Consumption function basics

WEBVTT
Kind: captions
Language: en

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Male: What I want to do in
this video is introduce you

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to the idea of a consumption function.

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It's a very simple idea.

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It's really just the notion that income,

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income in aggregate in an economy

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can drive consumption in
aggregate in an economy.

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Just to make things
tangible, I will construct

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a consumption function for
a hypothetical economy,

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and we can debate whether we
can construct a better one.

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All the numbers don't have to be exactly

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what I'm about to do, but this is just

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to make things concrete in your mind.

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Maybe we have a hypothetical economy

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where consumption is
going to be equal to ...

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well, maybe there's some
base level of consumption

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even if there's no aggregate
income in our economy.

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It's hard to image, but
let's say there isn't.

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There will still be consumption.

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Maybe people can do it by
digging into their savings.

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They're essentially using resources

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that they've already
accumulated in some way.

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Let's say that base level of consumption,

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let's call that 500.

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It could be billions of
dollars or gold coins

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or clamshells or whatever the unit

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of measuring economic
activity is in our economy.

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That's our base level of consumption.

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Then let's say if there
is some aggregate income,

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people will spend 60% of it.

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I'm just picking these
numbers somewhat arbitrarily.

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Let's say if there's some above and beyond

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the base level, they're going to spend 0.6

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of any aggregate income they have.

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Actually, to be a little
bit more particular,

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I'll write not just income,
I'll write disposable income.

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I'll want to do that in a different color.

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They will ... that's
not a different color.

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Above and beyond the base level,

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they'll spend 60% of
their disposable income.

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I make the distinction,
just to clarify our model,

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between income and disposable income

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because all of the aggregate
income in an economy

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does not end up in consumers' pockets.

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Just for a simplification, you might say,

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"Yeah, some of it ends
up in firms' pockets,"

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but the firms, at the end of the day,

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are owned by individuals, so it can end up

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in individuals' or consumers' pockets.

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But some of it goes off to the government.

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When you think about
income, and if you spend

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any time looking at
your pay stub this will

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become familiar to you,
you have your income

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but you don't end up
with all of that in your

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checking account or your pocket

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or your savings account.

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A good fraction of that
is taken out for taxes.

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What you have left over when you subtract

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taxes out of income, that
is your disposable income.

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That's why I write this
here because that's actually

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a more reasonable thing to say.

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People will spend 60% of
their disposable income.

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They obviously can't spend
a fraction of stuff that

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they don't have, the stuff
that's taken out for taxes.

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Just to visualize this, we can draw it.

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This will be a line.

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This might ring a bell from
your early algebra days.

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Just the variables are different.

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Instead of a y, we have a c,

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but that's still the dependent variable.

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It's a function of disposable income.

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In algebra you'll often call
this the independent variable.

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The most typical variable is x.

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It's really the same idea over here.

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Let me draw this a little bit neater.

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We can graph this, what's
essentially going to be a line.

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It doesn't have to be a line.

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We just constructed a consumption function

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that happens to be a line.

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This is consumption right over
here in the vertical axis.

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That could be in billions of dollars

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or clamshells or whatever else.

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Then right over here we
have disposable income.

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If there is zero disposable income,

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maybe I'll draw a little table over here.

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This is I'll call it disposable income

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and this is consumption.

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If there's zero disposable income,

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then this whole term right over here is 0.

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Then you have 500 billion dollars,

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or whatever our units
are, of base consumption.

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This would correspond to
this point right over here.

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In the horizontal axis
you don't move at all

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because this is 0.

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Vertical axis is 500.

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So you have 500.

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Let's say disposable income is 1,000

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whatever our units are.

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So this is 500.

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Let's say this is 1,000
billion clamshells.

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This could be in billions of clamshells.

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I don't want to keep having to say that

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over and over again.

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What is our consumption
going to be in our units?

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Our consumption is going to be equal to

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500 + 0.6 x 1,000 which is equal to

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500 + 600 which is equal to 1,100.

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That would correspond,
this right over here,

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would correspond to; so 1,000,

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so this might be 1,000 on this axis

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so this would be 1,100 to
this point right over here.

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That would be the
coordinate: 1,000; 1,100.

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This is a line.

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Two points make a line.

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In this particular case we have

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a consumption function that looks

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something like this.

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We picked two points to draw it.

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If you remember a little
bit of your slope,

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you could view this as your y intercept,

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or in this case your c intercept,

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and that your slope would be the .6,

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and we'll talk more about
that in future videos

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when we dig into the marginal propensity

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to consume a little bit more.

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But the one thing I just want to highlight

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is it's a very simple idea.

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This does not have to be
the consumption function.

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The consumption functions
that we tend to study

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in introductory economics
classes will look like this.

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It will be a line that
has some intersection,

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some base level of consumption.

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But one could argue it
might be very different.

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Maybe the consumption
function looks like this.

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Maybe when income is low,

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for every incremental dollar of income,

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people are probably going to spend a lot.

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As they become richer
and richer and richer,

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as their income goes higher and higher,

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they're going to spend less and less

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a fraction of their disposable income.

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Essentially what I'm describing here

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is a marginal propensity
to consume changes.

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In our first model, we had a very basic

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marginal propensity to consume.

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It was constant.

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For every incremental
dollar, .6 of that got spent.

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So we had a marginal propensity to consume

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that was constant of 0.6.

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Marginal propensity to consume.

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But, you could argue, that maybe a more

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complex model is justified.

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That when you have a very high marginal

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propensity to consume, when
people have very little

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because they have a very
low standard of living,

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they really want to just
get a little bit more

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just so they can live a decent life,

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but as they get more and
more income they say,

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"Hey, I'm starting to max
out my standard of living,

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"I'll save more and more
of it for a rainy day."


Mathy version of MPC and multiplier (optional)

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Kind: captions
Language: en

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In this video I'm going to
work through the exact same

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scenario that we saw in the last video

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but it will be a little bit more mathy.

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The reason why I'm going to make it

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a little bit more mathy

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is so that you see it's a same idea

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it's just going to have a
little bit more cryptic notation

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but it allows us to generalize

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the ideas that we saw in the last video.

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Let's just assume, instead of saying

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that the marginal propensity to consume

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in our little island is .6,

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let's just say our marginal
propensity to consume is C.

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What we want to do is
we want to figure out,

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given some initial change in expenditure

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and this guy's change in expenditure

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will be this guy's change in income.

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That cycle is round and round

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due to the multiplier effect.

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What is going to be the
total change in our GDP?

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This is what we care about,

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we care about our total change in the GDP.

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Y could be viewed as expenditure

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or it could be viewed as income

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depending on how you think about things.

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Let's say this guy, instead
of saying that's he's going to

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spend all in the thousand dollars,

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let's just call his incremental
change in expenditure,

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let's just call that delta Y nought.

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Delta just means change in,

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and Y, we could view this
as aggregate expenditure.

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I'm putting this little zero here.

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This is our first iteration,

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this is the first time that
we're doing one these deltas.

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Then as we keep doing them
we're going to have Y1,

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Y2, Y3 and so on and so forth.

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If we think about the total change in GDP,

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you're definitely going to have this.

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In the last example this was $1000.

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This guy is $1000 expenditures,

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this guy is a $1000 income.

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Then you have delta Y nought.

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Then we saw that this guy,

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his marginal propensity to consume is C.

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He's going to spend of the income he gets,

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he's going to spend C times that.

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He's now going to do Delta Y1.

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This is the next incremental
bump in our GDP we're seeing

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and that's going to be equal
to C times what he just got.

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Now, after doing the zero
iteration in the first iteration

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our total change is going to be ...

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Actually let me write it this way,

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times delta Y1, and delta Y1,
this is just the same thing

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as C x delta Y nought.

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It's fancy notation

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but it's just saying
something fairly basic,

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The exact same thing that
we said in the last video.

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Now this guy, all of a sudden,

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above and beyond what he spent
in that zeroth iteration,

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he's now getting delta Y1.

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He has a marginal propensity to consume,

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we're just assuming of C.

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Now he is going to spend C times that.

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He's now going to make an expenditure of,

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I'll do this just in the same color,

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he's now going to do delta Y2

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which is equal to C x delta Y1.

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Now we have delta Y2,
this new incremental bump

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and they're getting smaller
and smaller and smaller

00:02:53.477 --> 00:02:55.404
but we can go an infinite number of times.

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Just to remember what this is,

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delta Y2 is the same
thing as C x delta Y1.

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Delta Y1 is the same thing
as C x delta Y nought.

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So this thing right over here,

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this whole thing could be written as

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C^2 x delta Y nought.

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This right over here C x delta Y nought.

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This of course is equal to,
this is just delta Y nought.

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We can just keep going.

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If this guy would then get this amount

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and he'll spent C times that to the farmer

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and so if we had a Y3,

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it would just amount to C times this

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which is C^3 x delta Y nought

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and we could keep going on and on and on

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an infinite number of time

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but each of these terms are
going to smaller and smaller

00:03:47.001 --> 00:03:48.532
because we're going to assume,

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in order for this to actually work,

00:03:50.733 --> 00:03:56.067
we're going to assume
that C is between 0 and 1.

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Obviously, when someone gets new income

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and thinking of the simple case,

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someone is not going to spend more,

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the marginal propensity to consume,

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they can't spend more than they just got.

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In general they're not going
to spend the whole thing.

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So we're going to assume
that it is less than 1.

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This is exactly the same idea
that we did in the last one

00:04:13.734 --> 00:04:14.808
but now it is general

00:04:14.808 --> 00:04:17.003
and we can simplify this a
little bit mathematically.

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This is all equal to our
delta Y, our total bump in GDP

00:04:23.040 --> 00:04:26.069
due to that initial spark.

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If we factor that initial spark out

00:04:28.133 --> 00:04:30.413
with the delta Y nought.

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Actually, let me do
that in different color

00:04:31.470 --> 00:04:33.201
just so the math becomes clear.

00:04:33.201 --> 00:04:35.612
We have the delta Y
nought, delta Y nought,

00:04:35.612 --> 00:04:37.952
delta Y nought, delta Y nought.

00:04:37.952 --> 00:04:40.068
When I say nought, I'm talking
about that zero subscript.

00:04:40.068 --> 00:04:45.648
If we factor that our, we
get our total bump in GDP.

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Whether you want to do
this output, expenditure

00:04:47.006 --> 00:04:51.468
or income, is equal to, we're
going to factor that out,

00:04:51.468 --> 00:04:54.203
the delta Y nought times,

00:04:54.203 --> 00:04:56.133
and then we're just left with,

00:04:56.133 --> 00:05:00.704
you factor the change in
Y nought here you get 1

00:05:00.704 --> 00:05:07.064
and then over here, + C + C^2 + C^3

00:05:07.064 --> 00:05:09.737
and you go on and on and on.

00:05:09.737 --> 00:05:12.294
In the last video I told you
that this right over here

00:05:12.294 --> 00:05:16.935
is going to simplify to 1 over 1 - C.

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This is equal to, this
part over here is equal to

00:05:19.954 --> 00:05:22.801
1 over 1 - C.

00:05:22.801 --> 00:05:24.468
Now, you might have not been satisfied

00:05:24.468 --> 00:05:26.292
and since this is a more mathy video

00:05:26.292 --> 00:05:28.003
it's a good place to actually show you

00:05:28.003 --> 00:05:31.806
that it would sum up to 1 over 1 - C.

00:05:31.806 --> 00:05:33.791
Not to introduce too many variables,

00:05:33.791 --> 00:05:36.138
but let's just call this thing X.

00:05:36.138 --> 00:05:40.801
Let's just say that X is
equal to this whole thing

00:05:40.801 --> 00:05:42.378
right over here.

00:05:42.378 --> 00:05:46.627
It's equal 1 + C + C^2 + C^3,

00:05:46.627 --> 00:05:49.210
so on and so forth.

00:05:49.210 --> 00:05:51.138
Now let's imagine what we would get

00:05:51.138 --> 00:05:53.068
if we multiply X x C.

00:05:53.068 --> 00:05:54.665
What happens if I multiply,

00:05:54.665 --> 00:05:56.135
and I'll do this in a different color.

00:05:56.135 --> 00:05:59.206
What happens if I multiply C x X?

00:05:59.206 --> 00:06:00.705
Well then, each of these terms

00:06:00.705 --> 00:06:02.733
I can multiply by C.

00:06:02.733 --> 00:06:08.672
1 x C is C, C x C is C^2, C^2 x C is C^3,

00:06:08.672 --> 00:06:13.265
C^3 x C is C^4, so on and so forth.

00:06:13.280 --> 00:06:17.347
Now, what happens if I
subtract this from that?

00:06:17.347 --> 00:06:20.278
If I subtract the left hand sides

00:06:20.278 --> 00:06:28.600
I get X - CX on the left hand side.

00:06:28.600 --> 00:06:31.925
I'll do that in that pink color.

00:06:31.925 --> 00:06:32.787
Where did it go?

00:06:32.787 --> 00:06:34.534
Actually I think I changed
the color on my ...

00:06:34.534 --> 00:06:38.367
I'll just write X - CX and
that's going to be equal to,

00:06:38.367 --> 00:06:40.802
if you subtract this stuff
from that stuff over there,

00:06:40.802 --> 00:06:43.869
you have a C - C, they'll cancel out.

00:06:43.869 --> 00:06:45.271
Let me do this in yellow.

00:06:45.271 --> 00:06:47.364
C^2 - C^2, that will cancel out.

00:06:47.364 --> 00:06:49.201
C^3 - C^3, that would cancel out.

00:06:49.201 --> 00:06:51.664
Every term other than 1
is going to cancel out.

00:06:51.664 --> 00:06:53.136
Everything is going to cancel out

00:06:53.136 --> 00:06:54.864
and you're just going to
be left with the 1 here

00:06:54.864 --> 00:06:57.531
which is a pretty neat trick in my mind.

00:06:57.531 --> 00:06:59.951
Then we can factor out
the X right over here.

00:06:59.951 --> 00:07:04.334
You get X x 1 - C = 1

00:07:04.334 --> 00:07:06.465
and then you divide both sides by 1 - C,

00:07:06.465 --> 00:07:09.536
you get X = 1 over 1 - C.

00:07:09.536 --> 00:07:12.266
X was exactly this thing right over here.

00:07:12.266 --> 00:07:17.669
This thing is equal to 1 over 1 - C.

00:07:17.669 --> 00:07:19.296
This right here, we just showed you

00:07:19.296 --> 00:07:23.214
exactly what we told you in the last video

00:07:23.214 --> 00:07:26.333
that the total bump in GDP,

00:07:26.333 --> 00:07:27.294
this right over here,

00:07:27.294 --> 00:07:29.376
you could view this as
the total bump in GDP

00:07:29.376 --> 00:07:32.069
is going to be equal to
that initial bump in GDP

00:07:32.069 --> 00:07:33.999
which we called delta Y nought.

00:07:33.999 --> 00:07:36.714
That was that initial spending

00:07:36.714 --> 00:07:39.871
that that farmer did and
the builders initial income,

00:07:39.871 --> 00:07:41.467
that the total bump is going to be equal

00:07:41.467 --> 00:07:44.667
to that initial bump times this expression

00:07:44.667 --> 00:07:46.734
which we view as the multiplier.

00:07:46.734 --> 00:07:48.803
This is the multiplier right here

00:07:48.803 --> 00:07:52.133
is a function of the marginal
propensity to consume.

00:07:52.133 --> 00:07:56.467
This right over here, let me label it all.

00:07:56.467 --> 00:07:57.736
Actually, let me just rewrite it.

00:07:57.736 --> 00:08:01.667
The total bump in our
aggregate expenditure

00:08:01.667 --> 00:08:04.138
or output or income

00:08:04.138 --> 00:08:07.906
is going to be equal to the initial bump

00:08:07.906 --> 00:08:11.532
times the multiplier which
ends up being a function

00:08:11.532 --> 00:08:14.123
of our marginal propensity to consume.

00:08:14.123 --> 00:08:20.852
This right over here is our multiplier

00:08:20.852 --> 00:08:21.939
and this right over here is,

00:08:21.939 --> 00:08:23.679
you could view that as our initial bump.

00:08:23.679 --> 00:08:25.133
Just to make sure that it works out

00:08:25.133 --> 00:08:26.347
from what we saw in the last video.

00:08:26.347 --> 00:08:28.685
In the last video our
marginal propensity to consume

00:08:28.685 --> 00:08:30.763
was .6.

00:08:30.763 --> 00:08:36.091
C was 0.6 and our initial bump,

00:08:36.091 --> 00:08:39.682
our initial expenditure
was equal to 1,000.

00:08:39.682 --> 00:08:42.465
If you put .6 in here you will get 2.5

00:08:42.465 --> 00:08:44.345
and so you get the exact same multiplier

00:08:44.345 --> 00:08:47.013
and you get the exact
same total bump in GDP

00:08:47.013 --> 00:08:48.425
as we got in the last video.

00:08:48.425 --> 00:08:50.067
At least now we have a little general

00:08:50.067 --> 00:08:51.932
and you're hopefully a
little bit more comfortable

00:08:51.932 --> 00:08:53.806
with some of these
notation that I'm using.

00:08:53.806 --> 00:08:55.538
Unfortunately, you'll
see different notation

00:08:55.538 --> 00:08:57.408
almost every economics textbook.

00:08:57.408 --> 00:08:58.432
I just want to make sure

00:08:58.432 --> 00:09:02.000
that this makes reasonable sense to you.


MPC and multiplier

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:03.000
Going with my habit of
overly simplified economy,

00:00:03.000 --> 00:00:05.840
let's then imagine an economy
that has only two actors in it.

00:00:05.840 --> 00:00:08.260
So it has Mr. Farmer
right over here.

00:00:08.260 --> 00:00:10.220
Do my best to draw
the farmer, maybe he

00:00:10.220 --> 00:00:12.410
has a mustache of some kind.

00:00:12.410 --> 00:00:14.570
So it has Mr. Farmer
right over here.

00:00:14.570 --> 00:00:15.480
He's got a hat on.

00:00:18.490 --> 00:00:21.180
So that is the farmer
in this economy.

00:00:21.180 --> 00:00:22.990
And then let's say we
also have a builder.

00:00:22.990 --> 00:00:26.084
So this economy, they're
producing two things.

00:00:26.084 --> 00:00:27.750
They're producing
food, and this builder

00:00:27.750 --> 00:00:29.580
can help maintain stuff.

00:00:29.580 --> 00:00:31.340
So maybe he has
a lot more, maybe

00:00:31.340 --> 00:00:33.630
this is the builder
right over here.

00:00:33.630 --> 00:00:38.140
So this is Mr. Builder.

00:00:38.140 --> 00:00:41.440
And let's say, for the sake of
what we're going to do here,

00:00:41.440 --> 00:00:43.860
let's say that for this economy,
it's kind of a constant.

00:00:43.860 --> 00:00:47.470
If either of these fellows
gets an extra dollar to spend,

00:00:47.470 --> 00:00:49.969
he's going to spend 60% of it.

00:00:49.969 --> 00:00:52.260
And so, what I'm going to do
is introduce a formal word

00:00:52.260 --> 00:00:54.440
that really is just
another way of saying that.

00:00:54.440 --> 00:01:07.070
In this economy, the marginal
propensity to consume

00:01:07.070 --> 00:01:09.720
is-- and I'll put that
in parentheses, it's

00:01:09.720 --> 00:01:14.240
often referred to as
MPC-- that is equal to you

00:01:14.240 --> 00:01:18.530
could either say 60%
or is equal to 0.6.

00:01:18.530 --> 00:01:21.530
And all this is saying is that
if someone in this economy

00:01:21.530 --> 00:01:24.380
somehow finds another
dollar in their pocket,

00:01:24.380 --> 00:01:26.540
they're going to
spend 0.6 of that.

00:01:26.540 --> 00:01:28.124
Or they're going to
spend 60% of that.

00:01:28.124 --> 00:01:30.581
So if you give the builder--
if a builder all of the sudden

00:01:30.581 --> 00:01:33.470
gets an extra dollar, he's going
to spend another $0.60 on other

00:01:33.470 --> 00:01:33.970
things.

00:01:33.970 --> 00:01:35.840
And the person to really
spend it with is the farmer.

00:01:35.840 --> 00:01:37.550
If the farmer gets
another dollar,

00:01:37.550 --> 00:01:41.640
he's going to spend 60% of that,
or $0.60, with the builder.

00:01:41.640 --> 00:01:43.580
Now given this
assumption, let's think

00:01:43.580 --> 00:01:45.850
about what would
happen in this economy

00:01:45.850 --> 00:01:47.440
if all of a sudden
one of them decided

00:01:47.440 --> 00:01:49.260
to increase their
spending a little bit.

00:01:49.260 --> 00:01:51.520
So we'll assume that they
were all living happily.

00:01:51.520 --> 00:01:53.740
The economy was kind
of at a steady state.

00:01:53.740 --> 00:01:55.320
And let's say the
farmer discovers

00:01:55.320 --> 00:01:57.787
a sock in a drawer that he
didn't realize was there.

00:01:57.787 --> 00:02:00.120
And it's got a little bit of
their agreed upon currency.

00:02:00.120 --> 00:02:02.570
Maybe the agreed upon currency
in this island is a dollar.

00:02:02.570 --> 00:02:05.810
They've maybe got a stash when
their shipwrecked on this,

00:02:05.810 --> 00:02:06.720
or whatever.

00:02:06.720 --> 00:02:08.880
So the agreed upon currency
is actually the dollar.

00:02:08.880 --> 00:02:10.889
And the farmer
discovers that he's

00:02:10.889 --> 00:02:15.775
got-- he discovers a big
pile of dollars in his sock.

00:02:15.775 --> 00:02:17.650
And he says, well, I'm
going to spend $1,000.

00:02:17.650 --> 00:02:20.850
I need to do some
repairs to my buildings.

00:02:20.850 --> 00:02:25.330
So we have this kind of increase
in spending that's going on.

00:02:25.330 --> 00:02:30.800
So the farmer says, hey,
I'm going to spend $1,000,

00:02:30.800 --> 00:02:32.600
and I'm going to give
it to the builder.

00:02:32.600 --> 00:02:34.150
Now the builder
says, well, you know,

00:02:34.150 --> 00:02:37.070
gee, I've just gotten $1,000.

00:02:37.070 --> 00:02:41.610
I have a marginal propensity
to consume of 60%, or 0.6.

00:02:41.610 --> 00:02:43.670
I'm going to spend 60% of that.

00:02:43.670 --> 00:02:46.960
So he's going to spend,
and the only person

00:02:46.960 --> 00:02:48.770
he can spend it
with is the farmer.

00:02:48.770 --> 00:02:56.800
He's going to spend 60% times
$1,000, which is equal to $600.

00:02:56.800 --> 00:02:58.570
Well, now the
farmer says, well, I

00:02:58.570 --> 00:03:00.880
got above and beyond the
$1,000 that I just spent.

00:03:00.880 --> 00:03:02.920
Somehow the economy
seems to be picking up.

00:03:02.920 --> 00:03:05.490
The builder just
spent $600 more on me

00:03:05.490 --> 00:03:06.950
then he would have
otherwise done.

00:03:06.950 --> 00:03:08.910
He bought that much more food.

00:03:08.910 --> 00:03:10.580
I have $600 more.

00:03:10.580 --> 00:03:15.270
I have a marginal propensity
to consume of 0.6 or 60%.

00:03:15.270 --> 00:03:18.900
So I will spend 60% of
that $600 that I just got.

00:03:18.900 --> 00:03:23.020
And so it will be
60% of this thing.

00:03:23.020 --> 00:03:26.060
So it will be 60-- I'll
write it as a decimal-- it'll

00:03:26.060 --> 00:03:34.040
be 0.6 times this thing,
which is 0.6 times 1,000.

00:03:34.040 --> 00:03:37.570
Or you could say it is
60% of the $600, which

00:03:37.570 --> 00:03:40.870
is going to be equal to $360.

00:03:40.870 --> 00:03:42.760
Well, now the
builder says, well, I

00:03:42.760 --> 00:03:44.115
got that initial $1,000.

00:03:44.115 --> 00:03:44.990
I spent $600 of that.

00:03:44.990 --> 00:03:47.420
But now I've got
another $360, and I

00:03:47.420 --> 00:03:51.610
have a marginal propensity
to consume of 0.6.

00:03:51.610 --> 00:03:54.120
So I'm going to
spend 60% of that.

00:03:54.120 --> 00:03:55.720
So above and beyond
this spending,

00:03:55.720 --> 00:03:59.010
he also spends 60% of
this right over here.

00:03:59.010 --> 00:04:03.200
And 60% of this is 0.6
times this whole thing.

00:04:03.200 --> 00:04:07.780
So he's going to spend
0.6 times this thing--

00:04:07.780 --> 00:04:15.630
and I'll write it in green--
times 0.6 times $1,000.

00:04:15.630 --> 00:04:17.410
Now this number
right over here, I

00:04:17.410 --> 00:04:20.577
don't know what this
is, is it 60% of $360.

00:04:20.577 --> 00:04:22.160
I don't know, I could
get a calculator

00:04:22.160 --> 00:04:24.160
to figure out what
that is exactly.

00:04:24.160 --> 00:04:29.720
So let's say that I have
0.6-- we could actually

00:04:29.720 --> 00:04:32.860
say 0.6 to the third power.

00:04:32.860 --> 00:04:36.380
Or let's just write
that-- 0.6 to the third.

00:04:36.380 --> 00:04:40.830
And then I'm going to
multiply that times 1,000,

00:04:40.830 --> 00:04:43.850
gives us $216.

00:04:43.850 --> 00:04:47.070
So this guy-- so this right
over here gives us $216.

00:04:47.070 --> 00:04:49.350
This guy says, hey
got another $216,

00:04:49.350 --> 00:04:51.120
I'm going to spend 60% of that.

00:04:51.120 --> 00:04:53.210
And I think you see
where this is going.

00:04:53.210 --> 00:04:57.260
And 60% of that is going to be
0.6 times this whole quantity.

00:04:57.260 --> 00:04:59.240
So it's going to be--
I'll write it here--

00:04:59.240 --> 00:05:01.960
it's going to be 0.6
times this thing,

00:05:01.960 --> 00:05:05.240
which was already 0.6
times 0.6 times 0.6.

00:05:05.240 --> 00:05:08.580
So you're going to have 0.6
times 0.6 to the third power.

00:05:08.580 --> 00:05:15.330
That's going to be 0.6 to the
fourth power times 1,000, which

00:05:15.330 --> 00:05:17.930
is whatever 60% of 216 is.

00:05:17.930 --> 00:05:19.690
And I'll just calculated it.

00:05:19.690 --> 00:05:26.420
So times 0.6 gives us $130,
is going to get $129.60.

00:05:26.420 --> 00:05:29.000
Now this guy, the builder,
say, I got another $129.60.

00:05:29.000 --> 00:05:30.740
I'm going to spend 60% of that.

00:05:30.740 --> 00:05:32.940
And it goes on and on and on.

00:05:32.940 --> 00:05:35.390
So given this, let's think
about how much from that

00:05:35.390 --> 00:05:40.190
incremental increase of spending
of $1,000, how much total

00:05:40.190 --> 00:05:43.510
new production and spending
happened in this economy?

00:05:43.510 --> 00:05:48.850
So the way to think about
that, so the total-- and we

00:05:48.850 --> 00:05:49.970
could view it either way.

00:05:49.970 --> 00:05:51.735
Remember, you could
view kind of the GDP.

00:05:51.735 --> 00:05:53.770
You could view that as
the aggregate output.

00:05:53.770 --> 00:05:55.710
You could view that as
the aggregate income,

00:05:55.710 --> 00:05:56.680
aggregate expenditure.

00:05:56.680 --> 00:05:59.020
These are all views
because really the economy

00:05:59.020 --> 00:06:00.090
is a very circular thing.

00:06:00.090 --> 00:06:03.460
One person's expenditure turns
into another person's income.

00:06:03.460 --> 00:06:06.840
But we could say
total output here,

00:06:06.840 --> 00:06:09.590
measured in our agreed upon
currency, which is let's say

00:06:09.590 --> 00:06:10.520
dollars.

00:06:10.520 --> 00:06:13.320
This is now going to be,
it was this original $1,000

00:06:13.320 --> 00:06:15.800
that the farmer spent
for the builder.

00:06:15.800 --> 00:06:18.310
So it's going to be
that original $1,000

00:06:18.310 --> 00:06:21.580
plus this first, right
over here this 0.6 times

00:06:21.580 --> 00:06:23.990
1,000 that the builder
spent, that $600.

00:06:23.990 --> 00:06:29.140
So that's 0.6 times
1,000 plus-- then

00:06:29.140 --> 00:06:30.930
we had this time
the farmer said,

00:06:30.930 --> 00:06:32.260
I'm going to spend 60% of that.

00:06:32.260 --> 00:06:34.540
So that was 0.6
squared times 1,000.

00:06:34.540 --> 00:06:39.834
Plus 0.6 squared times 1,000.

00:06:39.834 --> 00:06:42.250
And then this guy said, oh,
I'm going to spend 60% of that

00:06:42.250 --> 00:06:44.520
now that I got that 0.6
squared times 1,000.

00:06:44.520 --> 00:06:46.760
So he's going to take
60% of that and spend it.

00:06:46.760 --> 00:06:49.650
And that gave us that 0.6 to
the third power times 1,000.

00:06:49.650 --> 00:06:54.840
Plus 0.6 to the third
power times 1,000.

00:06:54.840 --> 00:06:57.540
And then the last one we
did, it would keep going on

00:06:57.540 --> 00:07:02.040
and on forever,
theoretically, is

00:07:02.040 --> 00:07:07.180
you're going to have plus 0.6
to the fourth power times 1,000.

00:07:07.180 --> 00:07:09.510
And this would keep
going on and on forever.

00:07:09.510 --> 00:07:12.550
We could then would be plus 0.6
to the fifth power times 1,000,

00:07:12.550 --> 00:07:14.020
plus 0.6 to the sixth power.

00:07:14.020 --> 00:07:16.880
Keep going on and on forever.

00:07:16.880 --> 00:07:19.887
And one of the fascinating
things about mathematics,

00:07:19.887 --> 00:07:21.720
and maybe the next
video, I'll reprove this.

00:07:21.720 --> 00:07:23.410
I've proven this in
multiple playlists,

00:07:23.410 --> 00:07:26.760
is that you can actually
sum up because this value

00:07:26.760 --> 00:07:29.110
right over here is less
than 1, this actually

00:07:29.110 --> 00:07:30.970
ends up being a finite sum.

00:07:30.970 --> 00:07:32.720
You can actually take
this infinite sum

00:07:32.720 --> 00:07:34.530
and get a finite number.

00:07:34.530 --> 00:07:37.900
So just to simplify this,
the total output that's

00:07:37.900 --> 00:07:40.600
kind of sparked by
that original $1,000,

00:07:40.600 --> 00:07:44.110
we can factor out the 1,000--
I'll do this in a new color--

00:07:44.110 --> 00:07:46.390
so we can factor out the 1,000.

00:07:46.390 --> 00:07:48.820
And we are left with--
well if we factor of 1,000

00:07:48.820 --> 00:07:54.950
there you get 1 plus
0.6 plus 0.6 squared

00:07:54.950 --> 00:08:01.470
plus 0.6 to the third power
plus 0.6 to the fourth power.

00:08:01.470 --> 00:08:03.470
And it goes on and on and on.

00:08:03.470 --> 00:08:06.070
And in the next video, maybe
I'll prove it, just for fun.

00:08:06.070 --> 00:08:08.990
But this right over here,
it's an infinite sum

00:08:08.990 --> 00:08:10.680
of a geometric series.

00:08:10.680 --> 00:08:14.710
And this will actually
simplify to-- I'll

00:08:14.710 --> 00:08:20.040
do it in the same green
color-- as 1 over 1 minus 0.6.

00:08:20.040 --> 00:08:23.060
So whatever this number is right
over here, it'll be 1 minus 1

00:08:23.060 --> 00:08:24.080
over that.

00:08:24.080 --> 00:08:32.409
And so in this case, this
would be equal to 1 over 0.4.

00:08:32.409 --> 00:08:34.539
And 0.4 is 2/5.

00:08:34.539 --> 00:08:40.400
So this is equal to 1 over
2/5, which is equal to 5/2.

00:08:40.400 --> 00:08:50.050
So your total output is going
to be equal to 1,000 times 5/2.

00:08:50.050 --> 00:08:54.220
Or this is the same thing as
equal to 1,000 times 2 and 1/2,

00:08:54.220 --> 00:08:56.410
which is equal to 2,500.

00:08:56.410 --> 00:08:59.150
So there's two interesting
ideas that are going here.

00:08:59.150 --> 00:09:01.550
One is, when people get
a little bit more income,

00:09:01.550 --> 00:09:03.090
they're going to
spend some of it.

00:09:03.090 --> 00:09:05.160
And that's where the marginal
propensity to consume is.

00:09:05.160 --> 00:09:07.160
We're assuming it's linear,
that no matter how much you give

00:09:07.160 --> 00:09:09.540
them, they're just going
to spend 60% of that.

00:09:09.540 --> 00:09:12.740
And then given that, that 60%,
it keeps getting multiplied

00:09:12.740 --> 00:09:14.150
and going through the economy.

00:09:14.150 --> 00:09:15.650
You essentially have
this multiplier effect,

00:09:15.650 --> 00:09:17.720
that that 1,000 got spent,
some fraction of that gets

00:09:17.720 --> 00:09:19.720
spent, then some fraction
of that gets spent.

00:09:19.720 --> 00:09:23.690
And so what we ended up
doing is that first $1,000

00:09:23.690 --> 00:09:27.260
got multiplied by 2.5.

00:09:27.260 --> 00:09:29.380
And this 2.5 was
completely a function

00:09:29.380 --> 00:09:32.540
of what the marginal
propensity to consume was.

00:09:32.540 --> 00:09:34.480
So we have this
relationship here

00:09:34.480 --> 00:09:37.100
is that whatever the marginal
propensity to consume is,

00:09:37.100 --> 00:09:38.630
that drives the multiplier.

00:09:41.770 --> 00:09:43.980
And all the multiplier
is saying is

00:09:43.980 --> 00:09:46.780
if you spend an extra dollar
in this economy, given people's

00:09:46.780 --> 00:09:49.260
marginal propensity to
consume, how much will that

00:09:49.260 --> 00:09:51.794
increase total output?


Mega millions jackpot probability

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:03.210
I've been asked to calculate
the probability of winning

00:00:03.210 --> 00:00:05.080
the Mega Millions jackpot.

00:00:05.080 --> 00:00:07.650
So I thought that's what
I would do this video on.

00:00:07.650 --> 00:00:09.650
So the first thing is to
make sure we understand

00:00:09.650 --> 00:00:11.680
what does winning the
jackpot actually mean.

00:00:11.680 --> 00:00:15.840
So there's going to
be two bins of balls.

00:00:15.840 --> 00:00:19.920
One of them is going to have 56
balls in it, so 56 in one bin.

00:00:19.920 --> 00:00:23.290
And then another bin is
going to have 46 balls in it.

00:00:23.290 --> 00:00:26.564
So there are 46 balls in
this bin right over here.

00:00:26.564 --> 00:00:27.980
And so what they're
going to do is

00:00:27.980 --> 00:00:31.550
they're going to pick 5 balls
from this bin right over here.

00:00:31.550 --> 00:00:34.060
And you have to get the exact
numbers of those 5 balls.

00:00:34.060 --> 00:00:35.290
It can be in any order.

00:00:35.290 --> 00:00:36.470
So let me just draw them.

00:00:36.470 --> 00:00:39.820
So it's 1 ball-- I'll shade
it so it looks like a ball--

00:00:39.820 --> 00:00:47.376
2 balls, 3 balls, 4
balls, and 5 balls

00:00:47.376 --> 00:00:48.500
that they're going to pick.

00:00:48.500 --> 00:00:50.583
And you just have to get
the numbers in any order.

00:00:50.583 --> 00:00:52.255
So this is from a bin of 56.

00:00:55.515 --> 00:00:57.390
And then you have to
get the mega ball right.

00:00:57.390 --> 00:00:58.190
And then they're
going to just pick

00:00:58.190 --> 00:01:00.580
one ball from there, which
they call the mega ball.

00:01:02.926 --> 00:01:04.300
And obviously,
this is just going

00:01:04.300 --> 00:01:06.410
to be picked-- this is
going to be one of 46,

00:01:06.410 --> 00:01:09.000
so from a bin of 46.

00:01:09.000 --> 00:01:11.050
And so to figure out the
probability of winning,

00:01:11.050 --> 00:01:13.420
it's essentially
going to be one of all

00:01:13.420 --> 00:01:17.546
of the possibilities of numbers
that you might be able to pick.

00:01:17.546 --> 00:01:19.170
So essentially, all
of the combinations

00:01:19.170 --> 00:01:22.570
of the white balls times
the 46 possibilities

00:01:22.570 --> 00:01:24.294
that you might get
for the mega ball.

00:01:24.294 --> 00:01:25.710
So to think about
the combinations

00:01:25.710 --> 00:01:28.293
for the white balls, there's a
couple of ways you could do it.

00:01:28.293 --> 00:01:30.960
If you are used to thinking
in combinatorics terms,

00:01:30.960 --> 00:01:34.370
it would essentially say, well,
out of a set of 56 things,

00:01:34.370 --> 00:01:37.820
I am going to choose 5 of them.

00:01:37.820 --> 00:01:41.790
So this is literally, you could
view this as 56, choose 5.

00:01:41.790 --> 00:01:45.065
Or if you want to think of
it in more conceptual terms,

00:01:45.065 --> 00:01:48.865
the first ball I pick,
there's 56 possibilities.

00:01:48.865 --> 00:01:51.240
Since we're not replacing the
ball, the next ball I pick,

00:01:51.240 --> 00:01:54.300
there's going to be
55 possibilities.

00:01:54.300 --> 00:01:57.730
The ball after that, there's
going to be 54 possibilities.

00:01:57.730 --> 00:02:01.189
Ball after that, there's
going to be 53 possibilities.

00:02:01.189 --> 00:02:02.730
And then the ball
after that, there's

00:02:02.730 --> 00:02:06.330
going to be 52 possibilities,
because I've already

00:02:06.330 --> 00:02:07.931
picked 4 balls out of that.

00:02:07.931 --> 00:02:10.389
Now, this number right over
here, when you multiply it out,

00:02:10.389 --> 00:02:12.450
this is a number
of permutations,

00:02:12.450 --> 00:02:13.920
if I cared about order.

00:02:13.920 --> 00:02:15.870
So if I got that
exact combination.

00:02:15.870 --> 00:02:18.320
But to win this, you don't
have to write them down

00:02:18.320 --> 00:02:19.340
in the same order.

00:02:19.340 --> 00:02:21.806
You just have to get those
numbers in any order.

00:02:21.806 --> 00:02:23.180
And so what you
want to do is you

00:02:23.180 --> 00:02:26.190
want to divide this
by the number of ways

00:02:26.190 --> 00:02:28.760
that five things can
actually be ordered.

00:02:28.760 --> 00:02:31.040
So what you want to do
is divide this by the way

00:02:31.040 --> 00:02:32.670
that five things can be ordered.

00:02:32.670 --> 00:02:34.230
And if you're
ordering five things,

00:02:34.230 --> 00:02:36.940
the first of the five things can
take five different positions.

00:02:36.940 --> 00:02:39.240
Then the next one will have four
positions left, and then the

00:02:39.240 --> 00:02:41.130
one after that will have
three positions left.

00:02:41.130 --> 00:02:42.930
The one after that will
have two positions.

00:02:42.930 --> 00:02:45.116
And then the fifth one will
be completely determined

00:02:45.116 --> 00:02:46.990
because you've already
placed the other four,

00:02:46.990 --> 00:02:49.520
so it's going to have
only one position.

00:02:49.520 --> 00:02:51.800
So when we calculate this
part right over here,

00:02:51.800 --> 00:02:53.620
this will tell us all
of the combinations

00:02:53.620 --> 00:02:55.100
of just the white balls.

00:02:55.100 --> 00:02:56.640
And so let's calculate that.

00:02:56.640 --> 00:03:06.230
So just the white balls, we
have 56 times 55 times 54 times

00:03:06.230 --> 00:03:09.710
53 times 52.

00:03:09.710 --> 00:03:16.196
And we're going to divide that
by 5 times 4 times 3 times 2.

00:03:16.196 --> 00:03:18.070
We don't have to multiply
by 1, but I'll just

00:03:18.070 --> 00:03:19.870
do that, just to show
what we're doing.

00:03:19.870 --> 00:03:23.840
And then that gives
us about 3.8 million.

00:03:23.840 --> 00:03:27.150
So let me actually let
me put that off screen.

00:03:27.150 --> 00:03:28.830
So let me write
that number down.

00:03:28.830 --> 00:03:37.799
So this comes out to 3,819,816.

00:03:37.799 --> 00:03:39.590
So that's the number
of possibilities here.

00:03:39.590 --> 00:03:42.110
So just your odds of picking
just the white balls right

00:03:42.110 --> 00:03:43.960
are going to be one
out of this, assuming

00:03:43.960 --> 00:03:45.410
you only have one entry.

00:03:45.410 --> 00:03:47.539
And then there's
46 possibilities

00:03:47.539 --> 00:03:49.080
for the orange balls,
so you're going

00:03:49.080 --> 00:03:51.382
to multiply that times 46.

00:03:51.382 --> 00:03:52.840
And so that's going
to get you-- so

00:03:52.840 --> 00:03:57.070
when you multiply it times
46-- bring the calculator back.

00:03:57.070 --> 00:03:59.980
So we're going to multiply
our previous answer times 46.

00:03:59.980 --> 00:04:03.890
"Ans" just means
my previous answer.

00:04:03.890 --> 00:04:08.685
I get a little
under 176 million.

00:04:15.240 --> 00:04:17.329
Let me write that number down.

00:04:17.329 --> 00:04:25.470
So that gives us 175,711,536.

00:04:25.470 --> 00:04:28.267
So your odds of winning it,
with one entry-- because this

00:04:28.267 --> 00:04:30.600
is the number of possibilities,
and you are essentially,

00:04:30.600 --> 00:04:32.810
for $1, getting one of
those possibilities.

00:04:32.810 --> 00:04:35.839
Your odds of winning is
going to be 1 over this.

00:04:35.839 --> 00:04:37.630
And to put this in a
little bit of context,

00:04:37.630 --> 00:04:39.220
I looked it up on
the internet what

00:04:39.220 --> 00:04:40.780
your odds are of
actually getting

00:04:40.780 --> 00:04:43.004
struck by lightning
in your lifetime.

00:04:43.004 --> 00:04:44.420
And so your odds
of getting struck

00:04:44.420 --> 00:04:46.510
by lightning in your
lifetime are roughly 1

00:04:46.510 --> 00:04:50.470
in 10,000-- chance
of getting struck

00:04:50.470 --> 00:04:51.736
by lightning in your lifetime.

00:04:51.736 --> 00:04:54.360
And we can roughly say your odds
of getting struck by lightning

00:04:54.360 --> 00:04:56.070
twice in your lifetime,
or another way

00:04:56.070 --> 00:04:59.490
of saying it is the odds of
you and your best friend both

00:04:59.490 --> 00:05:01.800
independently being struck
by lightning when you're not

00:05:01.800 --> 00:05:05.330
around each other, is going
to be 1 in 10,000 times

00:05:05.330 --> 00:05:07.150
1 in 10,000.

00:05:07.150 --> 00:05:10.480
And so that will get you 1 in--
and we're going to have now

00:05:10.480 --> 00:05:14.980
eight 0's-- 1, 2,
3, 4, 5, 6, 7, 8.

00:05:14.980 --> 00:05:17.660
So that gives you
1 in 100 million.

00:05:17.660 --> 00:05:20.130
So you're actually
twice-- almost,

00:05:20.130 --> 00:05:22.460
this is very rough--
you're roughly twice

00:05:22.460 --> 00:05:26.170
as likely to get struck by
lightning twice in your life

00:05:26.170 --> 00:05:28.525
than to win the Mega jackpot.


The Caesar cipher

WEBVTT
Kind: captions
Language: en

00:00:04.460 --> 00:00:08.170
SPEAKER 1: The first well known
cipher, a substitution cipher,

00:00:08.170 --> 00:00:11.235
was used by Julius
Caesar around 58 BC.

00:00:11.235 --> 00:00:14.220
It is now referred to
as the Caesar Cipher.

00:00:14.220 --> 00:00:17.590
Caesar shifted each letter
in his military commands

00:00:17.590 --> 00:00:19.830
in order to make them
appear meaningless

00:00:19.830 --> 00:00:22.480
should the enemy intercept it.

00:00:22.480 --> 00:00:25.730
Imagine Alice and Bob decided
to communicate using the Caesar

00:00:25.730 --> 00:00:29.780
Cipher First, they would need
to agree in advance on a shift

00:00:29.780 --> 00:00:31.750
to use-- say, three.

00:00:31.750 --> 00:00:33.430
So to encrypt her
message, Alice would

00:00:33.430 --> 00:00:36.380
need to apply a shift
of three to each letter

00:00:36.380 --> 00:00:38.070
in her original message.

00:00:38.070 --> 00:00:43.280
So A becomes D, B becomes
E, C becomes F, and so on.

00:00:43.280 --> 00:00:45.940
This unreadable, or
encrypted message,

00:00:45.940 --> 00:00:48.200
is then sent to Bob openly.

00:00:51.310 --> 00:00:53.970
Then Bob simply subtracts
the shift of three

00:00:53.970 --> 00:00:58.480
from each letter in order to
read the original message.

00:00:58.480 --> 00:01:00.450
Incredibly, this
basic cipher was

00:01:00.450 --> 00:01:04.379
used by military leaders for
hundreds of years after Caesar.

00:01:04.379 --> 00:01:07.460
JULIUS CAESAR: I
have fought and won.

00:01:07.460 --> 00:01:10.600
But I haven't conquered
over man's spirit,

00:01:10.600 --> 00:01:12.934
which is indomitable.

00:01:12.934 --> 00:01:14.350
SPEAKER 1: However,
a lock is only

00:01:14.350 --> 00:01:16.520
as strong as its weakest point.

00:01:16.520 --> 00:01:19.100
A lock breaker may look
for mechanical flaws.

00:01:19.100 --> 00:01:21.400
Or failing that,
extract information

00:01:21.400 --> 00:01:25.450
in order to narrow down
the correct combination.

00:01:25.450 --> 00:01:29.540
The process of lock breaking and
code breaking are very similar.

00:01:29.540 --> 00:01:31.140
The weakness of
the Caesar Cipher

00:01:31.140 --> 00:01:34.540
was published 800 years later
by an Arab mathematician

00:01:34.540 --> 00:01:36.210
named Al-Kindi.

00:01:36.210 --> 00:01:38.960
He broke the Caesar Cipher
by using a clue based

00:01:38.960 --> 00:01:41.210
on an important
property of the language

00:01:41.210 --> 00:01:43.350
a message is written in.

00:01:43.350 --> 00:01:45.700
If you scan text from
any book and count

00:01:45.700 --> 00:01:47.360
the frequency of
each letter, you

00:01:47.360 --> 00:01:49.850
will find a fairly
consistent pattern.

00:01:49.850 --> 00:01:53.410
For example, these are the
letter frequencies of English.

00:01:53.410 --> 00:01:57.010
This can be thought of as
a fingerprint of English.

00:01:57.010 --> 00:01:58.500
We leave this
fingerprint when we

00:01:58.500 --> 00:02:00.810
communicate without
realizing it.

00:02:00.810 --> 00:02:03.090
This clue is one of
the most valuable tools

00:02:03.090 --> 00:02:05.192
for a codebreaker.

00:02:05.192 --> 00:02:07.500
To break this
cipher, they count up

00:02:07.500 --> 00:02:10.759
the frequencies of each
letter in the encrypted text

00:02:10.759 --> 00:02:14.010
and check how far the
fingerprint has shifted.

00:02:14.010 --> 00:02:16.820
For example, if H is
the most popular letter

00:02:16.820 --> 00:02:19.430
in the encrypted
message instead of E,

00:02:19.430 --> 00:02:22.130
then the shift was likely three.

00:02:22.130 --> 00:02:23.890
So they reverse
the shift in order

00:02:23.890 --> 00:02:26.020
to reveal the original message.

00:02:26.020 --> 00:02:27.960
This is called
frequency analysis,

00:02:27.960 --> 00:02:31.840
and it was a blow to the
security of the Caesar cipher.


Probability Space

WEBVTT
Kind: captions
Language: en

00:00:09.786 --> 00:00:10.727
In the 16th century,

00:00:10.727 --> 00:00:13.043
an Italian mathematician named Cardano

00:00:13.043 --> 00:00:15.651
had a well-known gambling addiction.

00:00:15.651 --> 00:00:17.141
He wrote letters in which he bragged

00:00:17.141 --> 00:00:20.906
about his ability to beat his friends at dice games.

00:00:20.906 --> 00:00:22.759
His trick was to place his bets

00:00:22.759 --> 00:00:24.866
using his ideas from mathematics –

00:00:24.866 --> 00:00:28.564
instead of hunches or luck.

00:00:28.564 --> 00:00:30.192
He came up with the method of calculating

00:00:30.192 --> 00:00:32.968
the exact probability of random events,

00:00:32.968 --> 00:00:36.391
such as, say, rolling 'snake eyes' – (a pair of 1's).

00:00:36.391 --> 00:00:39.807
It is based on a powerful property Cardano noticed.

00:00:39.807 --> 00:00:42.511
Every outcome – no matter how many dice you roll –

00:00:42.511 --> 00:00:44.570
is equally likely.

00:00:44.570 --> 00:00:46.566
This allowed him to calculate the probability

00:00:46.566 --> 00:00:50.722
by developing what's now called a 'probability space.'

00:00:50.722 --> 00:00:53.785
First, he counts all possible outcomes –

00:00:53.785 --> 00:00:55.506
known as the 'sample space.'

00:00:55.506 --> 00:00:59.211
For a single dice, these are the 6 possible faces.

00:00:59.211 --> 00:01:01.881
Then, he defines the event in question –

00:01:01.881 --> 00:01:03.338
such as rolling a one –

00:01:03.338 --> 00:01:05.521
which can occur in one way.

00:01:05.521 --> 00:01:07.174
The probability is then found

00:01:07.174 --> 00:01:10.369
by dividing the event by all possible events

00:01:10.369 --> 00:01:13.358
which in this case works out to 1/6.

00:01:13.358 --> 00:01:16.047
Realize the cold, calculating logic here.

00:01:16.047 --> 00:01:17.956
There is no such things as a 'lucky number' –

00:01:17.956 --> 00:01:19.662
no 'divine intervention.'

00:01:19.662 --> 00:01:23.840
The probability of rolling any number is exactly 1/6.

00:01:23.840 --> 00:01:27.358
Now the same logic applies when we roll multiple dice.

00:01:29.297 --> 00:01:32.981
Imagine he needed to know the probability of rolling a pair.

00:01:32.981 --> 00:01:35.485
First, he'd count the size of the sample space.

00:01:35.485 --> 00:01:36.748
With two dice rolls,

00:01:36.748 --> 00:01:42.056
there are 36 possible outcomes: 6 x 6.

00:01:43.839 --> 00:01:47.215
Then, he'd count the number of ways this event can occur.

00:01:47.215 --> 00:01:50.291
There are six different pairs.

00:01:52.353 --> 00:01:56.992
So, 6 divided by 36 is the probability of rolling a pair –

00:01:56.992 --> 00:01:58.532
also 1/6.

00:01:58.532 --> 00:02:01.088
This simple yet powerful idea allowed Cardano

00:02:01.088 --> 00:02:03.199
to bet according to the true probability –

00:02:03.199 --> 00:02:04.907
while his opponents placed their bets

00:02:04.907 --> 00:02:08.406
based on hunches and lucky numbers.

00:02:08.406 --> 00:02:10.434
Remember, this works with multiple rolls.

00:02:10.434 --> 00:02:11.730
[So,] Imagine we needed to know

00:02:11.730 --> 00:02:15.538
the exact probability of rolling three 1's.

00:02:15.538 --> 00:02:16.884
Simple!

00:02:16.884 --> 00:02:19.404
First, we'd figure out the size of the sample space.

00:02:19.404 --> 00:02:24.533
For three dice, this is 6 x 6 x 6, – or 216.

00:02:24.533 --> 00:02:27.886
And there is only one way to roll three 1's,

00:02:27.886 --> 00:02:32.370
so, the probability is 1 divided by 216 (or 1/216).

00:02:32.370 --> 00:02:33.636
This was the trick:

00:02:33.636 --> 00:02:37.492
It was not based on magic, but mathematics.

00:02:37.492 --> 00:02:40.962
Remember, to calculate the probability of a random event –

00:02:40.962 --> 00:02:42.242
such as a dice roll –

00:02:42.242 --> 00:02:45.494
you divide the number of ways that event can occur

00:02:45.494 --> 00:02:48.061
by all possible outcomes.


The fundamental theorem of arithmetic

WEBVTT
Kind: captions
Language: en

00:00:04.580 --> 00:00:07.330
Imagine we are living
in prehistoric times.

00:00:07.330 --> 00:00:09.510
Now, consider the following.

00:00:09.510 --> 00:00:12.870
How did we keep track
of time without a clock?

00:00:12.870 --> 00:00:15.650
All clocks are based on some
repetitive pattern which

00:00:15.650 --> 00:00:18.980
divides the flow of time
into equal segments.

00:00:18.980 --> 00:00:20.730
To find these
repetitive patterns,

00:00:20.730 --> 00:00:23.060
we look towards the heavens.

00:00:23.060 --> 00:00:26.310
The sun rising and falling
each day is the most obvious.

00:00:26.310 --> 00:00:28.960
However, to keep track of
longer periods of time,

00:00:28.960 --> 00:00:30.980
we looked for longer cycles.

00:00:30.980 --> 00:00:32.659
For this we looked
to the moon, which

00:00:32.659 --> 00:00:36.650
seemed to gradually grow
and shrink over many days.

00:00:36.650 --> 00:00:39.080
When we count the number
of days between full moons,

00:00:39.080 --> 00:00:40.960
we arrive at the number 29.

00:00:40.960 --> 00:00:42.980
This is the origin of a month.

00:00:42.980 --> 00:00:46.090
However, if we try to
divide 29 into equal pieces,

00:00:46.090 --> 00:00:47.700
we run into a problem.

00:00:47.700 --> 00:00:49.320
It is impossible.

00:00:49.320 --> 00:00:51.730
The only way to divide
29 into equal pieces

00:00:51.730 --> 00:00:54.780
is to break it back
down into single units.

00:00:54.780 --> 00:00:57.050
29 is a prime number.

00:00:57.050 --> 00:00:58.930
Think of it as unbreakable.

00:00:58.930 --> 00:01:02.160
If a number can be broken
down into equal pieces greater

00:01:02.160 --> 00:01:04.780
than one, we call it
a composite number.

00:01:04.780 --> 00:01:07.870
Now, if we are curious, we may
wonder how many prime numbers

00:01:07.870 --> 00:01:10.430
are there, and how
big do they get?

00:01:10.430 --> 00:01:13.800
Let's start by dividing all
numbers into two categories.

00:01:13.800 --> 00:01:16.540
We list the primes on the
left, and the composites

00:01:16.540 --> 00:01:17.890
on the right.

00:01:17.890 --> 00:01:20.530
At first they seem to
dance back and forth.

00:01:20.530 --> 00:01:22.960
There is no obvious
pattern here.

00:01:22.960 --> 00:01:25.950
So let's use a modern technique
to see the big picture.

00:01:25.950 --> 00:01:29.070
The trick is to
use a Ulam spiral.

00:01:29.070 --> 00:01:32.130
First we list all
possible numbers in order

00:01:32.130 --> 00:01:34.160
in a growing spiral.

00:01:34.160 --> 00:01:37.220
Then we color all the
prime numbers blue.

00:01:37.220 --> 00:01:41.420
Finally, we zoom out to
see millions of numbers.

00:01:41.420 --> 00:01:45.340
This is the pattern of primes,
which goes on and on forever.

00:01:45.340 --> 00:01:48.100
Incredibly, the entire
structure of this pattern

00:01:48.100 --> 00:01:50.330
is still unsolved today.

00:01:50.330 --> 00:01:52.080
We are on to something.

00:01:52.080 --> 00:01:55.790
So let's fast forward to around
300 BC in ancient Greece.

00:01:55.790 --> 00:01:58.240
A philosopher known as
Euclid of Alexandria

00:01:58.240 --> 00:01:59.760
understood that
all numbers could

00:01:59.760 --> 00:02:02.860
be split into these two
distinct categories.

00:02:02.860 --> 00:02:06.330
He began by realizing that
any number can be divided down

00:02:06.330 --> 00:02:09.310
over and over until you
reach a group of smallest

00:02:09.310 --> 00:02:10.770
equal numbers.

00:02:10.770 --> 00:02:13.020
And by definition,
these smallest numbers

00:02:13.020 --> 00:02:15.780
are always prime numbers.

00:02:15.780 --> 00:02:17.670
So he knew that all
numbers are somehow

00:02:17.670 --> 00:02:20.660
built out of smaller primes.

00:02:20.660 --> 00:02:23.440
To be clear, imagine the
universe of all numbers,

00:02:23.440 --> 00:02:25.730
and ignore the primes.

00:02:25.730 --> 00:02:30.620
Now, pick any composite
number and break it down,

00:02:30.620 --> 00:02:33.447
and you are always left
with prime numbers.

00:02:33.447 --> 00:02:35.030
So Euclid knew that
every number could

00:02:35.030 --> 00:02:37.810
be expressed using a
group of smaller primes.

00:02:37.810 --> 00:02:40.120
Think of these as
building blocks.

00:02:40.120 --> 00:02:42.220
No matter what
number you choose,

00:02:42.220 --> 00:02:46.270
it can always be built with
an addition of smaller primes.

00:02:46.270 --> 00:02:48.110
This is the root
of his discovery,

00:02:48.110 --> 00:02:52.060
known as the fundamental theorem
of arithmetic, as follows.

00:02:52.060 --> 00:02:55.420
Take any number, say 30, and
find all the prime numbers

00:02:55.420 --> 00:02:57.350
it divides into equally.

00:02:57.350 --> 00:02:59.930
This we know as factorization.

00:02:59.930 --> 00:03:01.610
This will give us
the prime factors.

00:03:01.610 --> 00:03:05.982
In this case, 2, 3, and 5
are the prime factors of 30.

00:03:05.982 --> 00:03:07.440
Euclid realized
that you could then

00:03:07.440 --> 00:03:10.080
multiply these prime
factors a specific number

00:03:10.080 --> 00:03:12.850
of times to build
the original number.

00:03:12.850 --> 00:03:15.400
In this case, you simply
multiply each factor once

00:03:15.400 --> 00:03:16.260
to build 30.

00:03:16.260 --> 00:03:20.290
2 times 3 times 5 is the
prime factorization of 30.

00:03:20.290 --> 00:03:23.260
Think of it as a special
key, or combination.

00:03:23.260 --> 00:03:25.090
There is no other
way to build 30

00:03:25.090 --> 00:03:28.980
using some other groups of prime
numbers multiplied together.

00:03:28.980 --> 00:03:32.600
So every possible number
has one, and only one

00:03:32.600 --> 00:03:34.140
prime factorization.

00:03:34.140 --> 00:03:36.430
A good analogy is to
imagine each number

00:03:36.430 --> 00:03:38.140
as a different lock.

00:03:38.140 --> 00:03:40.050
The unique key for
each lock would

00:03:40.050 --> 00:03:42.080
be its prime factorization.

00:03:42.080 --> 00:03:44.120
No two locks share a key.

00:03:44.120 --> 00:03:47.576
No two numbers share
a prime factorization.


What is cryptography?

WEBVTT
Kind: captions
Language: en

00:00:07.987 --> 00:00:10.409
Imagine two people who share an important secret

00:00:10.409 --> 00:00:11.977
have to split up.

00:00:14.669 --> 00:00:16.411
This requires them to communicate

00:00:16.411 --> 00:00:19.053
private information from a distance.

00:00:19.053 --> 00:00:21.240
However, an eavesdropper named Eve

00:00:21.240 --> 00:00:22.653
also wants this information,

00:00:22.653 --> 00:00:25.856
and has the ability to intercept their messages.

00:00:25.856 --> 00:00:27.718
So, Alice decides to communicate

00:00:27.718 --> 00:00:31.636
using letters written in some kind of secret code.

00:00:31.636 --> 00:00:33.954
The following analogy is helpful.

00:00:33.954 --> 00:00:36.421
First, Alice locks her message in a box,

00:00:36.421 --> 00:00:38.026
using a lock that only she and Bob

00:00:38.026 --> 00:00:39.951
know the combination to.

00:00:39.951 --> 00:00:42.669
This is known as 'encryption.'

00:00:42.669 --> 00:00:45.768
Then, the locked message is sent to Bob.

00:00:45.768 --> 00:00:47.982
When Bob receives the box, he opens it

00:00:47.997 --> 00:00:51.221
using the code they shared in advance.

00:00:51.221 --> 00:00:54.792
This is called 'decryption.'

00:00:54.792 --> 00:00:57.866
Cryptography begins when we abandon physical locks

00:00:57.866 --> 00:01:00.183
and use 'ciphers' instead.

00:01:00.183 --> 00:01:02.862
Think of [ciphers] as virtual locks.

00:01:02.862 --> 00:01:04.837
Ciphers allow Alice and Bob to scramble

00:01:04.837 --> 00:01:06.534
and descramble their messages

00:01:06.534 --> 00:01:08.222
so that they would appear meaningless

00:01:08.222 --> 00:01:11.289
if Eve intercepted them.

00:01:11.289 --> 00:01:13.956
Cryptography has been around for thousands of years.

00:01:13.956 --> 00:01:15.977
It has decided wars, and is at the heart of

00:01:15.977 --> 00:01:18.917
the worldwide communication network today.

00:01:18.917 --> 00:01:20.817
The fascinating story of cryptography

00:01:20.817 --> 00:01:23.824
requires us to understand two very old ideas

00:01:23.824 --> 00:01:28.134
related to number theory and probability theory.


Simple fractional reserve accounting (part 2)

WEBVTT
Kind: captions
Language: en

00:00:00.374 --> 00:00:01.198
Voiceover: In the last video,

00:00:01.198 --> 00:00:03.550
we saw how a bank would account for

00:00:03.550 --> 00:00:06.701
fractional reserve lending
on its balance sheet,

00:00:06.701 --> 00:00:07.602
and we did it with kind of

00:00:07.602 --> 00:00:08.549
the conceptual understanding

00:00:08.549 --> 00:00:09.410
that we've been talking about

00:00:09.410 --> 00:00:11.546
fractional reserve
lending the entire time.

00:00:11.546 --> 00:00:14.204
Someone deposits 100 million in reserves,

00:00:14.204 --> 00:00:16.963
and 90 million of it gets lent out.

00:00:16.963 --> 00:00:18.290
Of course, the offsetting liability

00:00:18.290 --> 00:00:20.035
is that person could come at any time

00:00:20.035 --> 00:00:22.271
and demand their money back.

00:00:22.271 --> 00:00:25.001
When that 90 million of
currency is lent out,

00:00:25.001 --> 00:00:26.905
the asset that it's
gotten in exchange for it

00:00:26.905 --> 00:00:29.801
is 90 million worth of IOUs.

00:00:29.801 --> 00:00:30.806
Now what I want to do in this video

00:00:30.806 --> 00:00:33.036
is to clarify that this
is conceptually a good way

00:00:33.036 --> 00:00:34.810
of thinking about
fractional reserve lending,

00:00:34.810 --> 00:00:36.633
but what the bank can actually do

00:00:36.633 --> 00:00:37.839
is slightly different than this.

00:00:37.839 --> 00:00:39.272
They can actually create,

00:00:39.272 --> 00:00:40.898
they can actually create the

00:00:40.898 --> 00:00:44.470
they can expand both the
asset and the liability side

00:00:44.470 --> 00:00:45.204
of their account

00:00:45.204 --> 00:00:46.803
with just 10 million of reserves

00:00:46.803 --> 00:00:49.140
to make this exact same thing happen.

00:00:49.140 --> 00:00:50.805
One thing I do want to clarify.

00:00:50.805 --> 00:00:51.361
These videos,

00:00:51.361 --> 00:00:52.189
they are not an attempt

00:00:52.189 --> 00:00:54.141
to either justify
fractional reserve lending

00:00:54.141 --> 00:00:56.473
or in some way indict
fractional reserve lending.

00:00:56.473 --> 00:00:59.007
It's really just to show
how it is accounted for.

00:00:59.007 --> 00:01:00.957
You can take that debate on your own side,

00:01:00.957 --> 00:01:02.677
whether you think it's worth doing or not,

00:01:02.677 --> 00:01:04.137
fractional reserve lending.

00:01:04.137 --> 00:01:05.602
Let's take the same example,

00:01:05.602 --> 00:01:07.392
but now let's take an example where

00:01:07.392 --> 00:01:09.371
so we're going to start the
same way that we started

00:01:09.371 --> 00:01:10.666
in the previous video,

00:01:10.666 --> 00:01:12.346
where I go buy,

00:01:12.346 --> 00:01:15.069
I go buy $10 million worth of assets,

00:01:15.069 --> 00:01:16.072
which are essentially the building

00:01:16.072 --> 00:01:17.291
and things for my bank:

00:01:17.291 --> 00:01:19.207
The buildings, the ATM,
the computer systems,

00:01:19.207 --> 00:01:20.269
all of that.

00:01:20.269 --> 00:01:21.355
I didn't take a loan to do it.

00:01:21.355 --> 00:01:22.866
Let's just say I had that money,

00:01:22.866 --> 00:01:25.470
so once again, I am
the owner of this bank,

00:01:25.470 --> 00:01:27.618
and so I get 10 ...

00:01:27.618 --> 00:01:30.406
I have all of the assets are owned by me,

00:01:30.406 --> 00:01:33.209
so my owner's equity is $10 million,

00:01:33.209 --> 00:01:34.575
is $10 million.

00:01:34.975 --> 00:01:35.957
Now, in this example,

00:01:35.957 --> 00:01:38.376
instead of getting $100
million of deposits

00:01:38.376 --> 00:01:39.470
like we saw in the last one,

00:01:39.470 --> 00:01:41.201
let's say that person A shows up

00:01:41.201 --> 00:01:44.200
and gives us $10 million of deposits.

00:01:44.200 --> 00:01:44.804
So they come,

00:01:44.804 --> 00:01:48.473
and they deposit $10 million of currency,

00:01:48.473 --> 00:01:52.072
so $10 million of federal reserve notes.

00:01:52.072 --> 00:01:53.528
So write over there, $10 million,

00:01:53.528 --> 00:01:55.959
and they can demand,

00:01:55.959 --> 00:02:00.056
person A has a right to
demand their $10 million.

00:02:00.056 --> 00:02:02.009
So this person, let's call them person B,

00:02:02.009 --> 00:02:04.620
person B is one-tenth
as wealthy as person A,

00:02:04.620 --> 00:02:06.555
so this is person B.

00:02:06.555 --> 00:02:10.751
I'll just call it B's checking,

00:02:10.751 --> 00:02:12.803
B's checking account.

00:02:12.803 --> 00:02:14.904
Now, this is going to
seem very unintuitive,

00:02:14.904 --> 00:02:16.410
what I'm about to do.

00:02:16.564 --> 00:02:18.422
Because a bank only has to keep

00:02:18.422 --> 00:02:20.801
of the amount of checkable
deposits they have,

00:02:20.801 --> 00:02:23.376
only 10% of that has to be in reserves,

00:02:23.376 --> 00:02:24.675
and we saw that over here,

00:02:24.675 --> 00:02:26.804
instead of just only being able to lend

00:02:26.804 --> 00:02:27.679
this money over here,

00:02:27.679 --> 00:02:29.093
the bank could keep these reserves,

00:02:29.093 --> 00:02:31.802
but then automatically
expand their checking,

00:02:31.802 --> 00:02:33.840
their checkable deposits.

00:02:33.871 --> 00:02:35.808
Let's say I go to this
bank right over here,

00:02:36.300 --> 00:02:39.292
and I want a $50 million loan.

00:02:39.292 --> 00:02:40.137
They're going to say,

00:02:40.137 --> 00:02:41.903
"Okay, is he good for
the $50 million loan?

00:02:41.903 --> 00:02:42.804
"Is he going to put it to good use?

00:02:42.804 --> 00:02:43.756
"Is he likely to pay?"

00:02:43.756 --> 00:02:45.268
Let's say they do decide

00:02:45.268 --> 00:02:47.204
that Sal is good for the money.

00:02:47.204 --> 00:02:48.876
what they can do,

00:02:48.876 --> 00:02:50.204
what they can do,

00:02:50.204 --> 00:02:51.805
they're going to lend me the money,

00:02:51.805 --> 00:02:54.203
but they don't even have $50 of currency

00:02:54.203 --> 00:02:55.366
to lend the money with.

00:02:55.366 --> 00:02:57.081
What they will do is that they will create

00:02:57.081 --> 00:02:59.840
a $50 million checking account for me.

00:02:59.840 --> 00:03:03.086
So they will create a $50
million checking account,

00:03:03.701 --> 00:03:08.195
so Sal's checking,

00:03:08.503 --> 00:03:09.822
Sal's checking account,

00:03:09.822 --> 00:03:11.245
and obviously, the bank
isn't in the business

00:03:11.245 --> 00:03:12.836
of just giving away money.

00:03:12.836 --> 00:03:15.425
What they will do is they'll
have an offsetting asset

00:03:15.425 --> 00:03:16.669
that they will get from Sal,

00:03:16.669 --> 00:03:18.540
which is an IOU from Sal.

00:03:18.540 --> 00:03:20.219
So let me write it this way.

00:03:20.219 --> 00:03:22.374
Loan to Sal would be an asset,

00:03:22.374 --> 00:03:23.124
because in the future,

00:03:23.124 --> 00:03:24.811
Sal's going to pay the bank.

00:03:25.165 --> 00:03:26.772
We could call this "Loan to Sal"

00:03:26.772 --> 00:03:31.551
or we could call this "IOU from Sal".

00:03:31.551 --> 00:03:33.736
Let's say that Bill comes along,

00:03:33.921 --> 00:03:34.942
I'm just making up names,

00:03:34.942 --> 00:03:36.224
let's say Bill comes along,

00:03:36.224 --> 00:03:38.430
and he wants to borrow another,

00:03:38.430 --> 00:03:39.824
let's say, $40 million,

00:03:39.824 --> 00:03:42.835
and the bank determines
that it's a good investment,

00:03:43.158 --> 00:03:44.171
and so let me actually,

00:03:44.171 --> 00:03:44.866
this is a,

00:03:44.866 --> 00:03:45.746
just to make clear,

00:03:45.746 --> 00:03:47.645
this was a $50 million,

00:03:47.645 --> 00:03:50.179
this was a $50 million IOU from Sal,

00:03:50.179 --> 00:03:53.846
and this is, I have 50 million worth of,

00:03:53.846 --> 00:03:55.770
I guess I can write
checks up to $50 million

00:03:55.770 --> 00:03:56.760
to go buy,

00:03:56.760 --> 00:03:58.025
this was a $50 million loan,

00:03:58.025 --> 00:04:00.022
so I can write checks against this now

00:04:00.022 --> 00:04:02.854
to go and build my business or whatever,

00:04:02.854 --> 00:04:04.348
or I could even take those checks,

00:04:05.040 --> 00:04:06.337
and I could cash them out,

00:04:06.337 --> 00:04:07.674
and of course the bank has to make sure

00:04:07.674 --> 00:04:08.767
it has enough reserves.

00:04:08.767 --> 00:04:10.079
It wouldn't want me to show up

00:04:10.079 --> 00:04:12.341
and try to cash out more than $10 million.

00:04:12.341 --> 00:04:13.829
If that started to happen,

00:04:13.829 --> 00:04:15.496
they would have to go and borrow reserves

00:04:15.496 --> 00:04:17.468
from either another bank
or, as a last resort,

00:04:17.468 --> 00:04:19.171
from a central bank.

00:04:19.171 --> 00:04:20.133
But let's just continue this

00:04:20.133 --> 00:04:21.826
just to show that we can
actually end up having

00:04:21.826 --> 00:04:24.350
identical balance sheets.

00:04:24.873 --> 00:04:27.602
Let's say another businessman,

00:04:27.602 --> 00:04:28.528
let's call him Bill,

00:04:28.528 --> 00:04:29.146
comes along,

00:04:29.146 --> 00:04:31.871
and let's say that he wants
to borrow $40 million.

00:04:31.871 --> 00:04:33.023
So the exact same thing,

00:04:33.023 --> 00:04:34.553
the bank decides to do it,

00:04:34.553 --> 00:04:35.417
so what they will do

00:04:35.417 --> 00:04:37.498
is they will lend Bill $40 million,

00:04:37.498 --> 00:04:38.147
but once again,

00:04:38.147 --> 00:04:39.405
they don't have that much in reserves.

00:04:39.405 --> 00:04:40.603
They will essentially create

00:04:40.603 --> 00:04:42.359
a checking account for Bill.

00:04:42.359 --> 00:04:49.023
So, Bill's $40-million checking account,

00:04:49.023 --> 00:04:50.135
and of course they don't want to just

00:04:50.135 --> 00:04:50.871
hand him the money,

00:04:50.871 --> 00:04:51.770
there's going to be an offsetting asset

00:04:51.770 --> 00:04:52.940
they get from Bill,

00:04:52.940 --> 00:04:57.927
which is essentially a 40-million IOU,

00:04:57.927 --> 00:05:02.494
IOU from Bill.

00:05:02.494 --> 00:05:03.643
Now you might say,

00:05:03.643 --> 00:05:05.849
well, can't the bank just keep doing this?

00:05:05.849 --> 00:05:08.280
Just creating, keep
getting more and more IOUs,

00:05:08.280 --> 00:05:09.893
keep, kind of, creating money

00:05:09.893 --> 00:05:12.159
because these checking
accounts really are money.

00:05:12.159 --> 00:05:12.876
You're money-creating.

00:05:12.876 --> 00:05:14.280
These people can now write checks

00:05:14.280 --> 00:05:17.725
against the bank's ability
to cash those checks,

00:05:17.725 --> 00:05:18.415
and the answer is

00:05:18.415 --> 00:05:20.655
what's limiting this bank right over here

00:05:20.655 --> 00:05:22.406
is the reserve requirements.

00:05:22.406 --> 00:05:23.346
The bank can only,

00:05:23.346 --> 00:05:26.696
the ratio of checkable
deposits to reserves

00:05:26.696 --> 00:05:29.068
can only be 10 to 1,

00:05:29.068 --> 00:05:31.003
or reserves have to be at least,

00:05:31.003 --> 00:05:32.996
and this varies from country to country,

00:05:32.996 --> 00:05:33.912
and this can change,

00:05:33.912 --> 00:05:36.249
depending on the policies
of the federal reserve,

00:05:36.249 --> 00:05:38.417
and that's one way they
have of controlling money,

00:05:38.417 --> 00:05:40.071
although that's not the most typical way.

00:05:40.071 --> 00:05:41.944
They have a reserve requirement here.

00:05:41.944 --> 00:05:43.278
You have a 10%.

00:05:43.278 --> 00:05:46.994
So, 10% of checkable deposits,

00:05:46.994 --> 00:05:48.672
and this is true for
large banks in the US,

00:05:48.672 --> 00:05:50.568
have to be held as reserves.

00:05:50.568 --> 00:05:52.950
There has to be reserves for,

00:05:52.950 --> 00:05:56.015
reserves for,

00:05:56.015 --> 00:06:00.071
10% of checkable deposits.

00:06:00.071 --> 00:06:01.664
That's what essentially keeps these banks

00:06:01.664 --> 00:06:02.671
from doing this forever.

00:06:02.671 --> 00:06:04.251
Now, this bank is all tapped out.

00:06:04.251 --> 00:06:06.421
It's limited by the amount of loans it has

00:06:06.421 --> 00:06:07.339
by its reserves.

00:06:07.339 --> 00:06:08.467
I know it looks a little bit,

00:06:08.467 --> 00:06:11.073
it looks a little bit suspect,

00:06:11.073 --> 00:06:12.110
that they were able to essentially

00:06:12.110 --> 00:06:15.061
create these checking
accounts out of scratch,

00:06:15.061 --> 00:06:15.940
and only have,

00:06:15.940 --> 00:06:17.986
they're essentially telling people,

00:06:17.986 --> 00:06:20.083
"Look, there's 100
million that you can have

00:06:20.083 --> 00:06:22.077
"on demand now to do whatever you need,"

00:06:22.077 --> 00:06:24.032
when they only have 10 million in reserves

00:06:24.032 --> 00:06:24.811
to back that up.

00:06:24.811 --> 00:06:26.811
The rest of their assets
are IOUs from people,

00:06:26.811 --> 00:06:28.167
but this is exactly what's happening

00:06:28.167 --> 00:06:30.032
with the other conceptual version.

00:06:30.032 --> 00:06:32.763
I guess the more traditional
conceptual reserve,

00:06:33.626 --> 00:06:35.956
the more traditional
conceptual understanding

00:06:35.956 --> 00:06:37.373
of fractional reserve lending.

00:06:37.373 --> 00:06:39.031
You're telling someone
that they have 100 million

00:06:39.031 --> 00:06:39.814
on demand,

00:06:39.814 --> 00:06:41.287
but you're loaning 90 million of it out.

00:06:41.287 --> 00:06:42.069
What they really have,

00:06:42.069 --> 00:06:43.595
truly in the vault,

00:06:43.595 --> 00:06:45.169
is $10 million.

00:06:45.169 --> 00:06:46.984
So these two things,

00:06:46.984 --> 00:06:47.940
these two things,

00:06:47.940 --> 00:06:49.068
are actually functionally,

00:06:49.068 --> 00:06:51.350
these two things are
completely equivalent,

00:06:51.350 --> 00:06:53.595
and if you have a problem
with one of these,

00:06:53.595 --> 00:06:55.126
if you feel like just
money is being created

00:06:55.126 --> 00:06:55.694
by the bank,

00:06:55.694 --> 00:06:57.439
it's actually happening in both cases.

00:06:57.439 --> 00:06:59.319
In that case, you would be having trouble

00:06:59.319 --> 00:07:01.658
with fractional reserve lending,

00:07:01.658 --> 00:07:04.295
not just this idea right over here.


Simple fractional reserve accounting (part 1)

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:01.501
Voiceover: What I want
to do in this video is

00:00:01.501 --> 00:00:05.242
start to visualize the balance
sheet for a simple bank

00:00:05.242 --> 00:00:07.271
so we can start to understand
the actual mechanics

00:00:07.271 --> 00:00:11.346
for how a bank accounts for
its assets and liabilities

00:00:11.346 --> 00:00:14.516
in the context of a
fractional reserve system.

00:00:14.716 --> 00:00:16.543
First, let's just give a general idea

00:00:16.543 --> 00:00:17.795
of what a balance sheet is,

00:00:17.795 --> 00:00:20.137
and I go into a lot more
depth in other playlists,

00:00:20.137 --> 00:00:22.145
but when we talk about a balance sheet,

00:00:22.145 --> 00:00:23.437
we're really just talking about

00:00:23.437 --> 00:00:25.217
how many assets does something have,

00:00:25.217 --> 00:00:26.905
and how many liabilities offset it,

00:00:26.905 --> 00:00:30.052
and how much is left over
for the owners of the firm

00:00:30.052 --> 00:00:31.833
or whatever we're talking about.

00:00:31.833 --> 00:00:33.206
For example,

00:00:33.206 --> 00:00:35.692
So, for example, if I have, let's say,

00:00:35.692 --> 00:00:38.520
let's just say, generalize
it to any type of company.

00:00:38.520 --> 00:00:39.689
Let's say that they have,

00:00:39.689 --> 00:00:42.215
so over here, I'll draw their assets,

00:00:42.215 --> 00:00:45.388
so their assets, I'll
do it in this green box.

00:00:45.388 --> 00:00:46.791
The height of it is kind of the magnitude

00:00:46.791 --> 00:00:47.947
of their assets.

00:00:47.947 --> 00:00:49.230
Let's say there's some company

00:00:49.230 --> 00:00:52.494
that has $100 million in assets,

00:00:52.494 --> 00:00:53.984
and assets, you probably understand.

00:00:53.984 --> 00:00:55.963
It's something that gives
you some type of benefit.

00:00:55.963 --> 00:00:57.172
The more formal definition

00:00:57.172 --> 00:00:59.024
is something that gives
you some future value,

00:00:59.024 --> 00:01:00.695
and it's generally considered to have

00:01:00.695 --> 00:01:02.216
some positive economic value,

00:01:02.216 --> 00:01:04.197
so it could be cash because
cash can be converted

00:01:04.197 --> 00:01:05.691
into other things.

00:01:05.691 --> 00:01:06.553
You can go buy a cow,

00:01:06.553 --> 00:01:08.122
and that cow can provide milk for you

00:01:08.122 --> 00:01:09.727
and give you future benefit.

00:01:09.727 --> 00:01:11.118
A cow itself would be an asset.

00:01:11.118 --> 00:01:12.218
A building would be an asset,

00:01:12.218 --> 00:01:13.871
because it gives you the future value

00:01:13.871 --> 00:01:15.786
of giving you shelter,

00:01:15.786 --> 00:01:16.880
so assets could be anything,

00:01:16.880 --> 00:01:18.666
but here for the sake of this company,

00:01:18.666 --> 00:01:21.507
we could even visualize
it as cash, if you like.

00:01:21.507 --> 00:01:23.794
It has $100 million of assets,

00:01:23.794 --> 00:01:25.741
and let's say it has some liabilities,

00:01:25.741 --> 00:01:27.566
so let's say this company right over here

00:01:27.566 --> 00:01:29.854
has 60 million in liabilities.

00:01:29.854 --> 00:01:31.939
I'm trying to do it roughly
equal to the height.

00:01:31.939 --> 00:01:33.102
It's not exact,

00:01:33.102 --> 00:01:37.553
but let's say that they have
60 million in liabilities.

00:01:37.553 --> 00:01:39.917
Liabilities are just obligations,

00:01:39.917 --> 00:01:43.919
so it owes people $60
million worth of stuff,

00:01:43.919 --> 00:01:45.185
and so when you look at it this way,

00:01:45.185 --> 00:01:46.720
this entity here,

00:01:46.720 --> 00:01:47.966
it could be a company, a firm,

00:01:47.966 --> 00:01:49.651
you could even call this a person,

00:01:49.651 --> 00:01:50.805
if this was a person.

00:01:50.805 --> 00:01:52.804
They have $100 million of assets,

00:01:52.804 --> 00:01:55.265
but they owe 60 million of that 100,

00:01:55.265 --> 00:01:56.538
or you could say they owe 60,

00:01:56.538 --> 00:01:58.377
and you could view it of that 100 million,

00:01:58.377 --> 00:02:00.051
so they would have 40 million left over

00:02:00.051 --> 00:02:00.947
for themselves.

00:02:00.947 --> 00:02:03.780
If you were to say, "What
is the value of this?"

00:02:03.780 --> 00:02:05.387
How much do the owners of this entity,

00:02:05.387 --> 00:02:07.985
actually, how much are they
worth from this entity?

00:02:07.985 --> 00:02:10.283
It would be the 100 minus the 60.

00:02:10.283 --> 00:02:12.406
they have 100, they owe 60,

00:02:12.406 --> 00:02:14.692
so the owner's equity, right over here,

00:02:14.692 --> 00:02:17.222
would be $40 million.

00:02:17.222 --> 00:02:18.784
That's really kind of the value

00:02:18.784 --> 00:02:20.726
of what the owners have,

00:02:20.726 --> 00:02:25.280
and it's called owner's equity.

00:02:25.280 --> 00:02:26.848
That's just a basic primary

00:02:26.848 --> 00:02:28.456
primer in assets and liabilities,

00:02:28.456 --> 00:02:29.346
and now I want to use,

00:02:29.346 --> 00:02:30.843
I want to build on that to think about

00:02:30.843 --> 00:02:31.787
what's actually happening

00:02:31.787 --> 00:02:33.957
in a fractional reserve
system with the bank,

00:02:33.957 --> 00:02:35.102
and what we're going to see is,

00:02:35.102 --> 00:02:36.526
the way it's actually done mechanically

00:02:36.526 --> 00:02:37.924
in a modern fractional reserve system

00:02:37.924 --> 00:02:39.072
is slightly different than

00:02:39.072 --> 00:02:40.493
the way you would conceptualize it,

00:02:40.493 --> 00:02:41.009
the way you,

00:02:41.009 --> 00:02:43.614
actually, I've been
conceptualizing it for you guys,

00:02:43.614 --> 00:02:44.570
because that's just an easier way

00:02:44.570 --> 00:02:46.074
to think about things.

00:02:46.074 --> 00:02:48.235
Let's just say we were
going to go start a bank.

00:02:48.235 --> 00:02:52.126
Let's say I want to start a bank,

00:02:52.126 --> 00:02:55.146
and what I do is I go and I take,

00:02:55.146 --> 00:02:57.001
I go buy a, I don't know.

00:02:57.001 --> 00:03:00.514
Let's say I go buy a $10
million existing bank.

00:03:00.775 --> 00:03:02.462
Here, I have an asset,

00:03:02.462 --> 00:03:05.143
which is my equipment and the building

00:03:05.143 --> 00:03:07.933
and all of the computers
and all of the things,

00:03:07.933 --> 00:03:09.942
all of the things that can
essentially run a bank,

00:03:09.942 --> 00:03:13.491
and that's worth $10 million,

00:03:13.491 --> 00:03:15.192
and this is my owner's equity.

00:03:15.192 --> 00:03:17.492
So i have $10 million of owner's equity.

00:03:17.492 --> 00:03:19.506
Maybe I'll do it in those
same colors that I did,

00:03:19.506 --> 00:03:21.583
so let me do this in that green color.

00:03:21.583 --> 00:03:22.758
This is an asset,

00:03:22.758 --> 00:03:24.073
and I have no liabilities yet.

00:03:24.073 --> 00:03:26.016
Let's just say that I
inherited that money,

00:03:26.016 --> 00:03:27.828
or that was just money
that I had saved up,

00:03:27.828 --> 00:03:29.934
so I went in and bought
a $10 million asset,

00:03:29.934 --> 00:03:31.196
and so my equity,

00:03:31.196 --> 00:03:33.155
since there's no offsetting liabilities

00:03:33.155 --> 00:03:34.683
is $10 million,

00:03:34.683 --> 00:03:37.663
so this is my owner's
equity right over here,

00:03:37.663 --> 00:03:39.657
is $10 million,

00:03:39.657 --> 00:03:42.656
so I'll just call it equity.

00:03:42.656 --> 00:03:44.378
Now, let's say that, you know,

00:03:44.378 --> 00:03:46.439
you were impressed with my building,

00:03:46.439 --> 00:03:47.883
and my IT systems,

00:03:47.883 --> 00:03:50.765
and the number of ATMs
that I have around town,

00:03:50.765 --> 00:03:52.326
so you decide that you want to deposit

00:03:52.326 --> 00:03:54.130
some money with me,

00:03:54.130 --> 00:03:56.135
so let's say that you take your,

00:03:56.135 --> 00:03:57.190
you take a wheelbarrow,

00:03:57.190 --> 00:04:00.315
and in your wheelbarrow,
you come and you deposit,

00:04:00.315 --> 00:04:03.099
let's say you deposit
$100 million in my bank,

00:04:03.099 --> 00:04:04.268
in cash.

00:04:04.268 --> 00:04:05.649
These are cash reserves.

00:04:05.649 --> 00:04:07.081
These are federal reserve notes

00:04:07.081 --> 00:04:08.511
that you're depositing in my bank,

00:04:08.511 --> 00:04:09.827
so I'll draw these as assets.

00:04:09.827 --> 00:04:10.782
So this is ...

00:04:11.089 --> 00:04:13.078
So, let me do $100 million,

00:04:13.078 --> 00:04:14.663
so it should be about 10 times as high

00:04:14.663 --> 00:04:15.909
as what I've already drawn,

00:04:15.909 --> 00:04:17.128
so you're going to come here,

00:04:17.128 --> 00:04:18.369
and you're going to deposit.

00:04:18.799 --> 00:04:22.168
you are going to deposit $100 million.

00:04:22.168 --> 00:04:24.315
So this is $100 million,

00:04:24.960 --> 00:04:29.027
100 million of, I'll call it cash,

00:04:29.027 --> 00:04:29.675
of cash.

00:04:29.675 --> 00:04:31.193
We'll visualize it as physical cash,

00:04:31.193 --> 00:04:33.683
and it goes into these
vaults that I had purchased,

00:04:33.683 --> 00:04:35.532
and so that's the asset that I got,

00:04:35.532 --> 00:04:37.672
but obviously, you're not
just giving me this cash.

00:04:37.672 --> 00:04:39.149
Then I would be $100 million richer.

00:04:39.149 --> 00:04:40.050
You're keeping that,

00:04:40.050 --> 00:04:41.913
you want that on demand.

00:04:41.913 --> 00:04:42.891
You want that in a checking account

00:04:42.891 --> 00:04:44.221
so that you can write checks against it

00:04:44.221 --> 00:04:45.809
and access it from your ATM,

00:04:45.809 --> 00:04:47.805
and so I have an offsetting liability.

00:04:47.805 --> 00:04:50.814
My offsetting liability

00:04:50.814 --> 00:04:54.797
is that this is essentially
a demand deposit for you,

00:04:54.797 --> 00:04:55.975
so this is,

00:04:55.975 --> 00:04:57.623
I guess the way we can view it is,

00:04:58.222 --> 00:05:00.229
the way we can view it is,

00:05:00.229 --> 00:05:02.431
we can write it as a checkable,

00:05:02.431 --> 00:05:06.594
checkable deposit,

00:05:06.594 --> 00:05:08.661
and I'm viewing it from
the bank's perspective.

00:05:08.661 --> 00:05:09.990
That's why it's a liability

00:05:09.990 --> 00:05:12.263
because someone can hand me a check,

00:05:12.263 --> 00:05:14.520
and I would have to give them some money.

00:05:14.520 --> 00:05:15.926
This is an obligation.

00:05:15.926 --> 00:05:17.227
If someone writes a check

00:05:17.227 --> 00:05:19.564
against these deposits to someone else,

00:05:19.564 --> 00:05:21.309
that's an obligation that I, as the bank,

00:05:21.309 --> 00:05:22.330
have to service.

00:05:22.330 --> 00:05:24.063
I could call this just a checking account,

00:05:24.063 --> 00:05:25.662
or checking accounts of person A.

00:05:25.662 --> 00:05:27.130
Maybe that makes it easier to,

00:05:27.637 --> 00:05:30.157
A's checking account
is a liability for me,

00:05:30.157 --> 00:05:31.171
so let me call it,

00:05:31.171 --> 00:05:32.523
if I haven't called them person A already,

00:05:32.523 --> 00:05:33.471
I'm calling them now.

00:05:33.471 --> 00:05:35.374
Person A's checking account,

00:05:35.774 --> 00:05:39.023
checking account, and that's a liability

00:05:39.023 --> 00:05:40.917
because person A can come at any time

00:05:40.917 --> 00:05:46.532
and they can demand $100 million of cash.

00:05:46.532 --> 00:05:48.296
Now, this, right over here,

00:05:48.296 --> 00:05:49.793
I haven't done anything fractional yet.

00:05:49.793 --> 00:05:52.068
This is just regular, so far,

00:05:52.068 --> 00:05:53.885
this would be equivalent
to full reserve banking.

00:05:53.885 --> 00:05:56.804
I'm just keeping person A's money safe.

00:05:56.804 --> 00:05:59.092
We know in a fractional reserve system,

00:05:59.092 --> 00:06:00.991
I can lend out a good bit of money,

00:06:00.991 --> 00:06:03.734
so that's, essentially,
what I could then do,

00:06:03.734 --> 00:06:05.840
if we're talking about fractional reserve.

00:06:05.840 --> 00:06:07.780
I can lend out 90% of this money.

00:06:08.195 --> 00:06:10.640
I could lend out 90% of this,

00:06:10.640 --> 00:06:12.076
so let me take out 90%,

00:06:12.076 --> 00:06:14.754
so let me clear this right over here.

00:06:15.354 --> 00:06:17.057
Let me clear that,

00:06:17.395 --> 00:06:18.936
and so let's say I took out 90% out of it,

00:06:18.936 --> 00:06:20.119
and lent it out,

00:06:20.119 --> 00:06:21.665
and so we only have 10 million

00:06:21.665 --> 00:06:23.800
of the original cash there as reserves,

00:06:23.800 --> 00:06:24.795
and I'll call them reserves now.

00:06:24.795 --> 00:06:26.800
But that's 10 million of the original,

00:06:26.800 --> 00:06:31.401
so I'm going to have 10
million of reserves left,

00:06:31.401 --> 00:06:33.271
and everything else I lent out,

00:06:33.271 --> 00:06:35.895
so everything else I lent out,

00:06:35.895 --> 00:06:38.882
so 90 million, I lent,

00:06:39.697 --> 00:06:41.792
90 million of lending,

00:06:41.792 --> 00:06:44.480
so we can even visualize
it as big stacks of cash

00:06:44.480 --> 00:06:46.046
that I handed out to people,

00:06:46.046 --> 00:06:46.717
and then you might say,

00:06:46.717 --> 00:06:48.996
"Well, I didn't just give
that to those people."

00:06:48.996 --> 00:06:51.800
In exchange for that, they are saying

00:06:51.800 --> 00:06:52.569
I'm going to pay me back.

00:06:52.569 --> 00:06:53.708
So that's an asset.

00:06:53.708 --> 00:06:55.822
If you borrow money from me,

00:06:55.945 --> 00:06:57.401
it's an obligation for you.

00:06:57.401 --> 00:06:58.407
It's a liability for you,

00:06:58.407 --> 00:06:59.796
but it's an asset for me.

00:06:59.796 --> 00:07:00.896
Let me make this clear.

00:07:01.111 --> 00:07:02.374
So, if I'm a bank,

00:07:03.128 --> 00:07:04.257
if I'm a bank,

00:07:04.257 --> 00:07:06.291
and there's a borrower,

00:07:06.291 --> 00:07:08.958
there is a borrower,

00:07:08.958 --> 00:07:10.498
there is a borrower,

00:07:10.498 --> 00:07:11.849
and if I give the borrower,

00:07:11.849 --> 00:07:14.481
if I give the borrower $1,

00:07:14.481 --> 00:07:16.270
if I give them $1,

00:07:16.270 --> 00:07:17.290
you could visualize it,

00:07:17.290 --> 00:07:18.668
although that's not exactly how it works,

00:07:18.668 --> 00:07:20.212
is that they give an IOU.

00:07:20.212 --> 00:07:22.202
They give the bank an IOU.

00:07:22.202 --> 00:07:25.136
I owe you $1 at some future date.

00:07:25.136 --> 00:07:26.932
Now, from the bank's point of view,

00:07:26.932 --> 00:07:28.805
this IOU is an asset.

00:07:28.805 --> 00:07:30.309
They're essentially exchanging assets.

00:07:30.309 --> 00:07:31.889
The bank is giving it a $1,

00:07:31.889 --> 00:07:33.976
the borrower is giving an IOU.

00:07:33.976 --> 00:07:35.254
From the borrower's point of view,

00:07:35.254 --> 00:07:36.889
the dollar is an asset,

00:07:36.889 --> 00:07:38.620
and this IOU is a liability.

00:07:38.620 --> 00:07:39.882
But from the bank's point of view,

00:07:39.882 --> 00:07:41.599
it's like, "Oh, I have this IOU.

00:07:41.599 --> 00:07:43.065
"Maybe I could give this to someone else.

00:07:43.065 --> 00:07:44.245
"Maybe I could sell this IOU.

00:07:44.245 --> 00:07:46.107
"This IOU is going to
give me future benefit."

00:07:46.107 --> 00:07:47.615
Because assuming this person's good

00:07:47.615 --> 00:07:48.362
for their money,

00:07:48.362 --> 00:07:50.522
they're going to give that money back.

00:07:50.522 --> 00:07:51.586
That's the same reason why a check

00:07:51.586 --> 00:07:53.571
is a liability of the bank.

00:07:53.571 --> 00:07:54.890
If you write a check to someone,

00:07:54.890 --> 00:07:57.188
the bank has a responsibility to,

00:07:57.188 --> 00:07:58.920
if someone were to give
that check to the bank,

00:07:58.920 --> 00:08:00.779
to give them cash.

00:08:00.779 --> 00:08:01.776
So, in a similar way,

00:08:01.776 --> 00:08:03.558
when the bank lends out all of this money,

00:08:03.558 --> 00:08:04.801
they're going to get IOUs

00:08:04.801 --> 00:08:06.274
from all the people that they lent it to,

00:08:06.274 --> 00:08:07.978
so they're going to have,

00:08:07.978 --> 00:08:11.420
they're going to get 90 million of IOUs.

00:08:11.420 --> 00:08:13.921
We could say 90 million worth of loans,

00:08:13.921 --> 00:08:15.305
but you really could just view those

00:08:15.305 --> 00:08:16.864
as these are IOUs to other people.

00:08:16.864 --> 00:08:18.898
This is an asset because
it's going to give

00:08:18.898 --> 00:08:21.973
some future benefit at some future time.

00:08:21.973 --> 00:08:22.787
I'm going to leave you there,

00:08:22.787 --> 00:08:24.225
because what I did here,

00:08:24.225 --> 00:08:25.469
this is conceptually identical

00:08:25.469 --> 00:08:26.808
to everything we've been talking about.

00:08:26.808 --> 00:08:28.799
This is, frankly, how
most people visualize

00:08:28.799 --> 00:08:30.204
fractural reserve lending.

00:08:30.204 --> 00:08:33.229
You get 100 million reserves,

00:08:33.229 --> 00:08:35.823
you lend out 90 million of that reserves,

00:08:35.823 --> 00:08:37.149
and you exchange that for an asset,

00:08:37.149 --> 00:08:38.825
which is essentially an IOU.

00:08:38.825 --> 00:08:39.814
What we'll see in the next video

00:08:39.814 --> 00:08:41.329
is this isn't exactly true.

00:08:41.329 --> 00:08:42.465
What a bank could actually do

00:08:42.465 --> 00:08:43.386
is it could actually create.

00:08:43.386 --> 00:08:45.778
It could actually take just
the 10 million of reserves

00:08:45.778 --> 00:08:47.866
and then it could create these assets,

00:08:47.866 --> 00:08:49.562
which are functionally equivalent.

00:08:49.562 --> 00:08:50.508
It looks a little bit shady

00:08:50.508 --> 00:08:52.175
the first time you think about it,

00:08:52.175 --> 00:08:53.990
but they're actually
functionally equivalent,

00:08:53.990 --> 00:08:55.466
so it's not as shady

00:08:55.466 --> 00:08:57.869
as you might initially think it to be,

00:08:57.869 --> 00:09:00.125
and we'll cover that in the next video.