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you today what we want to do is continue our discussion of money monetary policy and so forth and what we're going to talk about is something called the money multiplier which is kind of an interesting term that's what I need is a money multiplier this is really it comes down to some mathematical formulas and stuff like that it's not very complicated not very difficult but surprisingly economists didn't figure this out until in the 1960s I think in the mid to late 1960s and so until then this whole process that we'll be talking about today this whole process was going on and people didn't really understand it and we will see when we get done with all of this that part of the story behind what don't happen during the Great Depression part of that story is explained once you understand this money multiplier process what we're gonna do is build up to some formulas but we don't start off with the formulas we start off with a common-sense kind of an example and once you understand the common-sense example then the formulas you know we're where they come from what they mean and how to interpret them so anyway what we're going to do today is sort of make up a simple little economy it's mainly a people and a banking interaction but a little economy and just talk about how things would work out in that situation and then we'll see this money multiplier emerge as I say it was until the 1960s that economists had this figured out and I read the article you know when this was first done and I thought yeah so this is obvious because I had learned it as an undergraduate and I didn't realize when I learned it as an undergraduate just how recent it would have been I would have thought oh 100 years ago people would understand this so it's really not been that long ago as I said this has been going on forever if I wanted I could tell the story and say oh this is the way it worked during the days of the Goldsmith's and you remember the idea in England and the goldsmith and people put gold in there and they get these warehouse receipts they could use as money well this process took place then or this process took place during the early days of the United States from 1776 up to 1863 you remember what we had was the state charter banks and they were issuing their own currency well this process occurred then and nowadays it occurs with the Federal Reserve and so it's really the Federal Reserve that is driving the process now but I don't want you to think there's anything about all of this money multiplier stuff that's new or recent or just confined to Federal Reserve days what really causes this all to happen what drives it is this process of fractional reserve banking the fact that banks do not keep 100% reserves when you make a deposit they hold some of that on reserve and loan the rest out why do they make the loans for their profits and we've talked about how the high interest rate on bank loans the general idea is this and then we'll get into it is here's the economy and here's the Federal Reserve and this is our modern-day institution that we'll use as the outside agent the Federal Reserve injects a dollar let's say into the economy we'll call these bank reserves and then what happens is we notice that hey within the economy there's an increase in the money supply of let's say $3 and it's like how could this happen how could $1 become $3 and answers' there's a multiplier and how much is the multiplier is 3 in this particular case and I'm using these numbers as just you know hypotheticals now people didn't know about this before because you know if we went back 200 years ago and you told somebody hey $1 gets injected in the economy it turns into $3.00 people would have started scratching her head and said how can that be and they would have gone to work on that and figured out the answer because the math is not hard the only thing is MS a hundred years ago nobody knew these numbers there was nobody measuring the money supply and that being the case you go OK money comes in the economy there it is and that's the end of the story well the thing is if you don't measure how the money supply is then you can't realize that there's this money multiplier process at work it was not until 1963 I believe as a year of publication that two people Milton Friedman and a woman named Anna Schwartz published a book monetary history of the United States and this monetary history of the United States went back to the time of the Civil War and came forward to 1960 and what they said is this and they wrote this monetary history and told all about money and how it affected the economy but before they could do that they had to have money numbers yeah how much was the money supply and what they found out is you can't write a story of the monetary history of the United States without knowing how much money there was and nobody knew and so what they did is they went back this is a monumental task they went back and got records from old banks I mean banks that were still in operation banks that had gone bankrupt and so forth but they collected all of these numbers that were out there and would look at the banks balance sheets to find out basically how much were deposits and so forth and they put all these numbers together for thousands of banks at one point there were 30,000 banks in the United States and they put all these numbers together and said here's a money supply series all the way from the time of the Civil War up to modern days 1960 and so it's at that point that you could say oh look at this there's a certain amount of money being put into the economy by our monetary authorities and yet the money supply is a multiple of that how can that be and then you'd start going to work and say oh I got the answer well 1963 is when this book was published and so what I'm saying to you is five years later then the article came out that said hey here's the money multiplier here's why it occurs here's the formula for it and so forth and this stuff that we're getting ready to talk about it's essentially the same way that the Federal Reserve officials who make policy it's the same discussion that they have it's not like we're giving you the easy version of it here and there's a harder version later on you know that the that the authorities rely on anyway so what we're going to do is we're gonna start off with the Fed injects a thousand dollars into the economy we'll talk about how that is in a minute and then I want to make a couple of other assumptions okay the first one is this is that banks hold 10% of checking deposit liabilities on reserve now there's two kinds of reserves you remember this when we talked about the bank's balance sheet as required reserves and excess reserves so I'm just saying that this 10% is the total so it includes both required reserves and excess reserves and right now we're not going to distinguish between those two just 10% on reserve okay and then the other assumption we make is that people and companies divide their monetary assets 20% currency or capital C and 80% checking deposits capital D I guess the other thing I will say is this is that banks loan excess reserves why for interest and so this is just the profit motive that's motivating them that is to say if you put a hundred dollars in the bank and bankers hold ten percent reserves of that hundred dollars then there's ninety dollars of the hundred that's an excess reserve that they say I'm gonna loan that out okay so this will motivate or I mean this will underlie everything we do okay and if you see me make a mistake on this you'd be sure and tell me so let's start off I'm just gonna call these transaction 1 and here's transaction 1 now how does the Federal Reserve inject dollars into the economy well you know it's possible they could do anything that could fly airplanes or a helicopter overhead and just throw a thousand dollars out too bad they don't cuz I'd like to find out but that's not what they do what they do is they purchase something they go out and buy an asset and pay with a thousand dollars okay now what assets do they buy in real life they buy Treasury securities okay Treasury bills Treasury notes Treasury bonds mainly as what they buy but we don't want to get into that now we'll come back to that later on we will assume that when they start this off just to make it an easier simpler discussion we will assume that the Federal Reserve just buys something from someone let's say a Treasury bond that person gives a Treasury bond and let's just say the Federal Reserve prints up a thousand dollars in cash and says here you go and so the Fed buys a bond and pays with $1000 your currency see this transaction increases the money supply by how much $1,000 you remember what the money supply is I'll put it someplace up here money supply is equal to currency plus checking deposits I also said traveler's checks but the amount in traveler's checks is tiny six seven eight billion dollars out of a money supply exceeding a trillion dollars so we're just gonna leave out the traveler's checks for now okay so anyway currency and checking deposits and so what's happened in our story here is that the Federal Reserve said to somebody here's a thousand dollars in currency and this is how this whole process gets started okay this is how money gets into our economy this is a Federal Reserve gets the ball rolling that's the central bank and this increases the money supply by a thousand dollars and this is the end of the story back in the old days that's what people thought happened oh look we get $1,000 injected into economy there's a thousand dollars the multiplier is one you put in a thousand there is a thousand end of story okay but what happens next transaction to person who receives this money deposits at the bank okay how much $800 deposit but if you'll remember we've got this assumption that people only deposit 80% and then they keep two hundred dollars in currency now let's look at this what's the impact on the money supply in transaction 2 this person received a thousand dollars so the money supply went up now what this person all the person did it said you know I think I'll keep hold on to two hundred to that and I'll put the other 800 in the bank the total money supply did not change all that happened is we got $800 less in currency and $800 more in checking deposits so transaction two has no effect on the money supply okay and that's the way it is in real life if you do business with your bank put money into your checking account or take it out that doesn't affect the money supply it affects the composition of the money supply transaction three bank and we'll just work with one bank here so that we don't get involved in banks and shifting funds among themselves the bank I'll say hey not just bank the bank holds reserves of 10% of the deposit equals how much $80 are you with me on that it's an $800 deposit so we've got a hold reserves because that's our assumption of 10% and so then it says hey we got $800 coming in somebody slid $800 across the counter to us that's vault cash those are our reserves we only have decided to hold 10% of those we've got seven hundred and twenty dollars in cash what should we do with this answer we loan it out and loans this is the 90 percent or 720 dollars this making sense to you why do they do that for the interest okay maybe you're getting 8% on the loan and 0% on the vault cash that's pretty simple you don't want to keep all this money just laying around okay so here's the key and here's what's driving our multiplier the person who came into the bank and borrowed that money they walk out with 720 bucks okay so this increases the money supply increased money supply by 720 dollars hey thank you 720 bucks and so our money supply was a thousand dollars and now it's risen by 720 dollars what makes this possible is fractional reserve banking the banks only holding 10% and it loans out 90% and so now there's seven hundred twenty dollars the money supply at this point is one thousand seven hundred twenty dollars okay so here's transaction for the borrower of 720 spins it that makes sense right that's why people borrow money I could say to purchase goods and services what goods and services makes no difference now transaction four is moving money from one person to another right if I buy a go-cart from you for seven hundred twenty dollars I give you seven hundred twenty dollars you give me go-karts the money supply doesn't change and nor does the supply of go-karts it doesn't change the ownership of those assets changes okay so then no change in money spot is still seventeen hundred and twenty dollars transaction five the seller of the goods and services this person that we just talked about deposits what 80 percent of the 720 and the bank and holds 20 percent because that was our assumption as of our monetary assets will keep 20 percent as currency keep 20% as currency and 80% in the bank okay and so if we do the calculation 80% of the 720 deposits equal 500 $18.40 and currency is 20% what would it be 144 dollars what impact does this have on the money supply huh I just received 720 from somebody else and now I'm just deciding how much to hold in cash how much to put in the bank it doesn't affect the money spy transaction fives really like transaction - okay where all I do is decide how much to hold on to and how much to put in the bank so no effect on the money supply transaction six is that right six yeah what's the banker do bank holds 10% of deposit on reserve hey how much is that pardon me by how much I'm sorry 576 well I'm glad that somebody's checking yeah that was a test I told you didn't affect the money supply 10% of the deposit on reserve how much is that fifty seven dollars and sixty cents did I do wrong no I know what I did wrong so 5760 and then it loans out the rest right loans 90% how much is that point nine times the 726 48 I'll put that in red pardon me okay okay okay hey you know this is all a test right 0.9 times you know I'm getting so 576 that's exactly right five eighteen forty there's the number I had a moment ago I don't know how I got one step ahead five eighteen forty is that right this goes into somebody's check into their hands here you go somebody comes in says hey I'd like to apply for a loan how much do you want five hundred eighteen dollars and forty cents here you go and so this increases the money supply by five eighteen forty how much is the money supply now a moment ago it was seventeen twenty and so now it's twenty two hundred thirty eight dollars and forty cents twenty two did I say thirty eight forty now there's more steps to all this but right now if we had to calculate what's the multiplier a thousand dollars got pushed into the economy we've now got $2,200 2238 dollars in the money supply the multiplier is already two point two three eight four what's making this happen it's the fact that we're holding fractional reserves I'm lending the rest and what would make a loan that adds to the money supply okay I'm gonna erase this just because I don't want a lot of this sort of trivial stuff put on here so transactions seven the borrower spins five eighteen forty to buy goods and services okay we're gonna buy goods and services what are we gonna buy I don't know five hundred eighteen dollars and forty cents worth of stuff how much does that affect the money supply anybody zero okay so transaction eight the seller that is of the goods and services deposits 80 percent of the five eighteen forty in the bank and holds twenty percent of the five eighteen forty and so we'll see if we can figure out how much that is five eighteen point four times point two twenty percent so this the currency Holdings you know I just saw and forgot one hundred and three dollars and sixty eight cents is that right no okay and deposits for 1472 this alright looks right that's 80% how much did this transaction affect the money supply zero right you get some money in your hands five hundred and eighteen dollars and forty cents and you hold onto some of it and you put some in the bank and what you put in the bank is money supply just a different form of money supply checking account money supply okay and then transaction nine the bank receives four 1472 on deposit reserves ten percent
f that so forty one dollars and forty seven cents right and loans three hundred seventy-three dollars and twenty five cents is this right I think it is and this loan is made to somebody they slide that across the counter to the borrower and that increases the money supply by 317 25 and we had money supply a moment ago of whatever I said $2,200 now it's over $2,500 $2,600 I'm gonna do one or two more of these but I want to go back and just show this pattern that repeats here's transaction three the bank made a loan of a deposit well let me first of all transaction two was there was a deposit at the bank and then if I jump three transactions again there's another deposit okay we get a deposit in the bank and if we jump ahead three more there's a deposit in the bank now we move down one two transaction three the banker that received that deposit holds some reserves at 10% and makes a loan of 90% and that loan of 90% increases the money supply and if we jump three transactions ahead a bank receives a deposit hold someone reserved and makes a loan of 90% and that increases the money supply and now we've got transaction nine a bank receives a deposit holds ninety per ten percent makes a loan of 90 percent increases the money supply guess what's going to happen in transaction twelve it will increase the money supply you've been reading ahead okay let's do a couple more and then I will reveal the secrets transaction ten transaction tens going to look like transaction seven three transactions earlier the borrower receives how much 370 325 the bank slides it across the counter here's 370 325 and a person says thank you how much does that affect the money supply none and spins it right that's what we do with money that's what I do with all my money in just a little bit more transaction 11 which explains the whole idea credit transaction 11 then the seller of the goods and services sold things to that borrower and right that's why we borrow money from the bank you know you going to the bank saying I got a plan I won't buy a car I want to buy a motorcycle one buy a house or a business manager goes in says I want to borrow some money to buy a delivery truck or a dump truck or a road grader or something like this we go in and take out these loans so we can't spend that money and so every time we've got a borrower then the next thing that happens is that borrower takes that money and buy something so the seller what receives 370 325 and deposits 80% of it how much is that deposit 0.8 did you say to 9860 that's what I got and the rest is in currency 7465 how much did this transaction affect the money spike not at all I got some money if I'm the seller I got some money from that person that bought merchandise for me I put some of it in a bank and what I have in the bank now my checking account is money so I just transformed one form of money cash into another form checking account money okay transaction twelve now we've already heard from hope what's going to happen next it's like transaction nine the bank pulls reserves how much 10% of the deposit that deposit was to 9860 so I'll write the word down reserves holds reserves 10% of 298 60 $29 and 86 cents and loans 90% right to 6874 and loans 268 dollars and 74 cents and that increases the money supply let's go through here quickly to 6874 I'm gonna add these amounts up that the money supply is going up plus three seventy three twenty five plus five fifteen five eighteen forty plus what was our last one seven twenty plus $1,000 2880 thirty-nine is I wouldn't anybody else say that yeah I think you've been rounding off too much 2880 thirty-nine and of course we're not done but at this point the money supply when I say twenty eighty eighty thirty-nine if we were at this point somebody said hey how much is the multiplier I would say this a thousand becomes two thousand eight hundred eighty dollars and thirty nine cents then the multiplier would be two point eight eight zero three nine now that's enough of that we can go on by the way here's in real life you get to a point where bankers say you know it's not worth doing the paperwork to make a loan of eleven dollars or whatever and that's what's happening is each one of these loans get smaller here it was 725 18 414 373 two nineties the 268 the numbers keep getting smaller and smaller and smaller and you'll get to a point where a banker says no I'm not going to do it but suppose we took this out and right down to the last penny when there you go oh we have one penny over and above that 10% make a one penny loan and then we say now we're done okay and that's what would happen each time each one of these numbers is 72% as big as the one before here's what's happening and I'll explain to you why this is 72% let's say that we started off with $100 and then 20% of that hundred dollars would be held as cash and the banker would only receive 80 percent of that because I mean that's what we're doing is we're talking about how big are these loans the banker doesn't get a chance to loan out 20% because that person puts it in their pocket there's only 80 percent that goes into the bank and then the bank takes another 10% and sets it aside and reserves and there's only 90 percent of what remains that could be loaned out this is a these are called drains this is the currency drain that is to say it's not available for additional loans and then this is a reserve drain sort of like a bathtub we've got a couple of holes in here and we're draining this these funds out of the banking system where the bank just cannot lend it all out and so anyway what is 80 percent times 90 percent is 72 percent and so each time we go one more round and we give people an opportunity to hold some currency and bankers a chance to hold some reserves then there's only 72 percent as much available for lending the next time around and this is obvious this what I said okay let's start off with a hundred percent or a hundred dollars or whatever we start with a thousand but let's just start off with this and say hey how about just lend it and Linda and Linda it and no that can't happen because what happens to that hundred dollars is once somebody gets it into their hand I've got a hundred dollars in my hand then when I go to the bank I say you know I'm not giving you this full hundred dollars I'm gonna put in my pocket and I'm only going to deposit $80 80% and so the banker says thank you here comes 80% in and then the banker says oh of the 80% that came in I'm going to set aside the banker didn't know that was 80% but of the $80 that came in I'm gonna set aside 10% in reserve and I've only got 90 percent now of what remains for loans and so this if you've came at the hundred dollars then this becomes $80 is deposited and then 10 percent of that $8 would be set aside and then $72 would be available to make a loan and so that hundred dollars in one round becomes the next loan is 72 and so you can see we started with a thousand this became 720 the next time around and there's no question about that being 72 percent but 720 times 0.72 equals 5 1840 where is that and then that five 1840 ends up being well loaned out to somebody that somebody spins it and the next person in holds 20 percent makes a deposit of 80 percent of the five 1840 the banker then takes that deposit come in and holds 10% loans out 90% and so we're didn't get down to that five 1840 times 72 percent is what oh well we already had four fourteen seventy two and then the four 1472 is a loan somebody borrows it spins it the recipient puts aside 20 percent deposits 80 percent the banker sets aside 10% loans 90 percent so now we got 72 percent of that 373 then I've got point two four eight you know it rounds off to 25 cents 373 25 and then times 0.72 equals to 6874 is that what we have so what would we have in transaction 15 times 0.72 equals the next one be 193 dollars and 49 cents that would be transaction would I say 15 transaction 18 and these are the only ones that affect the money survived when a loan is made so this is times point 7 2 equals 1 39 31 and you can see this is going to get down to a penny if we go long enough in real life of course it takes a few minutes to figure out do all the paperwork for a loan and in real life the banker gets a percent like 8 percent interest and so in real life a banker goes just a second I'm gonna get 10 dollars in interest on this loan for a whole year no I don't think I want to mess with it that's in but we're trying to work out the theoretical possibility and also the Federal Reserve's Reserve doesn't start off with a thousand they start off with a billion and so these numbers are a million times as big this would be 139 million dollars and so banks gonna continue making those loans somebody had their hand up well they can make a loan of one penny will they I don't know it just depends on the banker and you know like if let's say that you're a banker and here's your best customer and this customers been doing business with a few years and they bring in their son or daughter and said you know Joanie wants to borrow three dollars would you say no would you just go no Joanie I don't care just get out of here did you give her three dollars but your customer wants you to make a loan what would you do you will make a loan of three dollars what if Joanie want to borrow three cents you know what you do transaction 21 how much Joanie's gonna get $100 and 31 cents this time 72 percent as much every time what are these all add up to well only I know and we'll talk about that in just a moment by the way all of these other things are 72 percent as much too so for example there's the bank holding reserves of $80 in this round three if we go three rounds later from transaction three to transaction six this is 80% of the 7mm order than $80 72% of that's this and then if we go to transaction nine 72 percent of fifty seven sixty is 41 47 and so because of these two drains that we're talking about every round just the entire thing every little piece of this is being scaled down by except for the money supply because the money supply is growing but the changes in the money supply and the changes of bank reserves and the amount of currency that people hold where was the currency there's two hundred dollars and seventy two percent that's one hundred and forty-four dollars where is it here mmm holds 28 well there's one hundred and forty-four dollars and then three transactions later eight then this would be 72 percent of 144 s103 68 and so forth everything is 72 percent is big it's sort of like a pyramid only its inverted okay we started off with a thousand and then 720 and then whatever I said 500 mmm $76 is that right Oh 518 40 and so forth and finally these are gonna get down to where Joanie gets her one penny loan and then we say that's the end yes we could start lending out fractions of a penny does that legal yeah anything legal you know we used to have in this state fractions of a penny you know when you see gasoline it would say like three dollars and 4.9 but there that's point nine nine tenths of a cent there used to be tokens in this state that were what's it called anybody know it was a mill a mill is one tenth of a penny and they never used them when I was growing up but I saw him before and there was a red one and it was about the size of a nickel but it was made of plastic there was a red one and that was one mill and then I don't have a green marker but there was a green one and that was five mills I ridiculous that's back when something like a pack of cigarettes was you know 14 cents or whatever right didn't it start charging you sales tax on 14 cents and then you start getting into fractional pennies anyway have any of you seen those mmm Mills nobody my I had an aunt and she passed away and we were going through and sort of cleaning out her house and putting everything together and she had these roles that you've seen like quarters rolled up or something like that and and I said oh look there are you know rolls of coins and so I picked them up and they didn't weigh anything and so I opened up to look inside and it was these mill tokens and red ones and green ones really kind of weird I mean you know anyway so made by the state yeah anyway sort of a private money wasn't it wasn't a national currency so anyway and so if we wanted to add all these up we could obviously just do a huge number of these transactions 80 of them or whatever and add them all up but if once we know about this process then we don't have to do that here's what we have and we're gonna do some more of this next time but what we have is this is that we have the money supply is equal to and this is by the way currency plus checking deposits traveler's checks are not a part of it I'm gonna put a B here this is from the Fed and I said that that's only under the institutions we have today goldsmith days it would have been whatever the gold miners fine and works its way into the Goldsmith's shop and so forth times and now I'm gonna have some brackets in the numerator one plus the ratio of check of currency to checking deposits and this is determined by the public right you decide how much currency to hold you decide how much to keep your checking deposit and our story here what it was that ratios anybody remember it was twenty over eighty so this is 0.25 that's just what I assumed now in real life all of us are different all of us make our own choice but in real life this number is pretty stable from one month to the next okay and in the denominator C over D again so here that would be 0.25 plus the ratio of bank reserves over checking deposits and this is at banks bankers decide how much reserves to hold bankers and the Fed as a ratio of checking deposits and so here what we had was ten to a hundred that is to say if $100 deposits made in the bank they will hold $10 on reserve this is point one zero and now get your calculators out so here's what we have B this is from the feds a thousand dollars times 1.25 / 0.35 how much is 1.25 / 0.35 three point five seven then what one four don't hold back let's make it three okay so $1,000 times that is equal to three thousand five hundred seventy one dollars and forty three cents because I know what your next question is and here it is do we have to know that yeah one plus the currency deposit ratio divided by the currency deposit ratio and the reserve deposit ratio and final point this reserve deposit ratio is partly set by the Federal Reserve saying you must hold certain reserves but also bankers can decide to hold some excess reserves that they want were you going to say something yes I'll finish that next time so long
