so many things!
I guess that stevea thinks I'm too much of a retard for him to respond to nowadays and no doubt, Tippit has formed the same opinion about you.
So, now we know that Tippit at least does not think of either of us as being retarded (at least that is what Tippit said). I do not think Tippit commented on either of our woo factors though. I have a woo factor myself of somewhere between 0.1 to 0.2. I will leave it to you to determine how one determines woo factor, or what yours is. That is half the fun of having a woo factor!
OTOH you can't argue with mathematics so maybe that is why they stopped posting on this thread?
Maybe. I read in the intro to a book an author (please do not ask me who, just take this as apocryphal) who said each equation in a book cuts readership in half (E = mc^2 too?). To be honest, the first post you did with equations I looked at for quite some time, mostly I think because of variable naming (I think I have my head wrapped around it, but I still have yet to do pen and paper examination). The next two threads after that seem like a blur of equations because I am finding it hard to get context for the equations. I feel bad about that, but hopefully I will rectify that soon.
While it is true you can not argue with correctly applied math, I think it is definitely possible to argue against the assumptions used before any math is applied

Often it is paramount to do so in fact, lest the math amplify initially false ideas into monstrously false conclusions.
There are two factual errors in your analysis:Required Reserves = 0.1 * Deposits.
I have to say, this caused me to go into deep analysis mode. I looked over MMM and found several quotes saying what the reserve ratio meant. It said that the reserve ratio was of reserves to deposits (I will find the quotes if desired). After that, I did some number crunching / numerology on the steps they give in MMM. What I figured out was that for any given bank the following is supposed to be true:
R / D > 0.1
(assuming a 9:1 ratio, R is Reserves, D is deposits, plus let RR be required reserves and ER be Excessive Reserves)
Given the formula above, the smallest R can be without breaking the inequality (assuming D is positive of course, which it must be), is 0.1 * D. This is the required reserves. So,
RR = 0.1 * D.
In the post it was said there were two factual errors. You only listed one. Let me give the other correction I think you were probably referring to.
ER = R - RR.
By the way, MMM kind of sucks as a document to understand FRB. It is long, boring, not many equations, and presents such simplified scenarios that one could easily misinterpret things if one does not read between the lines.
In fact, the bank has started out with $10,000 in deposits. This is an inexactitude rather than a straight out error. However, banks don't have to pay out from their capital, only deposits - on demand!
This introduces Capital. I am wondering if you can tell me where in MMM or somewhere else they talk about bank capital. I am now getting to the point where I feel much more confident that I understand how FRB works, to the point that I want referrences!
That said, from what I have read, a bank's reserves is all vault money (coin, which is actually coins and physical notes), money held in an account with a local fed branch bank, or money the bank has on its own accounts with itself (although, I have not found a referrence about banks holding accounts with themselves, so maybe that is a fiction of my own imagination, I have found quotes of banks holding accounts with central banks so that part is presumeably safe).
At this point, I will write the corrected version of your equations:
Let me introduce here all the equations and some motivation behind them. psionl0, I think this part is the most important part of this post. I hope you will give it a good look over.
First off though, let there be a triple (R, D, L), which represents one bank's reserves (R), loans and investments (L), and deposits of various kinds (D). Each of these quantities can be made up of a number of other quantities, but I will not cover that (for instance, D is made up of all the deposit accounts of bank account holders, say D = D1 + D2 + ... etc. That kind of thing...).
Basic Equations:
R = D - L
RR = r * D
r is reserve ratio, which for M:N reserve ratio means
r = N / (M + N)
ER = R - RR
Now come the actions a bank can do. Some are multistep in a sense.
Transfer money:
Let (R1, D1, L1) be the triple for bank 1 and (R2, D2, L2) be the same for bank2. Let the transfer amount be t. Let the transfer be from bank 1 to bank 2. Then the two triples will change like so:
bank 1: (R1, D1, L1) -> (R1 - t, D1 - t, L1)
bank 2: (R2, D2, L2) -> (R2 + t, D2 + t, L2)
Possible problems: If t > R1, If t > ER1, or in words, if the transfer is for more then the bank has in reserves or if the transfer amount is greater then the excessive reserves of bank 1 then the bank will not meet the reserve requirements or even have a run on its hands.
Make a Loan:
Let the loan amount be q. The bank triple will go like the following.
(R, D, L) -> (R, D + q, L + q)
Possible problems: after most bank loans a transfer occurs to another bank, or possibly even into cash (several other less likely scenarios, the loan money stays at the originating bank or even is transfered to several other banks, which might happen with a signature loan, for instance).
Covering the most likely scenario then of transfer of funds to another bank, we should set up two banks like before. The series of transforms of each bank triple then becomes as follows (bank1 originates the loan, bank 2 recieves the transfer after the loan).
bank1: (R1, D1, L1) -> (R1, D1 + q, L1 + q) -> (R1 - q, D1, L1 + q)
bank2: (R2, D2, L2) -> (R2 + q, D2 + q, L2)
There is no downside to this for bank 2, but for bank 1 the possible problems for it are the same as occured before, but with q replacing t. In general then banks should look at their ER and make sure that q < ER (and then some probably, because the bank will have other expenses that can mess with reserves).
Pay off part of loan:
I do not want to get into the whole P/P+I dilemma of FRB yet. I am holding off on that for a section below. Let this then just be pay off loan while only taking into consideration principal and not the interest (as per noted by you previously). The most likely scenario is that the loan will be paid from the same bank that originated it. I will also include the case of this not being true.
So let the principal part to be repaid on a loan be p.
One bank case:
(R, D, L) -> (R, D - p, L - p)
Two bank case:
Principal p on a loan is being paid from bank 1 to bank 2. Note that first a transfer happens, and then part of the loan is paid.
bank1: (R1, D1, L1) -> (R1 - p, D1 - p, L1)
bank2: (R2, D2, L2) -> (R2 + p, D2 + p, L2) -> (R2 + p, D2, L2 - p)
hmmm... or is this the way it goes? Well, a point to debate about I suppose.
It is interesting that in the scheme above total reserves stayed constant, total deposits and total loans went down by p, which is very much similar to the one bank case.
So starting off we have no Loans. (this part is correct)
Assets:
Reserves = Required + Excessive = 1,000 + 9,000 = 10,000
Loans = 0
Liabilities:
Deposits = 10,000
Bank makes a Loan.
------------------
Assets:
Reserves = Required + Excessive = 1,500 + 8,500 = 10,000
Loans = 5,000
Liabilities:
Deposits = 15,000
Bank transfers deposit money.
-----------------------------
After the Bank Deposit Transfer one has
Assets:
Reserves = Required + Excessive = 1,000 + 4,000 = 5,000
Loans = 5,000
Liabilities:
Deposits = 10,000
Bank borrower repays part of the Loan. (principal only)
--------------------------------------
We get
Assets:
Reserves = Required + Excessive = 950 + 4,050
Loans = 4,500
Liabilities:
Deposits = 9,500
In all of the above equations, (total) Reserves = Deposits - Loans.
Agreed to section above. Thanks for the correction. I love being shown I am wrong because then I learn something. I do not love being shown I am wrong too often though, because it means I am either crazy or lazy in my analysis. Either way, my honor is intact (I hope some of the other subscribers learn something here, it is *good* to admit when you are wrong! Tippit, Sceptic-PK, lomiller), so all is good.
The deposit account that the "bank has with itself" should not be considered "part of Total Deposits". It is actually the bank's capital - the sum of its paid in shareholder capital and undistributed profits. (Undistributed profits are also known as the company's "reserve" which is not to be confused with the reserves that the bank holds to back its customer deposits).
Again, I am concerned somewhat with the term capital for the moment.
The point is that banks do not have to make a "demand" withdrawal from this capital account. So whenever money is transferred from the bank's customer deposit accounts to its capital account it decreases the bank's required reserves and increases its excess reserves.
It seems capital would be reserves? Whatever the case is for the above, bank customer withdrawals lead to reduction in reserves and deposits in equal amount.
Bank borrower makes an interest payment of $100
--------------------------------------
We get
Assets:
Reserves = Required + Excessive = 940 + 4,060
Loans = 4,500
Liabilities:
Deposits = Demand + Capital = 9,400 + 100
Notice that the total Reserves are now the difference between the bank's Demand+Capital
deposits and the bank loans.
hmmm, still just not sure where this capital thing fits in exactly.
In double-entry bookkeeping, the accounts always balance. This is because every debit in one account is matched by credits in other accounts and vice versa.
This is the part that you want to describe with your mathematical equations. Hopefully, by adding the interest payment case to your equations, I have helped show you how *I* account for it.
Oh, but I never said the books don't balance, I said the
situation is unbalanced, two
very different things. If the books do not include something relevant then even if what is covered balances, the things the books do not cover might or might not ballance.
If D is the total deposits in the system and T the total debts, then T is always greater than D (T > D). The amount that T is greater than D is the interest, I. In the *books* used for FRB, there is no column for T or I (at least, not that I have seen, correct me if you know better).
Let's say X dollars is created by a government selling bonds to a central bank. The government then gives someone X dollars for some good or service. This someone puts the money in a bank.
The bank then has the (R, D, L) of (X, X, 0). Now, at this point the situation is already unbalanced, the money created is X, which is less than the debt T the government owes back! The books are ballanced though!
Then the bank does its thing and makes someone a loan of L (assuming that all rules are being followed here). The loan means that the triple becomes (X, X + L, L). Now, MMM does not cover how interest works as far as changing the triple, but it seems that the most logical possibility is that the interest subtracts from deposits and adds to reserves.
(R, D, L) -> (R + i, D - i, L)
The problem is banks charge a lot of interest! That and the imbalance that occurs due to government borrowing makes for a very unbalanced situation, with the banks being on the top no doubt.
Now, about the solution I presented.
I have to admit that there are two things I was incorrect about, so far as I can tell, up until now. The first is the formulas for excessive and required reserves. The second is in considering exactly how interest worked. In this error I think it was a lack of consideration in that I did not consider how interest worked and therefore how things might even out because of it (aka, the bank spend the i back into D from R as it were). As far as I can tell though the other fomulas involving (R,D,L) are correct (as per MMM).
That said, it is interesting that after looking at the solution I have advocated for I still think that it might be sound. The complaint given before about the government spending the interest into existence was that the banks would just use it to make more loans.
For starters, if the government spends money into existence instead of borrowing it (one of the main ideas in terms of Greenbacker notions btw), the main blackhole (a real debt blackhole as it were, instead of the kind-of debt blackhole of interest payments, which to be honest, is still in all likelyhood a serious black-hole in its own way -- more hardcore analysis required {or what of the other blackhole of debt, derivatives?}) would be eliminated.
But what of the new interest money?
Well, I am sure banks would use whatever money they can get their hands on to increase loans. The second part of the plank of ideas was to only have certain types of taxes be the only ones allowed, ever! (taxes on monopolies, financial instruments and profits accrued due to ownership of natural resources).
These taxes would not include the productive economy (ughgh, psionl0, you really should read Henry George. I am sure his ideas would nock your socks off. It is from his work I am advocating these types of taxes), no sales taxes, no wage taxes, as well as many others. The taxes I outlined would be on the main ones banks actually make money from. So while the government spends into existence interest, it taxes it into nothing back again. The rate of money creation / destruction would be of main concern then. But this would be determined by the people democratically choosing how many loans they want to go into.
To make sure banks do not make irresponsible loans (still possible in the system so far covered without any added rules), there would be two main types of reserves. The first would be a default reserve, the second a fractional reserve. The fractional reserve would act like how the total reserves acts now (with excessive and required reserves and all of that).
The default reserves would be in place so that if a borrower does not repay (subject to standardized default rules), the money comes from the default reserves. Since a bank would be allowed to move money from default to fractional reserves if requirements are met (I don't know, just think about what sounds reasonable here with the main hint being some of the default reserves would be covering loans, some of it would not, so the part that is not is rightfully the banks to do with what it wants), and defaulting would eat into this money, hopefully banks would act more responsibly.
The other thing that recently occured to me was that there is a problem when it comes to how banks currently foreclose on houses. If you spend 20 years on a 30 year home loan as a good borrower but you loose your house because you loose a job, it hardly seems right that the bank will just foreclose on your house, sell it as quickly as it can and then you loose that 20years of value.
I think the correct solution is that the house gets sold and from the proceeds of the sale the borrower gets whatever percent they spent into the loan, the bank a nominal fee (minus default reserve coverage), and whatever is left (if any is left) goes to the government to spend into the economy (apply as necessary to other types of loans). Any deficit comes from default reserves as noted parenthetically above. Benifit of the doubt goes to the borrower, and everyone gets what they rightly deserve.
But, now I come back to reality. The chances of the above ideas coming true are about a zillion to one. As an excercise in logic though it is at least fun to think about. I know it probably sounds complicated but it is really just taking the knowledge of how FRB works and changing FRB so that everyone gets what they really deserve.
{ Sorry for the wall of text above, I have at least tried to make it readable }
{ by breaking things up and doing my best to make it flow somewhat........ }
If total reserves go down to zero (they can't go negative) then we are in the middle of a bank run ("TAXPAYERS TO THE RESCUE!"

). Inter bank loans or loans from the fed can help a bank through a temporary liquidity problem but they can't bail out a failing bank.
Well, I think we are more or less on the same page here. I should note that if a bank even has its reserves go below required reserves too often (discount window to the rescue) the bank should be considered insolvent, put into recievership, and so on. I am sure Stephen K. Black has quite a number of things to say on this matter.
Books always balance. The key is the bank's capital account (excess of assets over liabilities). If this account does not have a credit balance then the bank has more liabilities than assets and is insolvent.
Sounds good to me, make sure and tell your democratic representatives and I will tell mine and then nothing much is likely to happen about it! Sorry, we have so many insolvant banks right now it is like whak-a-mole except no one seems to have the will to hammer them down.
Always happy to criticize!

Seriously though, take all the time you need to come to grips with your equations and mine. Once you have done this you should be able to return the favour (criticize me!)
Just did! Tomorrow I will start up on the other posts of yours. Sorry, best I could do. I kind of wanted to cover this first as it was on my mind. All the best to you all!
