These diagrams basically try to illustrate the quantity called surplus which is defined as the difference between the utility achieved by a consumer and the cost it takes to provide that kind of service. So here is reason number one. Illustrated through this kind of, a demand price diagram. In, most economy, economics textbooks, they plot p versus demand of p. Okay? A different kind of orientation of this graph. Here, we are plotting d of p versus p, Okay? So this is price on the x axis and demand on the y axis. Of course, it's a decreasing function. Let's say it's a straight line, for, Graphically, simplicity here. Now if you pick a certain price point as the carrier. Okay? So, P sub U for usage based. Okay? You say that this is the kind of the, the unit price. I need to provision capacity at, at this in this scheme here. Then according to a demand curve, with usage price, then you get a sort of X of U as a demand. Now, what is the utility? To the user, is basically. The area under this curve. Right? Why? Because u prime inverse is p, is d, Right? So if I flip the d curve, I'll going to get a u prime. So, turn your head 90 degrees.'Kay? You see that this is that curve. Right? And then, I'm going to integrate this. Then I'll get the utility value cuz I'm integrating the first derivative. That means I look at the area under the curve and that is this area, Okay? So utilities aB. + b. The two areas labeled as a and b. Now, what is the cost it takes to provision this much utility while the carrier is saying the per unit cost is p sub u and your consumption is x sub u. So, the product, that's this rectangle area b, is the cost. The difference is the surplus. And that is the difference between A plus B and B, which is exactly eight. So this part is the good part, the surplus. Now that's assuming you do usage based. Now, what if you do flat? So denote that by subscript F. Well, if you do flat, that's effectively saying that if a consumer were to consume all the weight as if the price is zero. It's a very disturbing pricing signal, free, okay? This skews the demand-supply relationship. So now the supply will be all the way to this high, okay, and, therefore, the extra cost to provision. This is c + d compared to the usage base case. This is extra cost, the cd + d area. The extra utility you achieve however is only area c. So the negative surplus is area d. This is negative surplus. And in fact, you can have enough negative surplus so D can be so big that it overwhelms A. So d can be bigger than area a here. And therefore, even the net surplus becomes negative as you switch from usage to flat in this comparison. So, that is reason number one that a flat rate pricing leads to less surplus because it sends the wrong pricing signal to consumers. Here's another reason, very different one. Here I'm plotting three different demand curves, representing three kinds of users, typical users. A light user x, a medium user y, and heavy user z okay. So, the heavier user you are the higher your, your demand curve is for the same price. Now, again, if it were a flat rate, then it's as if the price set to zero, and you get these three demand consumption points, okay. Now the price that carrier need to charge for the flat rate is to be high enough, okay, so that the area under this rectangle, marked by r, r must be large enough. Now, I cannot control this curve, but I can control this point. So I need to pick the price for flat-rate pricing scheme to be large enough so that the resulting r curve is large enough. But, if this point is large enough, then you can see that in certain cases. Say the light user, okay? The total surplus the total utilities on here under the curve, this, this T region, but the price is this much. So surplus is negative for light user. Now of course for the heavy user, this whole area under the curve is the utility subtracted this cost surplus is positive for heavy users. For light users however it is negative. This quantifies the simple intuition we've been alluding to a few times already. That is light users subsidize heavy user's lifestyle. And the reason is because flat rate pricing is inflexible. You need to set this to be large enough and when that happens the, surplus can become negative for light users, Reason number two. Reason number three, okay. You can have also a carrier think about upgrading the service. Okay? Upgrading the service. In order to upgrade service, you have to pay for the expense associated with that. On the one hand, as you upgrade service, the demand curve for every user will be shifted to, to the right. Say under the same shape. Why? Because, for the same price, I will be getting a better service. And therefore, all the demand will be higher, Okay? And now on the other hand, the carrier also has to pay more to upgrade and therefore issue a higher price. Let's say again, it's under this flat rate, so everything is subscript by f here, you go from p to p bar, okay? So that you can recover the cosst that is, the area originally under this rectangle suffixes now you need a bigger rectangle, Okay? Now as you do this however you can see that if the a user is actually light enough, Okay? Were light enough, then the surplus, that's the difference between utility. Area under the triangle curve, These are the consumption points minus the cost that's the rectangle area is actually shrinking as you go from a lower service to a better service. This, this surplus actually reduces as you go through an upgrade. Okay, this counter-intuitive behavior is again due to the fact that recovering cost through a single flat price is inflexible. This is reason number three, Okay? So now, somewhere you've seen a graphic illustration of three quantitative notions using utility and demand curve on these demand price diagrams. Reason number one is that, it leads to waste. Number two is that light user subsidizes heavy user. Number three is that it discourages, service upgrade in some cases. So there's plenty of evidence. In fact back in 1998. Uc Berkeley had an experiment called index experiment. So one of the few quantitative approaches to suggest why usage pricing is a good idea. But, of course back then supply per dollar can catch up with demands projected growth rate, and it was more important to get the market demand going up. So even though it was demonstrated, it took actually more than ten years for the industry, at least in US mobile industry, to say that we're going to shift to usage based because of this jobs in a qualitive demand. Alright let's conclude this lecture with a simple example at this point.