# Quantity equation

the quantity equation, quantity formula, transaction equation or traffic equation is the formal, mathematical expression of a version of the quantity theory in such a way specified of the money. How there are different forms of the quantity theory, there are also different forms of the quantity equation.

## the transaction form of the Fisher equation

the quantity or traffic equation, how it decreases/goes back on Irving Fisher, is described by the following equation:

[itex] T \ cdot P = G \ cdot U< /math>

It expresses itself, like the quantity of all material-economical transactions (transaction volume T), the price level (P), which and the peripheral speed of the money ( U ) hold back money supply (G) to each other:

[itex] (transaction volumes) \ cdot (price level) = (money supply) \ (peripheral speed) /math< cdot>

Hereunder applies for the individual factors:

 Variable explanation unit quantity of all material-economical transactions the “physical” quantity of all goods and services exchanged in a certain time interval against money. Empirically this quantity can hardly be determined. (Example: 1658234 yogurt cups + 36587 tractors per month) unpaid services like e.g. the child education (correct-proves) by the equation are not seized. The unit is of the type commodity/time. Price level the average cost per quantity unit of the transactions measured in a certain currency. Theoretically the price level is determined as a price index. The unit is of the type currency/commodity. (The price level determines the purchasing power of a currency.) peripheral speed the average number of transactions per monetary unit of the given currency in mentioned time interval. The peripheral speed is calculated theoretically simply by the remaining sizes of the equation. The unit is of the type 1/Zeit, thus a frequency, e.g. 1 y. Money supply the entire quantity of the money of mentioned currency. The unit is of the type currency.

### derivation

starting point is the consideration that at the market the exchanged objects, money and goods, at the time of a transaction represent related to value equivalents.

(Value of the river of the goods and services from salesman to buyer) = (value of the river of the money from buyer to salesman)

with the fact it is to be noted that both goods and money can change the owner several times.

The value of the river of the goods and services from salesman to buyer is accept-proves T*P.

The value of the river of the money from buyer to salesman is by definition G*U.

It follows:

[itex] T \ cdot P = G \ cdot U< /math>

## the income form of the Fisher equation

two of the sizes of the Fisher equation are statistically hardly to be seized: That applies to the entire quantitative transaction volume, like to the associated average price level of all transactions. Alternatives to it were among other things therefore developed, among them the income form of the Fisher equation:

[itex] Y \ cdot P = G \ cdot U< /math>

It expresses itself like the material gross domestic product (Y), the price level (P), which and the peripheral speed of the money (U) hold back money supply (G) to each other:

(nominal gross domestic product) = (material gross domestic product) * (price level) = (money supply) * (peripheral speed)

hereunder applies for the individual factors:

• nominal gross domestic product: The entire gained the income, which corresponds to the value of all goods and services provided inland, inland, which were supplied in a certain time interval of a domestic use, plus the external contribution. One can call the growth of this variables also nominal economic growth. Empirically the nominal gross domestic product is statistically in principle raisable.
• material gross domestic product: With the help of price index deflationierte nominal gross national product. One can call the growth of this variables also material economic growth. The material gross national product is a size derived from the statistically raisable sizes nominal gross national product and the selected price index.
• Price level: The average price of the goods and services measured in the national currency, seized in the material gross national product. Empirically that is determined price level as a price index. (The price level in the income form and the transaction form conceptionally different sizes are.)
• peripheral speed: The average number from transactions to the acquisition of goods and services of the last use of a unit of the regarded currency in the time interval. (The peripheral speeds in the income form and in the transaction form are conceptionally different sizes. It is calculated by the remaining - statistically raisable - sizes of the equation.)
• money supply: The quantity of the money of the regarded currency.

## interpretation

without further acceptance over the sizes of the two quantity equations concerns it thereby purely tautological connections, which are always fulfilled to ex post office, there z. B. the peripheral speed is calculated simply by the remaining sizes.

Among other things therefore the quantity theory of the money from the quantity equation without corollary assumptions, which maintains a last dependence of the price level on the money supply, does not follow. Because if the central bank does not even increase the money supply beyond the economic growth, the prices could rise nevertheless due to a growth of the peripheral speed. (Actually the statistic data according to the Federal Bank the peripheral speed of the money supply M1 from 1990 to 2001 of 1,58/a sank on 0,82/a.) empirical is however well occupied the systematic connection between money supply and price level.

## application

over neither producer, consumer, to give preference to or disadvantage debtor still creditor and around the economic calculation of the entrepreneurs simplify, is meaningful a firm Preisstand. Also the German Federal Bank had itself always for the purchasing power stability of the German Marks well-known. As also the German Federal Bank, the price level tried to essentially affect other central banks over the money supply. Practical ones like political factors can make it however difficult for a central bank to operate (possibly endogenous and by wage conflicts affected) the economic growth appropriate a money supply policy.