Velocity

We have had some spirited debate about inflation here at TLRB. One concept that keeps arising is that you can't have inflation without growth in the money supply. That is, prices are a function of dollars chasing goods. If the number of dollars grows faster than the amount stuff to buy with them, then prices rise. In a recent post, a commenter took me to task (which everyone is welcome to do) for saying "generally speaking, growing demand increases upward price pressures." I didn't respond in full because the length of the response is worthy of a post in itself, so here it is.

It is true that inflation is a monetary phenomenon- that is dollars per stuff.  Increase the amount of dollars per amount of stuff to buy with those dollars, and we get higher prices. We're in agreement there. What is not obvious however, is that not all money is used. Let's take an imaginary economy where the money supply of currency (dollars) is fixed- no banks, no printing presses, no borrowing or lending and thus no money is created or destroyed. Further assume production of goods and services in this economy is static and there is no outside interraction. In such an economy, there can be no overall inflation or deflation right?

Not so fast. Say citizens of this economy have a habit of saving 10% of their money. So out of the entire money supply, only 90% is actually circulating and participating in economic activity. One particularly delightful spring, the citizens are feeling extra happy. On average, they decide it's time to spend some of that savings, perhaps half of it. Suddenly, demand (in aggregate) grows 5.6% (5%/90%). But output is static, so we have 5.6% more dollars chasing the same amount of goods- voila, inflation! Yet the money supply didn't change at all.

Economists have a term to describe the average frequency a unit of currency is spent- the velocity of money. Back to our example, say this economy consisted of just Bill and Ted and $100 in money. Bill sell a surfboard to Ted for $100. Then Ted buys togas from Bill for $100 and this happens four times per year. Our excellent economy has $800 in GDP ($100 per transaction x 8). Each unit of currency has transacted 8 times (the velocity is 8). In fact, econ textbooks present this neat formula: G=MxV or GDP is the product of the money supply multiplied by velocity (frequency). With me so far?

Suppose that Bill magically has Bill Jr. who wants to get into his own business. Assuming equal output, GDP could now go to $1200 (both Bill and Ted contributed $400 each to GDP, another person should be able to contribute the same).  But if the money supply is fixed at $100, that $100 must change hands 12 times to generate the potential GDP. Or suppose the opposite- say Bill and Ted (forget about Bill Jr), transact twice a year instead of four times- GDP falls to $400.

So where am I going with this? In the real world, velocity is not fixed. When the willingness to borrow, lend, spend, invest and transact slows, so does velocity. If the entrepreneur can't get a loan, that economic activity doesn't materialize. When investors are afraid to fund new projects and everyone hoards cash, money transacts less often. Thus, a falling velocity must result in falling GDP- a recession, possibly a very severe one if accompanied by deflation.

When confronted by a massive deleveraging, greatly increased risk aversion, tightening credit, illiquidity and losses, the Fed can do nothing and watch velocity plummet and GDP contract. Or the Fed can flood the economy with money in an effort to keep GDP from falling too much (G=VxM) while the economy adjusts to the new paradigm of risk and leverage. If velocity is falling fast enough, even a dramatically increased money supply will not result in inflation. The "dollars per unit of stuff" framework for understanding the money supply and inflation is only so useful.