Simplified Exposition of Axiomatic Economics

*Section I: First Axiom*

Definitions to which one or more phenomena may conform do not exist at one point on one's value scale but rather in a series of points labeled "1st occurrence", "2nd occurrence",... The intensions of the definitions are the same at each of these points, the importance of each position being different because of factors not contained in the definitions, that is, how many phenomena have come before or are expected to come. The spacing of the definitions in a series is not even but is determined by diminishing utility. Phenomena that conform to the definitions in such a series are fungible, meaning interchangable. Being interchangable, they cannot each have a different value (importance), for the loss of one being employed for an important purpose can be met simply by replacing it with the one that conforms to the definition of marginal utility. Because any of the phenomena conforming to definitions in a series can be replaced by the one with the least utility of those being satisfied, one does not value any of them more than the last one. Marginal utility is all that is ever at stake when risking a unit of fungible phenomena. When considering the acquisition of another unit of fungible phenomena, the value of that unit is the utility of the next want to be satisfied in its series. In either case, the value of a phenomenon is never determined by the use to which it happens to be applied but by the use on the margin between satisfaction and nonsatisfaction; hence the term "marginal utility."

When defining marginal utility, the quantity of phenomena conforming to a definition was considered to be a constant of which value was a function. Where units of a phenomenon can be bought and sold and more of them produced out of the necessary labor and capital, the quantity of phenomena is variable and it must be shown to be a function of a constant lest two variables be defined with one equation.

Because one's wealth at any time is constant, it is applied first to the high end of one's value scale, producing phenomena or exchanging phenomena already acquired for those which conform to definitions at the top of one's value scale and continuing down until all of one's wealth is exhausted. In this finite quantity of definitions with phenomena conforming to them, there are a fixed number of definitions in each series of similar definitions which have phenomena conforming to them. Marginal utility is defined with the quantity of phenomena conforming to each definition, not an arbitrarily fixed constant, but a function of wealth.

I assert that one is capable of determining which of any two phenomena or sets of phenomena conform to a definition at a higher place on one's value scale than the other. If one fails to determine which of the two is higher, it can only mean that they are equal. In other words, one's value scale is a total (linear) ordering of phenomena. This is the first of three axioms which the reader is asked to accept. The plausibility of this axiom is derived mainly from analogy with the other dimensions (space and time), which are also totally ordered. A total ordering is included in the assertion of Absolute Geometry that every line has a coordinate system.

Because of this axiom, for every definition on one's value scale to which phenomena might conform, there stands beside it the number of units of money to which one is indifferent as to which one received. This supposition demands only that money be infinitely divisible, which it is for all practical purposes. As there are an infinity of distinct points on one's value scale, however, it cannot be expected that one is conscious of them all. In fact, one does not need to know exactly what one's point of indifference is to conduct many transactions.

The graph of the distribution of points of indifference, c(*m*), can be pictured as an aerial view of the people who value a phenomenon assembled along a line marked "money", where they are asked to stand by the number of monetary units that are equal to a unit of that phenomenon. If more than one person has the same valuation, they stand behind the corresponding number. The stock of that phenomenon naturally tends toward the high end, as anyone who possesses a unit of it who sees his neighbor to the right without one will sell it to him. Only use value and expected exchange value in other markets not represented on this graph are counted because, though one may value a phenomenon greatly in anticipation of exchanging it at a high price, if one fails to get that price, one has to lower one's asking price until it eventually equals the value of keeping that phenomenon for one's personal use. While money has very little use value, it does have expected exchange value in other markets not represented on this graph, and it is with this in mind that people withhold their money from this market if the price rises too high. The expected exchange value of money is historically derived from its use value. If it were a function of today's prices, we would have a contradiction because we are now deriving today’s prices from the demand distribution, c(*m*), which includes expected exchange value.

If a phenomenon has a steeply diminishing utility for most people (after acquiring one unit, the importance of the next is very low because one easily becomes sated), most people are only represented once and c(*m*), is very close to c_{0}(*m*), the distribution of people's point of indifference for their first unit. If there is a gradually diminishing utility among people, many come back again and again before they become sated, each time with a lower point of indifference, and consequently the low end of c(*m*) rises. \(R = \int_{0}^{\infty}c(m)dm\) is the requirement for a phenomenon by a population. Because stock is limited, however, only those with the highest use value of it relative to their value of money possess any of the phenomenon. The price is less than the point of indifference of the last person who possesses a unit of the phenomenon or he would sell it, and it is greater than the point of indifference of the first excluded individual or he would buy. These two points of indifference are the marginal pair which determine the upper and lower limit of price, between which is the zone of indeterminacy. The formula relating price and stock to the demand distribution, c(*m*), is \(S(m) = \int_{m}^{\infty }c(t)dt\) with S(*m*) the stock, *m* the price, and c(*t*) (*t* is a dummy variable for the integration) the distribution of points of indifference between the use value of a unit of a phenomenon and t units of money. Of course, the expression above does not have any meaning until it is proven that stock converges. It will be used informally, however, until the convergence of stock is proven.

Both the people traditionally labeled "consumers" and those labeled "producers" appear in the demand distribution. The conceptual separation of consumers and producers is a great mistake of mainstream economics. They are all just people, each with a bit of the stock, and they are all prepared to sell if the price is above a certain point and buy if the price is below that point. The only thing that distinguishes people from one another is their point of indifference. This has little to do with who produced different bits of the stock, the event of production having occurred in the forgotten past. When economists draw one curve called "supply" and another called "demand", they are implying that the two are independent, for one cannot solve two simultaneous equations for two variables if the two equations are just versions of the same relation. Their dependence is well known at the macro level, but I assert that supply and demand are not independent at the micro level either. It is a mistake to inquire whether I support Say's assertion that "supply creates its own demand" or Keynes' assertion that "demand creates its own supply"; Axiomatic Theory of Economics is detached from that debate. I anticipate that the greatest block to the understanding of my theory will be people trying to interpret it in terms of supply and demand. I do not believe in supply and demand. I believe in the demand distribution, which is a mapping between price and stock. Supply has no place at all in Axiomatic Theory of Economics. My theory is not even divided into “micro” and “macro” sections. These terms were invented by mainstream economists when it became necessary to paste Keynes’ theory over the top of Marshall’s theory. They are clearly incompatible and their association in modern textbooks is entirely due to the bookbinder, not the economist.

By what criterion does mainstream economics distinguish people represented on a supply curve from those represented on the associated demand curve? This is a particularly pressing question for people dealing in narcotics because the penalties are so much greater for being on one curve than the other. But, if one visits a neighborhood where such trade takes place, any of the people one encounters would sell if the price were right and would buy if offered a bargain. There is really only one relation and it is called the demand distribution. Since there are two variables, price and stock, this (single) relation can provide a mapping from one variable to the other but cannot fix them. However, later in this pamphlet, existence and uniqueness proofs are given for a point toward which price and stock tend. Thereafter, it will be assumed that they are fixed at that point, called saturation.

The method of mainstream economics really has a third variable which is never mentioned and that is the time unit for supply and demand. It is well known that elasticity is a function of this time unit and, if this is true, one calculates a different price depending on whether one speaks of weekly or monthly supply and demand. This is an inconsistency since there can only be one price and it is not dependent on the caprice of an economist when he decides how often to conduct his surveys. This is a point that is glossed over in mainstream texts. A detailed discussion of the time unit chosen for supply and demand is never given and many texts neglect to mention the need for choosing one at all. Yet in their chapter on elasticity, every textbook lists time as a factor, sometimes as the most important factor.

Mainstream economists have two variables, price and quantity per unit of (some usually unspecified) time, and two equations, supply and demand. For this to work at all, the equations must be independent, which means that each individual must be either a buyer or a seller. The economist's decision to put people on one curve or the other can-not depend on the price that they would buy or sell because both equations are defined for all prices. (Price is one of the independent variables.) So what is the economist's decision based on? Ask him repeatedly until he admits that there is really only one distribution. Also, press him to acknowledge that the demand distribution independently exists at each instant of time. Supply and demand curves are different depending on the time unit chosen. Mainstream economists provide no proof that their predicted prices are independent of their choice of time unit. For example, will thirteen predicted weekly quantities be the same as three predicted monthly quantities?

A large part of the problem with supply and demand is that it is used descriptively, but called predictive. It is easy to predict the past. Economists just observe the quantity produced one month and what it sold for and they put a little × over that spot. Then, by pure conjecture, they draw four tails on their × to fill their graph paper. Supply and demand has never been used predictively, not even to make bad predictions. × marks the spot is a purely descriptive technique. Since they are using the 20-20 vision of hindsight, they can do this for three months in a row and, to nobody’s surprise, the sum of the quantities is the quarterly quantity. In the real world, price is constant for years at a time but, for most companies, their weekly and monthly sales figures swing wildly and unpredictably, sometimes by several fold from one month to the next. Mainstream economists have no explanation for this, which they should since their theory is called __supply__ and demand and the horizontal axis of their graph is labeled weekly (or monthly) quantity. When I have been asked to help predict sales, I have told them that price is related to stock, not supply, and that they should stop watching their sales chart so ardently. At most companies, there is someone in accounting who feeds sales figures to the employees so that they can predict layoffs. They know that every dip in sales will send hundreds of them to the unemployment office, and that every rise will have their bosses clapping each other on the back and extolling their brilliant and farsighted management. They also know that nobody can predict sales. Supply never means anything in economics, though sometimes (for non-durable phenomena) it can pass for stock.

It is well known that mainstream economics is in trouble. Nobody in the hard sciences respects economists and even within their own ranks, a number of books and articles have appeared questioning why economics is not yet a science. There is considerable debate among economists about methodology, what it takes to qualify as a science, and what distinguishes economics from other fields. Implicit throughout is the understanding that mainstream economics does not work. To qualify as a science, economics must be axiomatic. But one must address price and stock; supply and demand does not work. Also, to deduce mathematical expressions from axioms, the axioms must be of a mathematical nature and they must specify actual functions from which equations can be derived. Fortunately, however, there is nothing fundamental about economics that prevents it from being made into a science just as physics was made into a science by Newton and mathematics by Euclid. This is what I propose to do.