Does Principal less than Principal Plus Interest Imply Default?

There has been some conflict over the idea that, since the majority of money (95%) is created as debt, the problem is that while what money is owed is principal plus interest, (P + I) and what money exists is merely the principal (P), it is always impossible to pay back the total, (since P < (P + I),) and so there will always be default.

Paul Grignon, from whose excellent movie   “Money as Debt II” http://www.youtube.com/watch?v=jQuEOUzA9P8 I originally gained this idea, now says the primary cause of default is secondary lending.  

http://peemconference2013.worldeconomicsassociation.org/?paper=proposed-new-metric-the-perpetual-debt-level If I understand him right.

We examine this.

WE consider a steady state economy, one which is neither growing nor contracting.  The velocity of money V we consider constant.  Banks lend out $100 at the beginning of the year.  This is all the money there is in the economy.  All money is debt.  At 6% interest.

All loans are to be paid in full at the end of the year.  Otherwise, there is no interaction between the banks and the rest of the economy.  $106 is required at the end of the year, but only $100 exists.  If we look at all of the actions internal to the economy, that is, the economy separate from the banks, none change the money supply. Only the paying back of loans, which extinguishes the money, or creating new loans, which creates money, changes the money supply.  If loans are paid early, the interest is collected. Paying early extinguishes the money, whether on principal or interest.   If the money supply is to be maintained, the loans are lent out again.  In this case $106 is still required at the end of year. Of course, the next year, $106 can be lent out, thus allowing the $6 in interest to be rolled over, along with the rest of the money in the economy,  the debt compounding. But see below.

Internal lenders, (secondary non-bank lenders,) who must first borrow the money from the banks at the beginning of the year, before they lend it, do not change the money supply. They may sell the loan, for money, but that doesn’t change the total supply of money.   Neither do they change the default rate to the banks.  In this sense: Default to secondary lenders is passed on as default to the banks.  They transmit, but do not originate.  

But this is the basic point.  If we keep secondary lenders separate from banks, the net default rate to banks does not change. The default rate is still just a consequence of the original shortage of money to pay the interest, unless the money supply is expanded.  Anyway, if the default rate is greater than the 6% interest rate, then there is money retained in the economy by other actors.  If the default rate is 8%, then 2% is retained as cash by the economy for the next year.  Indeed, we would expect a certain amount of this kind of default in an economy in any year.  Call this distributional, as opposed to secular, default. Roughly, the distributional default rate would be a constant, although this might depend on the growth rate or inflation. We will ignore this, as it is not brought about by a shortage of money, but by the distribution of money in the economy.  Because of distribution, some people will have more than enough to pay back their loans, some people will not have enough, and this will even out.  But because P < P + I, there will in addition always be some who will not have enough money to pay back their loans.

Suppose now instead the banks spend $6 throughout the year. (Interest to savers may be some of this.)  Essentially they are giving away this money, although they may demand real services for it. Then there would be $106 at end of year.  There would be no secular default, but there would be 6% inflation, with constant velocity, as the money supply has expanded by 6%, while the economy has, by assumption, remained at a steady state. The same result would happen if the banks were just to lend out $106 at the beginning of the second year, as above, thus covering what would otherwise be defaulted upon at the end of the first year.

Suppose the banks spend $10 throughout the year.  Then there would be $110 at the end of the year, and 10% inflation, with $4 remaining in circulation at end of year, when all loans were called due, and $106 collected.   But $106 would still have to be lent out, at the next cycle, as the required base money supply is now $110, and anything less, (or more,) would change the money supply, and if less, cause deflation, from $110, and if more, inflation.    

Suppose the banks spend just $3 through out the year.   Then the money supply increases by 3%, and there is 3% default.  This suggests an equation: rate of Money added + Default rate = mean interest Rate. (Rate of Money added in a steady state economy will equal the inflation rate, but it will not equal the inflation rate in a growing economy.)

Let’s look at this some more.  The increase in the money supply need not be just the banks spending money.  It could also be the government issuing money.  And this increase in the money supply could be greater than the interest rate.  Then default would be ‘negative,’ (by which we mean there would be net cash at beginning of the next cycle,) and inflation greater than the interest rate.  

Another thing that could happen is the banks could increase the rate of loaning money above $100, the first cycle.  But this would just set the base at say $110. Thus the increase in bank lending would also contribute to inflation.

Suppose now an economy growing at 3%.  Then if the banks put in $6, 6%, we would have 3% inflation:  Rate of Inflation = rate of Money added – Growth rate.  As before, zero secular defaults.  But suppose instead the banks just spend nothing.  This will lead to 3% deflation. The default rate would still be at 6%, though, because there is the 6% shortage of money. So in a growing economy, our first equation still is: rate of Money added + Default rate = mean interest Rate. These terms are the purely monetary terms.  Inflation and the Growth rate are the terms involving the real economy.  Substituting for rate of Money added, from one equation to the other, we have: rate of Inflation + Growth rate + Default rate = mean interest Rate. Note we allow the default rate to be ‘negative’ if there is a sufficient increase in the money supply.  (Note also that if we include the distributional cause of default, we actually have:  rate of Inflation + Growth rate + Default rate > mean interest Rate.   But distributional default is a complication we are ignoring. I think it averages out as roughly a constant over time, and so does not affect the secular default rate.) 

Back to a steady state economy. Instead of all money being created by loans, we are told that there is $5 in the economy, not created by the banks as loans.  Banks lend out $100 at 6% interest at the beginning of the year.  So there is $105 at the beginning of the year.  All loans to be paid in full at the end of the year.  No other interaction between the banks and the economy.  So $106 is required at the end of the year, but only $105 exists.  All internal actions, in particular the actions of internal lenders, add to zero.  Paying early extinguishes the money.  However, unless $5 is put into the economy the next year, then the banks will have all the money. ($105) Then the next year all the money which is in the economy will be lent, that is, all the money will be created as debt.   Which the banks loan out at 6%, requiring $111.30, or default to the amount $6.30.  So we see an amount equal to the interest on all money must be pumped into the economy each year to avoid defaults.  This leads to inflation, at the rate of interest.

So we see that, in a steady state economy, unless new money is created each year, at the mean rate of interest, there will be default.  If new money is created each year, there will be inflation.    

Consider instead overlapping periods of loans.  Banks lend out $100 at beginning of year: $50 for a year;  $50 for 6 months.  Then the banks loan out the $50 again at mid year, for a year, etc.  Assume as before the velocity of money V is constant.   Then $51.50 is taken out of the economy at the end of 6 months. If then only $50 is lent back in, the banks keeping the $1.50 interest, then only $98.50 will remain in circulation.  But if we assume business as usual, and that the money will be distributed throughout the economy, then the $1.50 interest due after 6 months will be defaulted on.  This default is required to maintain the money supply, in the economy. If it is not defaulted, the money supply will contract by $150, unless the banks now lend out $51.50.

Suppose instead the banks will lend just the $50 out again.  After 1 year, then, on the first year loan $53 will be taken out, so only $95.50 will remain in circulation. So we see that with overlapping loans, the result will still be some combination of deflation, default, or increasing indebtedness with inflation.

What about with deflation?  Indebtedness can still compound.  The banks keep all interest to themselves. Then after one year, $100 is owed on $94 in circulation, and after two years $100 is owed on just $88 in circulation, etc.  This is a cumulative 6%, or $6 on the $100 which is owed.  This is constant, so the reduction in circulation each year is constant, although the percentage decrease in money in circulation increases.  6.38% decrease in the 2^nd year, 6.82% decrease in the 3^rd year, 10.35% the 7^th year, when $100 will be owed on just $52 in circulation.  This is independent of any growth, or contraction, in the in the real economy.

In this toy economy, we have either default or compounding debt, just because P < P+I.

Finally, we note again the odd consequence of distributional default, which is that the economy retains cash not owned by the banks.  Peculiarly, except for this small percentage, plus any money issued by government each year, or given away by banks, each year, all money is effectively owned by the banks.