Today's lecture is all about the power of complements. But at the very start, before we even start thinking about what strategies to use, once we go into complements or once we're looking at complements, let me give you some examples and the formal definition of what complements actually are and what they do economically. So, let's take some examples. An obvious one would be computers and software. You can take this computer, and you can do all sorts of things with it. You can go on the internet, you can write documents and so on. But if you use particular software, in this case game software, if you use that game software to play with that computer, it's going to increase in value. If you're thinking about skis and skiing sticks, skis on their own are good for getting down the hill. But it's definitely safer and is more fun if you have skiing sticks as well. Skiing sticks on their own are pretty useless if you don't have skis. Now think of Smartphones and apps, if you don't have any apps, then using a Smartphone as a phone is still fine, so you get some utility from using the phone as such. But the power of smartphones really comes from the fact that you can install little programs, applications, that you can then use basically as a computer on your phone, and that's where the main utility, the extra utility comes from. So these are all examples of complements, of complementary products that increase each others utility. So, formally speaking, two products, A and B, are complements if the usage of B increases the user's utility from A and vice versa. Formally, if we wanted to express that, that would mean that the utility from using A and B together is higher than the utility of using A on its own plus the utility of using B on its own. And let me give you a numerical example, just plucked out of thin air of course. The utility from using a laptop, and again that's probably the utility you get from using word processing software and so on, let's say that the utility you get is 50. The utility from software as such without a computer is 0. By the way what do we mean by utility. Utility is basically how much you're better off using the particular good in question. So if you use a laptop we're assuming that you're 50 units better off, than if you didn't. So what would happen if you combined laptop and software and you were able to use those together? It would be worth more than just a laptop and it would definitely be worth more than just the software. And it would even be worth more than the sum of the two. So we can imagine a situation where using the laptop and the software is worth 100. So that's the definition of a complement in terms of the user utility. An implication from this is when we think about cross price elasticity. So that sounds complicated, but it's fairly straight forward I think. So two products A and B are complements if the demand for B increases when the price of A drops, and vice versa. So, in other words, if the price for product A goes down then people are going to buy more of good B. Okay, and how is that going to happen? Well, first of all, this is what we call, negative cross price elasticity. Meaning that, the price of one product and the demand for the other product go in opposite directions. Now, cross price elasticity, as I said, sounds complicated, it's fairly easy. Basically, how does the demand for 1 product depend on the price of another product. So let's think of the example of our laptop and the software again. What happens if the price for the laptop goes down? The price for the laptop goes down, then demand for software is going to increase. And why did that happen? How can that happen? Well, price for laptops going down does two things. First of all, we might have more demand for laptops to begin with. So there's more people buying laptops in the first place. And secondly, people that do buy a laptop anyway, will have a larger budget for additional software. So that means that in both cases, so both from new consumers and from consumers that now have more disposable budget for buying software, the demand for software goes up. So so far, the complements we've looked at where fairly obvious. I mean, you know software and computers, skis, and skiing sticks, and so on. That's fairly, fairly obvious, but sometimes complements can show up in the most surprising places if we think about it, and if we look around. So even substitute goods, so goods that would typically be bought, either one or the other, can have complementary effects. So for example, if a price cut of the substitute good may decrease market share, but at the same time, it can increase the size of the market, the net result, the net effect, can be positive. So, again, let me give you an example of this. If we have two cloth shops in the same mall, okay, so you can buy all sorts of cloth. If shop A now initiates a price cut, that price cut is going to do 2 things. First of all, the people that went to the mall already might go to shop A rather than shop B because it relatively speaking has become cheaper. On the other hand, it also makes the whole mall more attractive. So words going to get around, hey there is shop A and it's just cut its price. So lets go to that mall and lets have a look around. So this is going to mean that for shop B, even though their prices have not changed and even though the prices of a competitor have decreased, I might still see a sales increase, because I have additional consumers that went to the mall and end up buying from me. So these are surprising complements in some sense, because we wouldn't think of substitute products as complements as well. But there maybe particular complementary effects. So hopefully, by now you've got some intuition of what we mean when we talk about complements. So for now let's move on and talk in the next couple of lectures about the kind of strategies that firms can implement in the light of complements. So stayed tuned and see you in a few minutes.