- [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.
Yay! This guy is super great. Really helped me learn more about economics and ecology and some practical mathematics. This one was a bit simple, I felt, but maybe I've just learned this lesson sometime recently.
If you're new to this channel, it's best to watch them in order of upload, because they regularly build on one another. There's not many and they're all short! But if you see an exciting topic in your scroll down to the bottom, just go for it and do your best to keep up.
I think my favourites were Simulating Natural Selection and Simulating Supply and Demand.
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The mangos could be anything, here.
Like a Crunchwrap Supreme, or a Mexican Pizza.
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