Does the Quantity Theory of Money derive from the Quantity Equation?

The short answer is no. 

A quick look at the historical origins of the Quantity Theory of Money (QTM) and the Quantity Equation makes things clear. 

Historical Origins

QTM traces its origin to as far back as the 16th century when Jean Bodin (French philosopher and economist) and some others asserted that the European inflation of the time was being driven in significant part by the inflow of gold and silver (metals used as currency) from South America. Subsequently, influential thinkers including John Locke (1632-1704), Richard Cantillon (1680s - 1734) and David Hume (1771-76) did important work on QTM, adding substance to the theory. By the 1800s, despite opposition, QTM had become the largely accepted theoretical guide to monetary policy. 

The Quantity equation came much later. Since the sharpest minds through history have often worked and come up with the same formulations around the same time, attribution is sometimes a complicated affair. While John Stuart Mill (1806-73) developed the concept of the “Equation of Exchange” (what the Quantity equation was originally called), the mathematical formulation of the Equation of Exchange is attributed to Irving Fisher (1867-1947), who in turn credits Simon Newcomb (Canadian-American mathematician) as the first thinker to come up with this equation. 

The Equation of Exchange 

Given below is the original ‘Equation of Exchange’ (the form that Newcomb came up with and Fisher adopted):

MV=PT                    where

M = the stock of money in circulation 

V = velocity of circulation of money or the number of times a unit of money changes hands during the year

P = general price level 

T = total no. of transactions carried out during the year

Irving Fisher’s Contribution 

What Fisher did (and why history remembers him), was take Newcomb’s equation and formulate the Quantity Theory of Money around this equation. He gave QTM a mathematical framework that did not exist before, and in doing so, allowed those who came after him, to empirically test QTM in a scientific way. 

This framework also made it possible to clearly state one’s assumptions. Fisher assumed that V and T were constant or stable. Based on these assumptions, he theorized that the general price level (P) varies in direct proportion to the quantity of money in circulation (M). Makes complete sense; if MV=PT, and V and T are stable, P has to be directly proportional to M. 

Naturally, this framework also made it easier to refute the theory by attacking these assumptions. For example, if V or T are not stable, then QTM as it is traditionally formulated, falls apart. 

Conclusion

The Quantity Theory of Money does not derive from the Quantity Equation, since QTM was around centuries before the Quantity Equation was formulated and employed to give the theory mathematical form and vigour. The Quantity equation is simply a tool employed by economists to justify the validity or the invalidity of QTM by critically analyzing the theory’s assumption and its fit with empirical data.