# Mill discusses the Quantity Theory of Money in 1848

From Mill’s Principles:

If we assume the quantity of goods on sale, and the number of times those goods are resold, to be fixed quantities, the value of money will depend upon its quantity, together with the average number of times that each piece changes hands in the process . The whole of the goods sold (counting each resale of the same goods as so much added to the goods) have been exchanged for the whole of the money, multiplied by the number of purchases made on the average by each piece. Consequently, the amount of goods and of transactions being the same, the value of money is inversely as its quantity multiplied by what is called the rapidity of circulation. And the quantity of money in circulation [M] is equal to the money value of all the goods sold [PT], divided by the number which expresses the rapidity of circulation [V]. (Mill [1848] 1871: 494 – letters in parentheses inserted into the text)

Note that the money value of all goods sold is PT, with the T standing for Transactions. This is the accurate rendering of the concept since the same item might be sold many times over. A sack of flour might find itself sold first to a distributor, and then to a retailer and then finally to a consumer. It is the number of transactions that matter. The transactions also incorporate all of the sales between input producers that occur well before, perhaps years before, some item is sold as a final good to a consumer.

Thereafter we come to the quantity equation which is actually a quantity identity since it is true by definition. It is true only because it could not be anything else.

M ≡ PT/V

Or in its more typical formulation:

MV ≡ PT

The number of times a unit of money is exchanged is equal to the total money value of all sales that take place inside an economy. Since there is no means to calculate T or the average price of all of the items that are turned over in the market, PT is a number that can never be calculated.

Following that para from The Principles are a large number of additional considerations that help make sense of the point and also make it more comprehensible in relation to the operation of an economy.

Whatever else Mill is or is not trying to do, what he is not trying to do is provide some means to regulate an economy by trying to adjust any of the four elements within the identity.