Instructor: Jon Nash

Jon has taught Economics and Finance and has an MBA in Finance

This lesson explains the quantity theory of money and how to apply it, including the idea that an increase in the money supply leads to inflation in the long run.

One Man’s Economic Decisions

Go with me to the town of Ceelo, where one man’s economic decisions are affecting the lives of many others. At the Federal Reserve Bank of Ceelo, Ben the Banker oversees the money supply within this part of the country. Joe the Plumber remodels kitchens and bathrooms for $50 an hour. Margie the Cake-baker offers her legendary chocolate cake for $10 each, both in the bakery as well as in the grocery stores, while Sheila runs a restaurant by the name of The Salad Shaker. Her signature salad entree sells for $15. This week, Ben the Banker has increased the money supply by around 20% by purchasing government bonds in the open market.

Let’s take a look at what happens in the lives of these Ceelo professionals both in the short run and the long run. Once Ben increases the supply of money, almost immediately there are more dollars floating around the economy. This means more customers for Joe, Margie, and Sheila.

All three of them are overjoyed with the increase in sales they’re observing. Joe is happier because he’s getting more phone calls requesting remodeling jobs. To satisfy these new customers, Joe works longer days and even starts working on Saturdays. After a solid week of higher sales volume, Joe realizes he can raise his hourly charge from $50 to $60 without losing any customers. Joe is already thinking about things he’ll be able to buy and enjoy for himself, including Margie’s cakes and Sheila’s salads, which have been recommended time and again by the food critic at the local news service.

All the while that Joe is experiencing an increase in business, Margie and Sheila are going through the same experience. Margie begins working longer hours to keep up with extra demand and realizes that she can raise the price of her chocolate cake from $10 to $12, making her even more profit that she can spend by remodeling her basement with Joe’s help. She’s also imagining the benefit of going out to eat at Sheila’s Salad Shaker with the extra income she’s currently earning. Sheila is thrilled to see her salads are flying out of the kitchen as fast as she can create them, and she raises the price of her signature salad from $15 to $18. Throughout the day, she daydreams about cheating on her diet by enjoying Margie’s delicious frosting.

Now the plot thickens, and so does the frosting and the salad dressing, for that matter. When Joe shows up to start buying additional cakes at Margie’s bakery, he’s quite shocked to see that the price of her cakes has risen substantially. Sheila and Margie both find the same thing when they show up to buy the goods and services that they’ve been wanting recently. Each of them has been tricked into thinking their sales increased and that they’re now more wealthy. In reality, economic output rose in the short run (because of Ben’s increase in the money supply) but not in the long run. The only thing that happened in the long run is that prices went up, which means that the value of the money has gone down.

Let’s take a look at the theory that economists use to describe this scenario as well as the key equation that central banks have used in the process of conducting monetary policy.

The quantity theory of money describes the relationship between inflation, the money supply, real output, and prices. It’s a theory that explains how much money is needed in order for an economy to function.

The quantity theory of money started in the early 1900s by Irving Fisher. Challenged by Keynesian economists, it was later updated and reinvigorated by the new monetarist school of economics. Monetarism is the economic viewpoint that excessive expansion of the money supply leads to inflation and that economic output will grow steadily as long as the money supply grows steadily as well.

Economist Milton Friedman was a monetarist and was quoted as saying ‘Inflation is always and everywhere a monetary phenomenon.’ Although Milton opposed the existence of the Federal Reserve, he did believe that, in order to avoid inflation, the best way for the central bank to reach its goals is by keeping the growth rate of the money supply at a certain predetermined rate, a process that is known as targeting the money supply. While the central bank doesn’t follow this wholeheartedly today, many economists accept the wisdom in this theory. At the heart of the theory is the equation of exchange.

The Equation of Exchange

The equation of exchange shows the relationship between the money supply, velocity, the price level and economic output. Here’s the equation:

where M = the money supply, V = the velocity of money, P = the price level, and Y = real GDP. Another way to think about the equation is to say that M x V = nominal GDP, because nominal GDP is simply real GDP times the price level. This means that the money supply times the velocity of that money is equal to the price level times real GDP. At the center of this equation is the velocity of money.

The Velocity of Money

I’m sure you’ve had times when you received cash from a bank or a retail store that seemed brand-new — it was so untouched and crisp that the bills actually stuck together. Why does currency start out brand-new in circulation like that and then get worn out and replaced with new currency within a short amount of time? Because the same $20 bill will be used in transactions to buy and sell goods many, many times throughout the course of a single year.

The velocity of money is how many times single unit of currency gets turned over within the economy during the year. It measures how fast money changes hands. Now that you’re familiar with the components of the equation of exchange, you can use it, along with the variables you do know, to solve for the one that you don’t know.

Solving for Velocity

As with any equation, if I know three out of four things and only one unknown, I can solve for the one missing item. If you know any three of these four variables — the money supply, velocity of money, the price level, or nominal GDP — then you can solve the equation and find the missing piece.

To keep things easy, let’s just say that in Ceelo, the price level (P ) is 1, while the real GDP (Y ) is $200, and suppose that the money supply (M ) is $100. What we want to know is — what is the velocity of this $100 supply of money?

Plugging in these numbers to the formula gives us:

$100 x V = 1 x $200

When we solve for V. we get:

$100 x 2 = 1 x $200

That means that the velocity of money is 2. The average dollar bill in circulation is getting spent 2 times during the year; money is turning over at a rate of 2 times per year. If Joe spends $20 at Margie’s bakery, then Margie goes to eat salad at Sheila’s restaurant with the same $20, this would be an example of a velocity of 2.

Of course, this makes sense logically — in order for a $100 money supply to create $200 worth of transactions, the same money in circulation had to be used twice.