Macroeconomics and equilibrium

Question

Preliminary note: I have nearly zero economical background, I am a physicist and my question is probably very naive, but I would like a clear and simple explanation.

If I am not wrong, the global economy can be seen as an isolated system (ie we do not have any non-Earth economic exchanges). At any given time $t$, there is a given amount of money $M$ in the world. As worldwide economy is an isolated system, $M$ can vary only if it is created or destroyed within the system. To my knowledge, the only way to create money is by creating a debt at $t_{0}$ and when money is reimbursed at $t_{1}$, the money that was created out of thin air is destroyed. I see no problem when the interest rate is $0\%$, because globally the system stays balanced.

Now, if the interest rate is stricly positive, that means that the amount of money $|m_{1}|$ that will need to be reimbursed at $t_{1}$ is higher than the debt $|m_{0}|$ that was created at $t_{0}$. But the thing is that $dm = |m_{1}|-|m_{0}|$ does not exist in the total amount of money available worldwide at $t_{0}$, $M_{0}$. So for the debt to be reimbursed with the interests, $dm$ will need to be created. And the only way to create money... is by creating a debt... with interest. So the system diverges very rapidly with an ever growing debt.

The other way I can see to make the system stable is by inflation/deflation: if $dm$ exactly corresponds to the inflation/deflation rate, then the system can remain at equilibrium without an ever growing debt. The last way I can see to remain at equilibrium, is by crisis so that $dm$ is never reimbursed.

I would like an explanation in simple words about what is wrong about this naive view.

Answer 1

The world economy is a closed system as regards economic exchanges, but it is not a closed system as regards productive resources: earth as a natural system still has resources outside the human economic system that are continuously transformed by willful human activity and enter the economic system. Also, human time (enhanced with productive know-how) is something that continuously flows into the system as a productive resource.

The issue with the quantity of money therefore, is not its absolute level and magnitude, but its quantity relatively to produced output. A small village with a monetized economy, needs a certain amount of money to function economically. A large country needs a much higher quantity of money for the same purpose.

When a person borrows an amount of money, he essentially borrows an amount of productive resources, raw (investment loan) or in finished/ready-to-consume form (consumption loan). And indeed, he undertakes the obligation to return a higher amount that includes the interest.

If, when the time comes to repay loan+interest, he liquidates some already existing asset of his, then we do not really have additional money creation to cover the interest. If it manages to pay loan+interest by the output he produced in the meantime through his activity, then the additional money that needs to be created in order for the monetary transaction to be completed, "makes no harm" since it matches and reflects underlying real value that has already been created.

Certainly, "value" is not objective, and we have the price system that fluctuates, creating defaults, bankruptcies, hyperinflations, sudden re-distributions of wealth, etc. But in the very large picture you are looking at, these are fluctuations and deviations around the structure delineated above.

Answer 2

You seem to be confusing the concepts of value and money. There are ways of repaying a debt without having any money. I.e. you can pay with assets, such as a painting or your house, etc. as long as the other side accepts.

The speed of value creation and the speed of money creation need not coincide. When a new painting (or company or diamond) is valued at a million dollars, no bank needs to issue new debt.