what is the equation of exchange 
the equation of exchange is an economic identity that shows the relationship between the money supply the velocity of money the price level and an index of expenditures it says that the total amount of money that changes hands in the economy will always equal the total money value of the goods and services that change hands in the economy understanding the equation of exchangethe original form of the equation is as follows m v p t where m the money supply or average currency units in circulation in a year v the velocity of money or the average number of times a currency unit changes hands per year p the average price level of goods during the year t an index of the real value of aggregate transactions begin aligned m times v p times t textbf where begin aligned m text the money supply or average currency units in text circulation in a year end aligned begin aligned v text the velocity of money or the average number of text times a currency unit changes hands per year end aligned p text the average price level of goods during the year t text an index of the real value of aggregate transactions end aligned m v p twhere m the money supply or average currency units incirculation in a year v the velocity of money or the average number oftimes a currency unit changes hands per year p the average price level of goods during the yeart an index of the real value of aggregate transactions m x v can then be interpreted as the average currency units in circulation in a year multiplied by the average number of times each currency unit changes hands in that year which is equal to the total amount of money spent in an economy in the year on the other hand p x t can be interpreted as the average price level of goods during the year multiplied by the real value of purchases in an economy during the year which is equal to the total money spent on purchases in an economy in the year so the equation of exchange says that the total amount of money that changes hands in the economy will always equal the total money value of the goods and services that change hands in the economy 1later economists restate the equation more commonly as m v p q where q an index of real expenditures p q nominal gdp begin aligned m times v p times q textbf where q text an index of real expenditures p times q text nominal gdp end aligned m v p qwhere q an index of real expendituresp q nominal gdp so now the equation of exchange says that total nominal expenditures are always equal to total nominal income 2the equation of exchange has two primary uses it represents the primary expression of the quantity theory of money which relates changes in the money supply to changes in the overall level of prices additionally solving the equation for m can serve as an indicator of the demand for money in a macroeconomic model the quantity theory of moneyin the quantity theory of money if the velocity of money and real output are assumed to be constant in order to isolate the relationship between money supply and price level then any change in the money supply will be reflected by a proportional change in the price level 3to show this first solve for p p m v q p m times left frac v q right p m qv and differentiate with respect to time d p d t d m d t frac dp dt frac dm dt dtdp dtdm this means inflation will be proportional to any increase in the money supply this then becomes the fundamental idea behind monetarism and the impetus for milton friedman s dictum that inflation is always and everywhere a monetary phenomenon money demandalternatively the equation of exchange can be used to derive the total demand for money in an economy by solving for m m p q v m left frac p times q v right m vp q assuming that money supply is equal to money demand i e that financial markets are in equilibrium m d p q v m d left frac p times q v right md vp q or m d p q 1 v m d left p times q right times left frac 1 v right md p q v1 this means the demand for money is proportional to nominal income and the inverse of the velocity of money economists typically interpret the inverse of the velocity of money as the demand to hold cash balances so this version of the equation of exchange shows that the demand for money in an economy is made up of demand for use in transactions p x q and liquidity demand 1 v 