You pick up your iPhone while waiting in line at a coffee shop. You google a not-so-famous actor, get linked to a Wikipedia entry listing his recent movies and popular YouTube clips of several of them. You check out user reviews on Amazon and pick one, download that movie on BitTorrent or stream that in Netflix. But suddenly the WiFi logo on your phone is gone and you're on 3G. Video quality starts to degrade, but you don't know if it's the server getting crowded or the Internet is congested somewhere. In any case, it costs you $10 per Gigabyte, and you decide to stop watching the movie, and instead multitask between sending tweets and calling your friend on Skype, while songs stream from iCloud to your phone. You're happy with the call quality, but get a little irritated when you see there're no new followers on Twitter. You may wonder how they all kind of work, and why sometimes they don't. Take a look at the list of 20 questions below. Each question is selected not just for its relevance to our daily lives, but also for the core concepts in the field of networking illustrated by its answers. This course is about formulating and answering these 20 questions. All the features of this course are available for free. It does not offer a certificate upon completion.
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Del curso dictado por Princeton University
Networks: Friends, Money, and Bytes
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Why Do Mobile Carriers Charge Me $10/GB?
In recent years, mobile carriers have introduced a usage-based component to their data plans, where you are charged proportionally to the amount of data you consume. In this lecture, we will look at the reasons behind the switch to usage-based pricing, in terms of fundamental economic principles.
Conoce a los instructores
Mung ChiangProfessor
Electrical Engineering
Christopher BrintonLecturer
Electrical Engineering
In this simple example, we'll be asking the following question.
Okay, suppose you have users, all uniform, they all look the same with a certain
utility function which is a weighted log utility function for certain given
capacity bits per second measured, Okay, and denoted by x.
I look at the log of x weighted by sigma. Okay.
So, sigma parameterized is, basically, now they log utility functions.
And the user, or the carriers is charging a price based on the consumption amount.
This is a typical chart we've seen. There's a flat rate component g dollars,$
it doesn't matter how much you consume, plus a usage base h dollar per amount of
consumption, okay. So now, if I look at the graph, it looks
like this. Okay?
This is g dollars, Right?
And this part is h dollars per unit of consumption, say, per gigabyte.
So, I'm going to look at these two functions.
On the consumer side, it's the utility function sigma times log of x.
And on the carrier sides, p of x, g + hx. And I'll ignore this horizontal shift in
the demand because by paying g, you actually get a fixed amount of up to a
certain fixed amount of data. So, I'm going to ignore this to simplify
the notation. It does not change the gist of either
presentation or the conclusions. So, question number one.
Given the baseline usage price, is given g dollars and h dollar per gigabyte what is
the demand? And second, given such demand, how to
optimize the price. Now you see this feedback loop, right?.
Consumers have utility functions. Carriers decide the price,
Right? You give a different price to consumer,
they give you a different demand. And that will shift to your price again.
Now, this kind of loop we'll see a few times.
We will see it in TCP, in a network context.
We will see next lecture in SDP, Smart Data Pricing in a more elaborate way and
the general notion of you design something and then the agents will react, was
certainly even h, broader in its application, since we have seen in auction
and so on. Alright.
So, let's write down the equations. First of all on the consumer side, you say
that, you know what I'm going to look at my net utility,
Which is sigma x log of x - minus the price of ghx.
Plus hx, okay? This is my net utility.
I will set its derivative against x to be zero.
What is the derivative? Was just sigma over x minus h equal to
zero, That means,
My x star is just sigma over h. Alright, that make sense?
Bigger h, steeper slope, I consume less. How much less?
Well, governed by sigma phi. This is the answer, by setting the
derivative of that utility to be zero. Now, what about the carriers?, Price
settings, that is the g and h settings, the two parameters for you to play with.
The base line and the slope. Well, in this case, you are not setting
the derivative to zero, instead, instead we say that this is a poor monopoly
carrier. It has a price setting power. Meaning that it can squeeze your net
utility itself, now the derivative itself, to zero.
This assumes that this is a very powerful carrier, it got the price setting,
Power, Meaning that you can set the g of h such
that your utility is zero. This is clearly an extreme case of
modeling monopoly power. It's not realistic in our mobile data
market. But for a simple illustration, it
suffices. Okay.
So, this leaves no utility to the consumers.
It can't be negative, cuz if it's negative, the users won't participate.
Okay? And to properly use this monopoly price
setting power, We'll set it to be zero.
So, we can solve this second equation The second equation that says, sigma log of x
equals g plus hx, So now, I got two equations.
One is by the demand modeling, the others by the monopoly price setting modeling.
We can stick this x into this equation and now, we have the following result.
Sigma times log of sigma over h equals g plus h sigma over h equals g plus sigma.
Okay. That means, We can set the flat rate g to be sigma log
of sigma over h minus one. Now, this assumes that you know that, as a
carrier, you know the consumers are taking the logatative function with a known sigma
value. Which again, is unrealistic to assume.
But, let's say, that's the case now. So, now we have the answer.
Okay, so you give me a sigma. Okay.
And then, I can pick out a h slope, Then that will give me a g.
For example, let's say, sigma is set to be a 100 unit.
Alright Then let's look at two cases. One is one h is two dollar a gigabyte.
That's the slope. Then, plug in the equation, sigma and h,
you get the g, which is the flat rate, $70,
Alright? So, $70 a month is the baseline, then
extra gigabyte, you pay $two. This implies that the revenue for ISP,
gHX=$170 plus hx, a $170 a month, Okay? And the flat rate component is 41%
of the total revenue. Case A.
Case B. Suppose I increase h now to $five per
gigabyte, okay? Then, apply it in the equations, sigma
100, h is five, G Is 30.
That means an alternative is to set the baseline to be $30, and every gigabyte get
$5.. This actually is quite close, reasonably
close to the actual pricing points used by AT&T and Verizon Wireless.
This implies, on average, the ISP monopoly power ISP under our assumption, guess a
$130 as the revenue and the flat rate component is not only 23% of the total
revenue. Now, you can look at many more cases.
But you get the trend, the trend says, that actually, you should make h real
small, okay, very shallow slope. Okay.
So that you can afford to make a g, the constant part, very high.
This will max out your revenue, and the flat rate part will be dominant, okay?
Now, say, that's actually somewhat counterintuitive conclusion, isn't it?
Indeed it is, that's because we have made up three unrealistic assumptions.
Number one is that we assume there is only one bottleneck link.
In lecture fourteen, we'll take this away in TCP congestion control at a much faster
time scale than monthly bills. Number two is there's no capacity cost of
constraints of any kind. And that was the fundamental reason why we
got that somewhat counterintuitive conclusion from this simple numeric
illustration. Once we put capacity either as a
constraint, you can exceed a certain capacity, or as a cost.
Then you see that we cannot make h arbitrarily small and g arbitrarily large,
because that would induce a tremendous amount of traffic that will violate the
constraints or increase the costs to the point of not making it worthwhile.
The last one is that ISP was soon to be a monopoly.
And therefore, price setting power to squeeze your utility as a consumer to
zero. This is unrealistic.
So, later in the course, we'll, perhaps we'll keep this assumption, but certainly
remove these two assumptions. In fact, in the advanced material, we'll
remove this assumption. In lecture fourteen, we'll remove this
one. Now, having gone through this perhaps
unrealistic small numerical illustration, Let's highlight that we did touch upon a
very important conceptual and methodological tool called utility
maximization. It generalizes the payoff function ideas
we mentioned before. So far, we haven't seen network cuz
there's no network constraints or coupling get, but that's coming up in lectures
ahead. This utility maximization models consumer
behavior. We've seen utility function, demand
function, and induced elasticity of demand.
We've also seen a very, very powerful notion that the pricing, whether it's on a
single link of a network, it can coordinate demand versus supply.
Whether that's done on a monthly bill time scale, or a 50 millisecond round trip
scale of the internet. Whatever timescale, if you can design a
proper pricing, then it could help just demand supply.
Just like we've seen proper pricing in auction, like second price, can't
correctly internalize certain type of negative externality.
But improper pricing can also create a tragedy of comments.
Finally, for the specific topic of why usage-based pricing, why, you know the
answer. It's because of jobs inequality of
capacity. Where do we go now from $ten a gigabyte?
Is this the end of story or more? We'll look at smart data pricing in the
next lecture.
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