For example, some people believe the world is flat and some believe that it is round. So, we can classify these people into two groups: flaties and roundies. These classifications leave out those people who think the world is neither flat nor round. There may be some who think it is flat on one side and round on the other. We could add a third class: floundies. But there are many other shapes. With this method of classification we must add a new classification for every possible shape. Hardly practical when there are many possibilities.

Fortunately there are other methods of classification. One particularly useful method is binary classification. This method classifies all people with an opinion either as those who believe or those who do not. This allows us to consider any possible opinion using only two classifications. We can classify people who believe the world is flat as flaties and all other people as non-flaties. Likewise, we can classify roundies and non-roundies, floundies and non-floundies. Each pair includes all people.

Among economists there are those who believe inflation can only be caused by too much money, deflation by too little and stable prices by the proper quantity. This belief is based on the quantity theory of money. Believers of this theory were called "monetarists." (There is now another definition of monetariststhat reflects the beliefs of Milton Friedmen. I still prefer the older definition.) As with floundies and non-floundies, economists can be classified as monetarists and non-monetarists.

The two most famous proponents of the quantity theory of money were, perhaps, Milton Friedman and Irving Fisher.

Milton Friedman has interpreted this theory to mean that the money supply should be increased at a steady rate equal to the long term growth rate of the economy. (Believers in this proposal are the ones now called monetarists.) He uses several items of very strong evidence and logic to support this proposition. They are:

(1)  There is a very good correlation between     
     current prices and the money supply measured 
     several years earlier.                       
(2)  This time lag makes it impractical to be     
     certain of the quantity of money needed      
     to stabilize prices.                         
(3)  Therefore, to minimize the effect of money   
     supply on prices, the rate of growth of the  
     money supply should equal the long term rate 
     of growth of the economy.                    

(1)  Equating Gross National Product (GNP) to    
     money supply (M) times money velocity (V)   
     is an over simplification of the equation   
     of exchange. (The equation of exchange is   
     the subject of the next chapter and will    
     be fully explained there.)                  
(2)  The definition of the velocity of money as  
     V = GNP/M (from GNP = MV) does not describe 
     the concept of money velocity.              
(3)  The errors introduced by (1) and (2) average
     over time and give the appearance of a lag  
     between changes in money supply and changes 
     in money value.                             

Irving Fisher did his analysis of the quantity theory of money without the aid of the considerable data on money and money substitutes that is now available. It is, in fact, a result of his work that this data is now available. In the preface to the first edition of his The Purchasing Power Of Money (copyright 1911, rev. 1913) he presented the following proposition:

"...The purchasing power of money - or its
 reciprocal, the level of prices - depends
 exclusively on five definite factors:    
  (1)  The volume of money in circulation;
  (2)  Its velocity of circulation;       
  (3)  The volume of bank deposits subject
       to check;                          
  (4)  Its [checkable deposits] velocity; 
       and,                               
  (5)  The volume of trade."              

  (6)  The volume of trade conducted     
       without the use of money;         
  (7)  The volume of trade not included  
       in the Gross National Product.    

  (1)   In reference to barter:              
          "Checks aside, we may classify     
           exchanges into three groups: The  
           exchange of goods against goods,  
           or barter,; the exchange of       
           money against money, or changing  
           money; and the exchange of money  
           against goods, or purchase and    
           sale. Only the last named species 
           of exchange makes up what we call 
           the 'circulation of money'...     

          "The chief object of this book is  
           to explain the causes determining 
           the purchasing power of money..." 

                (Purchasing Power Of Money, 
                   Chapter II, Section I.)  

  (2)  And book credit:                          
          "Such an exchange of goods against     
           a later payment may be resolved       
           into two successive exchanges. The    
           first occurs at the start when the    
           credit is given for the goods. The    
           purchaser then buys goods in          
           exchange for a promise to pay. The    
           second exchange occurs at the close   
           of the transaction, when the debt     
           is liquidated...                      
          "...if time credit is being contracted 
           faster than it is being extinguished, 
           prices tend to become higher, but as  
           soon as the paying of these debts     
           become as rapid as the making of them,
           prices will fall back to their old    
           level...                              
          "...These equal and opposite items     
           nearly cancel..."                     
                
                    (Purchasing Power Of Money,
                      Appendix to Chapter V)

Factor (7) is actually redundant to his factor (5). It is added because of the modern convention of using GNP as the value of transactions in the equation of exchange. There is nothing in The Purchasing Power Of Money to imply he would do this. Quite the contrary, it appears evident that his intent was to account for all economic transactions except those specifically excluded for the reasons he gave in his book. These are the barter and credit transactions previously discussed.

Although not specifically addressed in Purchasing Power Of Money, the existence of a lag between the creation of money and a rise in prices was clearly not a part of his proposition. All of his calculations and demonstrations used concurrent periods for his measured and estimated factors.

That he was aware of the possibility of time effects is also quite clear. The effect, however, he assigned to interest rates.

"...Rising prices, therefore, in order that the            
 relations between creditor and debtor shall be the same   
 during the rise as before and after, require higher money 
 interest than stationary prices require.                  
"Not only will lenders require, but borrowers can          
 afford to pay higher interest in terms of money; and to   
 some extent competition will gradually force them to      
 do so. Yet we are so accustomed in our business dealings  
 to consider a "dollar as a dollar" regardless of the      
 passage of time, that we reluctantly yield to this        
 process of readjustment, thus rendering it very slow      
 and imperfect..."                                         
                          (Chapter IV, Section  1)