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.