# Money Growth and Inflation

We begin by presenting a framework to highlight the link between money growth and inflation over long periods of time. [1] The quantity theory of money is a relationship among money, output, and prices that is used to study inflation. It is based on an accounting identity that can be traced back to the circular flow of income. Among other things, the circular flow tells us that nominal spending = nominal gross domestic product (GDP). The “nominal spending” in this expression is carried out using money. While money consists of many different assets, you can—as a metaphor—think of money as consisting entirely of dollar bills. Nominal spending in the economy would then take the form of these dollar bills going from person to person. If there are not very many dollar bills relative to total nominal spending, then each bill must be involved in a large number of transactions. The velocity of money is a measure of how rapidly (on average) these dollar bills change hands in the economy. It is calculated by dividing nominal spending by the money supply, which is the total stock of money in the economy:

velocity of money = nominal spending money supply

= nominal GDP money supply

.

If the velocity is high, then for each dollar, the economy produces a large amount of nominal GDP. Using the fact that nominal GDP equals real GDP × the price level, we see that

velocity of money = price level × real GDP And if we multiply both sides of this equation by the money supply, we get the quantity equation, which is one of the most famous expressions in economics: money supply × velocity of money = price level × real GDP. Let us see how these equations work by looking at 2005. In that year, nominal GDP was about $13 trillion in the United States. The amount of money circulating in the economy was about $6.5 trillion. [2] If this money took the form of 6.5 trillion dollar bills changing hands for each transaction that we count in GDP, then, on average, each bill must have changed hands twice during the year (13/6.5 = 2). So the velocity of money was 2 in 2005. Toolkit: Section 16.16 “The Circular Flow of Income” You can review the circular flow of income in the toolkit. The Classical Dichotomy So far, we have just written a definition. There are two steps that take us from this definition to a theory of inflation. First we use the quantity equation to give us a theory of the price level. Then we examine the growth rate of the price level, which is the inflation rate.