So now we'll consider two graphs to illustrate the differences between usage
and flat-rate pricing. And specifically they will show the
advantages of usage based pricing over flat-rate.
And so, before we do that we have to define what's called the user surplus.
Which is the difference between the utility that a customer gets and the cost
of the provider needs to to satisfy the network.
And clearly we want that to be as high as possible, right.
because we want the customers to have high utility and we want the providers to
incur low costs for the network. So the higher that is, the better.
So under usage-based scheme let's see kind of what the user surplus is.
and so, we've defined the utility, the customer, the cost of the provider, and
then the surplus. So we'll consider our standard graph
again, here. And just very simply we know already we,
we really did this before and we'll write this as usage-based up top.
That the utility is going to be A plus B in this graph and the cost is going to be
just B, right? So it's the dollars per gigabyte times
the number of gigabytes that are being consumed.
And as for the surplus, it's just A plus B minus B, right, because this is the
cost of the provider. Right because the provider,
We're assuming that, again this is going to be, the cost, that the, provider's
going to incur. And that is what we're looking at over
here. And then if he's charging his [UNKNOWN]
then the users will, you know, consume this many gigabytes.
So, then the surplus is going to be A plus B minus B which is A, just as we've
said before. Now let's consider under flat rate
pricing what this graph looks like, so write up here flat rate.
So now flat rate's interesting because even though the provider's incurring this
cost, right, remember that we're doing flat rate pricing.
So this isn't really what's being charged.
This just at the beginning of the month this fixed amount.
And everything after that is essentially free, right, so the price then is
essentially dropping down to zero. Okay.
So, really everyone's going to kind of consume all the way up to the top of the
demand curve. Right?
Because we're not here anymore. We're all the way back down at the
origin. Because the price is zero for the entire
month. So everybody will consume as much as
possible until they can't have any more added, gain in utility.
And so, If we call, we'll just draw these arrows out here.
And we'll call this region in here C. Let's call this region here D.
So first thing we have to do is find out what the user's utility is.
So remember just like last time, the utility is just everything that's to the
left of the demand curve such as this big triangle right here, right?
So nothing outside the demand curve, always inside, just this area.
So we have this region plus this region in here.
So we have A plus B plus C, that's being the utility.