GDP deflator | GDP: Measuring national income | Macroeconomics | Khan Academy

Relationship between the GDP deflator, nominal GDP and real GDP

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In the last video, we studied
a super simplified economy

that only sold one
good or service.

But now let's think about things
a little bit more generally,

or a little bit more
complex economies.

And let's say that in
year one economists

have determined that the
level of prices of the goods

and services produced
in that economy is 100.

So they've essentially
just multiplied

and divided by
the right numbers,

so that their index
that they generate just

says that that is 100.

And they do this so that
they can measure the prices

in other years
relative to year one.

So let's say in year
two, using their index,

they realize that
prices are now 110.

Now, this is not a
simple thing to do.

This would have been
a very simple thing

to do if there was only one
good or service in the economy,

like in our last
example, apples.

You could have just taken
the price of apples.

It went from $0.50 to $0.55.

In the real world, this is
not a simple thing to do.

You have a gazillion
goods and services.

Some prices go up.

Some prices to go down.

The quantities of the
goods and services change.

In fact, there might
be goods and services

that were offered
in year one that

don't exist anymore in year two.

And there are goods and
services in year two

that didn't exist in year one.

But for the sake of
this video, let's just

assume that economists
are able to say this.

If you call the general level
of prices 100 in year one,

it's now 110.

Or another way to think
about it is things

have gotten 10% more expensive.

Now, assuming that we know this
relationship-- and once again,

it's not an easy
thing to figure out,

and it actually turns out
there's no perfect way

to do this-- how
can we figure out

a relationship between
real GDP and nominal GDP?

And remember, whenever
we talk about real GDP--

so we're going to talk
about real GDP in year two--

whenever you talk
about real GDP,

you're talking
about GDP in terms

of the prices in some base year.

So in this example, we'll
think about real GDP

in year two in terms
of a year one dollars.

So whatever were the
goods and services

that were produced in year two,
we're going to think about,

well, what if they were at the
same prices as in year one?

And that will give us
the real GDP in year two.

So one way to think about
it is really just a ratio.

So let me write nominal GDP.

So this is GDP in
year two, measured

in year two dollars,
divided by-- I

guess we could call
this a proportion,

really-- divided by the
real GDP in year two.

And this is measured
in year one dollars.

Well, that's going
to be the same thing

as the ratio of the prices
between year two and year one.

This is going to be the ratio
of-- we use this indicator

right over here-- 110 to 100.

And I want you to just sit and
think about this for a second.

It's just saying, look, these
are measuring the same goods

and services.

The real GDP is measuring
them in year one prices.

The nominal GDP is measuring
them in year two prices.

So if things got
10% more expensive

between year one and
year two, the nominal GDP

should be 10% larger
than real GDP.

We should have the
exact same ratios.

And now we can manipulate this
thing using any type of algebra

that we want.

For example, we could
say, well, nominal GDP--

And I'll just write nominal now.

This is where I
kind of specified

exactly what we're
talking about.

This is a nominal
GDP of year two.

So now we could say
nominal GDP is equal

to-- we can multiply both
sides times the real GDP--

is equal to 110 over
100 times the real GDP.

And remember, this is
nominal GDP in year two.

This is real GDP in year two,
measured in year one dollars.

Or we can divide both
sides of this equation

by this 110 over 100.

And then we get nominal
GDP in year two divided

by 110 over 100 is equal
to real GDP in year two.

This is nominal GDP in year two.

And writing it this
way kind of feels

like you're taking your
nominal GDP in year two,

and there's been
a general increase

in the level of prices.

That's called price inflation.

We see that right over here.

And now we're deflating
it to get real GDP.

We're dividing it by
the ratio of the prices.

We're dividing it essentially by
how much the prices have grown,

or I guess you could say the
ratio between the year two

prices and the year one prices.

So this quantity right
over here is 1.1.

So another way you
could think about it,

we're deflating the
nominal GDP in year two

to get the real GDP in year two.

We're getting it in, remember,
this is in year one prices.

And because of that, this
number right over here

is referred to as a deflator.

This is our GDP deflator.

You pick a base here, in
this case, it was year one.

That base year could
have been 1985.

It could've been 2006.

Who knows what it could be.

It could be anything.

Your GDP deflator is going to
be relative to that base year.

It's going to say, well,
if that base here was 100,

your deflator's going to
say how much things are now

in this year.

And you can even go
backwards in time.

Year zero, the deflator
might have been 85,

because maybe things
have gotten cheaper.

Or you could actually
had prices go down.

You could have
actually had deflation.

So maybe in year two your
deflator would be at 98.

But the reason why
it's called a deflator

is because generally you have
inflation as time goes on,

and generally you're going to
be deflating your nominal GDP.

You're going to be dividing it
by a value greater than one.

It's going to be something
over 100 divided by 100,

which is your base year,
to get your real GDP.