firm in California, 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 OVERALL 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 by consumption. 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 today, 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 fractional reserve banking using commodity money as a base currency, which is a fascinating topic in and of itself, but far outside the scope this basic, introductory 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 arbitrage risk-premium that also results 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 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. Which is exactly why exchange method A under Roosevelt only became efficient in the United States after World War II started and even under WWII, method A was primarily efficient due to the Pareto-efficiency of commerce that resulted from Roosevelt using A 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 trade 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 slavery in the US, or Communist China or 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 must be controlled in order for 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 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 today? Just units. Electronic ledger entries. M2 doesn’t really exist. It is just a unit of measure, called the US 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.
WHICH IS TO SAY THAT
[money IS to you a unit in which the relative prices of what you buy and sell are measured, which is why money is-also to you a means of exchange]
[which is why money is-also to everyone a means of exchange]
[which is why money is-also to you a means of exchange]
[which is why money is-also to everyone a means of exchange]
[which is why money is-also to you a means of exchange]
and so on, under infinite recursion, which is to say recursively-induced-also!
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 needed 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 rank order-able subjective ex ante utility of exchange? This was only possible because the RANK-of(ex-ante-[subjective-utility]-of-[EXCHANGE]) as measured in subjectively perceived unit-of-relative-price first-primary MONEY is 100% correlated with the RANK-of(ex-ante-[subjective-utility]-of-[EXCHANGE]) as measured in means-of-[EXCHANGE] recursively-induced-also MONEY, such as M2 as a result of MONEY ITSELF being defined RECURSIVELY! Otherwise, we must make assumptions that frequently turn out to be wrong. And you can go ahead and re-read this paper as carefully as you want. 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 seems to have a cause and 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 a medium-of-exchange. The original, UNIQUE-ONE-TRUE-MONEY as defined in this paper under the 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 so to speak. 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, 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 one-truth postulate, ALL axioms, not only those that ARE based on assumptions, but also those that ARE NOT, as represented by recursive definitions such as maximum-likelihood itself, 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 the first-dual at once! Similar to how particles such as electrons have properties that we can not measure at the same time, because they may be inherently recursive? Maybe economists can finally teach theoretical physicists something for a change. Under the one-truth postulate under maximum-likelihood it is easy to see that in reality, clearly inherent-randomness and inherent-recursion co-exist.