Equation of Exchange

Today we're going to introduce an important tool for thinking about issues in macroeconomics -- the quantity theory of money. Let's imagine the journey a dollar bill might take in a year. Imagine that the dollar bill starts with Tyler, who buys a pupusa from Don, the street vendor. Don gives it to his daughter, who spends it on a pony ride at the fair. It ends up in the hands of Alex, who, after losing it and then finding it in his couch cushions, buys a cup of coffee while on a road trip to see his favorite polka band. So, in a year, this dollar has been spent three times -- on the pupusa, the pony ride, and on a cup of coffee.

Okay, we've got the building blocks to understand the quantity theory of money already. Our dollar bill -- well, that's money, which we represent with the letter "M" -- how many times that dollar gets used in a year is called the “velocity of money,” which we'll label with a "V." In this case, V is 3, as our bill was spent three times in a year. The pupusa, pony ride, and coffee are real goods and services, which we'll call "Y." And the price of those goods and services, we'll call "P." These are the variables in the quantity theory of money.

Now, let's think about this for an economy as a whole. M would be the money supply -- all the money in the economy. V would be how many times a dollar is spent purchasing finished goods and services. Some people hoard cash under their mattress so their dollars have a low velocity, while others spend or invest their money quickly and their dollars have a high velocity. V is the number of times the average dollar is spent. P would the price level of all finished goods and services in an economy, and Y would be all the finished goods and services sold in an economy. So, Y is real GDP, and when you multiply it by a measure of the price level, you get nominal GDP.

Same thing over here. You take all our money, M, and multiply it by how many times the average dollar was spent, or V, and you get nominal GDP as well. Both sides represent nominal GDP in a different way. So, these are equal by definition, which is why we call this equation an identity. One way to think about it is that how much money we have in total times how many times the money is spent covers the actions of buyers. The stuff we sell times the prices we charge covers the actions of sellers. Given that everything that is sold is, by definition, bought by someone, this equation is true by definition. There are important questions about the variables and how they are measured. How do we measure M, for example? However, the core identity, that M times V must equal P times Y, gives us a lot of insight, and a way of organizing our thought about important macroeconomic issues.

So, we'll return to this tool often. For example, what can this identity equation tell us about the causes of inflation? That's the topic we'll turn to next.