In our planned expenditure model we've been assuming that planned investment is fixed. And what I want to do in this video is think about how real interest rates drive planned investment. Think about the function - investment as a function of real interest rates. Planned investment as a function of real interest rates. And when I'm talking about real interest rates I'm really just talking about nominal interest rates, factoring out or discounting what's going on with inflation. And there's other videos where we go into more depth on that. Another way to think about that is if there were no inflation real and nominal interest rates would be the same thing. And I want to tackle it with a very tangible example. So, let's say in this upcoming year there is a bunch of potential planned projects, so let's call this "Projects"... so these are really potential investments. So you have projects and then you have some level of expected return. So each of the people who are thinking about these projects, they all have their spreadsheets out and have taken in risk and probabilites and all of the rest and they've come up with their expected return numbers. And let's say Project A has an expected return of 20% B 18%, C 16%, I'll do a couple more, D 10%, E is 5% and then let's say F is 2% And let's say, initially, in one state of affairs interest rates are relatively high. So let's say r1 is equal to 19% interest rates So if we have 19% real interest rates and these are the real expected returns, which of these projects will actually be invested in? Which ones will people actually do? Well if someone has the cash, they say "I could either lend my money out for 19% or I could do this Project A and get 20%" So if they have the cash, they would definitely do this, and if they don't have the cash, they could say "Well, I could borrow money for 19% and I can invest it at 20%, I'll make money off of that!" So Project A - Project A will definitely be done. Now what about Project B? Well, Project B, if the person actually has the cash on hand to do Project B, they say "Well, I could do Project B and get an 18% real return, or I could lend that money out and get a 19% real return." So actually I would not do Project B and obviously I would not do anything that has an even lower real return. And, if I could potentially do Project B, but I had to borrow the money, well if I had to borrow the money at 19% real interest and I'm only getting 18% on it, that's a money-losing proposition. So I wouldn't do B, and I definitely wouldn't do all of these things that get a lower return. So when I have high interest rates over here, the only thing I would is Project A. Project A. So now let's think about what would happen if interest rates went down, if real interest rates went down. So let's say real interest rates, we'll call that r2, go down to 3%. Well, once again, Project A you're definitely going to do. If you have the money on hand, you get 20% doing Project A. You definitely don't want to lend it out at 3%. If you don't have the money on hand you can borrow at 3% and invest at 20%. And so, by the same logic, people would do Project B. You could borrow at 3% and make 18%. Or if you have the money, you get 18% versus 3% on your money, so you definitely do this. You do all of these, you would even do Project E. If you have the money you would rather put that money and get 5% than lend it out and only get 3%. So you'll even do Project E. If you need to borrow it, it still makes sense. Borrow money at 3%, invest it at 5% and you're making some real return. The only one you would not do is Project F right over here, because here you aren't actually covering your cost of borrowing. If you had to borrow at 3% and invest at 2%, doesn't make sense. If you have the money you would rather lend your money out at 3% than do Project F, so you're definitely not going to do Project F in this scenario. And you obviously do it in neither scenario. So right over here... you'd do all of the above. So you would do A, B, C, D, all of the above except for F. A, B, C, D and E. So let's just think about the rough level of investment. If we were to plot on this axis right over here, if we were to plot the investment as a function of real interest rates. And over here we actually have our indepedent variable - real interest rate. At a high real interest we had a low level of investment. We only did Project A. So that's right over there: That is A only. So this is when we were at r1. And when we lowered interest rates to r2, we had a much higher level of investment. We did all of these projects right over here. So you had a much higher level of investment. So this is A, B, C, D and E. And so you see that you have an inverse relationship: The lower the real interest rate, the more investment is going to go on. The higher the interest rate, the less investment that goes on. And you can debate whether it's a curve or a line but for sake of simplicity we'll assume that it looks something like this... I'll draw a dotted line, it's easier for me to do that. It might look something like that. And now we can use this insight to start thinking about how a change in real interest rate might shift our planned expenditures on our Keynesian cross. And from that we can start to think about the IS curve, the famous IS curve from the IS-LM model.