Going with my habit of overly simplified economy let's imagine economy that
has only two actors in it: so that's Mr Farmer right over here
I'll do my best to draw the farmer, maybe he has the mustache of some kind
so that's Mr Farmer right over here, he's got a hat on
so it has Mr Farmer So that is the Farmer
in this economy, and we'll also have a Builder
so this economy they are producing two things: they are producing food and this Builder
can help mantain stuff so maybe
so maybe this is Mr Builder right over here
is Mr Builder. And let's say, for the sake of
do here let's say that for this economy it kind of a constant that
either of these fellows gets an extra dollar to spend
he is going to spend 60% of it so I'll introduce a formal word that
that really is another way of saying that: in this economy
the marginal propensity to consume: MPC
propensity to
consume is
open parentesis is often MPC
that is equal to say 60%
and or is equal to 0.6
And all this thing if someone in this economy somehow finds another dollar
in their pocket they're going to spend 0.6 of that or
60% of that, so if you give the Builder, if the builder gets some extra dollar
he is going to spend another 60 cents on another things Farmer
if the Farmer gets another dollar he is going to spend 60%
or 60 cents with the builder. Now, given this assumption let's
think about what'll happen in this economy if all of the sudden one of them decided to
increase their spending over there: so all the sum
economy let's say the farmer discovers
a sac in a drawer that he didn't realise was there
currency maybe get a
maybe currency in that is
dollar and the farmer discovers that he
he discovers a big power dollar in the sac
and he say and do some repairs to my building
so let's we have this kind of increase in
spending that's going on, so the farmer says I'm going to spend
I'm going to spend 1000 dollars and I'm going to
give it to the builder, now the builder says
1000 dol, I have the marginal propensity to consume or 0.6
he is going to spend
with the farmer he is going to spend 60%
times 1000 dol, which is equal to 600 dol
well now the farmer says
1000 somehow the builder to spend
more on me much more
I had 600 more I have the marginal propensity
to consume of 0.6 or 60% so I'll spend
60% of that 600 dol that I've just got
it will be 60% of that thing so it will be
60 decimal so it will be 0.6
times this thing which is 0.6
times 1000 or you can say 60%
of this 600 dol which is going to equal to 360 dol.
now the builder says
I gave the initial 600 dol another 360 dollars
and I have the amrginal propensity to consume of 0.6 so I'll
spend 60% of that bothered on this spending
he also spends 60% of this right over here and 60% of this
is 0.6 times this whole thing
0.6 times this thing
times 0.6 times this thing - times 0.6
times 1000 dol. Now this
number right over here 60% of 360 dol
I'd like to calculator to figure what it is exactly
so let's say that I have
it's 0.6 to the 3rd power
0.6 to the third
multiply that times 1000
gives us 216 dollars. so this guy
write it over here
I'm going to spend 60% of that
is going, and 60% of you see where it's going
so it's going to be 0.6
times this thing which is already 0.6 times 0.6
0.6 times 0.6 to the 3rd power
0.6 to the 4th power times
1000 which is whatever sixty
percent of
0.6 gives us 115 dollars
129, and this guy Oh I have
spend 60% of that, and this goes on and on
so given this think how much from that incremental
increase of spending of a 1000 dollars how much total
new production and spending happen in this economy
so the way to think about that - so the total
we can do the either way we can do kind of GDP
output income expenditure
these all views because economy is a very thing
one persone's expenditure turns into another person's income
we can say total output here measured in our agreed currency
which is dollars this is now going to be
original 1000 farmer spend for the builder
original 1000 plus this 1st right over here
this that the builder spent
.6 times 1000 plus
than we have this time the farmer said I'm
6 square
times 1000 and than this guy
I spend 60% of that
and spend gives 3rd power
1000 + 0.6 to the 3rd power times
1000 and that the last
keep going on and on forever theoretically
6 + 0.6 to the 4th power
times 1000 and this will keep going on and on
forever plus 0.6 to the 5th power
0.6 to the 6th power and going on and on forever
and one of those things about mathematics
equall multuply is that you can actually sum
up because this value right over here is less than one
ends up being infinite sum
you can actually take this infinite sum and find number so just to simplify this
the total output from that's kind of original 1000
we can factured 1000 new colour
so we can fracturate 1000 left with
one plus 0.6 plus
0.6 square + 0.6
to the third power plus 0.6 to the 4th power
on and on and on and on the next video
just for fun, but his write over here it's an infitinite sum
geometric series and this actually simplify to
as one over one
minus 0.6, so whatever this number is
here that will be
this will be equal one over
0.4 and 0.4
is two fifths one over two fifths
which is equal to 5 halfs
so your total output is going to be equal to
1000 times 5 halfs
and this the same thing as equal to 1000 times 2,5
which is equal to 25 hundret (2500)
there is two interesting ideas going here. one is when people get a bit of more income, they're going to
spend some of it adn that's the marginal propensity to consume
how much you 60% of that
60% it keep going multiplied throw the economy
multiplier fraction of that get spent
some fraction of that get spent
1000 that first 1000 dollars got multiplied
by 2,5 and that 2,5 was completely a function of what the
MPC was, so we have this relationship here
is that whatever the marginal propensity to consumer is that drives
the multiplier that drives the multiplier
all the multiplier say if you spend an extra dollar in this economy
given people's MPC how much
will than increase total output