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These diagrams basically try to illustrate the quantity called surplus which is

Â defined as the difference between the utility achieved by a consumer and the

Â cost it takes to provide that kind of service.

Â So here is reason number one. Illustrated through this kind of, a demand

Â price diagram. In, most economy, economics textbooks,

Â they plot p versus demand of p. Okay?

Â A different kind of orientation of this graph.

Â Here, we are plotting d of p versus p, Okay?

Â So this is price on the x axis and demand on the y axis.

Â Of course, it's a decreasing function. Let's say it's a straight line, for,

Â Graphically, simplicity here. Now if you pick a certain price point as

Â the carrier. Okay?

Â So, P sub U for usage based. Okay?

Â You say that this is the kind of the, the unit price.

Â I need to provision capacity at, at this in this scheme here.

Â Then according to a demand curve, with usage price, then you get a sort of X of U

Â as a demand. Now, what is the utility?

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Right? Why?

Â Because u prime inverse is p, is d, Right?

Â So if I flip the d curve, I'll going to get a u prime.

Â So, turn your head 90 degrees.'Kay? You see that this is that curve.

Â Right? And then, I'm going to integrate this.

Â Then I'll get the utility value cuz I'm integrating the first derivative.

Â That means I look at the area under the curve and that is this area,

Â Okay? So utilities aB.

Â + b. The two areas labeled as a and b. Now, what is the cost it takes to

Â provision this much utility while the carrier is saying the per unit cost is p

Â sub u and your consumption is x sub u. So, the product, that's this rectangle

Â area b, is the cost. The difference is the surplus.

Â And that is the difference between A plus B and B, which is exactly eight.

Â So this part is the good part, the surplus.

Â Now that's assuming you do usage based. Now, what if you do flat?

Â So denote that by subscript F. Well, if you do flat, that's effectively

Â saying that if a consumer were to consume all the weight as if the price is zero.

Â It's a very disturbing pricing signal, free, okay?

Â This skews the demand-supply relationship. So now the supply will be all the way to

Â this high, okay, and, therefore, the extra cost to provision. This is c + d compared

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to the usage base case. This is extra cost, the cd + d area.

Â The extra utility you achieve however is only area c.

Â So the negative surplus is area d. This is negative surplus.

Â And in fact, you can have enough negative surplus so D can be so big that it

Â overwhelms A. So d can be bigger than area a here.

Â And therefore, even the net surplus becomes negative as you switch from usage

Â to flat in this comparison. So, that is reason number one that a flat

Â rate pricing leads to less surplus because it sends the wrong pricing signal to

Â consumers. Here's another reason, very different one.

Â Here I'm plotting three different demand curves, representing three kinds of users,

Â typical users. A light user x, a medium user y, and heavy

Â user z okay. So, the heavier user you are the higher

Â your, your demand curve is for the same price.

Â Now, again, if it were a flat rate, then it's as if the price set to zero, and you

Â get these three demand consumption points, okay.

Â Now the price that carrier need to charge for the flat rate is to be high enough,

Â okay, so that the area under this rectangle, marked by r, r must be large

Â enough. Now, I cannot control this curve, but I

Â can control this point. So I need to pick the price for flat-rate

Â pricing scheme to be large enough so that the resulting r curve is large enough.

Â But, if this point is large enough, then you can see that in certain cases.

Â Say the light user, okay? The total surplus the total utilities on

Â here under the curve, this, this T region, but the price is this much.

Â So surplus is negative for light user. Now of course for the heavy user, this

Â whole area under the curve is the utility subtracted this cost surplus is positive

Â for heavy users. For light users however it is negative.

Â This quantifies the simple intuition we've been alluding to a few times already.

Â That is light users subsidize heavy user's lifestyle.

Â And the reason is because flat rate pricing is inflexible.

Â You need to set this to be large enough and when that happens the, surplus can

Â become negative for light users, Reason number two.

Â Reason number three, okay. You can have also a carrier think about

Â upgrading the service. Okay?

Â Upgrading the service. In order to upgrade service, you have to

Â pay for the expense associated with that. On the one hand, as you upgrade service,

Â the demand curve for every user will be shifted to, to the right.

Â Say under the same shape. Why?

Â Because, for the same price, I will be getting a better service.

Â And therefore, all the demand will be higher,

Â Okay? And now on the other hand, the carrier

Â also has to pay more to upgrade and therefore issue a higher price.

Â Let's say again, it's under this flat rate, so everything is subscript by f

Â here, you go from p to p bar, okay? So that you can recover the cosst that is,

Â the area originally under this rectangle suffixes now you need a bigger rectangle,

Â Okay? Now as you do this however you can see

Â that if the a user is actually light enough,

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Area under the triangle curve, These are the consumption points minus the

Â cost that's the rectangle area is actually shrinking as you go from a lower service

Â to a better service. This, this surplus actually reduces as you

Â go through an upgrade. Okay, this counter-intuitive behavior is

Â again due to the fact that recovering cost through a single flat price is inflexible.

Â This is reason number three, Okay?

Â So now, somewhere you've seen a graphic illustration of three quantitative notions

Â using utility and demand curve on these demand price diagrams.

Â Reason number one is that, it leads to waste.

Â Number two is that light user subsidizes heavy user.

Â Number three is that it discourages, service upgrade in some cases.

Â So there's plenty of evidence. In fact back in 1998.

Â Uc Berkeley had an experiment called index experiment.

Â So one of the few quantitative approaches to suggest why usage pricing is a good

Â idea. But, of course back then supply per dollar

Â can catch up with demands projected growth rate, and it was more important to get the

Â market demand going up. So even though it was demonstrated, it

Â took actually more than ten years for the industry, at least in US mobile industry,

Â to say that we're going to shift to usage based because of this jobs in a qualitive

Â demand. Alright let's conclude this lecture with a

Â simple example at this point.

Â