In this video, we'll get to know what direct network effects are and how they influence the development of network goods utilities, which can at best continue exponentially. Just like you would imagine, all the reflections in a mirror multiplying, just like these two mirrors. So, getting back to that notion of positive consumption externalities, let's now have a look at direct network effects. So, direct network effects again using the example of the telephone. Where did direct network effects come from? Well, the idea is that the utility from using the good or from having the good increases with each additional user who uses the same. So, to call other people you need other people to have a telephone as well. Which means that the utility, i.e. the number of people that I can call increases with the number of possible interaction partners. So, this leads to an exponential growth of the number of connections that you could potentially make, which is what's called the Metcalfe's Law. So, if you're on your own in your network, then you cannot call anyone. As you add one additional person to the network, you can see that the number of possible interactions here increases in a non-linear way, and in an exponential way, basically. So, each additional user becomes more useful to the overall network, because he can add additional connections to the rest. So, this is going to mean that there are positive consumption exponalities through additional people coming into the network. Now, how does a network good diffuse? So, how does it penetrate the overall market? So, interestingly if you think of a technology, adoption of a technology takes time. In other words, if a new technology comes out it's not adopted immediately by the entire market, but you get a fairly slow process of additional people joining the network. In fact, it's a very strong regularity that diffusion follows an S-shape meaning that you have a period of slow diffusion at the start, a period of very fast diffusion in the middle, and then it starts tapering off. And in network markets, you can see that the S-shape is often much more pronounced. As we'll see in this graph here, so, a usual s-shaped diffusion curve is going to be more pronounced if we have a technology with network effects. So, where does that come from? Well it comes from the fact that if you have very few users, these very few users are less inclined, they convey less utility and they are less inclined to adopt even more. So, only if you reach a critical mass then a large number of people will end up adopting pretty much at the same time. So, what does this imply for the utility function of a network good? Well, a utility function basically consists of a number of components here. The utility that a consumer, let's call him i, derives from a network good, depends on, first of all the stand alone value of the network good. What does that mean? Well, if you have a telephone and you can use the phone as an ornament, as a decorative device, then that would give you some stand alone value, okay? Now, as you can see from my example that may not be very large if that product is really designed as a network good. On the other hand, it depends on the number of users of the network that you're part of. And it depends on the strength of the network effect. So, if you combine the strength of the network effect and the number of users, you'll get what we call the network benefit. So, if we wanted to put it in the generic form, you can see here that the utility that a consumer i derives from a network good is a function of a, the stand alone value of the network good, and it's a function of the users of the network. And the function of course is determined by the alpha, the strength of the network effect. So, how would these look like in terms of their shape? Well, what's interesting is that of course they strongly depend on the alpha, on the strength of the network effect. So, if we take, as an example, a function or a network good that has no stand alone value, everything that it depends on is the n and the alpha. So, if we take a network good with a very strong alpha, so here, we took alpha equal to 2, so we have n to the power of 2. It's basically an exponential function that looks very much like the one we saw in Metcalfe's Law. If we take alpha equal to 1, then the utility you get from a network good is simply a linear function of n and if you take an alpha that's that less than 1, so here 0.5, it means that basically as you add on additional consumers the added utility that you get is going to be decreasing in the number of additional or of existing users. Now, are these utility functions the same for all consumers? Well, they're not. So, we have different kinds of adopters and these will have different preferences. These will have different values depending on a, the standalone value and, n to the power of alpha, which is the value of the network benefit. So pioneers like Ludwig II, for example who was a very early mover when it came to telephone networks. He will have a different utility function from lets say medium adopters, like you and me, so the mass market of adopters and late adopters will be even less inclined to adopt the technology, and they will have a different utility function again. So, just looking at this, a pioneer will have a fairly high stand alone value, so the a is going to be fairly large and the utility he gets is not going to depend a great deal on the number of users that also use the same product. Median adopters are our typical adopters who have a critical mass. So, their stand alone value is quite small but the number of adopters will lead to a threshold value. So, once you get beyond a certain number of adopters, their utility, the utility of a median adopter is suddenly going to increase sky high, so it's going to be this middle period that leads to critical mass and then it starts tapering off. And finally, late adopters have a very low stand alone value and only if basically the entire market has adopted, so when we're at the very high n we're late adopters we'll end up adopting the technology, after all. Okay, so this is basically looking at direct network effects and giving you a bit of information on utility functions, how they look like, what they depend on, and so on. And we're going to use that in the next couple of videos. So you see, direct network effects are a strong mechanism but they are not the only kind of network effects. There are also indirect network effects which you will get to know in the following video. END