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## IS-LM

# 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.