Enjoy.
Credit Cards
The concept behind this post is, more or less, entirely my own, and fits well into the discussion at hand, albeit in an oblique manner. Behind this answer, however, is the original question that created it - and it is, in my mind, a very important question.
Last year, in my senior capstone class, my professor asked the class about what the impact of credit cards is on the quantity theory of money. I had a rather incomplete answer at the end of class that I discussed with him briefly, and this answer is based on that one.
But first, a better explanation of the general form of this question...
Last year, in my senior capstone class, my professor asked the class about what the impact of credit cards is on the quantity theory of money. I had a rather incomplete answer at the end of class that I discussed with him briefly, and this answer is based on that one.
But first, a better explanation of the general form of this question...
The Quantity Theory of Money
MV = PQ. This one equation sums up the central concept of the quantity theory of money. A somewhat good explanation can be found here, but if you are unwilling to read it, I will instead provide a quick explanation at less cost.
M is the total amount of money in the economy. What measure? Unimportant, at least for the moment.
V is the velocity of that money - that is, how often that money is used to purchase something.
V is the velocity of that money - that is, how often that money is used to purchase something.
MV, then, is the total value of all transactions that occurs within a certain economic unit. For now, think of it as a country - in fact, just keep thinking of it as a country, because we're not going to be dealing with anything else for the moment.
P is the column vector representing the price of all sorts of transactions. (You can also simply think of this as dividing all transactions into price levels, without worrying about other attributes of the transaction.)
P is the column vector representing the price of all sorts of transactions. (You can also simply think of this as dividing all transactions into price levels, without worrying about other attributes of the transaction.)
Q is the row vector representing the quantity of each sort of transaction.
PQ, then, is also the total value of all transactions that occurs within a certain economic unit.
PQ, then, is also the total value of all transactions that occurs within a certain economic unit.
Hence, MV must be equal to PQ, or something is really quite wrong with your numbers, and both are analogous to GDP.
In addition, as these are fairly important concepts, changes in M are changes in the supply of money, while changes in P are changes in the price level - inflation if positive, deflation if negative.
There's a lot to be said about the quantity theory of money, but I'm not writing this to say it. My sole intent as of the moment is to answer the question that spawned this article in as general a manner as possible.
So, how do I generalize the question?
It's quite simple, really. Credit cards are, in essence, loans. Very small loans that require no clearing outside of changes in cap, but they are still loans. They also tend to be very expensive loans in terms of interest rate, but that is not currently important.
Our question, then, is how loans effect the quantity theory of money, if they do so at all.
Before examining this, we can go one step further in our generalization - all loans are a form of investment, and it is the impact of investment on the quantity theory of money that I will be examining for the rest of this article.
There are, in my mind, two ways of treating this problem. The simpler method is to treat the M in our equation as representing all money, from M1 all the way up to M3 (For those unfamiliar with this, these are different 'sorts' of money, mostly representing liquidity and, in this case, velocity. You can read more here.).
There is a separate method that yields a similar result in which you treat M as only M1, but that requires treating investment as a method of increasing and decreasing the actual money supply - something that it usually is not.
For the moment, then, we will treat our M value as representing the entirety of the money supply.
So, what does investment do?
It takes money from low-velocity categories and moves it to high-velocity ones. That is, money that might otherwise be in, say, the M3 category, might be invested - or loaned - into the M1 category, which has a much higher velocity.
Put simply, then, investment tends to increase velocity in the short-run.
However, all investment desires a return. This means that high-velocity money right now requires a greater removal of high-velocity money in the future. Although some of it may return quite quickly, we don't yet have an inkling of how much.
As such, we can say that investment tends to increase velocity in the short-run, while its impact on long-run velocity is, at least for the moment, ambiguous.
At some point in the future, these investments require some amount of money to be paid back, Mrtrn, and this money moves from Vinvst to Vrtrn. In the majority of cases, Mrtrn will be larger than Minvst, but it is possible for the opposite to be true - for instance, at the beginning of a major financial crisis.
Now, we are fairly certain that Vinit is less than Vinvst - that is, the money enters a higher velocity level when invested than it would have been had it not been invested. This accounts for the short-run increase in velocity posited above.
In order to understand if there is a long-run increase or decrease in velocity as a result of investment, we need to decide how likely it is for Vrtrn to be less than Vinvst - assuming no additional investment, of course.
Well, first of all, let's think about Vinvst. People take out loans when they need money, presumably to spend on something or, in some cases, to invest in something. There are cases where this is not true, but the majority of loans are taken for the purpose of acquiring money to cover expenditures, whatever those may be.
As such, we can expect Vinvst to be fairly high.
Now, let's think about Vrtrn. Investors come in one of two kinds - institutions and individuals. The institutions are largely banks, but can also be a variety of other finance-related entities. Individual investors tend to be quite rich, as they otherwise would not be able to reasonably take the risk associated with investment.
Institutions tend not to spend much money outside of operating costs, and the rich tend to have a fairly low marginal propensity to consume.
As such, we can expect Vrtrn to be fairly low - assuming that we disregard the possibility of further investment, of course. (In fact, I would expect Vrtrn to be more or less equivalent to Vinit, but that's a very large assumption that I'm not willing tot ake for the moment.)
The long-run impact of a single investment, then, is to decrease velocity. Here's some equations...
Initial: Minvst * Vinit
Change by investment: Minvst * (Vinvst - Vinit)
Change by return: Mrtrn * (Vrtrn - Vinvst)
Total Change: Minvst * (Vrtrn - Vinit) + (Mrtrn - Minvst) * (Vrtrn - Vinvst)
If we assume Vrtrn and Vinit are the same, the first term of total change drops out and our entire long-run change equation is based upon the difference in velocity level of money between the investor and the investee, as well as the difference between the amount invested and the required return on investment - roughly correlated to interest rate, risk premium, and a handful of other concepts.
In addition, as these are fairly important concepts, changes in M are changes in the supply of money, while changes in P are changes in the price level - inflation if positive, deflation if negative.
Generalization
There's a lot to be said about the quantity theory of money, but I'm not writing this to say it. My sole intent as of the moment is to answer the question that spawned this article in as general a manner as possible.
So, how do I generalize the question?
It's quite simple, really. Credit cards are, in essence, loans. Very small loans that require no clearing outside of changes in cap, but they are still loans. They also tend to be very expensive loans in terms of interest rate, but that is not currently important.
Our question, then, is how loans effect the quantity theory of money, if they do so at all.
Before examining this, we can go one step further in our generalization - all loans are a form of investment, and it is the impact of investment on the quantity theory of money that I will be examining for the rest of this article.
Investment and Velocity
There are, in my mind, two ways of treating this problem. The simpler method is to treat the M in our equation as representing all money, from M1 all the way up to M3 (For those unfamiliar with this, these are different 'sorts' of money, mostly representing liquidity and, in this case, velocity. You can read more here.).
There is a separate method that yields a similar result in which you treat M as only M1, but that requires treating investment as a method of increasing and decreasing the actual money supply - something that it usually is not.
For the moment, then, we will treat our M value as representing the entirety of the money supply.
So, what does investment do?
It takes money from low-velocity categories and moves it to high-velocity ones. That is, money that might otherwise be in, say, the M3 category, might be invested - or loaned - into the M1 category, which has a much higher velocity.
Put simply, then, investment tends to increase velocity in the short-run.
However, all investment desires a return. This means that high-velocity money right now requires a greater removal of high-velocity money in the future. Although some of it may return quite quickly, we don't yet have an inkling of how much.
As such, we can say that investment tends to increase velocity in the short-run, while its impact on long-run velocity is, at least for the moment, ambiguous.
Long-run Impact of Investment
We know that some amount of money is invested, and this investment moves money from one velocity level to another. Let us denote these levels as Vinit and Vinvst, and the amount of money moving between them as Minvst.At some point in the future, these investments require some amount of money to be paid back, Mrtrn, and this money moves from Vinvst to Vrtrn. In the majority of cases, Mrtrn will be larger than Minvst, but it is possible for the opposite to be true - for instance, at the beginning of a major financial crisis.
Now, we are fairly certain that Vinit is less than Vinvst - that is, the money enters a higher velocity level when invested than it would have been had it not been invested. This accounts for the short-run increase in velocity posited above.
In order to understand if there is a long-run increase or decrease in velocity as a result of investment, we need to decide how likely it is for Vrtrn to be less than Vinvst - assuming no additional investment, of course.
Well, first of all, let's think about Vinvst. People take out loans when they need money, presumably to spend on something or, in some cases, to invest in something. There are cases where this is not true, but the majority of loans are taken for the purpose of acquiring money to cover expenditures, whatever those may be.
As such, we can expect Vinvst to be fairly high.
Now, let's think about Vrtrn. Investors come in one of two kinds - institutions and individuals. The institutions are largely banks, but can also be a variety of other finance-related entities. Individual investors tend to be quite rich, as they otherwise would not be able to reasonably take the risk associated with investment.
Institutions tend not to spend much money outside of operating costs, and the rich tend to have a fairly low marginal propensity to consume.
As such, we can expect Vrtrn to be fairly low - assuming that we disregard the possibility of further investment, of course. (In fact, I would expect Vrtrn to be more or less equivalent to Vinit, but that's a very large assumption that I'm not willing tot ake for the moment.)
The long-run impact of a single investment, then, is to decrease velocity. Here's some equations...
Initial: Minvst * Vinit
Change by investment: Minvst * (Vinvst - Vinit)
Change by return: Mrtrn * (Vrtrn - Vinvst)
Total Change: Minvst * (Vrtrn - Vinit) + (Mrtrn - Minvst) * (Vrtrn - Vinvst)
If we assume Vrtrn and Vinit are the same, the first term of total change drops out and our entire long-run change equation is based upon the difference in velocity level of money between the investor and the investee, as well as the difference between the amount invested and the required return on investment - roughly correlated to interest rate, risk premium, and a handful of other concepts.
What This Means
Taken by themselves, investments have a tendency to decrease velocity over the long-run.
Fair? Not particularly. Let's take a look at what happens when we take a huge number of them all at once...
Fair? Not particularly. Let's take a look at what happens when we take a huge number of them all at once...
Taking an infinite sum assuming constant reinvestment of returns and Vrtrn = Vinit, you will find that the overall change in velocity is zero.
However, the world is not ideal, and not only is Vrtrn likely not equivalent to Vinit, constant reinvestment of all returns is simply not a reasonable assumption. Transaction costs alone will cause loss, and any loss begins to accrue to very large velocity changes over time, with the amount dependent on the interest rate charged on the investments.
We can then conclude that investment will generally decrease the velocity of money over time.
Why does this matter?
Velocity is very important. It is a key indicator of demand, as it shows how often you buy things with a specific unit of money - usually the dollar, as that is also the unit in which the money supply tends to be denoted. A decrease in velocity indicates a decrease in demand, which in turn can lead to economic problems, i.e. a recession.
So, how do we fix this problem?
To do so, we need an accurate analog for investment. For this, we shall use growth.
Why? Think about it for a moment. In an economy like the one we have here, the majority of growth is a direct result of investment. Small businesses, which create the majority of new jobs over the course of any given year, come into existence as a result of investment. Most major projects undertaken by large corporations are funded by the sale of securities, another form of investment. Even the government finances its chronic overspending with bonds.
We can then conclude that growth is a fairly accurate analog for investment - that is, there is some sort of function that directly relates the two, and the function is meaningful.
Now we know how much investment there is that must be counteracted to prevent a decrease in velocity. How do we counteract it? You create more money - specifically, money with the highest possible velocity. You increase the supply of total M by increasing the supply of M1, and this will increase total velocity.
And this, friends, is one of many reasons why you find the majority of healthy capitalist economies have a strong correlation between growth and increase in the money supply.
Now we know how much investment there is that must be counteracted to prevent a decrease in velocity. How do we counteract it? You create more money - specifically, money with the highest possible velocity. You increase the supply of total M by increasing the supply of M1, and this will increase total velocity.
And this, friends, is one of many reasons why you find the majority of healthy capitalist economies have a strong correlation between growth and increase in the money supply.
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