Equation of Exchange
In its modern form, the quantity theory builds upon the following definitional relationship.
where
- is the total amount of money in circulation on average in an economy during the period, say a year.
- is the transactions velocity of money, that is the average frequency across all transactions with which a unit of money is spent. This reflects availability of financial institutions, economic variables, and choices made as to how fast people turn over their money.
- and are the price and quantity of the i-th transaction.
- is a column vector of the, and the superscript T is the transpose operator.
- is a column vector of the .
Mainstream economics accepts a simplification, the equation of exchange:
where
- is the price level associated with transactions for the economy during the period
- is an index of the real value of aggregate transactions.
The previous equation presents the difficulty that the associated data are not available for all transactions. With the development of national income and product accounts, emphasis shifted to national-income or final-product transactions, rather than gross transactions. Economists may therefore work with the form
where
- is the velocity of money in final expenditures.
- is an index of the real value of final expenditures.
As an example, might represent currency plus deposits in checking and savings accounts held by the public, real output (which equals real expenditure in macroeconomic equilibrium) with the corresponding price level, and the nominal (money) value of output. In one empirical formulation, velocity was taken to be “the ratio of net national product in current prices to the money stock”.
Thus far, the theory is not particularly controversial, as the equation of exchange is an identity. A theory requires that assumptions be made about the causal relationships among the four variables in this one equation. There are debates about the extent to which each of these variables is dependent upon the others. Without further restrictions, the equation does not require that a change in the money supply would change the value of any or all of, or . For example, a 10% increase in could be accompanied by a 10% decrease in, leaving unchanged. The quantity theory postulates that the primary causal effect is an effect of M on P.
Read more about this topic: Quantity Theory Of Money
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