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Bank balance sheet free response question | APⓇ Macroeconomics | Khan Academy - YouTube
Channel: Khan Academy
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the following is the balance sheet of
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first superior bank and so let's see on
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the asset side it has 200 of reserves
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and 1800
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of loans so its total assets are 2 000
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and then that should be the same as its
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liabilities and equity and we see here
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that it has two thousand dollars in
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demand deposits that's a liability
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because people can come to the bank and
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say hey i want that money these are
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checkable deposits they could even try
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to withdraw that money and since all of
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that two thousand dollars is on the
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liability side there is no equity right
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over here these two should sum up to two
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thousand dollars the same as you have on
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your asset side
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assume that the required reserve ratio
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is 10
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and just as a review that's the percent
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of deposits that the bank needs to keep
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as reserves and we can see that it's at
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that reserve ratio right now it has 2
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000
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in deposits and so it needs to keep ten
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percent as reserves ten percent of two
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thousand dollars is two hundred dollars
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so it's at its minimum reserves already
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part a says what is the dollar value of
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new loans that first superior bank can
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make explain
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pause this video and see if you can
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figure that out yourself
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well as i just mentioned this bank is
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already at its minimum reserves it's
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already loaned out as much as it could
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if you get two thousand dollars in
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deposits and you have a ten percent
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reserve ratio that means you can loan
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out ninety percent of that two thousand
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dollars and it has already loaned out
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ninety percent of the two thousand
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dollars so what is the dollar value of
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new loans that first superior bank can
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make well it's zero dollars zero dollars
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because
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because already
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already
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at
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minimum reserves
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minimum
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reserves
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all right let's do part b
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mr smith deposits 100 of cash in a
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demand deposit account in first superior
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bank
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calculate the maximum amount of new
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loans that first superior bank can now
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make so pause this video again and see
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if you can figure that out
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well there's a couple of ways you could
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think about it before mr smith makes
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that deposit we already saw in part a
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that first superior bank can't make any
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new loans and so now if it gets a
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hundred dollars of cash in a demand
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deposit account because the reserve
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ratio is 10
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the bank needs to keep 10 of that
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deposit as reserves and it can loan out
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the other ninety percent so you could
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just say well i could loan out ninety
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percent of that new deposit and so it'd
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be ninety percent
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times
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one hundred dollars
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which is equal to ninety dollars
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of new loans
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another way that you could think about
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it is after mr smith's deposit the
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demand deposits right over here goes to
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2100
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and that increase in liabilities is
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offset by an increase in assets it just
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got a hundred dollars of cash so the
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reserves go from two hundred dollars to
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three hundred dollars
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now this point first superior bank is
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clearly above its minimum reserve
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requirements 300 over 2100 is more than
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10
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so it can loan out some money how much
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can it loan out well it has to keep 10
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percent of this 2100 as reserves so it
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needs to keep
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210
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right over here and so that other 90 it
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could loan out and so this could be
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1890
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and so it can make 90
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in new loans
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as a result of mr smith's 100 cash
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deposit calculate the maximum change
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over time in each of the following in
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the banking system
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so part one is loans so what's the
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maximum change over time in the banking
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system of loans pause this video and try
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to figure it out
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well as we just said mr smith by
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depositing one hundred dollars
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first superior bank can make ninety
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dollars of loans so that would be ninety
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dollars of new loans but then whoever
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they loan that money to they could then
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deposit that in a bank and then that
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bank could depo could loan out 90 of
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that so then it would be zero plus 0.9
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times 90.
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now this bank that got 0.9 times 90
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dollars which is 81 dollars it can then
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loan out 90 of that so it's going to be
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plus 0.9 times this so 0.9 squared times
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90 and you just keep going like this and
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then this gives us essentially the
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equation for the multiplier which you
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might have memorized this is just going
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to be equal to
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90
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times 1
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over
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1
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minus you could say this 0.9 or you
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could say this is the same thing as 90
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times 1 over the reserve ratio which is
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0.1 and 1 over 0.1 is 10 so this is
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going to be equal to
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900 dollars
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now what is going to be the maximum
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change over time in demand deposits
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pause this video again and try to figure
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that out
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when mr smith first deposits that
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hundred dollars in cash at first
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superior bank that creates a hundred
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dollar increased demand deposit here on
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first superior bank's balance sheet so
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that is let me just write it this way so
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you have 100 but then we already said
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that first superior bank could loan out
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as much as 90 of that and whoever they
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loan that to they could put all of that
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into a bank as a demand deposit and so
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that's going to be plus 0.9 times 100
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and then that bank could then loan out
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0.9 times this and then whoever gets
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that loan that
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that could be they could deposit into
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the bank creating a demand deposit so
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plus 0.9
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squared times 100 and it keeps going on
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and on and on and you could just view
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this as this is going to be equal to 100
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times 1
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over 1 minus 0.9 which is the same thing
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as 100 times 1 over the reserve ratio
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and so this is just going to be 100
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times 10 which is going to be 1
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000
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part d
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as a result of mr smith's 100 cash
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deposit calculate the maximum change
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over time in the money supply so pause
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this video again and try to think about
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it
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so you might be tempted to say hey maybe
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that's just going to be the same thing
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as a total maximum change in demand
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deposits but we have to be very careful
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that first hundred dollars already
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existed as cash in the money supply
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the maximum change is everything else
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it's this part right over here
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mr smith deposits 100 in cash that's not
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new money but then the bank can loan out
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ninety percent of that so that's ninety
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dollars in new money that someone could
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use to then deposit another bank and so
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that other bank could then load out
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ninety percent of that ninety and we've
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seen this drill before that was the
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exact same calculation for part one
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right over here this is just going to be
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equal to 90 times one over the reserve
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ratio
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which is equal to 900 dollars
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part e provide one reason why the actual
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change in money supply can be smaller
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than the maximum change you identified
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in part d
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pause this video and see if you can
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figure that out
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well there's actually two good reasons
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why the actual change in money supply
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might be smaller than what we just
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calculated
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one reason is if banks decide to keep
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more than the minimum reserves
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so banks
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banks
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might
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keep
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more
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than
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minimum
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minimum
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reserves
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so you could imagine even though by law
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according to this world they have to
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keep a reserve ratio of 10 percent if on
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average the banks decide to keep a
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reserve ratio of 20 percent then every
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time they would loan out 80
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of whatever they get in deposits and so
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you would have a lower number here
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there's another world where the people
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who get the loans don't deposit all of
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that into the banking system so if you
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wanted a second reason we've already
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answered their question we've given one
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reason but a second reason is people
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might not deposit all of their funds in
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the banking system
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so i will leave you there
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