Economics Exam > Economics Videos > Generalized linear consumption function - Economics
Generalized linear consumption function - Economics Video Lecture
FAQs on Generalized linear consumption function - Economics
| 1. What is a generalized linear consumption function? |  |
Ans. A generalized linear consumption function is an economic model that represents the relationship between consumption and income. It assumes that consumption is a linear function of income, but also takes into account other factors such as interest rates, government policies, and consumer expectations.
| 2. How does a generalized linear consumption function differ from a simple linear consumption function? | |
Ans. While a simple linear consumption function assumes that consumption is solely determined by income, a generalized linear consumption function incorporates additional factors that influence consumption. These factors can include interest rates, government policies, and consumer expectations, making it a more comprehensive model.
| 3. What are some examples of factors that can affect consumption in a generalized linear consumption function? | |
Ans. Factors that can affect consumption in a generalized linear consumption function include interest rates, government policies (such as tax rates or subsidies), consumer expectations about future income or prices, and demographic factors (such as age or household size). These factors can influence the propensity to consume and the marginal propensity to consume.
| 4. How can a generalized linear consumption function be used in economic analysis? | |
Ans. A generalized linear consumption function can be used in economic analysis to study the relationship between consumption and income, and to understand how other factors impact consumption. By estimating the parameters of the consumption function, economists can make predictions about how changes in income or other factors will affect consumption levels. This can be useful in analyzing the effects of government policies or changes in interest rates on consumer behavior.
| 5. Are there any limitations to using a generalized linear consumption function? | |
Ans. Yes, there are limitations to using a generalized linear consumption function. The model assumes a linear relationship between consumption and income, which may not always hold true in reality. Additionally, the inclusion of other factors in the model may introduce additional complexity and make it more difficult to estimate the parameters accurately. Furthermore, the model does not account for all possible factors that can influence consumption, and individual behavior may vary significantly from the assumptions of the model.
Text Transcript from Video
Male: In the last video,
we began our exploration
of what a consumption function is.
It's a fairly straightforward idea.
It's a function that describes how
aggregate income can drive
aggregate consumption.
We started with a fairly
simple model of this,
a fairly simple consumption function.
It was a linear one.
You had some base level of consumption,
regardless of aggregate income,
and then you had some level of consumption
that was essentially induced by having
some disposable income.
When we plotted this linear
model, we got a line.
We got a line right over here.
I pointed out in the last video
this does not have to be the only way
that a consumption
function can be described.
You might use some fancier
mathematical tools.
Maybe you can construct
a consumption function.
You have an argument.
You would argue that
the marginal propensity
to consume is higher at lower levels
of disposable income and
that it kind of tapers out
as disposable income, as aggregate
disposable income goes up.
You might think that maybe you should have
a fancier consumption function
that when you graph it
would look like this
and then you would have to use things
fancier than just what
we used right over here.
What I want to do in this video
is focus more on a linear model.
The reason why I'm going to focus on
a linear model is because,
one, it's simpler.
It'll be easier to manipulate.
It's also the model that tends to be used
right when people are starting to digest
things like consumption functions
and building on them to learn about things
like, and we'll do this in a few videos,
the Keynesian Cross.
What I'm going to do is,
I'm going to do two things.
I'm going to generalize this linear
consumption function,
and I'm going to make it
a function not just of disposal income,
not just of aggregate disposable income,
which is what we did in the last video,
but as a function of
income, of aggregate income.
Then we will plot that generalized one
based on the variables.
It's really going to be the same thing.
We're just not going to use these numbers.
We're going to use
variables in their place.
Let's give ourselves a
linear consumption function.
We can say that aggregate consumption
where we're going to have some base level
of consumption no matter
what, even if people
have no aggregate income,
they need to survive.
They need food on the table.
Maybe they'll have to dig
in savings somehow to do it.
So, some base level of consumption.
I'll call that lower case c sub zero.
Or lowercase c with a subscript
of zero right over there.
That's the base level
of aggregate consumption
or it's sometimes referred
to as autonomous consumption.
This is autonomous
consumption because people
will do it on their own, or in aggregate
they will do it on their
own, even if they have
no aggregate income.
Then we will have the part that is due,
directly due, to having
some aggregate income.
We call that the induced consumption,
because you can view it as being induced
by having some aggregate income.
Above and beyond what the
base level of consumption,
people are going to consume some fraction
of their disposable income.
So we'll say disposable income.
They're not going to consume all
of their disposable income.
They might save some of it.
So they're going to consume the fraction
that's essentially their
marginal propensity to consume.
This right over here, I'll
do that in this orange color.
Marginal propensity to consume.
Hopefully this makes intuitive sense.
This says, look, if this was 100,
people are going to
consume 100 no matter what,
100 billion whatever
your unit of currency is.
Now, if their marginal propensity
to consume is, let's say, it is 1/3.
You have now above and beyond this
people have disposable
income of let's say 900,
this is saying that
they want to consume 1/3
of that disposable income they're getting.
That is, if you give them 900 of extra
disposable income, they're propensity
to consume that incremental income,
they're going to consume 1/3 of it.
So this would be 1/3, so it would be 900.
Let me give an example.
If you had a situation,
you could have a situation,
where c-nought is equal to 100.
If you have disposable
income is equal to 900,
and c1 is equal to 1/3, or we could say
0.333 repeating forever, c1 is 1/3.
Then this makes sense.
On their own people
would consume this much,
but now they have this disposable income.
Their marginal propensity to consume
if you give them 900 extra of income,
they're going to consume 1/3 of that.
So then you're going to
have, your consumption
is going to be equal to, for
this case right over here,
your consumption is going to
be 100 plus 1/3 times 900.
So your consumption in this situation,
your induced consumption, 1/3 times 900,
would be 300, maybe it's
in billions of dollars,
300 billion dollars.
Then your autonomous
consumption would be 100.
They would add up to 400.
Once again, this is autonomous
and this is induced.
Autonomous, this right over
here is induced consumption.
Now, I did write it in general terms.
I'm using variables here
instead of, or constants, really
instead of using the numbers
we saw in the last example.
But I also said that I would express
aggregate consumption
as a function not just
of disposable income
but of aggregate income;
not just of aggregate disposable income
but aggregate income.
The relationship is fairly simple between
disposable income and overall income.
We saw over here, in
aggregate, you have income,
but the government in
most modern economies
takes some fraction of that out for taxes.
What's left over is disposable income.
Just a reminder, income in aggregate,
aggregate income is the same thing as
aggregate expenditures,
which is the same thing
as aggregate output.
This right over here is GDP.
So this right over here is, let me do this
in a color, I've used
almost all my colors.
This is equal to GDP.
Disposable income is essentially GDP,
or you could say aggregate
income, minus taxes.
I'm going to do the taxes
in a different color.
Minus taxes.
So we can express disposable income
as aggregate income, this right over here
is the same thing as
aggregate income minus taxes.
We could rewrite our
whole thing over again.
Aggregate consumption is equal
to autonomous consumption
plus the marginal propensity to consume
times aggregate income,
which is the same thing
as GDP, times aggregate
income minus taxes.
We fully generalized
our consumption function
and now we've written it as a
function of aggregate income,
not just aggregate disposable income.
To make you comfortable
that this is still a line
if we were to plot it as a function
of aggregate income instead
of disposable income,
let me manipulate this thing a little bit.
We could distribute c1, which is our
marginal propensity to consume, and we get
aggregate consumption is equal
to autonomous consumption
and then we're going to distribute this,
plus c, so we're going to multiply it
times both of these terms,
plus our marginal propensity to consume
times aggregate income,
and then minus our marginal
propensity to consume
times our taxes.
Since we want it as a
function of aggregate income,
everything else here is really a constant.
We're assuming that those
aren't going to change.
Those are constant variables.
What we could do is we could rewrite this
in a form that you're
probably familiar with.
Back in algebra class
you probably remember
you can write it in the form y=mx+b where
x is the independent variable,
y is the dependent variable.
If you were to plot this,
on the horizontal axis is your x axis,
your vertical axis is your y axis.
This right over here
would have a y intercept,
or your vertical axis intercept
of b, right over there.
Then it would be a line with slope m.
If you were to take your
rise divided by your run,
or how much you move up
when you move to the right
a certain amount, that gives you your m.
Slope is equal to m.
The same analogy is here.
We can rewrite this in that form,
where our dependent
variable is no longer y.
Our dependent variable
is aggregate consumption.
Our independent variable is
not x, it is aggregate income.
So let's write it in that form.
We can write it as dependent variable, c,
which we'll plot on the vertical axis,
is equal to the marginal
propensity to consume
times aggregate income,
I'll do that purple color,
times aggregate income,
plus autonomous consumption,
minus marginal propensity
to consume times taxes.
It looks all complicated, but you just
have to realize that this
part right over here,
this is all a constant.
It is analogous to the
b if you were to write
things in kind of
traditional slope intercept
form right over here.
When we plot the line, if you have no
aggregate income, this is what your
consumption is going to be.
Let me draw that.
Once again, our dependent
variable is aggregate consumption.
Our independent variable
in this is no longer
disposable income like
we did in the last video.
It is now aggregate income.
If there's no aggregate income,
this is the independent
variable right over here,
if there's no aggregate income,
then your consumption is just going to be
this value right over here.
So your consumption is just going to be
that value right over
there, which is c-nought
minus c1 times t.
Then as you have larger values of
aggregate income, c1, that fraction of it,
is what's going to contribute
to the induced consumption.
What you essentially
have is this is the slope
of our line, this right
over here is our slope.
Just to kind of draw the analogy,
if you were to say y
is equal to mx plus b.
Actually, maybe I'll write it like this.
If you were to write c is equal to m ...
and I don't want to
confuse you if this m and b
seem completely foreign.
It comes from kind of
a traditional algebra
grounding in slope and y intercept.
If I were to say c is equal to my plus b,
this is the slope.
This is our vertical or our
dependent variable intercept
right over here.
That's where we intercept the dependent
variable axis.
And this is our slope.
It's our marginal propensity to consume.
Our line will look something like this,
where the slope is equal to the marginal
propensity to consume,
which is equal to c1.
If people all of a sudden are more likely
to spend a larger
fraction of their income,
then the marginal propensity to consume
would be higher and our
slope would be higher.
We would have a line that looks like that.
We always assume that the marginal
propensity to consume will be less than 1.
So we'll never have a slope of 1.
We'll also never have a negative slope
because we assume that this is positive.
If people are more likely
to save than consume
when they have extra
income, then this line
might look something like that.
It might have a lower slope.
we began our exploration
of what a consumption function is.
It's a fairly straightforward idea.
It's a function that describes how
aggregate income can drive
aggregate consumption.
We started with a fairly
simple model of this,
a fairly simple consumption function.
It was a linear one.
You had some base level of consumption,
regardless of aggregate income,
and then you had some level of consumption
that was essentially induced by having
some disposable income.
When we plotted this linear
model, we got a line.
We got a line right over here.
I pointed out in the last video
this does not have to be the only way
that a consumption
function can be described.
You might use some fancier
mathematical tools.
Maybe you can construct
a consumption function.
You have an argument.
You would argue that
the marginal propensity
to consume is higher at lower levels
of disposable income and
that it kind of tapers out
as disposable income, as aggregate
disposable income goes up.
You might think that maybe you should have
a fancier consumption function
that when you graph it
would look like this
and then you would have to use things
fancier than just what
we used right over here.
What I want to do in this video
is focus more on a linear model.
The reason why I'm going to focus on
a linear model is because,
one, it's simpler.
It'll be easier to manipulate.
It's also the model that tends to be used
right when people are starting to digest
things like consumption functions
and building on them to learn about things
like, and we'll do this in a few videos,
the Keynesian Cross.
What I'm going to do is,
I'm going to do two things.
I'm going to generalize this linear
consumption function,
and I'm going to make it
a function not just of disposal income,
not just of aggregate disposable income,
which is what we did in the last video,
but as a function of
income, of aggregate income.
Then we will plot that generalized one
based on the variables.
It's really going to be the same thing.
We're just not going to use these numbers.
We're going to use
variables in their place.
Let's give ourselves a
linear consumption function.
We can say that aggregate consumption
where we're going to have some base level
of consumption no matter
what, even if people
have no aggregate income,
they need to survive.
They need food on the table.
Maybe they'll have to dig
in savings somehow to do it.
So, some base level of consumption.
I'll call that lower case c sub zero.
Or lowercase c with a subscript
of zero right over there.
That's the base level
of aggregate consumption
or it's sometimes referred
to as autonomous consumption.
This is autonomous
consumption because people
will do it on their own, or in aggregate
they will do it on their
own, even if they have
no aggregate income.
Then we will have the part that is due,
directly due, to having
some aggregate income.
We call that the induced consumption,
because you can view it as being induced
by having some aggregate income.
Above and beyond what the
base level of consumption,
people are going to consume some fraction
of their disposable income.
So we'll say disposable income.
They're not going to consume all
of their disposable income.
They might save some of it.
So they're going to consume the fraction
that's essentially their
marginal propensity to consume.
This right over here, I'll
do that in this orange color.
Marginal propensity to consume.
Hopefully this makes intuitive sense.
This says, look, if this was 100,
people are going to
consume 100 no matter what,
100 billion whatever
your unit of currency is.
Now, if their marginal propensity
to consume is, let's say, it is 1/3.
You have now above and beyond this
people have disposable
income of let's say 900,
this is saying that
they want to consume 1/3
of that disposable income they're getting.
That is, if you give them 900 of extra
disposable income, they're propensity
to consume that incremental income,
they're going to consume 1/3 of it.
So this would be 1/3, so it would be 900.
Let me give an example.
If you had a situation,
you could have a situation,
where c-nought is equal to 100.
If you have disposable
income is equal to 900,
and c1 is equal to 1/3, or we could say
0.333 repeating forever, c1 is 1/3.
Then this makes sense.
On their own people
would consume this much,
but now they have this disposable income.
Their marginal propensity to consume
if you give them 900 extra of income,
they're going to consume 1/3 of that.
So then you're going to
have, your consumption
is going to be equal to, for
this case right over here,
your consumption is going to
be 100 plus 1/3 times 900.
So your consumption in this situation,
your induced consumption, 1/3 times 900,
would be 300, maybe it's
in billions of dollars,
300 billion dollars.
Then your autonomous
consumption would be 100.
They would add up to 400.
Once again, this is autonomous
and this is induced.
Autonomous, this right over
here is induced consumption.
Now, I did write it in general terms.
I'm using variables here
instead of, or constants, really
instead of using the numbers
we saw in the last example.
But I also said that I would express
aggregate consumption
as a function not just
of disposable income
but of aggregate income;
not just of aggregate disposable income
but aggregate income.
The relationship is fairly simple between
disposable income and overall income.
We saw over here, in
aggregate, you have income,
but the government in
most modern economies
takes some fraction of that out for taxes.
What's left over is disposable income.
Just a reminder, income in aggregate,
aggregate income is the same thing as
aggregate expenditures,
which is the same thing
as aggregate output.
This right over here is GDP.
So this right over here is, let me do this
in a color, I've used
almost all my colors.
This is equal to GDP.
Disposable income is essentially GDP,
or you could say aggregate
income, minus taxes.
I'm going to do the taxes
in a different color.
Minus taxes.
So we can express disposable income
as aggregate income, this right over here
is the same thing as
aggregate income minus taxes.
We could rewrite our
whole thing over again.
Aggregate consumption is equal
to autonomous consumption
plus the marginal propensity to consume
times aggregate income,
which is the same thing
as GDP, times aggregate
income minus taxes.
We fully generalized
our consumption function
and now we've written it as a
function of aggregate income,
not just aggregate disposable income.
To make you comfortable
that this is still a line
if we were to plot it as a function
of aggregate income instead
of disposable income,
let me manipulate this thing a little bit.
We could distribute c1, which is our
marginal propensity to consume, and we get
aggregate consumption is equal
to autonomous consumption
and then we're going to distribute this,
plus c, so we're going to multiply it
times both of these terms,
plus our marginal propensity to consume
times aggregate income,
and then minus our marginal
propensity to consume
times our taxes.
Since we want it as a
function of aggregate income,
everything else here is really a constant.
We're assuming that those
aren't going to change.
Those are constant variables.
What we could do is we could rewrite this
in a form that you're
probably familiar with.
Back in algebra class
you probably remember
you can write it in the form y=mx+b where
x is the independent variable,
y is the dependent variable.
If you were to plot this,
on the horizontal axis is your x axis,
your vertical axis is your y axis.
This right over here
would have a y intercept,
or your vertical axis intercept
of b, right over there.
Then it would be a line with slope m.
If you were to take your
rise divided by your run,
or how much you move up
when you move to the right
a certain amount, that gives you your m.
Slope is equal to m.
The same analogy is here.
We can rewrite this in that form,
where our dependent
variable is no longer y.
Our dependent variable
is aggregate consumption.
Our independent variable is
not x, it is aggregate income.
So let's write it in that form.
We can write it as dependent variable, c,
which we'll plot on the vertical axis,
is equal to the marginal
propensity to consume
times aggregate income,
I'll do that purple color,
times aggregate income,
plus autonomous consumption,
minus marginal propensity
to consume times taxes.
It looks all complicated, but you just
have to realize that this
part right over here,
this is all a constant.
It is analogous to the
b if you were to write
things in kind of
traditional slope intercept
form right over here.
When we plot the line, if you have no
aggregate income, this is what your
consumption is going to be.
Let me draw that.
Once again, our dependent
variable is aggregate consumption.
Our independent variable
in this is no longer
disposable income like
we did in the last video.
It is now aggregate income.
If there's no aggregate income,
this is the independent
variable right over here,
if there's no aggregate income,
then your consumption is just going to be
this value right over here.
So your consumption is just going to be
that value right over
there, which is c-nought
minus c1 times t.
Then as you have larger values of
aggregate income, c1, that fraction of it,
is what's going to contribute
to the induced consumption.
What you essentially
have is this is the slope
of our line, this right
over here is our slope.
Just to kind of draw the analogy,
if you were to say y
is equal to mx plus b.
Actually, maybe I'll write it like this.
If you were to write c is equal to m ...
and I don't want to
confuse you if this m and b
seem completely foreign.
It comes from kind of
a traditional algebra
grounding in slope and y intercept.
If I were to say c is equal to my plus b,
this is the slope.
This is our vertical or our
dependent variable intercept
right over here.
That's where we intercept the dependent
variable axis.
And this is our slope.
It's our marginal propensity to consume.
Our line will look something like this,
where the slope is equal to the marginal
propensity to consume,
which is equal to c1.
If people all of a sudden are more likely
to spend a larger
fraction of their income,
then the marginal propensity to consume
would be higher and our
slope would be higher.
We would have a line that looks like that.
We always assume that the marginal
propensity to consume will be less than 1.
So we'll never have a slope of 1.
We'll also never have a negative slope
because we assume that this is positive.
If people are more likely
to save than consume
when they have extra
income, then this line
might look something like that.
It might have a lower slope.
About this Video
Apr 18, 2026 Last updated
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