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# Investment and real interest rates

## Video transcript

In our planned expenditure remodel we've been assuming that planned investment is fixed. 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. Talking about real interest rates, I'm really just talking about nominal interest rates factoring out or discounting what's going on with inflation. There's other videos where we go into more depth about that. Another thing if there were no inflation real and nominal rates would be the same thing. I want to tackle it with a very tangible example. Let's say this up coming year there's a bunch of potential planned projects. Let's call this projects. Theses are potential investments. You have projects, and then you have some level of expected return. Each of the people who are thinking about these projects, they all have their spreadsheets out, and they've taken in risk and probabilities and all of the rest. They've come up with their expected return numbers. Let's say project A has an expected return of 20%, B 18%, C 16%. I'll do a couple more. D is 10% , E is 5% and F is 2%. Let's say initially in one state of affairs interest rates are relatively high. Let's R1 is equal to 19% interest rates. We have 19% real interest rates. These are the real expected returns. Which of these projects will actually be invested in? Which of the ones will people actually do? If someone has the cash, they say well, I could either lend my money out for 19%, or I could do this project and get 20%. If they have the cash they would definitely do this. If they don't have the cash, they could say, well, I could borrow the money for 19%, and I could invest it at 20%. I'll make money off of that. Project A will definitely be done. What about project B? Project B, if the person actually has the cash on hand to do project B, they say I could do project B and get an 18% real return, or I could lend that money out and get a 19% in real return. Actually, I would not do project B. I'll just say I would not do anything that has a even a lower real return. If I could potentially do project B, but I had to borrow the money, if I have to borrow the money at 19% real interest, and I'm only getting 18% on it, that's a money loosing proposition. I wouldn't do B, and I definitely wouldn't do all these things that get a lower return. When I have high interest rates right over here the only thing I would do is project A. Let's think about what would happen if interest rates went down. If real interest rates went down. Let's say real interest ... let's call that R2. Real interest rates go down to ... let's say they go down to 3%. Once again, project A you are 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%. By the same logic, people would do project B. You could borrow at 3% and make 18%. If you have the money, you get 18% verses 3% on your money, so you definitely do this. You do all of these up to project E. If you have the money, you would rather put that money and get 5% then lend it out and only get 3%. You'll even do project E if you need to borrow it and still makes sense. Borrow money at 3%, invest it at 5%, your making some real return. The only one that you would not do is project F right over here. Here you aren't actually covering your cost of borrowing. If you have to borrow at 3% and invest at 2%, doesn't make sense. If you have the money, you would rather lend your money at 3% then do project F. So, your definitely not going to do F in this scenario. Obviously do it in neither scenario. Right over here, you'd do all of the above. You would do A, B, C, D, not all of the above. All of the above except for F. A, B, C, D, and E. Let's just think about the rough level of investments. If we were to plot on this axis right over here, if we were to plot the investments as a function of real interest rate, and over here we actually have the ... independent variables are real interest rate. At a high real interest we had a low level investment. We only did project A. That's right over there. That's A only. This is when we were at R1. When we lowered interest rates to R2, we had a much higher level of investment. We did all of these projects right over here. You had a much higher level of investment. This is A, B, C, D, and E. You see that you have an inverse relationship. The lower the real interest rate, the more investment that's going to go on. The higher the interest rate, the less investment that goes on. You can debate whether it's a curve or a line, bur for the sake of simplicity, we'll assume that it looks something like ... I'll draw a dotted line it's easier for me do that. It might look something like that. Now, we can use this insight to start thinking about how a change in real interest rate might shift our plan expenditures on our [unintelligible 05:50] and from that we can start to think about the IS curve. The famous IS curve and the ISLM model.