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If the central bank is the only institution that can increase the monetary base (create both, digital and paper money), how can any institution that borrows from it (mostly banks) satisfy its interest requirements? In other words, how can you pay back more than what left the central bank?

A dumbed down example would be: Only I can create money, I (the central bank) loan you (the banks) 10 dollars expecting 11 dollars back (10 dollars principal + 1 dollar interest). Where will you get that 1 dollar from to pay me the interest if there are only 10 dollars in existence?

This question can be easily answered if there were any way in which new money can leave the central bank without being paid back. Are there such transactions I don't know about?

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    $\begingroup$ Your same reasoning would apply for any kind of debt: Assume the amount of outstanding currency is fixed, say 10 dollars, and it is held by a single agent A. Now agent A lends to agent B expecting 11 dollars back. But the total amount is 10, so what? To put it very simple, the interest is a right, so it is in a sense independent of the actual availability of currency. $\endgroup$ – user4385 Apr 8 '15 at 10:24
  • $\begingroup$ The thing is that private banks lend the money with a higher interest rate than the one they have to pay to the central bank, so in the end the question is how everyone else can pay back the private banks. I think the answer is that they can't. $\endgroup$ – agemO Jul 8 '15 at 9:35
  • $\begingroup$ In fact they can : of course the private bank will spend the money from the interest by buying stuff to the rest of the economy, so it's possible not to exponentially accumulate debt, but if a private bank decides to use its constant flow of money to buy lands or gold, it will accumulate forever. $\endgroup$ – agemO Jul 8 '15 at 9:56
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You anticipate the answer when you ask:

This question can be easily answered if there were any way in which new money can leave the central bank without being paid back. Are there such transactions I don't know about?

Indeed, there is always a way that money leaves the central bank without being paid back: the central bank does something with its net interest earnings, usually sending them to the central government, which treats them as part of its revenue, and is therefore able to get by on a little less tax revenue than it would otherwise need. For instance, in 2013 the Federal Reserve remitted $78 billion in profits to the US Treasury.

Let's incorporate this observation into an augmented version of your example. Suppose that the central bank keeps the supply of money at \$10, with a corresponding loan of \$10 to banks, and the annual nominal interest rate is 10%. Suppose that the central government spends \$5 per year and runs a balanced budget.

Each year, banks pay \$1 in interest to the central bank. This is profit and is sent to the central government, which then only needs to raise \$4 in taxes to pay for its \$5 in spending. The net effect of this is to put \$1 in the hands of the public, which ultimately finds its way to paying for the \$1 in interest that banks owed to the central bank. (After all, these banks are presumably lending out the money and collecting interest from the public themselves.)

One can make the example much more intricate, but the key point is that we don't get an exponentially growing debt owed to the central bank by the rest of the economy - because the central bank sends its profits to the government, and then they're recycled into the rest of the economy.

(As user4385 points out in a comment, the situation is similar for any kind of debt. Suppose, for instance, that Connecticut is a net creditor to the rest of the country - where does the rest of the country get the money to pay interest to Connecticut? The answer is that Connecticut eventually spends its interest earnings on goods and services from the rest of the country - funds flow in both directions.)

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  • $\begingroup$ Money is just a form of currency. It only represents value to the extent a seller will accept it in exchange for a good or service. For example, $A$ can loan $B$ 10 fish and charge 1 fish in interest. $\endgroup$ – Mowzer Jul 15 '16 at 15:24
  • $\begingroup$ This answer still does not explain where the money that made up the "first" profit of the Central Bank came from. Furthermore, since the profit increases year after year, where does the money that makes up the difference between this year's profit and last year's profit come from? $\endgroup$ – AxiomaticNexus Aug 12 at 12:27
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A good starting point would be to see what an open market operation is, which is the main way to adjust the money supply. FYI, the banks may borrow from the ECB but they are reluctant to do so (they prefer borrow from each others). The interest rate you're referring to is mere a "focus" point (for later arbitrage).

I let someone else give you a more complete answer...

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The answer lays in the way liquidity provision of the central bank works. Conventional framework is probably best represented by the ECB.

The ECB sets the amount of liquidity provision so that the interest on the money market would match their key rate. The demand for central bank liquidity stems from the need to service interbank payments and to meet reserve averaging requirements of the central bank.

In your simplified example the volume of central bank lending appears out of thin air, but in fact the offered volume is calculated so that the banking system is able to meet reserve averaging requirements set by the central bank. So for the sake of clarity assume that the only outflow of reserves from the banking system is interest payments to the central bank. Then the central bank would offer increasingly higher amounts so that to meet the demand of the banking system.

I think that the mechanism is best described in (ECB,2002) and a bit more at length in (Fullwiller,2008).

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The principle is that the central bank acquires government bonds and in return increases the money flow, i.e increases inflation. I think that Keynes's objective was to ensure market liquidity and to stimulate growth, this market growth should take care of the interests, I guess. Check a summary of all the Goals of Monetary policy developed in : John Maynard Keynes, The General Theory of Employment, Interest and Money.

Government bonds in a country's own currency are sometimes taken as an approximation of the theoretical risk-free bond, because it is assumed that the government can raise taxes or create additional currency in order to redeem the bond at maturity.

"Payments in kind" through disposal of assets, e.g public privatization.

Extreme measures taking care of debt are clearing and defaults.

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  • $\begingroup$ Most major economies of the world, if not all, have similar central banks just like the U.S. $\endgroup$ – AxiomaticNexus Apr 10 '15 at 18:32
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    $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post. $\endgroup$ – BKay Apr 10 '15 at 21:09
  • $\begingroup$ @ BKay I've considered your advice and changed my answer, is it still not providing any insight on the question? $\endgroup$ – Ziezi Apr 13 '15 at 19:48
  • $\begingroup$ @simplicisveritatis People do not always come back to posts they've voted down. It might have been better to simply delete the old answer and post the real answer. Also: Note that you have a space between @ and Bkay - he didn't receive a notification. $\endgroup$ – FooBar Apr 25 '15 at 23:00
  • $\begingroup$ @FooBar Thank you for the reconsideration! I'll make sure to use your advice in future posts. $\endgroup$ – Ziezi Apr 26 '15 at 7:20
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I hope this helps. It helped me.

https://mises.org/library/what-does-debt-based-money-imply-interest-payments

Edit: As pointed out by others, I'll include a short explanation of what the page says:

What happens is that the banks spend money to function (they pay their workers, their bills, ...) and so part of the money that is supposed to be at the bank is given back to the public. This way, people can pay back their interest. Basically it is the same money used all over again.

But this "problem" you point out is not unique to the our banking system. If you used gold and had a limited amount of it (no gold mined), you would have the same situation. Interest is paid by the circulation of the money. Otherwise, you would have to find new gold to pay for the one you borrowed.

TL;DR: The interest can only be paid by the banking system spending their money. So, as long as the banks don't keep their money to themselves, it should work out. But it does seem weird.

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    $\begingroup$ Let me reply to an unexplained link with an unexplained link. I hope this helps. It helped me. rationalwiki.org/wiki/Ludwig_von_Mises_Institute $\endgroup$ – HRSE Mar 29 '16 at 12:37
  • $\begingroup$ What do you want me to explain? The link answers the question asked... I am sure he can read for himself. $\endgroup$ – Telmo Mar 29 '16 at 12:59
  • $\begingroup$ Good point. I'll edit. $\endgroup$ – Telmo Mar 29 '16 at 14:03

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