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- [Justin] This video was sponsored
by Primer's new merchandise store on dftba.com.
Link in the description below.
This is a blob.
It lives in a forest eating mangoes
and burning wood for heat.
In this video, we're gonna take
the very first step towards building
a simulated economy by creating a model
for how this blob chooses
to spend its time gathering resources.
(gentle music)
Each day, the blob can go out
to collect mangoes and wood.
Each tree produce one mango per day
and it grows back the next day
if it gets chopped down.
(gentle music)
The blob's decision for how to spend its time
has two inputs.
First, what are its option for it to produce
with the time it has in the day,
and second, out of those options,
what makes it the happiest?
We'll start by looking at the production side.
To figure out what these options are,
let's see how many mangoes the blob
can get if that's all it looks for the entire day.
Alright, 17 mangoes total.
Now, let's try collecting only wood.
It does take a moment to chop down the trees,
so the blob probably won't get quite
as many pieces of wood.
Alright, looks about right.
It go 14 total.
Those are the two extreme cases,
but what about cases when the blob
tries to find some balance between the two?
We're dealing with two quantities,
so it'll be useful to keep track
of outcomes using a graph.
The two cases we've looked at so far
led to 17 mangoes and zero wood,
and zero mangoes and 14 wood.
Next, let's have the blob grab only one mango,
and then, spend the rest of its day on wood
just to see how much it can get.
Okay, it looks like we still get 14 pieces or wood
even if we sneak a mango in right away.
And to finish putting this together,
let's fast-forward a bit and have the blob
run through days getting two mangoes,
then three mangoes, then four, and so on.
(gentle music)
Okay, assuming the only thing
the blob can change is how much time
it spends on each resource,
these points represent all of the possible options.
You might here this called
the Production Possibilities Frontier.
It's the frontier, or the edge, of what's possible.
Or, if we draw a curve through the points,
the production possibilities curve.
The curve really only makes sense
when the numbers are big enough
for it to look continuous, though.
With all that done, we have a pretty good understanding
what the blob is able to produce
and what trade-offs it has available.
But we don't yet have any idea
what the blob wants to produce
and which trade-offs it's willing to make.
Maybe, the blob wants to balance its time
to get a decent amount of, both,
mangoes and wood.
Or, maybe, it doesn't care about wood at all
and it just wants as many mangoes as it can get.
So now, our goal it to make a computer model
that captures the full depth of the human experience.
How can we do that?
Well, I certainly can't,
but we don't have to be quite that ambitious.
All we need here is a way for the blob
to choose which of two situations it prefers.
So, and this might sound a bit silly at first,
we're going to try to give a happiness score
to every possible combination of mangoes and logs.
Then, when the blob has a decision to make,
it can just compare those happiness scores
and pick the higher one.
Again, we'll start with just mangoes.
Also again, we'll use a graph to keep track of things.
So what should the happiness score be
for one mango in a day?
We're making this up so let's just say 100.
That's pretty meaningless on its own,
but what about the second mango?
That first mango stopped the blob from starving,
which is pretty valuable.
So even though the second mango
is still delicious and nourishing,
the blob isn't quite as desperate for a mango
now that it's already eaten one
and it's not gonna starve.
And so, that second mango will give
fewer happiness points.
Say, here, about 60 for a total of 160.
And this trend will continue with each mango
being worth a little bit less than the previous one.
The term for this is diminishing returns.
Sometimes, people use the word, utility,
to talk about happiness points,
so you might hear this called diminishing marginal utility,
which just means you get fewer happiness points
for each additional mango or whatever it is
you're talking about.
That's the basic picture,
but we're gonna want to adjust these values a few times so,
instead of making up each number individually,
I used a logarithm function to get the values.
If the word, logarithm, makes your head hurt, don't worry.
We're not gonna go too deeply into them.
It's just a kind of function that follows
this idea of diminishing returns.
It's actually the opposite, or the inverse,
of an exponential.
When things grow exponentially,
they grow more and more and more quickly,
and when things grow logarithmically,
they grow more and more and more slowly,
and that slowing growth is all we're looking for here.
Alright, and before we keep moving,
we should note that this utility function
is an assumption.
Maybe, the first one just wakes up the blob's palate
and the second one is amazing,
and so, it's worth more than 100 happiness points.
And then, eventually, the blog gets full
and eats too many, making its total happiness
actually go down, which is known in some circles
as the Mo' Money Mo' Problems Effect or,
in my case, it's the Taco Bell Drive-Thru Phenomenon.
And Taco Bell, if you're watching,
I'm always looking for new sponsors.
Anyway, there's a whole field called behavioral economics
that focuses on how people make decisions.
So we'll explore more models in the future,
but this idea of diminishing returns
is a pretty decent starting point.
Alright, now, let's add wood to the picture.
At first, we'll assume the blob values wood
in the same way it values mangoes.
Now, our happiness point function
has two inputs and one output.
So to show it in the graph,
we need to add another axis for wood.
And now, instead of a curve,
we have a surface.
Any combination of mangoes and wood
leads to some point in this surface,
and that point's height reflects how happy
the blob is with that situation.
And that's how the blob decides what it wants.
In a minute, we'll combine it
with the production possibilities,
but I've thrown kind of a lot at you
over the past few minutes,
so don't be shy about pausing,
rewinding, and reexplaining it to yourself
to help it all sink in.
Now, we have everything we need to unleash
this blob and see how it behaves.
It'll start by just getting one mango
before switching to logs,
and each day, it'll adjust how many mangoes
it goes for until it seems to find the strategy
that gives the highest possible number
of happiness points.
This is the same forest, the same blob.
So the production possibilities
are the same as before.
So if wanted, we could just have the blob calculate
the optimal point ahead of time.
But, in real life, we have to try things out
and learn from our mistakes.
And so, we're gonna make the blob do the same thing.
(gentle music)
Alright, so it looks like the blob
is equally happy with 10 mangoes and nine pieces of wood,
or with nine mangoes and 10 pieces of wood.
It's not too surprising to see
that it's finding a happy medium
since the two resources are valued
in the same way and they aren't too different
in terms of production possibilities, either.
But now, what happens if the blob
has a little baby blob?
The baby can't collect anything,
but it does have to eat.
So now, let's say, the blob values mangoes
twice as much as it used to.
What do you think the new optimal strategy will be?
(gentle music)
It turns out that 13 mangoes and six pieces of wood
ends up maximizing the blob's utility.
The interesting thing here is that,
even though we, literally and precisely,
doubled the value of mangoes,
it didn't try to get twice as many mangoes.
Alright, one more situation before we go.
Let's rewind to before the baby blob came along.
So now, the blob is back to valuing wood
and mangoes in the same way.
This time, though, each mango tree
will bear two mangoes each day instead of just one and,
with the different forest,
the production possibilities will actually change.
Now, what do you think the blob will do?
(gentle music)
And we've landed on 12 mangoes and 10 pieces of wood.
It could've been natural to guess
that the blob would get twice as many mangoes,
but the blob ended up deciding to get only
a few more mangoes, and then,
use the time it saved to get more wood.
And the way it makes sense of this, intuitively,
is to think about if, say,
a cheesy gordita crunch was half the price.
I wouldn't actually eat twice as many.
I mean, don't get me wrong,
I'd eat more, but I'd probably put some
of those savings into buying a bigger Baja Blast,
which it comes in a zero-calorie version now,
by the way.
The point is, it's hard to predict ahead of time
how everything's going to balance out
when you make one simple change.
That's it for this video.
In the next video, we'll expand this economy
by introducing this blob to its neighbor,
and we'll get to see whether they decide
to trade with each other.
See you then.