Thursday, September 9, 2010

How Money Supply Limits Prices

Today I’d like to revisit an idea that was the focal point of my last blog, The Ca$h Bull: which is the relationship between money supply and prices.

It is common observation and defined in the Quantity Theory of Money that when money supply increases substantially and rapidly, prices tend to rise. That the reverse is true seems sensible as well, though it is rare for money supply to contract so historical examples would be uncommon.

I tried to more precisely define the relationship of money supply and inventory by equating the two: that the sum of all things for sale would self-adjust in price to equal the money supply. I did this because I was trying to define a value for cash, and postulated that the money supply is exactly equal to the sum of all goods that can be bought with it, much like all stock certificates added together would exactly equal the value of the corporation that sells them. The value of a dollar is the collection of all goods for sale, divided by the number of dollars in circulation. That was the theory.

It was pretty detailed how I built the argument and led to some concepts which I think are still valid, but as I delved into the nuts and bolts of the mathematics, I concluded it was completely wrong, and terminated the blog because I didn’t see any way to reconcile the rest of the blog with that realization. In short: inventory prices do not gravitate toward the standing money supply, rather inventory prices gravitate toward zero. In an ideal economy, everything is sold the moment it is produced. That which does not sell immediately becomes a burden on production, where either prices will have to drop or production will have to slow to accommodate standing inventory. The ideal inventory is zero. What inventory that does exist is simply a necessary error in real systems based on lag between production and sales.

So then, how can money supply and prices relate as we see in the Quantity Theory of Money? The relationship comes through both money and sales velocity, not standing amounts.

Inventory (in dollar amounts) cannot be sustainably produced in an amount that exceeds rate of spending. If goods are produced faster than money can be spent, then excess inventory goes unsold. In the next round of production, not only what is produced has to be sold, but it has to compete against unsold inventory, and if any inventory remains standing in a prolonged way, it means that producers are not being paid for their work. For standing items to sell, either production must slow or prices drop.

Now, say the money supply is doubled and dispersed through the population. Now twice the amount of money is capable of being spent per unit time, which either allows more to be produced at the same price, or more to be charged if production is kept the same. Say money supply stays the same but you double the rate people are inclined to spend it, then same thing. So absolute money supply is not a hard and fast limit on production capacity—to the degree people can be encouraged to spend money faster, prices can still rise even with a stable money supply.

But eventually there is a limit to the rate of spending—the rate people spend money cannot rise to infinity. Even with policies that encourage spending, eventually society reaches the upper limit, and at that point, whatever that rate of spending may be, money supply becomes the limiting factor of production.

So, if society is spending money at its natural rate, in a way that cannot be increased in a sustainable way, then the only way for prices to increase is for money supply to increase. The maximum production (in dollars) over a given time period is limited by maximum rate of spending over the same period of time.