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© 19992003 Douglas A. Ruby Revised: 01/15/2003 Financial Markets and Instruments Inflation and Inflationary Expectations Aggregate Demand Macroeconomic Principles Macroeconomic Theory 
An "identity" is an expression that is true by definition such as the the following: a triangle = a three sided geometric figure There is no debate about this equality, its truth comes from the nature of the definitions used. A popular identity defined by Irving Fisher is the quantity equation commonly used to describe the relationship between the money stock and aggregate expenditure:
The terms on the righthand side represent the price level (P) and Real GDP (Y). Taken together these two terms represent Nominal GDP or a measure of the total spending that takes place in an economy in a given time period. On the lefthand side, M represents some measure of the money supply, perhaps M_{1}, and 'V' represents the velocity of this monetary measure. Velocity represents the number of times money changes hands in support of the total spending in an aggregate economy. We might more accurately state the equation as follows: M_{1}V_{1} = PY^{R} denoting the use of M_{1}, its corresponding velocity and Real GDP 'Y^{R}'. If we chose to use M_{2} as our monetary measure then the expression would be: M_{2}V_{2} = PY^{R}The truth of the expression does not change. Even though, we find ourselves using a broader definition of money, and corresponding velocity measure will be smaller. For example, in 1999, Nominal GDP (PY) was equal to roughly $10 trillion. In that same year, M_{1} was measures at roughly $2.2 trillion with a corresponding velocity of 4.5. or $2.2(4.5) = $10.0In that same year M_{2} was measured at $4.0 trillion with a corresponding velocity of 2.5 Through logarithmic transformation and differentiation, the quantity equation can be transformed into the following: %ΔM+ %ΔV = %ΔP + %ΔY^{R}where each term represents growth in the money stock, growth in velocity, the rate of inflation, and the rate of Real economic growth respectively. If we are able to assume that velocity is a numerical constant (its value determined by institutions and habits that see little change over time), this expression can be written as follows: %ΔP = %ΔM  %ΔY^{R}The implications of this expression are that if growth rates in the money stock exceed the rate of real economic growth, inflation will be the result. The money stock growing by a smaller amount as compared to the rate of economic growth will lead to deflationary pressures in the aggregate economy. And, of course, price stability implies that growth in the money stock should match the [expected] rate of growth in a particular economy. Concepts for Review:
