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Simplified Exposition of Axiomatic Economics

Section V:  Glossary of Terms

Absolute Geometry: the four axioms common to Euclidean and non-Euclidean geometry, they make no mention of parallel lines.

Aggregate Utility: price times stock; F(m) = mS(m).

Central Bank: the only bank which can create money certificates ad libitum. Commercial banks can write checks of their own amounting to some multiple of the cash and central bank deposits that they hold, the exact multiple depending on the reserve requirement.

Credit Money: bills of debt (IOUs) that circulate as money before being redeemed. Existence alone is not a sufficient condition for credit instruments to be included in the stock of money; there must be an active secondary market for them in the community.

Demand Distribution: $$c_0(m) = \frac{e^{-\frac{1}{2}(\frac{ln(m)-μ}{\sigma })^2}}{\sigma m}$$, the distribution of people who will pay up to m monetary units for the first unit of a phenomenon. This is a simplification. The general theory uses $$c(m) = \sum_{r=0}^{\infty }c_0(x)$$ with $$x = \frac{mu(0)}{u(r)}$$to include all demand.

Federal Reserve: the United States’ central bank.

Fiduciary Money: money certificates created in excess of the commodity money (gold) for which they can be redeemed. For countries that have abandoned the gold standard, all of their money certificates are fiduciary.

First-Unit Demand: the value (in money) of the first unit of a phenomenon. It is described by Axiom Three of my theory.

Interest: Consider a man who wants to take out a loan at interest. He must think he will have more money in the future than he does now. (More money holdings, not necessarily more wealth.) If he does, the value of individual monetary units will tend to decrease over time relative to other phenomena. Traditionally, this has been assumed to be exponential decay; value changes each day by a proportion of the previous day’s value. Other decay functions are discussed in Appendix A: Alternative Distributions for First Unit Demand.

Kolmogorov: wrote Foundations of Probability in 1933. He began “The purpose of this monograph is to give an axiomatic foundation for the theory of probability”. He was sharply opposed by Keynes, who was involved in probability as well as economics.

Law of Price Adjustment: Increases in the importance of a phenomenon causes its price to rise exponentially and its stock to remain constant, that is, $$\frac{ds_p}{dµ} = p$$ and $$\frac{dp}{dµ} = p$$

Marginal Utility: u(s), the first derivative of total utility, it is described by Axiom Two of my theory. Also called diminishing utility.

Money: a medium of exchange which one can always expect others to accept as payment. 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 to which one received.

Money Certificates: cash and deposits at the central bank which are or were redeemable in commodity money (gold). Checking accounts are redeemable only in cash, not commodity money, and are limited by the reserve requirement. Thus, there are three levels of money.

National Debt: government bonds sold mostly to the central bank, some to commercial banks, and almost none to private savers. Since the central bank and the treasury are both branches of the government, they have effectively just printed some money and spent it. One possible exception is countries with a large trade deficit. This implies that foreigners own some of their assets and, while they usually prefer real estate and businesses, they may take government bonds.

Proportionate Effect: the value of a phenomenon is subject to change each day by a random proportion of its previous day’s value.

Reserve Requirement: the percentage (about 12.5%) of a commercial bank’s deposits that must be backed up with cash and central bank deposits. Commercial banks receive checks written on the central bank when it buys government bonds from one of their clients.

Requirement: the amount of a phenomenon needed; $$R = \int_{0}^{\infty }c(m)dm$$

Saturation: the price and stock such that aggregate utility is at its maximum, that is, its first derivative,
f(m) = S(m) - mc(m), is zero.

Stock: the amount of a phenomenon in existence. If the price is m then $$S(m) = \int_{m}^{\infty }c_{0}(t)dt$$or, in the general theory, $$S(m) = \int_{m}^{\infty }c(t)dt$$.

Total Utility: the value (in money) of the stock of a phenomenon that one possesses.

Utility: value. The position of a definition on one’s value scale.

Value Scale: the values (in money) that one assigns to phenomena, it is described by Axiom One of my theory.