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Male: In the last video,
we began our exploration

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of what a consumption function is.

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It's a fairly straightforward idea.

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It's a function that describes how

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aggregate income can drive
aggregate consumption.

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We started with a fairly
simple model of this,

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a fairly simple consumption function.

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It was a linear one.

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You had some base level of consumption,

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regardless of aggregate income,

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and then you had some level of consumption

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that was essentially induced by having

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some disposable income.

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When we plotted this linear
model, we got a line.

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We got a line right over here.

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I pointed out in the last video

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this does not have to be the only way

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that a consumption
function can be described.

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You might use some fancier
mathematical tools.

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Maybe you can construct
a consumption function.

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You have an argument.

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You would argue that
the marginal propensity

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to consume is higher at lower levels

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of disposable income and
that it kind of tapers out

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as disposable income, as aggregate

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disposable income goes up.

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You might think that maybe you should have

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a fancier consumption function

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that when you graph it
would look like this

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and then you would have to use things

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fancier than just what
we used right over here.

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What I want to do in this video

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is focus more on a linear model.

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The reason why I'm going to focus on

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a linear model is because,
one, it's simpler.

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It'll be easier to manipulate.

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It's also the model that tends to be used

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right when people are starting to digest

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things like consumption functions

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and building on them to learn about things

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like, and we'll do this in a few videos,

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the Keynesian Cross.

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What I'm going to do is,
I'm going to do two things.

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I'm going to generalize this linear

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consumption function,
and I'm going to make it

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a function not just of disposal income,

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not just of aggregate disposable income,

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which is what we did in the last video,

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but as a function of
income, of aggregate income.

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Then we will plot that generalized one

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based on the variables.

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It's really going to be the same thing.

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We're just not going to use these numbers.

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We're going to use
variables in their place.

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Let's give ourselves a
linear consumption function.

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We can say that aggregate consumption

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where we're going to have some base level

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of consumption no matter
what, even if people

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have no aggregate income,
they need to survive.

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They need food on the table.

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Maybe they'll have to dig
in savings somehow to do it.

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So, some base level of consumption.

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I'll call that lower case c sub zero.

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Or lowercase c with a subscript
of zero right over there.

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That's the base level
of aggregate consumption

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or it's sometimes referred
to as autonomous consumption.

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This is autonomous
consumption because people

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will do it on their own, or in aggregate

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they will do it on their
own, even if they have

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no aggregate income.

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Then we will have the part that is due,

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directly due, to having
some aggregate income.

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We call that the induced consumption,

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because you can view it as being induced

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by having some aggregate income.

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Above and beyond what the
base level of consumption,

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people are going to consume some fraction

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of their disposable income.

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So we'll say disposable income.

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They're not going to consume all

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of their disposable income.

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They might save some of it.

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So they're going to consume the fraction

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that's essentially their
marginal propensity to consume.

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This right over here, I'll
do that in this orange color.

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Marginal propensity to consume.

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Hopefully this makes intuitive sense.

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This says, look, if this was 100,

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people are going to
consume 100 no matter what,

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100 billion whatever
your unit of currency is.

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Now, if their marginal propensity

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to consume is, let's say, it is 1/3.

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You have now above and beyond this

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people have disposable
income of let's say 900,

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this is saying that
they want to consume 1/3

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of that disposable income they're getting.

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That is, if you give them 900 of extra

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disposable income, they're propensity

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to consume that incremental income,

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they're going to consume 1/3 of it.

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So this would be 1/3, so it would be 900.

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Let me give an example.

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If you had a situation,
you could have a situation,

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where c-nought is equal to 100.

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If you have disposable
income is equal to 900,

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and c1 is equal to 1/3, or we could say

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0.333 repeating forever, c1 is 1/3.

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Then this makes sense.

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On their own people
would consume this much,

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but now they have this disposable income.

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Their marginal propensity to consume

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if you give them 900 extra of income,

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they're going to consume 1/3 of that.

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So then you're going to
have, your consumption

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is going to be equal to, for
this case right over here,

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your consumption is going to
be 100 plus 1/3 times 900.

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So your consumption in this situation,

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your induced consumption, 1/3 times 900,

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would be 300, maybe it's
in billions of dollars,

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300 billion dollars.

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Then your autonomous
consumption would be 100.

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They would add up to 400.

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Once again, this is autonomous
and this is induced.

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Autonomous, this right over
here is induced consumption.

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Now, I did write it in general terms.

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I'm using variables here
instead of, or constants, really

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instead of using the numbers
we saw in the last example.

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But I also said that I would express

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aggregate consumption
as a function not just

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of disposable income
but of aggregate income;

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not just of aggregate disposable income

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but aggregate income.

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The relationship is fairly simple between

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disposable income and overall income.

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We saw over here, in
aggregate, you have income,

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but the government in
most modern economies

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takes some fraction of that out for taxes.

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What's left over is disposable income.

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Just a reminder, income in aggregate,

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aggregate income is the same thing as

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aggregate expenditures,

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which is the same thing
as aggregate output.

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This right over here is GDP.

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So this right over here is, let me do this

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in a color, I've used
almost all my colors.

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This is equal to GDP.

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Disposable income is essentially GDP,

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or you could say aggregate
income, minus taxes.

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I'm going to do the taxes
in a different color.

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Minus taxes.

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So we can express disposable income

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as aggregate income, this right over here

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is the same thing as
aggregate income minus taxes.

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We could rewrite our
whole thing over again.

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Aggregate consumption is equal
to autonomous consumption

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plus the marginal propensity to consume

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times aggregate income,
which is the same thing

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as GDP, times aggregate
income minus taxes.

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We fully generalized
our consumption function

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and now we've written it as a
function of aggregate income,

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not just aggregate disposable income.

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To make you comfortable
that this is still a line

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if we were to plot it as a function

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of aggregate income instead
of disposable income,

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let me manipulate this thing a little bit.

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We could distribute c1, which is our

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marginal propensity to consume, and we get

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aggregate consumption is equal
to autonomous consumption

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and then we're going to distribute this,

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plus c, so we're going to multiply it

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times both of these terms,

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plus our marginal propensity to consume

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times aggregate income,

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and then minus our marginal
propensity to consume

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times our taxes.

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Since we want it as a
function of aggregate income,

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everything else here is really a constant.

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We're assuming that those
aren't going to change.

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Those are constant variables.

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What we could do is we could rewrite this

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in a form that you're
probably familiar with.

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Back in algebra class
you probably remember

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you can write it in the form y=mx+b where

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x is the independent variable,

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y is the dependent variable.

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If you were to plot this,

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on the horizontal axis is your x axis,

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your vertical axis is your y axis.

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This right over here
would have a y intercept,

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or your vertical axis intercept
of b, right over there.

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Then it would be a line with slope m.

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If you were to take your
rise divided by your run,

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or how much you move up
when you move to the right

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a certain amount, that gives you your m.

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Slope is equal to m.

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The same analogy is here.

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We can rewrite this in that form,

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where our dependent
variable is no longer y.

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Our dependent variable
is aggregate consumption.

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Our independent variable is
not x, it is aggregate income.

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So let's write it in that form.

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We can write it as dependent variable, c,

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which we'll plot on the vertical axis,

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is equal to the marginal
propensity to consume

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times aggregate income,

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I'll do that purple color,

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times aggregate income,

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plus autonomous consumption,

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minus marginal propensity
to consume times taxes.

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It looks all complicated, but you just

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have to realize that this
part right over here,

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this is all a constant.

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It is analogous to the
b if you were to write

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things in kind of
traditional slope intercept

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form right over here.

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When we plot the line, if you have no

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aggregate income, this is what your

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consumption is going to be.

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Let me draw that.

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Once again, our dependent
variable is aggregate consumption.

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Our independent variable
in this is no longer

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disposable income like
we did in the last video.

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It is now aggregate income.

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If there's no aggregate income,

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this is the independent
variable right over here,

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if there's no aggregate income,

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then your consumption is just going to be

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this value right over here.

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So your consumption is just going to be

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that value right over
there, which is c-nought

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minus c1 times t.

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Then as you have larger values of

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aggregate income, c1, that fraction of it,

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is what's going to contribute
to the induced consumption.

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What you essentially
have is this is the slope

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of our line, this right
over here is our slope.

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Just to kind of draw the analogy,

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if you were to say y
is equal to mx plus b.

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Actually, maybe I'll write it like this.

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If you were to write c is equal to m ...

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and I don't want to
confuse you if this m and b

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seem completely foreign.

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It comes from kind of
a traditional algebra

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grounding in slope and y intercept.

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If I were to say c is equal to my plus b,

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this is the slope.

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This is our vertical or our
dependent variable intercept

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right over here.

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That's where we intercept the dependent

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variable axis.

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And this is our slope.

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It's our marginal propensity to consume.

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Our line will look something like this,

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where the slope is equal to the marginal

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propensity to consume,
which is equal to c1.

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If people all of a sudden are more likely

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to spend a larger
fraction of their income,

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then the marginal propensity to consume

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00:11:36,777 --> 00:11:38,941
would be higher and our
slope would be higher.

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00:11:38,941 --> 00:11:40,363
We would have a line that looks like that.

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00:11:40,363 --> 00:11:41,934
We always assume that the marginal

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00:11:41,934 --> 00:11:44,319
propensity to consume will be less than 1.

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00:11:44,319 --> 00:11:45,942
So we'll never have a slope of 1.

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00:11:45,942 --> 00:11:47,637
We'll also never have a negative slope

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00:11:47,637 --> 00:11:49,410
because we assume that this is positive.

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00:11:49,410 --> 00:11:51,780
If people are more likely
to save than consume

267
00:11:51,780 --> 00:11:54,612
when they have extra
income, then this line

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00:11:54,612 --> 00:11:56,101
might look something like that.

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00:11:56,101 --> 00:11:57,840
It might have a lower slope.