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## Production possibilities frontier

Current time:0:00Total duration:7:55

# Economic growth through investment

## Video transcript

In the last few
videos, we've been talking about the
production possibilities frontier as a relatively
static thing, something that you couldn't change
but you could move along. What I want to do in this
video is think about, maybe there are ways
to change or expand the production
possibilities frontier. And to do that let's assume that
our little hunter-gatherer has decided to become
a strict carnivore. So he's only focused
on rabbits now. And his whole happiness in
life is optimizing the number of rabbits he can catch
and eat in a given day. And so let's-- on
one axis let's draw, let's say the number of rabbits
that he can catch in a given day. Let's say it's 1,
2, 3, 4, 5, 6, 7-- I could keep going on and on. So this right over
here is rabbits that he can catch in a
given day, rabbits in a day. But remember, he wants
to optimize this. He wants to think about how he
can increase his productivity in terms of the
number of rabbits. And he knows-- we'll
just assume that he knows how to build rabbit traps. So now we're going to do
a production possibilities frontier, not between
rabbits and berries, but between rabbits and building
rabbit traps, so rabbit traps. So maybe he's able
to get twigs together and he builds something. Puts the twigs together
in a little thing. It's a little box that--
maybe he puts a little, I don't know some type of
carrot down over there. And then if the rabbit comes
then takes the carrot then the box falls on the rabbit
or something like that. We don't have to go into the
particulars of the actual trap. But he can also spends his
time building rabbit traps. So let's say, 1 rabbit
trap, 2 rabbit traps, and 3 rabbit traps. And let's say-- we're going to
hold all other things equal, ceteris parabus. So we're not worrying
about other things. And as we'll see, in most
introductory economics class, whenever you do a production
possibilities frontier you're only doing it
with two dimensions. And so that's why you
have a regular curve. You could have one with three
dimensions, where you're doing the trade off
between three things. But then you would have to
have a three dimensional graph, and essentially the production
possibilities frontier would be a surface. But let's just focus
on this right now. Maybe I'll do a surface in
the future, just for fun. So these are the rabbit traps. And let's say the production
possibilities frontier between rabbit traps and rabbits
look something like this. He could spend all his
time making rabbit traps, but in that case he
won't get any rabbits and he'll probably starve. And that wouldn't
be a good scenario. Or he could spend all of
this time hunting for rabbits and he would catch, on
average, 5 rabbits per day. But that would leave him no
time to make rabbit traps. So this is our
current production possibilities-- let
me just draw it. This is our current production
possibilities frontier. So I'll call this p, production
possibilities frontier. And I'll put a little
0 subscript there. That's our starting point. So he can he can sit
anywhere over here, and he would have achieved
productive efficiency anywhere on this curve. But as we saw, if he just spent
all of his time doing this over here, he'll never
get any rabbit traps. And so he won't
be able to change the productive
possibility frontier. But what happens if
instead he decides that he does want to
build some rabbit traps? So he decreases the number
of rabbits a day to 4 and that allows him to
make 1 rabbit trap per day. So he wants to hang
out in this scenario. So every day that
goes by, on average, he's going to make 4 rabbits. And he's going to
build a rabbit trap. So what's going to happen? So as we go into, maybe
into the next period, he would now have a rabbit
trap after just one day that he can use to
help catch rabbits. So that will actually change
the production possibilities frontier. So if he makes
this investment, it will actually allow him,
in a given amount of time, to actually catch more rabbits. So if he does that, the
production possibilities frontier-- having a rabbit
trap won't make him that much, won't allow him to make
more rabbit traps in a day. So the most rabbit traps
he can make in a day is still going to be 3. But maybe now he can
catch 6 rabbits a day. So now it might look
something like that. So now he could either
stop making rabbit traps, and catch 6 a day just
with that 1 rabbit trap he has, or he could
continue that. And now actually he can
catch 5 rabbits a day and still make 1
rabbit trap a day. And maybe he decides to do that. But it could be anywhere along
this production possibilities frontier. Or he could say, hey, I'm happy
eating the 4 rabbits a day. I'm going to make 2 rabbit
traps now every day. And now after another period
he gets even more productive. And so then the production--
so let me call this one, this is after one day. Production possibilities
frontier after one day, and then after two
days, let's say he did this scenario
right over here. Now he's produce 2 rabbit traps. And obviously, maybe I'm
exaggerating how quickly his productivity would grow. But maybe now the new production
possibilities frontier looks something like this. He now has 2 rabbit traps. Or he has 2 more rabbit
traps, he already had 1. So now he has 3 rabbit
traps after two days. And so now if he wanted to
devote themselves purely to rabbit trapping he
can get 8 rabbits a day. Or he could do some
combination in between. And actually this curve,
it shouldn't go up at all. I don't want to give
you the impression that it went up and then down. It just goes kind of
straight and does something like that right over here. So this right over
here, I'll call that the production
possibilities frontier 2. So what this hunter-gatherer
is doing in this scenario right here is, he is
making an investment. He is accumulating capital. This right over here,
this is capital. He is choosing, instead of to
consume all of his resources-- so there's two things he can do. He can either spend all of
his time in pure consumption, getting as many rabbits
as possible a day and then eating them
all, pure consumption. Or he could reduce
his consumption and then allocate
some of his resources towards and investment. So this right over here,
this is an investment. It makes him more productive. This right over
here is consumption. There's some base
level of consumption he needs to survive. But if he invests,
then it increases his overall productive capacity. So if you viewed
him as an economy by himself, by investing
instead of consuming all of his resources,
by investing some of his resources--
and in this case, his resources are his
time and his expertise-- by investing some of them
he's able to increase his productivity. And if you viewed
him as an economy, he's experiencing
economic growth. And so there's multiple
types of investments. And we'll talk about
these in multiple videos. In this case, he is doing
capital accumulation. He is building tools that
will make him more productive. Another type of
investment is essentially technological change,
technological improvement, which would actually make
his tools even better. So we could maybe draw another
production possibilities frontier between
making rabbit traps and then doing R&D on inventing
new types of rabbit traps. And so he could decide
which of those two things he wants to decide between. But what I wanted you to
just appreciate in this video is that the production
possibilities frontier can change. You can become more
productive if you do have investment in R&D
or capital accumulation. And in this case, that just
happened to be rabbit traps.