Constant money supply in a world with interest

[doodle]

Im a bit confused about interest on a macro level. Is it possible to have a steady money supply or one that grows less rapidly than interest rates without making it mathematically impossible for all interest bearing loans to be repaid?

For example, let's say base money supply is held steady and banks have loaned out funds to the maximum allowed by reserve ratio (which incidentally is another can of worms that I'm trying to grasp as existence of reserve ratio as limit on bank loans seems to be contested by post keynsians) and these loans were made at an average interest rate of 4%, how would it be possible to return the 4% interest without somehow expanding the base money supply or lowering the reserve ratio? Once interest is introduced into the system doesn't the money supply have to stay in a mode of constant expansion?

[moda0306]

Gumby, I think we'll leave this one to you...

[melveyr]

Im a bit confused about interest on a macro level. Is it possible to have a steady money supply or one that grows less rapidly than interest rates without making it mathematically impossible for all interest bearing loans to be repaid?

For example, let's say base money supply is held steady and banks have loaned out funds to the maximum allowed by reserve ratio (which incidentally is another can of worms that I'm trying to grasp as existence of reserve ratio as limit on bank loans seems to be contested by post keynsians) and these loans were made at an average interest rate of 4%, how would it be possible to return the 4% interest without somehow expanding the base money supply or lowering the reserve ratio? Once interest is introduced into the system doesn't the money supply have to stay in a mode of constant expansion?

I don't have an answer to your question, but about the post-keynesian thoughts about reserves... In your hypothetical example the banking system is by definition reserve constrained because you set total reserves constant. I think post-keynesians simply argue that the under our current regime banks can make the loans first and find the reserves later (either from each other or if it is a banking wide shortage from the discount window).

[AgAuMoney]

Once interest is introduced into the system doesn't the money supply have to stay in a mode of constant expansion?

I don't think that is a natural consequence of interest.

I think it may be a consequence of the excessive quantity of borrowing allowed to happen when money is created to lend.

In other words, if you are going to create money to lend, then you may have to create money to pay it back.  If the money to lend was borrowed from someone that actually had it, 1) there would be much less borrowing, and 2) that borrowing would likely be only for a productive purpose, 3) productive enterprise attracts capital from people who have it, 4) that greater capital flowing into the business allows the loan to be repaid.

If you think that does not sound like consumer credit, or borrowing for consumption, then you would be right.  A limited money supply would tend first to limit lending for such frivolity.

Perhaps also you might be ignoring bankruptcy or default, when a loan is simply not paid back.  It happens under any system, but especially if money is cheap and easy because the cheaper/easier the money, the more marginal the projects that borrowing can fund.

If money is lent, and not put to productive use, i.e. does not attract capital sufficient to pay the loan, then the borrower may default and the lender loses his capital (which went to some other enterprise and lender).  This risk of loss also limits lending such that lender and borrower must be reasonably certain that the loan is for a productive purpose or there is some other equally valid reason to suppose the borrower will be able to repay.  Perhaps by posting sufficient collateral to mitigate the risk to the lender...

But I also think you will never find a 100% static supply of money unless you have a monopoly such as the Fed enforcing that limit.  In the real world people will supplement the money supply somehow.  See Ithaca Dollars, or in a commodity money system the incentive increases to find more of the commodity(s).

Of course, there can also be deflation in prices if money becomes scarce (hence more valuable) whether thru actual reduction or simply failure to grow as fast as the economy.  That alone will serve to limit lending if it becomes the expectation, because borrowers will rightly be concerned about paying back more valuable money than they borrowed.  Reduced lending means fewer marginal projects get funded, resulting in more efficient allocation of capital.  (Only the most productive projects get funded)

[AgAuMoney]

I think post-keynesians simply argue that the under our current regime banks can make the loans first and find the reserves later (either from each other or if it is a banking wide shortage from the discount window).

That's what I'd argue, and have, but I'm more of a pre-Keynesian than a post-Keynesian. 

[doodle]

The economy can certainly be a complicated topic when trying to analyze its myriad twists and turns, therefore this issue works best when abstracted.

Lets say our economy starts off with $100 dollars that is in the hands of a private bank. The money does the private bank no good just sitting there, so it decides to lend it out at interest so that its money can grow.  So, the bank decides to write a one year loan for the $100 dollars at a 5% interest rate to a businessman who wants to build a general store to sell all of the things that the people in the economy produce and who up until now have been just trading and bartering their goods.  

So the businessman takes the $100 dollars and pays for the materials and workers to build the store and also uses the money to buy his supply of inventory. At this point the businessman has $0 dollars left over and this money now sits in the hands of the people who built his store and sold him his inventory. He isn't worried though because he is sure that they will come back in and use their money to buy things in his store.

At the end of the year, the businessman has done a tremendous job at providing a convenient store for the townspeople to buy goods from and sell goods to and the money has been flowing through his store constantly. Nevertheless, the businessman cannot seem to come up with $105 dollars to repay the bank loan because try as he might the reality is that there are only $100 dollars in the economy in total.

In order to get $105 dollars to repay back the loan, somehow $5 more dollars need to be introduced into the money supply. If not, the bank will take control of his business.

Now this is a simple example of one business, but it should hold true at the macro level. In other words, if the money supply is steady, and loans are being made at interest it is mathematically impossible for all of those loans to be repaid. In other words productive or not, a certain number of businesses are condemned mathematically to failure.

What are the implications or the lesson to be gathered from that, Im not quite sure at this point.

[Pointedstick]

That's a very good example, doodle. But I think it's important to introduce a refinement: instead of one loan for $105, let's say that instead the bank made 10 loans for $11 at different times, such that they came due across many years. It may be impossible for everyone to repay their loan at the same time without new money being created, but isn't it possible for this fragile system to function so long as the payments come due at different times, and the bank continues to loan out the money that gets paid back?

[AgAuMoney]

instead of one loan for $105, let's say that instead the bank made 10 loans for $11 at different times, such that they came due across many years. It may be impossible for everyone to repay their loan at the same time without new money being created, but isn't it possible for this fragile system to function so long as the payments come due at different times, and the bank continues to loan out the money that gets paid back?

Yes, and some loans will go bad which will enable to the others to be paid back. Of course, if everyone that received a loan spent it, and 100% of the recipients then just buried it in a mason jar out back, the economy would grind to a halt.

100% uniform behavior does not happen in the real world, so a contrived example/analogy does not prove anything in the real world.

[melveyr]

doodle,

Ancient societies used to clear out the financial system every 50 years with a "Jubilee." I think they had similar concerns to the ones you are expressing.
http://en.wikipedia.org/wiki/Jubilee_(Christianity)

I do think the system becomes more fragile as more private debts accumulate relative to GDP. Government giving everyone $40,000 could be a modern equivalent of a jubilee. The inflationary consequences would reduce the real value of the debts... But I think a slow mediocre recovery is in the in the financial interests of many bond holders. They want enough activity for default rates to be small, but not an economy booming enough to push up prices.

These thoughts really reinforce the role of Treasuries and Gold in a portfolio. Whichever path we choose to delever, one of those should do well.

[doodle]

Yes, and some loans will go bad which will enable to the others to be paid back.

Yes, but unless the money supply grows the bank will still not receive their interest, so why even make the loans in the first place then? You are taking a risk, for which there is no mathematically conceivable way for you to generate a return above and beyond the quantity of money that you originally loaned.

[Pointedstick]

Yes, and some loans will go bad which will enable to the others to be paid back.

Yes, but unless the money supply grows the bank will still not receive their interest, so why even make the loans in the first place then? You are taking a risk, for which there is no mathematically conceivable way for you to generate a return above and beyond the quantity of money that you originally loaned.

Oh but there is, so long as you're not dumb enough to be a monopoly provider of debt-backed currency who makes all your loans at once so that they come due at the same date.

In a real economy--with a debt-issuing government, many competing debt-issuing banks, and many people seeking loans at many different times--the total outstanding debt exceeding the quantity of money in circulation isn't a problem because people default, they repay their debts at different rates, and the debts come due at different times. Now, I think we can agree that this system is fragile as hell and causes inflationary pressures for goods financed by debt, but there's nothing "mathematically impossible" about it working so long as new loans are made constantly being made and old loans are paid off in a staggered fashion.

[Gumby]

I have to agree with much of what was said above. Though, in our current debt-based/credit-based monetary system, both private credit and public debt seem to increase exponentially.

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I could be wrong, but I'm pretty sure the exponential nature of the graphs are at least partially due to interest payments.

[AgAuMoney]

I could be wrong, but I'm pretty sure the exponential nature of the graphs are at least partially due to interest payments.

Actually the graphs are probably NOT exponential, because the RATE of increase is not shown to be increasing.  I wonder if FRED can plot on a log scale...

[AgAuMoney]

Some other bank will have to lose said amount in their deposits. 

But in the real world not from their deposits.  Defaults come from their lending which is far in excess of their deposits (see money multiplier in regards to the reserve ratio).

[AgAuMoney]

Thanks Slotine.  That was quite the job.  I didn't check all the numbers, but with a quick scan it looks to be a reasonable facsimile of how things work.

Of course, the original question posited a constant money supply. 

[AgAuMoney]

Actually the graphs are probably NOT exponential, because the RATE of increase is not shown to be increasing.  I wonder if FRED can plot on a log scale...

Turns out they can:

Very nice.  And in those we can easily see the growth is not exponential for either of them.