Subject: Re: TURMEL: On Social Credit vs Greendollars

From: [email-masked] (Timothy Huyer)
Date: 27 Nov 1995 22:53:23 GMT

John Turmel ([email-masked]) wrote:
:      On Nov 21 1995, in article #114196 in Newsgroups: can.politics, 
: [email-masked] (Timothy Huyer) wrote: 

I will attempt to deal with Turmel's positions by trying to cover briefly 
the various issues that he raises:

(I)  First, that interest is necessarily bad.  Whereas it is clearly 
obvious that the borrower, all else being equal, will prefer lower 
interest rates, not all else remains equal.
	An example.
Assume a two person-two period model, i.e., a model in which two people 
exist whose lifespan covers two periods.  Assume no uncertainty.
	Let money be continuously divisable.
All income goes to consumption, either in first or second periods.  All 
goods are perishable (i.e., goods not consumed in period one are not 
available in period two).  Let consumption by individual A or B be 
denoted C_Ai or C_Bi respectively, i=1,2 the period in which the 
consumption occurs.

Let the first person, A, have a utility function 
U_A := (C_A1)^0.7*(C_A2)^0.3  
and the second person, B,
U_B := (C_B1)^0.6*(C_B2)^0.4

Finally, assume that each individual has wealth w_Ai=w_Bi=$5000, i=1,2, 
that is, each person in each period earns $5000.

Clearly, each individual's utility without trade is 5000.   The issue is 
whether it is possible for _both_ A and B to be strictly better off, 
i.e., for both U_A > 5000 and U_B > 5000 by a transaction.
	In fact, this is clearly possible, and there actually exists a 
locus of possible trades which alllows for both individuals to be 
strictly better off.  Since A has greater preference for consumption in 
period 1, A could borrow money from B in period one and repay that money 
plus a premium to B in period 2.  I will skip calculating out the locus 
of solutions, but it is straightforward to show that the premium 
constitutes an amount of interest, and that, at very low rates of 
interest, B is not willing to lend (since B's utility would then be below 
5000) and at very high rates of interest A would not be willing to 
borrow.
	Rationality of assumptions.
(1)  Perfect information (no uncertainty).  Clearly a very strong 
assumption, but one which simplifies the math enormously.  The confident 
can, with the assistance of economics literature, look at math involved 
when uncertainty is introduced; however, the fundamental results in the 
simple model are not changed.
(2)  Multiple generations (i.e., more than 2 periods) are possible 
although needlessly complicate the math.  Also more than 2 agents are 
possible.  As more agents are added, the locus of mutually acceptable 
interest rates declines until, with infinite persons, a unique value exists.
(3)  Form of utility functions.  It can be proven that agents with 
rational preference ordering (an ordering over a set of possible 
consumption bundles which is complete, transitive, and anti-symmetric) 
which are continuous are necessarily represented by a continuous utility 
function.  Since utility is an ordinal ranking, the functions are 
equivalent over monotonic transformations.  I arbitrarily chose a utility 
function which is mathematically very simple, but the results hold over 
more complex utility functions.

Therefore, situations can occur under which mutual gains are made with 
positive interest rates.

(II)  Banks do not loan depositer's money.   The bank system is basically 
a means of making the above market more accessible.  By loaning or 
borrowing money through the intermediary -- the bank -- risk and 
transaction costs can be reduced.
	In a previous post, I attempted to demonstrate to some extent how 
money flows in the banking system.  I will attempt to quickly repeat 
(and possibly improve on) that here.
	Let there be one central bank and one charter bank, and all 
individuals deposit all of their money in the charter bank (no one keeps 
any cash).  All borrowing also occurs from the charter bank.  The charter 
bank keeps a set fraction of deposits in reserves, i.e., a reserve ratio 
of r, 0 < r =< 1 and loans out the remainder.  For the example, we will 
set r = 0.1
	Let the central bank buy a bond from any individual for $1, and 
pays for the bond by the creation of new money, $1 (all central bank 
operations on the open market involve creation/destruction of new 
money).  That person deposits the $1 in the charter bank.  The charter 
bank puts $0.10, or r*$1 in reserves, and loans out the remainder, 
$0.90.  That loan is used for some transaction and the recipient(s) of 
the money deposit it in the bank.  This process repeats infinitely.
	Note that deposits in the charter bank is the series
t=0->infinity, [$1*(1-r)^t], which, with r=0.1, has a value of $10.  
Reserves are necessarily r*deposits, or $1.  Loans are the series 
t=0->infinity, [$0.90*(1-r)^t] or $9.  Thus, liabilities of the bank 
(deposits) are $10 which equals assets (loans + reserves).  All loans are 
covered by deposits and then some.
	Boundedness of r.  I assumed earlier that r is in (0,1].  Note 
that it is impossible to maintain greater reserves then deposits, since 
all reserves come from deposits.  Hence r is bounded above by 1.  Note 
that the two series converge only if 1 - r < 1, which thus requires that 
r > 0.  If the reserve ratio is zero or negative (the latter if banks 
created their own money), the money supply would be infinite.
	With infinite money pursuing a finite amount of goods and 
services, it follows that prices, i.e., inflation, is also infinite.

Additional comment on the reserve ratio.  The assumption that depositors 
keep no cash is very strong.  In fact, people keep some function of their 
total wealth in cash on them; i.e., if wealth is w, cash held is 
f(w|e), 0 =< f(w|e) =< w (f(w|e) need not be linear), where e is some 
environment.  e can be conceived as needs for cash not tied directly to 
wealth, i.e., if planned major expenditures are occuring or other 
environmental considerations.  From the perspective of the bank which 
cannot perceive e, aggregating over all depositors gives an estimate of a 
random variable which represents the unknown demand for cash.
	Since banks must meet the demand for cash they keep reserves in 
order to cover the expected demand plus extra to cover risk.
	How do banks then choose r?  Obviously, it depends on the 
expected value and variance of e.  However, the charter banks also can 
borrow money directly from the central bank (the loaner of last resort) at 
the bank rate.  Thus banks choose to minimize the cost of holding 
reserves (measured in terms of possible income from loaning out the 
money) and the costs of borrowing from the central bank (measured in 
estimated short-fall of reserves*bank rate).
	Clearly, as the bank rate falls, so too falls the cost of 
borrowing from the central bank, and thus charter banks are less inclined 
to keep reserves -- reserve ratio falls, money supply increases.  The 
reverse if the bank rate rises.  
	It is much more complex to establish, although many of the 
necessary conditions have already been established, that the rate of 
interest is such that reserves cover interest, which, if I follow 
Turmel's arguments correctly, contradicts his claim that there is a 
shortage in the money supply.
	The (charter) banker here has not added any money to the pot, 
which is a correction of an error that I had made many many weeks ago and 
one which Turmel repeatedly brings up. 

(III)  Turmel proposes, in effect, abolishment of the charter banks and 
private lending (via the banks or otherwise) in favour of loaning 
directly from the central bank at zero interest.  Since the central bank 
can literally create money, it does not need any deposits to cover the 
loans.
	Note that as in (I), there is no incentive for anyone to loan at 
0% interest (besides altruism).  Even changing B's utility function to 
something like U_B := (C_B1)^0.4*(C_B2)^0.6 would mean that B would 
simply choose to save his/her own money at 0% interest and has no 
incentive to loan that money out (and with positive risk on default, 
incentive exists to not loan money out).
	Turmel restricts the infinite supply of money case by holding the 
supply of money equal to collateral.  In a sense we can view collateral 
to be (real) GDP -- if money supply always equals real GDP, then there is 
no inflation -- there is neither too much money chasing too few goods or 
too few goods chasing too much money -- and similarly no deflation.  This 
is already what central banks attempt to do when they decide by how much 
to increase the money supply, and the inflation that we have is simply 
the error resulting from incorrectly estimating the growth of real GDP 
(the error is consistently biased positive since too little money causes 
a recession, which is much worse than a little inflation).  Since 
estimation procedures are unlikely to be better under Turmel's system 
than present, inflation would still exist.
	Is there an equilibrium in Turmel's model?  Note that in (I), 
with the original utility for B, both A and B would want to borrow money 
at 0% interest.  Note that in (I), any equilibrium would have C_Ai + C_Ai 
= w_Ai +w_Bi, i=1,2; consumption equals supply in each period.  With both 
A and B being net borrowers in period 1, C_A1 + C_B1 > w_A1 + w_A2 and 
the reverse for period 2.  Demand exceeds supply in period one and the 
reverse in period 2.  Simple economics notes then that prices will rise 
in period one and fall in period 2.  But if the agents take prices as 
given, then there still would not be an equilibrium.  If agents 
understand their impact on prices, then the change in prices is 
implicitly equivalent to interest and an equilibrium is possible.  Note 
that when I commented on the LETSystem and implicit interest within 
prices a similar argument holds for that.
	The above paragraph follows from the simple reality that 
consumption is specific to certain time periods.  Note that money 
borrowed in period one is backed by collateral from period two.
	Should the central bank restrict the money supply such that the 
total supply of money in each period is backed by goods and services 
within that period, then no borrowing from the central bank can occur - the 
model (I) already has that equality established in both periods.  
	However, we shall allow for the supply of money to be less than 
the supply of goods and services.  For simplcity, then, assume that the 
supply of money is zero.
	First, note that the exchanges of goods is still entirely 
possible as a barter system.  Let any good which has non-zero value 
(i.e., is demanded by some individuals) be considered the numeraire, the 
good by which all other good's prices are established.  I.e., if we let 
apples be the numeraire, then other goods are worth x apples.  Under the 
barter system, the solution in (I) still occurs.  I had mentioned before 
in other posts that with n goods, prices form an n-1 dimensional simplex, 
and this is the logic that holds true.  Simply, it is only the relative 
prices that matter, not the absolute prices.
	But let everyone borrow $5000 from the central bank each period at 0% 
interest.  Note that from that point, both A and B can make mutual gains 
by loaning to each other following exactly the same logic used in (I).

A note on rationality.
	For an agent (an agent is an economic decision making unit, i.e., 
an individual, household, firm, etc.) to be rational, that agent must be 
trying to maximize an objective function subject to constraints.  For the 
case of the individual or household, that objective function is to 
max utility and the constraints are (real) wealth.
	Rational people can still do what anyone else might consider to 
be "stupid".  Utility functions need not be identical across individuals, 
nor need information sets.  I could be stupid enough to think that an IBM 
286 is better than a Pentium machine, but I would still be rational if I 
chose to buy the IBM 286 even if it cost more.  Rational people can make 
mistakes.  However, rational people also learn.  The cliche that "you 
can't fool all of the people all of the time" is true.  As agents aquire 
information, they change their actions resultingly, all according to 
their objective function.  In particular, if anyone repeatedly attempts 
something and it does not achieve the expected results, they will learn 
and try something else.
	I called Turmel's watches and toothpick model irrational since, 
in a perfectly random game, each agent expects to get 10 toothpicks back 
(what they started with) and thus not be able to buy back their 
collateral.  That is to say, each agent expects to be strictly worse off 
as a result of playing the game.
	Clearly, some people can be foolish enough to not realize that 
the game is stacked against them.  However, over time, more and more 
people will realize that playing the game is stupid, and the equilibrium 
result will be no one plays the game.  Thus, if the mortgage system 
really behaves as Turmel suggests in that model, then it can be expected 
that, within a reasonable learning time, everyone will stop playing, and 
there would not be any mortgages undertaken.  Turmel thus needs a very 
compelling reason why agents will continue to play the game -- i.e., a 
reason that makes playing the game rational.

Finally, on the creation of money.  Note that fundamentally, the creation 
of money first occurs when the central bank creates money in an open 
market transaction.  One could state, technically, that only the amount 
of money created by the central bank actually exists.  But the amount of 
money in deposits (and the amount loaned) greatly exceeds the amount of 
money physically in existence.  Hence the various definitions of money, 
M1, M2, M2+, M3, etc..  One could also argue that, since the money 
circulates multiple times through the charter banks and that, each time 
it loops back, deposits and loans increase, that the charter banks are 
also creating money, although they are not creating any physical currency 
or M1.
	This is probably why the explanation as to who creates money is 
often vague.  Fundamentally, it is always the central bank.  Even stating 
that charter banks create money since, after the money goes through a 
charter bank deposits (a measure of money) increases, the total money 
supply is still determined as a/r, where a := the amount of money created 
by the central bank.

:      Pretty good argument for linear service charges for our loans. 
: Now we pay $100 on the $1,000 transaction and $100,000 on the 
: $1,000,000 transaction. Every year. I'd rather pay the $15 service 
: charge one for both. 

If the linear service charge is r*loan, 0 < r < 1, charged per period, 
say, annually, then over multiple years we have exponential, or compound, 
interest.  Thus either your system is not linear or the current system is.

:      And if it's only part of the problem, why would I not still be 
: correct in criticizing economic systems? Why does the problem have to 
: "_simply and only-" the lack of money and not just a component of the 
: problem. Shall it be discarded because it doesn't solve everything all 
: at once but only one small part of the market mechanism? Actually, it 
: does solve everything all at once. 

I was simplifying myself.  I will allow, if the scarcity of money -- 
distinct from the scarcity of goods and services -- is part of the 
problem, then Turmel's criticisms have at least some validity.

:      To say scarcity occurs in nature and therefore not in the money 
: supply needs remedial Boolean algebra. Scarcity can and does occur in 
: both real life and in the money supply. One is real, one is 
: artificial. Looking at the real scarcity will not help you in your 
: examination of the artificial one we're discussing here. 

Well, take the (among economists) famous Fisher equation:
	M*V = P*T
Where M := supply of money, V := velocity of money, P := prices, and T:= 
transactions.
	The equality holds obviously -->  all goods and services that are 
sold are sold at some price and that price must come from some money.  
Since money circulates, each dollar is used in more than one transaction, 
and hence the velocity of money is important.
	If V is constant, as it normally is, and M is set by the central 
bank as it always is, we can use d to represent delta, for discrete changes.
	If dM > dT, then dP > 0 (too much money chasing too few goods 
causes prices to rise).  Clearly the reverse also holds.  Note similarly 
for changes in transactions being the first result.
	The above of course skips whether T is a function of M, but that 
is not relevant in this simple case.
	Note that for any finite T and any V > 0, infinite money (i.e., 
no scarcity in money) only results in infinite prices.  In fact, for any 
fixed T and V, increasing the money supply necessarily only increases 
prices -- which is why I claimed that scarcity of goods and services is 
the only problem and not supply of money.

:      No, lowering the interest rate does not lower the bank's reserve 
: ratio. Yes vice versa. The reserve ratio has been defined in 
: legislation by Parliament. Cutting it allows for more and therefore 
: cheaper borrowing into circulation. But whatever then happens in 
: circulation has no effect on the rate the Banker sets. 

Subsequent to the last amendment of the Bank Act, which occured under 
Mulroney's govt, the minimum legislated reserve ratio was abolished.  
This was done in part since charter banks were always maintaining 
reserves greater than the minimum ratio.  

:      But you don't comment on whether I used my plumbing model 
: correctly enough to have a pedagogical value in economics. We know it 
: works for engineers. You tell us it also works for economists. Did it 
: work for John The Engineer? 

Models only work if reasoanable assumptions are made and if the math is 
valid.  Certainly a plumbing model can have valid mathematics and is thus 
of potential pedagogical value.  However, I have attempted to note many 
of the fundamental failures in Turmel's analysis which makes those models 
incorrect.  Now incorrect models can still have pedagogical value (i.e., 
assignment question:  Is the following a correct model -- explain 
fully), and, as such, Turmel's models might still find their way into an 
economics classroom.  
	In fact, I hope that Turmel is clever enough to see that a 
plumbing diagram could be constructed from the model that I presented of 
the banking system.  Let money be injected from a tap, the central bank, 
into a charter bank.  Let the reserve ratio of the money go to the 
reserves, the rest goes to loans which loops back into the charter bank.  
Using liquid to represent money, if we measure the volume of liquid that 
enters the bank either from the central bank or from deposits (allows 
liquid to be double-counted) and the volume that is loaned out, we will 
find that the volume of liquid deposited is 1/r, the volume of liquid 
loaned is (1-r)/r, the volume of liquid in reserves (which is the 
reservoir of all money) = 1.  I haven't used any fancy diagrams, but I 
figure most people who can use internet can handle that much for themselves.

:      And who to better understand the usury banking system than the 
: engineer who first drew its Laplace Transform Control Circuit? Check 
: it out in my Mathematics of Usury. Other engineers have vouched for 
: it. 

I commented a while ago that mathematics + bullshit = bullshit.  The same 
holds true for economics.  I have no doubts that the math in your models 
is correct, it is the underlying economic assumptions which I am challenging.

: You're not supposed to continue to not understand when there's a 
: working model for you to get on and pedal. 

I would have to say ditto for the current system.

:      If the non-existence of interest cannot be sufficiently 
: demonstrated when it's been designed out of the blueprint,  then 
: you've got your eyes closed. I call this "judicial disease." 

Economics, at the very least, attempts to follow scientific methodology.  
Scientists like to isolate out other possible causes in order to 
sufficiently prove that two things are positively related.  Economists 
don't often have the normal luxury of doing experiments with control 
groups, but nevertheless attempt to use the same concept in our 
methodology.  Hence, the cateris paribus (all else being equal) statement 
that we use.  Hence models that unambiguously show the isolated effect.  
Because of scientific methodology, science is generally more reliable 
than speculation or opinion.  If Turmel wishes to merely use opinion 
versus economic science and claim that opinion carries more weight, then 
I see no reason for continuing in this thread.

--
Tim Huyer, Graduate Studies     |	"Masters are always and everywhere
Department of Economics	 	|	in a sort of tacit, but constant and
Queen's University, Canada  	|	uniform combination, not to raise the
[email-masked]	|	wages of labour above their actual
[email-masked]		|	rate."  Adam Smith
- My opinions do not necessarily reflect my views or those of anyone else -