Hi, welcome back. Okay, so, last lecture, we talked about how using models can make us more intelligent citizens of the world. How we could just sort of understand how the world works a lot better. How was sort of the new lingo [unknown]. Alright, in this lecture, we're going to talk about how models make us clear thinkers, and this is one of the big reasons why people use models, because they could help us think more logically about how the world works. Okay, so this is sort of a multi-step process. So, let's, let's see exactly how it place out. So, the first thing you do when you write down a model is you name the parts. So, let me take a simple examples. Suppose I just want to write a model of where people go for lunch. And suppose it's a small town, and there's really just sort of, you know, four restaurants. So, there's restaurant 1, restaurant 2, restaurant 3, restaurant 4. So, those are parts, right? But what else is parts? Another part is people, right? So, these individuals, and they've got to decide where to go, right? Which restaurant do I go to? Well, now, we have to ask, what are the relevant parts of the people? Well, you know, this guy is wearing shoes, but the thing is his shoes probably aren't a relevant part. So, we name the parts really, but what really matters, and the shoes probably don't matter. And what does it matter if he's wearing mittens or, and if we put a hat on him. His hat isn't going to have much of an effect on which restaurant he goes to, okay? So, what does matter? Well, one thing that matter is how much money he's got, right, and how expensive these restaurants are. So, this restaurant may be cheap and this restaurant may be expensive. But this may be someone that's got a lot of money. So, how much money you have is going to be one determinant with of which restaurant you choose. Another thing that's going to matter is how much time he has. Does he have only 15 minutes, right? Or does he have a whole half hour to go have lunch, and different restaurants make it in different amounts of time. A third thing, maybe and I'll write this fancy little signal here for preferences. This is how economists and social scientists write preferences down, these are just, you know, what he likes. Maybe one of these is a Mexican restaurant, maybe one of these is an Italian restaurant. So, he's got different preferences over the different restaurants. So, these are all things, these are all sort of relevant parts that go into the model, alright? Once we've laid down the parts, then we've got to think about the relationships between those parts. So, models help us sort of identify the specific relationship. What you see on the left is a simple game theory model. This is called a extensive form game where one player, here's player 1, takes, makes some sort of decision, and then another player, player 2 takes some sort of decision, and then the players get payoffs. So, once you sort of name the parts, then the next thing you're going to model is identify the relationships between those parts and how things play out. So now, you got the parts, you got the relationships. What you can do is you can think through the logic. So, let me show you how complicated this is and how models are so useful. Let's do sort of a, a simple thing that I sometimes play with my undergraduates. Suppose I want to build a rim for the earth to be shot through, build a big basketball. I'm going to shoot the earth through the rim, but I want to give a little bit of space so you can make it. So, I'm going to put one meter, sort of all the way around, right? So, there's a little bit of a gap of one meter, and then the earth can go through just that little bit of spacing, one meter all the way around. Well, now, I'm going to ask the question, what should the circumference of that rim be? How big around does that rim have to be, assuming that the earth is, let's just simplify it and say, it's 25,000 miles around the equator of the earth. How big around does that rim have to be if I want 1 meter of clearance all the way around? Think about it. Okay, now let's do a little math. So, we know the formula for circumference of a circle, right? Circumference is equal to pi times D, right? Now, what I want is I want to find the circumference of that rim and that's going to be pi but my diameter is going to be the diameter of the earth. And if I think about it, remember I've got this rim here, and I want the earth to go through, but I want 1 meter on this side, and I want one meter on that side, so it's going to be, the diameter of the earth plus 2 meters. So the circumference of my rim is going to be just pi times the diameter of the Earth plus 2 meters. Well, that's pretty easy to, to solve, right? Because that's just going to be pi times the diameter of the earth plus pi times 2 meters. Well, pi times the diameter of the earth, you already said, was 25,000, and pi times 2 meters is just going to be 6.28 meters. So, the circumference is going to be 25,000 and 6.28 meters. So, that's probably not what most of you guessed, right? So, by writing down a very simple model, just a, you know, model for the circumference of a circle, we're able to figure out exactly how big that room has to be, and it's often very different, right, from what our intuition would have suggested. Okay. So, working through the logic is a big reason why models make us clear thinkers. Now, the next thing models do is they allow us to inductively explore. So, let me give a, sort of a fun example of this. Suppose you have a room, right, and we've got this room here. And there's a door, there's one little door right here that people can come out of and the problem is jammed in the door, right, so that, you know, as people try to exit this room, somebody gets jammed in the door. So, the question is like, how do you figure out a better way to prevent people from getting jammed? But one thing you might do is you might put a post right here. And this post might prevent people from you know, bumping into each other as they come out because they come here and they sort of bump into the post and they have to go around and that prevents things from, from sort of getting bunched up near the door. So, the interesting here is once you construct a model of the room, when you put a bunch of people in the room, right, so heres people and then you have them run out, you can ask, whats the effect going to be of putting the post and can conductively explore better ways to sort of position things in the room to prevent people from getting piled up, okay? Now, once we've sort of went through the logic and explored things, we can ask what, what exactly happens in our model. Now remember, when we talked about types of outcomes earlier on. I said, theres only four things that can happen in a model. One is It can go to some sort of nice equilibrium, like the planets, you know, I mean, like, I'm sorry, like, if I drop my pen, it rests on the floor in equilibrium. It can be some kind of cycle, right, like the planets orbiting the sun. It can be completely random, right, it can be just, you know, totally unpredictable and random, or it can be complex. And so, one thing that models like, let us do is figure out which of those things is going to happen. So, let me throw something out there. Suppose we're looking at oil, which is a commodity and we want to ask what about the price of oil? What about the demand for oil? What can we say about those things. Well, let's think about it. The demand for oil is, you know, probably, you can depend on the size of the economy. And so therefore, you'd expect since the economy tends to grow at a fairly constant rate, you'd expect, you know, the demand for the total supply of oil to probably slope up, right? What about the price of oil? Well, the price of oil depends on a whole bunch people who are sort of have some, you know, they might have some in reserve, and they're bargaining and they're buying and selling, and all sorts of crazy stuff can go on. So, if I were going to make a guess, I would say, you know, that the supply of oil is some sort of nice pattern, right? The total world demand and supply of oil is probably a nice pattern, but if I look at the price of oil, it's probably crazy, okay? And so, in fact, if you look at it, that's exactly what we see. So, here's oil production right here, and that satisfy sort of this nice upward slope. But if you look at the price of oils, the price of oil which is down here, that's just crazy. It's completely unpredictable. It's what we call complex. It's not random, right, but it's complex. So, the model, sort of if we construct models of these two things, we can see why, you know, total production of oil goes up and why the price of oil is so hard to understand, okay? Next, identify logical boundaries. This is one of my favorites. So, there's a website called opposite proverbs. And on this website, you see these statements like these two. Two heads are better than one, and that's certainly true. Often, it's the case that two heads are better than one. And too many cooks spoil the broth and that's often true as well, right? It is true that too many cooks do spoil the broth. Well, here's the problem. There's, are the opposite, right? The same is with a stitch in time saves nine, and he who hesitates is lost. So, if you just have these sort of proverbs or mantras that you sort of follow, they're not going to do any good because there's always going to be an opposite proverb that you know, says, do the op, do the opposite thing. So, which one do you follow? What models enable us to do is find the conditions under which one thing holds and one thing doesn't. So later in this course, we're going to see, when is it exactly the case that two heads are better than one, and when is it exactly the case that too many cooks spoil the broth? So, even though these proverbs are opposite, there are conditions under which each one holds, alright? Okay. Last thing. Communicate. One of the real beauties of models is they allow us to communicate our ideas and what we know really simply. So, let's take politics, for instance. And suppose you want to ask me, Scott, how do you, how do people vote exactly? Now, I can say you know, petty [unknown] I think that people, you know, they like candidates, they don't like candidates. And then there's issues, there's these things called issues. And it, there's a question like, you know, is the candidate, did they take positions on issues that you like, or they don't take positions on issues you like and they, they balance these things and they watch debates. And it can go on and on and on and you might really have no idea, when I'm done, how I think people vote. Well, let's place some standards with our simple model and I said, okay, so, here's how it works. There's going to be a voter and there's going to be two candidates, so here's my voter and here's candidate 1 and here's candidate 2. Now, what the voter does for each of these candidates is, they've got some sort of likability. So, they can say, so there's likability of candidate 1 and there's likability of candidate 2. And this is just sort of like, you know, how friendly do they seem, do they seem trustworthy, do they seem honest, that sort of stuff. So, this is, you know, we'll put Likability here. Now, the second thing that I'm going to say is that people care about policy. Now, for policy, what they care about is sort of this set of issues. So you can think of policies, what I'm going to say is the voter, I'm going to put a little left right continuum, to say the voter over here is going to be a little bit conservative, right? And then, for these candidates, I'm going to say, well, candidate 1 is over here. He's kind of liberal. And candidate 2 is really conservative, right, over here. So, this is what candidate 2 is. So now, here's my model of how people vote. What they do is they sort of, say, okay, well, how likable is each candidate, right, so look at the likability of candidate 1 and the likability of candidate 2. And then, they ask, how far apart is, here's my sort of policy, you know, I may be a little bit to the right. How close are these candidates to me? Well, candidate 1 is, is pretty far away. Candidate 2 is a little bit closer. So then, how people vote depends on the combination of these two things, likability, and how close somebody is on policy space. Notice how that's a much clearer way of explaining exactly how I think and enables me to communicate much more clearly to other people how is it that I vote, okay? Alright. So, that's how models make us clearer thinkers. Now, what we're going to do next, once we sort of, you know, got this understanding of models helping us think logically, is we could take those logical models and bring them to data. Thank you.