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in our planned expenditure model we've been 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 how real interest rates drive how they drive planned investment or another 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 if there were no inflation real and nominal interest rates would be the same thing and I want to tackle it with a very a very tangible example so let's say in this upcoming year there's a bunch of potential planned projects so let's call this so let's call this so 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 they've taken in risk and probabilities 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 F is let's say F is 2% and let's say initially let's say in one state of affairs interest rates are relatively high so let's say r1 is equal to 19 percent interest rates so if 19 per we have 19 percent real interest rates and these are the real expected returns which of these projects will actually be invested in which of the ones will people actually do well if someone has the cash they say well I could either I could either lend my money out for 19 percent or I could do this project and get 20 percent 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 percent and I can invest it at 20 percent 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 adding it a 19% real return so actually I would not do project B and obviously I would not do anything with that has an even lower real return and if I wanted if I could potentially do project B but I had to borrow the money well if I had to borrow the money at 19 percent real interest and I'm only getting 18 percent 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 when I have high interest rates right over here the only thing I would do is project a project project a 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 rate like all that are - let's call that our two real interest rates go down - and let's say they go down to three percent well once again project a you are definitely going to do if you have the money on hand you get 20 percent doing project a you definitely 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 and and make 18 percent or if you have the money you get 18 percent versus 3 percent on your money so you definitely do this you do all of these up - you would even do project E if you have the money you would rather put that money and get 5 percent then lend it out and only get 3 percent so you'll even do project e if you need to borrow it it still makes sense borrow money at 3% invested at 5% you're making some real return the only one that you would not do is project F right over here because here you aren't actually covering your cost of borrowing if you have to borrow at 3% and invested 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 you're definitely not going to do F in this scenario and actually you obviously do it in either scenario so right over here you do all of the above so 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 so let's just think about the rough level of investment so if we were to plot if we were to plot on this axis right over here if we were to plot the relative less investment as a function of real interest rates and over here we actually have real we actually have the the independent variables our 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 that when we lower it 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 there 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 and you can debate whether it's a curve or a line but for sake of simplicity we'll assume that it looks something that it looks something like it looks I need drugs 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 in the is-lm model