Quantity equation

The quantity equation (also transaction equation , traffic equation or exchange equation ) provides clues about the relationship between money and goods transactions within an economy and is interpreted by quantity theory . In addition to different forms of quantity theory, there are also different forms of the quantity equation.

Explanation

The quantity equation is based on the assumption that all transactions are carried out using a determinable amount of money (in the form of banknotes and coins or book money ). (The barter trade is left out.) The money supply M would change several times through transactions from one hand to the next in a certain period of time, which is referred to as the velocity of the money V. This amount of money in circulation cannot be clearly defined and its velocity cannot be measured. Therefore, the speed of circulation is calculated in the quantity equation to match the selected quantity of money, so that M · V = P · T applies. By definition, the quantity equation is always true and empirically not falsifiable .

The quantity theory interprets the quantity equation so that the central bank controlled money supply directly the (assuming mostly as a constant rotational speed) price level would determine, without impact on the real economy . Thus the quantity equation is the basis of the money supply control and stability policy of monetarism . Milton Friedman declared inflation or deflation to be a purely monetary problem that the central bank could address by managing the money supply.

history

The basic ideas of the later quantity theory were already recognized by Jean Bodin . Building on Bodin, John Locke (English philosopher) introduced the concept of velocity and the function of money as a medium of exchange. Locke thus formulated the essential elements of quantity theory for the first time. This idea was later simplified by the Scottish economist David Hume and finally expanded and announced by John Stuart Mill . The quantity equation goes back to Simon Newcomb (1885) and was specified in 1911 by the economist Irving Fisher . Nobel laureate Milton Friedman was particularly important for neo-quantity theory .

The most common versions of the quantity equation

Transactions and quantity equation (transaction version)

The quantity equation is an identity equation. It is defined as follows:

${\displaystyle M\cdot V=P\cdot T}$

${\displaystyle {\text{Geldmenge}}\cdot {\text{ Umlaufgeschwindigkeit}}={\text{ Preisniveau}}\cdot {\text{Transaktionen}}}$

${\displaystyle M\,}$: Amount of money (average amount of money in circulation within a period).

${\displaystyle V\,}$: Circulation speed (indicates how often a monetary unit was used on average in a period under consideration).

${\displaystyle P\,}$: Price level (represents the average price of goods and services).

${\displaystyle T\,}$: Transactions (indicates the average number of transactions taking place in a period).

While the right part of the equation ( P · T ) shows the volume of the transferred goods and services (sales), the left side ( M · V ) shows the amount of money that is necessary for the execution of the transactions. As a result of the tautology, both sides must correspond, i.e. H. the sum of all sales is equal to the sum of all payments.

From Transactions to Income (Income Version)

However, the transactional form of the quantity equation poses problems. On the one hand, the number of transactions and, on the other hand, the associated average price level cannot be clearly determined. For this reason, alternatives to the original quantity equation were developed, such as the income form of the quantity equation. In this modified form, the transaction volume ( T ) is replaced by the total production (output, Y ). These two quantities are not completely identical, but they are very closely linked, as the amount of goods and services bought and sold increases as production increases. Since there are further empirical measures for the value Y in economics , Y corresponds to real GDP as well as total income.

${\displaystyle M\cdot V=P\cdot Y}$

${\displaystyle {\text{Geldmenge}}\cdot {\text{Umlaufgeschwindigkeit}}={\text{ Preisniveau}}\cdot {\text{Output}}}$

${\displaystyle {\text{Geldmenge}}\cdot {\text{Umlaufgeschwindigkeit}}={\text{ Preisniveau}}\cdot {\text{reales BIP}}}$

${\displaystyle {\text{Geldmenge}}\cdot {\text{Umlaufgeschwindigkeit}}={\text{nominales BIP}}}$

${\displaystyle Y\,}$: Output / real gross domestic product / total income

${\displaystyle P\,}$: Price level

${\displaystyle M\,}$: Amount of money

${\displaystyle V\,}$: Velocity of circulation / velocity of income circulation (indicates how often a monetary unit is used on average to pay income in a period.)

While the right part of the equation ( P · Y ) represents the value of the goods produced (nominal gross domestic product), the left side ( M · V ) reflects the monetary payments that are required for the purchase of these goods / services.

Cambridge version of the quantity equation

Another version of the quantity equation is based on the Cambridge equation, which states that the money supply is the product of nominal income ( P · Y ) and average cash holding time ( k ).

${\displaystyle M=k\cdot P\cdot Y}$

The circulation speed ( V ) already known to us now corresponds to the reciprocal of the average cash holding time ( k ) used here:

${\displaystyle V={\frac {1}{k}}}$

While V represents the turnover rate of a monetary unit within a period, k indicates the length of time a monetary unit is held by an economic subject . If you now replace the cash holding time in the Cambridge equation by the speed of circulation, you get the quantity equation after changing over. So it can be said that the Cambridge and quantity equations are in principle identical. The only difference is in the use of cash holding time and circulation speed.

From equation to theory

The quantity equation is not yet a theory , but it is easily convertible. Two assumptions are necessary for this. On the one hand, T (transactions) and Y (income) are set constant, since it is assumed that people hold a constant part of their income. On the other hand, V ( speed of circulation of money ) is set constant, since this variable depends on a large number of fixed payment habits (e.g. wages, salaries, taxes). These change only slowly and are therefore not subject to any short-term changes.

The quantity theory of money states that a change in the supply of money (M) results in a proportional change in the price. It can be concluded that a doubling of the money supply leads to a doubling of the price. Furthermore, the money supply influences the nominal income ( P · Y ).

Effect of a change in money supply

If the money supply increases at constant velocity, this has two possible reactions. On the one hand, if capacities are not yet fully utilized, the increased demand can increase the amount of goods produced (real GDP ). On the other hand, an increase in the amount of money when capacities are at full capacity causes a price increase, since the high demand meets a constant supply of goods. Money supply inflation occurs.

If the amount of money falls while the velocity of circulation remains constant, this results in a decline in demand, which means a decline in sales and inventory build-up for companies and can ultimately lead to price reductions.

literature

• Gregory Mankiw : Macroeconomics , 4th edition, Schäffer Poeschel, Stuttgart, 2000
• Felderer, Homburg: Macroeconomics and new macroeconomics , 8th edition, Springer Verlag, Berlin 2003
• Berlemann: Macroeconomics, "Modeling, Paradigms and Politics" , Springer Verlag, Berlin Heidelberg, 2005
• Klatt: Introduction to Macroeconomics , 2nd edition, Oldenbourg, Munich, 1989
• Dornbusch Fischer, Macroeconomics , 6th edition, Oldenbourg, Vienna, 1995
• R. Clement, W. Terlau: Fundamentals of Applied Macroeconomics , Verlag Vahlen, Munich, 1998
• Wachtel: Macroeconomics , from theory to practice, Oldenbourg, Munich 1994
• Gordon: Makroökonomie , 4th edition, Oldenbourg Verlag, Munich 1989
• Blanchard, Illing: Macroeconomics , 4th edition, Pearson, Munich, 2006
• Fuhrmann: Macroeconomics , 3rd edition, Oldenbourg, Munich, 1991
• A. Wagner: Macroeconomics , 2nd edition, Lucius & Lucius, Stuttgart, 1998

supporting documents

1. ↑ ^{a b c d} Cf. N. Gregory Mankiw, Macroeconomics 4th edition, Schäffer Poeschel, Stuttgart, 2000, page 185
2. ↑ See: Quantity Theory
3. ↑ See: Felderer, Homburg, Macroeconomics and New Macroeconomics, 8th Edition, Springer Verlag, Berlin 2003, page 80
4. ^ See: Gordon, Macroeconomics 4th edition, Oldenbourg Verlag, Munich 1989, page 466 f
5. ↑ See: Felderer, Homburg, Macroeconomics and New Macroeconomics, 8th Edition, Springer Verlag, Berlin 2003, page 81
6. ↑ See: R. Clement, W. Terlau, Fundamentals of Applied Macroeconomics, Verlag Vahlen, Munich 1998, page 111
7. ↑ See: R. Clement, W. Terlau, Fundamentals of Applied Macroeconomics, Verlag Vahlen, Munich, 1998, page 110