Loanable funds interpretation of IS curve

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.