What's exactly the T/Y value in the Quantity Theory of money simplified equation: MV=PT or MV=PY?

Question

I understood the basic fundamental principle of the theory, that all things being equal, a change in the money supply affects price level. Yet, now I am trying to understand this statement ‘ The QTM proposes that the exchange value of money is determined by the volume of transactions (or income) and the velocity of money in the economy.’ through playing with the formula. The problem stands with the fact that there is no consensus on the exacts definitions of one element in particular of the equation MV=PT or MV=PY- the T/Y value. Some sources like Wall Street Mojo defines it as the ‘ Total index of physical volume of transactions’ , Investopedia defines it as ‘ Volume of transactions of goods and services’ without specifically giving additional description of what they mean with volume whilst another source like ‘ PPT - TOPIC 5 PowerPoint Presentation, free download - ID:4345046 (slideserve.com)’ defines it as Real GDP , which I deem it as the most credible option as through this path, considering that the T/Y value in the equation is multiplied to the P value, you get nominal GDP out of the multiplication on the left hand side of the equation. I tried to use Chat GPT also but it confuses things more as it changes the definition of ‘T’ just based on the fact that I simply tell him that in this websites it states ‘…’ and on this other it states that’ …’. I would be very grateful if you could help me to understand it because I am a bit lost. Thanks

Answer 1

Both WSM and Investopedia are actually using the same definition (i.e. $T$ is volume of transactions). WSM just specifies that it can be measured as index of volume of transactions. Conceptually those are the same definitions except WSM is more specific in way how to measure it.

For example, $P$ which is price level could be measured as consumer price index (CPI) or using implicit deflator. If one source says that $P$ is CPI and another that it is implicit deflator, and third source just says its price level they do not have different conceptual definition of $P$, all sources in effect say $P$ is price level, some are just more specific.

Next the QTM given by $MV=PT$ is a simplification of the definitional relationship given by $MV=PY$, where $Y$ is a real output. There is some correspondence between real output and volume of transactions to buy goods and services, real output is slightly broader term that would include also production of unsold goods (i.e. inventory investment). Real output can be measured in multiple ways. Most popular way of measuring $Y$ is using real GDP. So many sources will just say $Y$ is real GDP.