MPC and Multiplier

Introduction to the marginal propensity to consume and the multiplier

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