Equation of exchange

In monetary economics, the equation of exchange is the relation: where, for a given period, is the total money supply in circulation on average in an economy. is the velocity of money, that is the average frequency with which a unit of money is spent. is the price level. is an index of real expenditures (on newly produced goods and services). Thus PQ is the level of nominal expenditures. This equation is a rearrangement of the definition of velocity: V = PQ / M. As such, without the introduction of any assumptions, it is a tautology. The quantity theory of money adds assumptions about the money supply, the price level, and the effect of interest rates on velocity to create a theory about the causes of inflation and the effects of monetary policy. In earlier analysis before the wide availability of the national income and product accounts, the equation of exchange was more frequently expressed in transactions form: where is the transactions velocity of money, that is the average frequency across all transactions with which a unit of money is spent (including not just expenditures on newly produced goods and services, but also purchases of used goods, financial transactions involving money, etc.). is an index of the real value of aggregate transactions. The foundation of the equation of exchange is the more complex relation: where: and are the respective price and quantity of the i-th transaction. is a row vector of the . is a column vector of the . The equation: is based upon the presumption of the classical dichotomy — that there is a relatively clean distinction between overall increases or decreases in prices and underlying, “real” economic variables — and that this distinction may be captured in terms of price indices, so that inflationary or deflationary components of p may be extracted as the multiplier P, which is the aggregate price level: where is a row vector of relative prices; and likewise for In 2008 economist Andrew Naganoff (Эндрю Наганов) proposed an integral form of the equation of exchange, where on the left side of the equation is under the integral sign, and on the right side is a sum from i=1 to .