## Why Modest Inflation is Necessary

Let me first say that I am no fan of inflation. I understand the desire to have money store value indefinitely and that $100, in my piggy bank, will purchase just as much ten years from now as it does today. The problem is that reality doesn’t bend to my feeling and will. I would like to fly in the air. I would like to not bother wearing a seat belt. I would like there to be no inflation.

I look for fundamental constrains in economics, in order to better understand what limits the economy. In problems of physics and engineering, these are often boundary conditions. There are physical laws that restrain the way physical quantities move. Then, given the specific situation, the performance of a system is further constrained by boundary conditions. As well, in physics and engineering, there are laws than can be deduced from basic principles. So, I look for basic principles and boundary conditions upon which to deduce some economic laws. It is always better if we can look at what is now, as physics does, to determine what must be. The law of gravity doesn’t depend on history or precedence, it just is. And, if we can look at the fundamental performance of economics in what is now, at least we might narrow things down a bit in terms of what can occur.

Here is the summary of my reasoning. Money serves two purposes, 1) as a medium of exchange and 2) as a store of value. The purpose of it as a medium of exchange takes precedence. Deflation is elevates the secondary purpose to a primary position and is then logically not allowed. Indeed, there must be some level of inflation, or money will store value forever and elevate this purpose to an equal standing with the primary purpose. The question then becomes one of inflation should occur. A simple linear decline doesn’t function well, as it either gets to zero at some arbitrarily chosen point or not at all. This leaves an exponential decline. In fact, the existing inflationary process is exactly this. I therefore conclude that the existing inflationary process is, at least, logically appropriate. The question then remains as to how much it should be. We can conclude that as little as possible is entirely appropriate. What, as little as possible is, remains an empirical question.

A course in macro economics suggests deflation creates serious problems as it creates a feedback issue where consumers delay purchases while prices fall which causes prices to fall which causes consumers to delay purchases. This downward spiral is a severe issue. As such, deflation is not allowed. The same course indicated that inflation is targeted to be about 3%. Are these then correct?

An article on the WSJ brought up some basic questions of money. It struck me that there is some deductive reasoning that determine if and how inflation should be considered based on the very nature of money. We need not go to precedence or history to determine whether inflation is necessary.

Here is an interesting reason of logic regarding money and inflation. Money, as we know, has two purposes, that of a medium of exchange and that of a store of value. The primary purpose is that of a medium of exchange. It’s secondary purpose is as a store of value. There is no need to go further than simply watch a person earn use money. We can simply go to the store and follow money as it moves from a consumer’s pocket book, into a cash register, to the bank, into some account, back out into a paycheck, then back to the store again. These are observable properties and few would disagree.

As a medium of exchange, it is this only during the moment of the transaction. The remainder of the time, it is serving it’s secondary purpose. Without it’s primary purpose, the secondary purpose is meaningless. Therefore, the primary purpose is as “primary” implies, a precedence over the secondary purpose.

We can also point out that deflation makes the secondary purpose mute and therefore deflation is logically forbidden. If money were to gain value indefinitely, then the secondary purpose, as a store of value, would be elevated to having precedence over the first. The simple accumulation and storage of money would be the primary motivator. As such, deflation is simply not an option. Indeed, having a zero rate of inflation elevates the storage of money as being of equal value as it’s primary purpose and, for this reason, there must be a non-zero rate of inflation.

We are left to conclude that the only other considerations are what the rate of inflation or decay of value should be. The rate of decay must be such that, at the very least, in the limit of an infinite amount of time, the value decays to zero. Perhaps it might be that the rate should be considerably greater but, at the very least, it must get to zero value in the limit.

There are mathematical options for a decay rate, one being a simply linear decay. In the limit of a zero slope, it goes to zero at infinity, but that is the only case. The problem with a linear decay is that it goes to zero at some arbitrarily chose point. We might choose some finite time for decay but this leads to an artificially determined length of time. Choosing some artificial length is to be avoided as it then leads to whole question of why that length, why not longer or shorter. It’s, well, artificial. In the graph below, three lines show what I mean by “in the limit”. Y1 decays to zero at 15. Y2 decays to zero at 30. Y3 decays to zero at infinity. In the limit, it gets to zero but it doesn’t actually decay.

So, a second choice must be found. What we need is a curve that always decays to zero, regardless of how quickly it decays. The second choice is any exponential decay. An exponential decay can decay to zero immediately, or it can decay so slowly that it takes an infinite amount of time to get to zero. Some forms of an exponential decay are shown.

Two forms are shown, one being a natural exponent, the other being base 2. Whatever the base, they all get there.

It seems that we do have such an exponential rate, the rate of inflation. Whatever the rate of inflation is, it it’s form, it is some sort of exponential decay. It would seem that, in the general part, the value of money is doing exactly what it should be doing. The CPI decay is shown below. For reference, a constant rate is also shown. This constant rate is Value(Year)=Value(Year-1)*(1-rate).

This leads to the question of what this numerical rate should be. At the very least, it can be as close to zero as possible. We have determined that it cannot be negative, this is a forbidden boundary. We have determined it cannot be zero, this is a boundary condition. But, there is yet to be determined what it should be above zero. There may be some reason, yet considered, but at least, we have a lower boundary condition.

In the reasoning that follows, I will postulate that inflation must be managed. There are fundamental reasons for this postulate. Left to it’s own devices, the value of money may deflate. The economy is huge under constrained system in which prices can go any which way. There is no fundamental law that guarantees that money will remain at a constant value or at some positive level. If, for whatever reason, the sufficient majority of consumers decide to save, then prices will adjust downward, at least according to basic economic principles of competition. And, given the feedback nature of the economy, if and when it goes negative for long enough, deflation becomes a catastrophic condition. There is no natural stabilization. (This contention of there being no natural stabilizer to deflation deserves further investigation.) This will be a postulate which then leads to the requirement of management.

It is established that it must be above zero. It must be managed above zero. And, lacking further reason, it can be as close to zero as possible. It is in the reality of managing that rests the answer to how close to zero it can be. The answer is “as close as can be managed”. The process of managing inflation is not exact. So, whatever this value is, it must be determined based on the variance inherent in the process of managing it. Considering the delay in determining the CPI, and the lack of precision in managing the CPI, it must be targeted at least high enough that it does not dip below zero for sufficiently long enough to result in perceptible deflation.

This is as far as reasoning needs to go, in defining the purpose and management of money and it’s value. The absolute number for the rate of inflation becomes an empirical issue.

The very nature of money requires that we do not have deflation. Indeed, it requires that there be some very slight level of inflation. The way that money devalues, best takes on an exponential decay. In fact, that is what it does. What this rate should be remains a question. Logically, it can be as little as possible. Exactly what , as little as possible is, is an empirical issue.

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