Hi. Remember we were talking about the concept of path dependence. In this lecture, I wanna focus on a very closely related topic, or concept, known as increasing returns. Increasing returns works as follows. Basically, it says, the more I have of something, or the more people that do something, the more that I want of it, or the more other people are gonna do it. So, for example, the more people to get [inaudible] typewriters, and the more other people are gonna wanna get [inaudible] typewriters. And there's two reasons for this. One is, you can then type of somebody else's machine if they have the same layout. And then also, from a production standpoint, if I'm producing [inaudible] typewriters. [inaudible]. Then it makes more sense to these other [inaudible] that it's gonna be costly to rearrange the keys on a computer. So there's these positive feedbacks. More produces more. Now, this idea that more produces more actually. Exist within the player process, right? The more blue balls I pick, then the more likely I am to get a blue ball in the future. So, that leaves a lot of people to think, well maybe it's increasing returns that causes path dependence. And in fact there are books that are called Path Dependence Increasing Returns, and they're not necessarily equating the two, they're just putting them in the same box saying that these are related concepts. And they are related concepts because both the sway of the paths process and the player process had increasing returns. And the balancing process, which did not produce path dependence, didn't have increasing returns. In fact, it had the opposite, it had decreasing returns. The more red balls I picked, the more blue balls I picked in the urn. So there's clearly a relationship between the two. What we'd like to do is understand, is it logically the same thing? Is increasing returns the same thing as path dependence, or is it something separate. Let's go back and look at our [inaudible] process. We've got one blue ball and one red ball. We select a ball and then we return it, and we add a ball of another color. This clearly has increasing returns. Because if I pick three red balls. Now I've got four red balls in there, and only one blue. And the odds of picking a red ball is gonna be four-fifths, whereas, initially, one-half. So the more red balls I pick, the more likely I am to pick red balls in the future. So there's clearly increasing returns in this setting. But what we wanna ask is, does that mean that increasing returns is the same thing as path dependence? Are the logically the same thing? Now here's where it's very useful to have a model. And what we're gonna do is we're just gonna use our earn model, and we're gonna see that, in effect, they're not the same thing. So here's something I call the Gas/Electric Model and what this is meant to represent is the choice between gas cars and electric cars. Now, both of these had positive feedback. So when automobiles are first being developed, the more gas cars that were going to be built, the cheaper it would be for other people to build gas cars because all the engines would be being built, in fact, because there would be all these subsidiary industries creating things like pistons and stuff like that and fuel injectors. And so gas would be get more gas and also would create gas stations and that sort of thing and a whole oil industry. And electric would also [inaudible] electric so there would be electric filling stations and that sort of stuff, so both had increasing returns. But the fact is, is that the turn of the century when automobiles were being [inaudible] gas had much larger increasing returns than did electric so here's how we can represent that. We're gonna start off with five blue and blue is gonna represent gas. And we're gonna start out with one red. Now let's suppose that somebody makes, a company rises up that's an electric car company. Well what that's gonna do, is that's gonna add another red car, another, another red ball in the air, because it's gonna make electric cars more likely. But it's also gonna add one blue. Why? Because you can just stick a gas engine on the electric car. And just like you could stick an electric engine on a, on a gas, so we're assuming there's one blue and one red. Well what happens initially I've got a one-fifth chance of getting a red ball, after I pick a red ball I've got, since I've added one red and one blue. What I'm gonna guess, I'm gonna have a two-sevenths chance. So the probability of picking a red ball has gone up. But I would assume that increasing returns to, to blue balls, are much larger. So if I pick a blue ball, then what I'm gonna add is ten blue balls. Well, clearly if I pick a blue ball, then I'm increasing returns in blue balls. So what I've got here, I've got increasing returns in red and increasing returns in blue. But if you run this process, what you get is every single time, you're gonna get the blue balls winning out. You're going to end up getting that blue balls are more likely than red balls. And so this process isn't path dependent, but it has increasing returns. It's just that the increasing returns are much larger for the blue balls than they are for the red balls. So if you reregistry 1,000 times, we'd get gas cars everytime. And the main reason is you couldn't carry electricity in a tank. [inaudible] just carry electricity around. Take it, you know, from one place to the next you couldn't store it and that storability meant that gas cars had much more, had much larger increasing returns which is why they won out. So, increasing returns themselves don't give path dependent. You can have increasing returns and not get path dependent. Then we can ask another question which is, could you. Get path-dependence without decreasing returns and the answer to that is also yes. So here's an example and this [inaudible] an example for symbiosis, so we've got a bunch of symbiots that get, now we've got four color blocks. We've got blue, red, green and yellow and the [inaudible] return it. But here's the idea, if I pick a red ball. I'm going to add a green. If I pick a green ball, I'll add a red. If I pick a blue ball, I'll add a yellow, a yellow ball, I'll add a blue. Well there's no increase in returns here. So if I pick a red ball, I'm actually increasing the odds of green. But if pick a blue ball, I increase the odds of yellow. The same goes for green and yellow, so there's no increasing returns. I'm actually helping another type. But if I call this. The red and green balls are star, for like the larger set of red balls. And I call this blue star. You can see that this is in fact just the player process renamed. If I pick a ball from this set, a red or green, I add another ball from that set. And if I pick a ball from the blue yellow set and I add another ball to the blue yellow set. So, this is going to be path dependent, but it doesn't have increasing returns. So, what we see from the gas electric process is that. You can have increasing returns, but not get path dependence. And what we see from symbiotic process is that we can have path dependence and not have increasing returns. So, does this mean that increasing returns doesn't matter? No, but it means that increasing returns is logically distinct from path dependence. So, yes it may be the case that a lot of the things that we out there in history in which we have path dependence are the result of increasing returns, but. Logically they're completely separate concepts, increasing returns can give path dependents but it doesn't have to path dependents can occur with increasing returns it can occur without it. And the earn models are really interesting, and they really help us clarify a lot of stuff. But I don't want you to think that they're the only way you can get path dependence. In fact, in my own opinion, I think most path dependence comes from a very different process. And so I think we oughta just move beyond earns, and talk about path dependence in the social realm occurring through something entirely different. And that something entirely different is gonna be externalities. It's gonna be interdependencies between decisions. Remember and externality is a situation where I make some choice, A and this is just me making this choice. So I choose A and I'm really happy, but when I choose that, if you're over here, this has an effect on you. And maybe it makes you happy or maybe it makes you sad, but my decision influences you. And these externalities, because of the inter-dependencies between the choices, can produce externalities that can do so in really obvious ways. So let me give something that worked on, on my dissertation, my dissertation was written on sort of externalities between large public projects. Now, why large public projects? Because public projects are big. If you think of the economic choices we make, me buying, me buying a loaf of bread is a little decision. Somebody building a nuclear power plant, somebody, you know, creating a giant national park. [inaudible], you know, creating [inaudible] interstate highway system. These are huge economic decisions, and they bump into a whole bunch of other stuff. And because they bump into a whole bunch of other stuff, they create extra [inaudible]. And let's see, now, how those same externalities create path dependence. So, here's my model. There's just gonna be five projects a, b, c, d, and e. Each one has a value of ten on their own. This can be 10,000,000, 10,000,000,000, it doesn't matter. There's a positive value of ten on their own. But, each project's also gonna create some externalities. So, it's gonna. Bump into the other projects. And we'll see how, now, we can get path dependence. So, here's how I'm gonna represent these externalities graphically. The A, these things on the diagonal, the A, B, C, D, E, it's just the value of the project. This minus twenty counts the size of the externality between project A and project B. And this minus ten tell the size of the externality between B and C, and this five. Gives the size of the externality between A and C. So let me, get rid of all of my drawings here, and now let's think about, supposed that I did project A first. I get a value of ten. Now I'm thinking, do I do B? If I do A and B, I'm gonna get ten for A, plus ten for B, but then minus twenty for A and B which is gonna be worth zero, so I'm not gonna do it. Now if I think about doing A and C. I'm gonna get ten for A, plus ten for C, but then I get plus five for AC, which is gonna be 25, which is bigger than this ten. So I'm gonna do AC. Well now I've gotta ask, do I do A, C, and D? And if I do A C and D, I'm gonna get ten for A. Plus ten for C, plus five for the externality, plus ten for D, but then minus ten. For the externality between A and D, and that's gonna mean that, you know, maybe I do it and maybe I don't, because I'm sort of indifferent between doing A and D. So you can see if I start with A, I'm not gonna do B, I'm gonna do C. Maybe I do D, maybe I don't. Well, let's suppose that for some reason, I start out by doing B first, and if I do B first, then I'm gonna get a path of ten, and for the reasons I didn't talk about before, A B is getting a dim value of zero, so I'm not gonna do A B. But now when I look at B and C. If I do B and C, I get ten for B, ten for C, but then the externality between B and C is -ten. And so I'm not going to get really any larger benefit from doing B and C, so I could decide to do it, I could decide to not do it. Let's suppose I decide not to do it. When I also get B and D, and I look at B and D, I get ten for B and ten for D. But the externality between B and D is 30. Which is positive right? So now that's [inaudible] 50, so I'm gonna do B and D. So what's interesting here is if I started out, doing A I might end up A and C. If I start out doing B I might do B and D. And so there's gonna be depending on not only the initial conditions but also sort of you can see as I moved down this path, what projects I do in the past, are going to effect. What projects I do in the future. So these externalities between projects create path dependencies along the way. And it's the positive externalities as well as the negative externalities between projects. And what I did in my dissertation was showing that if most of the externalities were positive, then you actually had less path dependence than if the externalities were negative because the positive externalities created, they gave me sort of increasing returns of public projects, and just made it more likely that you're gonna do more projects. And you didn't get as much contingency as when you had the negative externalities. The point I want you to take away from this is, a big cause of path. [inaudible] is externalities and increasing returns I guess to one type of externality between decisions. Okay, so let's think about this particular lecture. What have we done? We said that one thing that people often equate with path dependence is increasing returns and we've shown that although maybe empirically the case that a lot of path dependence does come from increasing returns, logically they're completely separate. You can have path dependence without increasing returns, you can have increasing returns and not get path dependence. We also talked about how one big cause of path dependence may be externalities. Inner dependencies between choices, especially big choices like public projects, and those externalities, whether they're positive or negative. Can create that dependence. But the negative [inaudible] may have a larger effect. All right, thank you.
