Help me understand how money is created via lending

I have a new idea for a business:  I will borrow tractors from farmers when they don't need them, paying them a small fee.  Then, I will lend them out to farmers who do need them, collecting enough to cover the fee I pay plus to make a profit for myself.  After borrowing one tractor, I don't think it will be safe to lend it out, because I don't know if the owner will want it back in a short time or a long time.  Therefore, I will just store the first tractor I borrow, and lend out the next nine, keeping the one in reserve.

Question:  after I have borrowed ten tractors and lent nine, how many tractors are in existence?  The answer seems obvious:  ten, one in my reserve and nine out on loan.  But while this seems obvious when dealing with tractors, when it comes to money I get a quite different answer.  After borrowing $10 and lending $9, I am told that there are $19 in existence.  This troubles me.

I used to think I understood the creation of money through borrowing, partly because I had seen it explained through the example of goldsmiths.  The story goes (I am told this is true) that people would leave their gold with goldsmiths for safe keeping.  In exchange, the goldsmith would give them a piece of paper entitling the bearer to however many ounces of gold had been deposited.  The gold's owner could keep the paper and collect his gold later, or he could trade it away like money for whatever the current price of gold entitled him.  Any bearer could redeem the paper.

Goldsmiths realized that this gave them an excellent opportunity to make money.  If someone needed cash, they could give the person a piece of paper exactly as though he had deposited gold, which the person could then spend like money.  (Of course, the goldsmith also kept an IOU from the borrower requiring repayment with interest of the gold's value.)  Since no one wanted to carry around actual gold, the certificates issued by the goldsmith were essentially money.  And since he could write certificates for more gold than he actually had in storage, he was effectively creating money by lending.  Of course, he was subject to a run on his "bank" if too many certificates were redeemed at the same time.  It would be a matter of chance whether he could collect from his borrowers and buy enough gold to refill his stores before going bankrupt.

This scenario makes perfect sense to me, but it is not the same scenario that we have with modern banking, at least as far as I can tell.  The "demand deposits" (checking accounts) that banks hold are not like the goldsmith's gold, because the bank does not issue certificates redeemable for money.  Instead, a person writes a check to draw on his deposits.  This check is made payable to a specific person and is valid only for a specific time.  Once the recipient cashes or deposits the check, the money is withdrawn from the person's checking account and deposited elsewhere.  The bank can, therefore, lend more money than it has in reserve, but the depositors cannot spend their money without affecting the bank's reserves.  In the goldsmith's case, the certificates can circulate indefinitely and never affect the goldsmith; in a modern bank, once a depositor spends his money, it is gone from the bank and is not available to be loaned to anyone else.  Or, to look at it another way, a borrower can spend the money the bank gives him only so long as depositors leave enough cash for the bank to cover the loan.  If they don't, there is a run on the bank -- but in a very different sense from a run on the goldsmith's bank.  In the goldsmith's case, he does not actually have reserves to cover the demands, and never did.  In the bank's case, the money is attached to specific borrowers whose loans can be called in.  The classic explanation from "A Wonderful Life" is that the depositors' money is not at the bank, it's on loan to their neighbours in the form of mortgages.  The money for the depositors exists, but it is already being used.

In one sense, you could say that banks and goldsmiths are doing the same thing:  both have books that balance, because the amount they owe in deposits is equal to the amount they are owed in loans.  The crucial difference is that banks must gets the deposits before it makes the loans.  The goldsmith makes the loans first, and is thus creating money where it didn't exist previously.

There are a couple of ways I can see how the modern scenario could be the equivalent of the practice of goldsmiths.  One is if bank notes circulated just like cash.  That's the goldsmiths' situation:  their notes that say "pay bearer X ounces of gold" are as good as cash (or close to it), and since no one wants to carry actual gold around, there is no reason for the notes to be redeemed under normal circumstances.  That's not how modern banking works, however.  If you write a check, it gets deposited at a different bank and the money withdrawn from your bank almost immediately.

There is, admittedly, a period when you have purchased something with a check but your bank has not yet handed over the money, and in that sense there is extra money in circulation for a period of time:  you purchased something, but your bank still had the cash to lend on the money market overnight -- the money effectively exists in two places.  This might be what people are talking about, but I don't think so.  First, the time that a check has to wait to be processed is short and getting shorter all the time.  Automated clearing houses have cut it down to a couple of days in most cases.  Second, only a small amount of money is normally in this transitional state.  You write a check for $100, even though you may have several thousand in your bank; by the time you write another check, your first check has cleared.  This is the case for all but the largest purchases (cars, down payments on houses), where you will pull most of the money out of your checking account.

Credit cards function similarly.  In their case, the money is transferred from the issuing bank to the merchant in a short period of time, I assume faster than checks since it is all electronic.  You don't pay the money back until the end of the month, but the time between your purchase and the transfer of money is quite short.  The bank forwards you the money in exchange for fees from the merchant, plus the chance to charge high interest rates if you don't pay off your balance.

There are some rare cases in which bank notes can circulate much like cash.  Traveller's checks, for instance, work that way if I understand correctly.  You can pay someone with a traveller's check, and that person can, in turn, sign it over to another party, and so on indefinitely.  I don't think this happens very often, and it certainly isn't a major part of the money in the economy, but the principle works.

Theoretically, other bank notes can also circulate.  Treasury bills are so safe that they can be used much like cash, and I believe they are sometimes exchanged in financial transactions by major corporations.  Again, I don't think this is a major part of the money supply, and it certainly has little to do with the creation of money through lending as explained in my college Money and Banking textbook.

The one place where lending clearly acts as a form of creating money is lending to sell a product.  Whether you take out a loan from the car dealer, the furniture store, or purchase groceries on store credit (rare now but apparently common in the past), you are spending money that doesn't exist.  No one has to give up money for you to make the purchase; instead, the store itself is providing you with a good on the promise of future payment.  (I'm not actually sure if this is even how store credit works any more; car dealers may need to procure actual cash to pay for the car which is it only borrowing.  But it certainly could theoretically sell you a car without getting any actual money up front.)  This may actually be a major part of the economy for all I know, but it is completely different from the model of banks creating money by lending to people.

The second way I can see borrowing as a way to create money is in the case of a bank that can actually print the money that it lends out -- i.e., the Federal Reserve.  Most of its loans don't involve physical cash, but rather theoretical accounts, but the premise is the same.  A Federal Reserve bank can credit a private bank on its books, creating a debit and credit out of thin air, and that is certainly a form of creating money.  This is much like the goldsmiths' case.  It is as though you go to the bank and ask to borrow money, and the bank, instead of securing deposits to lend you, simply goes in the back and prints a stack of bills.  Voila!  You can borrow money, and the bank doesn't need to worry about a run on its assets.

This, the example of the Fed, is probably the simplest and clearest explanation of how lending creates money.  I understand it clearly.  The problem is that it only works for the Federal Reserve, and not for private banks.  That is not how the creation of most money comes about, and it is not how the textbook explains it, since the textbook refers specifically to private banks.

So I am still confused.  I understand how money can be created by lending in various circumstances -- goldsmiths, store credit, and the Federal Reserve -- but none of it corresponds to the way I have seen it explained, either in my college course or anywhere on the internet that I have looked.  Those explanation look to me like we are conjuring tractors from thin air.  If anyone can help clear up my confusion, I would be glad to get your help.

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