Hi, I am looking for an a-priori proof that money printing always raises overall prices (even if all the printed money is hoarded and not spent). (when I say "raises prices" I mean ceteribus paribus.) I don't know if this is even true, but I am trying to prove it.
I have an idea and I am looking for comments or improvements.
Suppose that the central bank prints new money and gives it to A. Only three cases are possible: 1) A spends the money; 2) A invests (lends) the money; 3) A hoards the money.
We want to prove that prices will increase in all cases, in particular in case 3.
Case 1) A spends the new money on some good X. This is the easy case: we all know why the price of X will increase. (Demand for X increased, and supply has not increased, so the price for X must increase.) Then the seller of X in turn will have more money, which he is going to spend on some other good Y, so the price of Y will increase too, and so on.
Case 2) A lends the new money to some other person B. Then B has the new money and is faced with the same problem: he can either spend it, lend it, or hoard it. So we can ignore this case, because it must eventually resolve to case (1) or (3). Eventually, someone must either spend or hoard the money.
Case 3) A hoards the money (e.g. he keeps it under the mattress). This is the difficult case. We want to prove that even in this case some price will increase. How can this be, since A is not buying anything with the money? My answer: Even though A does not spend the money, something important has changed: A now has more money. So, money has now become less attractive to A (because he has more of it, and nothing else has changed). This is like saying that everything other than money (including leisure) has become more attractive to A. (Another way to say it is that his demand for money has decreased). This means that, in order to get the same amount of money as before, A will be willing to work less than before. Or, equivalently, it means that, to work the same amount of time as before, he will ask for more money than he did before. But to me this means that the price of A's services has increased. In general, we can say that the overall price of labour has increased as a consequence of money printing. And since, as far as I can see, nothing else has changed, we seem to have proved that overall prices have increased, even in the case where all the money was hoarded and not spent.
If this analysis is correct, it seems we can state that money printing always increases prices. But is it correct? Are there other ways to get to the same conclusion? Thank you.
@prime
"to work the same amount of time as before, he will ask for more money than he did before"
Is this true? Do all lottery winners who choose to continue working at their jobs always demand a raise?
Good point. I realize my statement is poorly phrased. What I meant is: for any given amount of time T, the minimum amount of money they require to work for T hours will increase. (In other words, their supply curve of labour will shift.) This does not imply that they will ask for a raise or quit, because their current wage could already be greater than the new minimum wage that they require (after the shift).
However, the fact alone that their supply curve of labour has shifted seems to me enough to conclude that price of labour will increase, so I think my point still stands.
Lets say I have a machine that can print dollars. I print 10 million bucks and then shove it all under my mattress. Here is my line of thinking:
A) According to your theory, I now value money less, and as such I demand more dollars for my labor.
B) My emplyer X decides to give me a substantial raise to compensate for my new demands. (If X declines no prices have risen)
C) X now has a decrease in profits and cannot afford to build a new factory.
D) The construction builder, who would have built the factory, is now unemployed.
E) This increases the supply of available labor, and as a result, decreases wages for everyone else.
F) There is no net increase in prices. My raise came at the expense of lower wages for everyone else
Remember, as an extreme hoader, he wants money to simply have money. Once more this calls into question the definition of hoarding. If hoardeers are literally never going to spend that money, then their actions lower prices. If they are merely extreme savers and will eventually spend that money on necessities like food and shelter, and eventually will it to heirs who spend it, then the operative function of that money will be to raise prices in the long term assuming it's printed money he's hoarding.
Xahrx, in my example the only money that is hoarded is what came from the printing press. He is not hoarding the money from his wages. In actuallity, it's as if the counterfeit money didn't even exist (except for in the mind of the hoarder). The OP's original point that printing money and then hoarding said money would increase the net price of wages. I think I have provided an example where there is no net gain.
I'm curious which invention the fella uses to distinguish regular money from QE money ?
Where there is no property there is no justice; a proposition as certain as any demonstration in Euclid
Fools! not to see that what they madly desire would be a calamity to them as no hands but their own could bring