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# Loanable funds interpretation of IS curve

## Video transcript

In the last video, we began to
explore the IS curve, which, as I think I mentioned,
stands for investment savings. And we really analyzed
it from the point of view of investment. We thought of it as
real interest rates driving the level of investment,
which drives the equilibrium level of real output. High real interest
rates, low level of investment, low
level of investment leads to low equilibrium output. So this scenario is closer
to that right over there. If real interest
rates are lower, then that leads to higher levels
of planned investment, which leads to a higher level
of equilibrium output. So that right over there. So that was more from the
investment point of view. What I want to do
in this video is explore the exact
same relationship, the exact same curve,
but think of it more from the savings
point of view. And in this
situation, we're going to have this exact
same thing, but instead of viewing real interest
rates as driving GDP, we're actually going to view GDP
as driving real interest rate. So let me leave this up here. But let's just break down
the expenditure model of GDP. So we know that aggregate
income, or aggregate GDP, or aggregate output-- however
you want to think of it-- is equal to, and you
could break it up into its component
expenditures, it's equal to aggregate
consumer spending, which is a function of
disposable income. y minus t is disposable income,
aggregate income minus taxes, plus investment plus
government expenditures. And I could do net exports. But for simplicity
for this discussion we'll just assume we
are in a closed economy. It makes good
conceptualizing saving and investment a
little bit easier. Now what I want to do
is solve for investment. So if I solve for
investment I'm just going to subtract this
piece and this piece from both sides
of this equation. And I get aggregate income
minus total aggregate consumer spending minus total
government spending is equal to-- on the
right hand side I'm just going to be left with, with
investment right over here. And this thing right
over here is interesting because this is total
income minus what-- and let me make sure that we,
I don't want to confuse you. Because that looks
like a lowercase c. And if we're talking about
aggregate consumption it's usually an uppercase C. So on the left hand side, we
have total aggregate income minus consumer spending
minus government spending. So you could really view this
as, this right over here, really is aggregate savings. This over here
really is savings. And as we see when on
one side of the economy, when people are saving, that
goes into banks and it gets lent out. And then it gets reinvested. Or you could save
directly by reinvesting. And so what we have here is
savings is equal to investment. And that's why it's
called an IS curve, because when you look at
the expenditure model, savings and investment
are really the same thing. They're really
just saying, look, there's two ways
to view this curve. It's investment driven
or its savings driven. And when you think
of it this way you have a slightly
different view of this curve. Because when you view
it from a savings point you say, well, what's going
to happen if GDP goes up? What happens if we have
a high GDP over here? So if we have a
high GDP, or let's say in particular
if GDP goes up, the consumer spending,
which is a function of GDP, it will go up. But it won't go up as much. It's going to go up by
this expression right here times, if we
assume a linear model, times the marginal propensity to
consume, which is less than 1, it's between 0 and 1. So this is going to
go up less than that. And then we can, for
the sake of this model, we'll assume right
now that happens without any change in
government expenditure. So if total aggregate
income goes up then savings are going
to go up, if we assume government expenditures
holds constant. So then we have savings goes up. And if savings
goes up, that means we have more loanable funds. There's more money to lend. And if there's
more money to lend, what's going to happen
to interest rates? Well interest rates
are just the price of borrowing money,
the price of money. So if you have more of something
the price of that thing goes down. So if savings goes up then
real interest rates go down. So if you have a
high GDP you're going to end up with low
real interest rates. So once again, is looking at
it from a point of view of GDP driving interest rates. We have high savings here. So we're going to have
low interest rates. And you view it the
other way around. If you have a lower
income this thing is going to also decrease. But is not going to decrease
as much as this did, because of the
marginal propensity to consume is less than
1, we saw that up here. We saw that all the way
over here, right over there. And so in aggregate, the
savings are going to go down. Once again, we hold
government spending constant. So in this situation,
savings are going to go down. And if you have
fewer loanable funds, there's less
savings to lend out. Then if you have less of
a supply of something, what's going to
happen to its price? It's price is going to go up. The price of borrowing
money is the interest rate. So in this situation
interest rates would go up. So that's going in this
direction, right over here. If aggregate income goes
down, loanable funds go down, interest rates are
going to be higher. So once again, the same
exact curve, IS curve. But there's two takeaways here. One is to realize
why it's called IS, that investment and
savings, when you view it from this point of view,
really are the same thing. One person's savings can be
another person's investment. And when we viewed it from
the investment point of view, we were viewing r as driving y. Now we're looking at it
the other way around. y is driving savings,
which is driving r. But it gives us the exact same
relationship for this model.