0:01

So, we just looked at utility. Now, let's look at demand.

And demand is really the desire for a given resource at different prices.

Right. So, it's how much you want depending upon

what the price is. And here, this shows a typical demand

curve you might see. as the price increases, as you would

probably expect your demand is going to go down until you want less of it, you

buy less of it. Something costs $10, you'll buy more if

it costs $100. This for instance, just simple basic

ideas. And so one thing to note about the demand

function is that it's never increasing, opposite of the utility.

If the utility was set, it was never decreasing.

And demand is never increasing, it's just because of what we're looking at here

that makes it different. here we're looking at how much you're

going to buy or the quantity or price. And, clearly as the price goes up, you're

never going to want to buy more. You'll only, you might want to buy the

same amount as you really need it, you know if it's gasoline and you really,

really needed gas. then you might buy the same amount even

if it costed more, but it's only going to either stay the same, maybe, in very rare

exceptions or go down. Typically you'll see it just go down.

And, so higher price is going to induce a lower demand as we said.

And we assume linear demand curves right, so we're assuming that this is a straight

line from some point down to the bottom here.

We don't have to make that assumption, it just makes it a lot easier to think about

and clearly not all demand curves are linear, it's just an approximation we

make. And so really, the usefulness of the

demand function comes into play is that for a given price per unit, we can

determine how much will be consumed. So, price per unit could be something

like $10 per gigabyte, right? So, that's the price that we're paying,

and the unit is gigabytes. And so then that's going to tell us how

much quantity we're going to pay. So, if this is 10 dollars per gigabyte

here, maybe we would consume 5 gigabytes. And that would be a total cost of 50

dollars, and down here might say, well, once it gets up to something like, 30

dollars per gigabyte. That's just too expensive for me so I

won't consume anything. And down here, if it was completely free

per gigabyte, right. So, if it was almost a flat rate, right?

After the end of the month, I consume up to something like 50 gigabytes or, just

making these numbers up. That so, you know, the idea is that,

again, as the price goes up, the demand's going to go down.

But if we knew the demand curve, we could tell depending upon what price we set how

much user was going to consume in a given month.

So, that's why demand is a very useful concept here.

2:44

So, let's look at the relationship between demand and utility.

it comes into play when we define what's called the net utility.

And so before we said that you know, utility was the basically amount of gain

and the amount of happiness. But the thing is that, you know, every

slice of pizza you have, you're going to have to pay for it, right.

So, the net utility is the pay off, or the user's internal quote, unquote

profit, right. which is really the difference between

what you're getting and what you're paying.

Right, so we say that the net utility, write net utility, is equal to the total

utility minus how much you're paying. so the price per unit.

Or per quantity whatever it is times the amount that you're consuming or the

quantity. And so, really what, whatever price per

unit is times whatever quantity it is, right so,

And the utility is of course a also function of the quantity.

So, that's how we define the net utility. And that should make sense, right.

So, that you're going to pay more if you consume more, right.

Your utility's also going to go up, so the question is where, where does that

go. And user's are going to try all these

things to maximize this net utility. Users do not want to maximize utility and

they do not want to minimize price, they want to do both of them at the same.

Whereas if you try to maximize utility, you consume How ever much was possible,

right? But that's the problem is that then you

have to pay so much more that it wouldn't be worth it.

And, at the same time, you're not going to want to just set this to zero

because, in that case, then your utility would be zero and your net utility would

go down to zero. So, they want to maximize this.

This is what they want to maximize. So, we can graphically interpret and show

the relationships between utility, demand to net utility and so forth.

And, we'll do that right now, this is a very important concept, for the remainder

of this, this lecture, just to see and understand this here.

4:48

So, I'm showing again the demand curve. Over here, we have demand and price on

the other axis and first thing I want to do is just label a few of the points in

this graph here and so we'll look at it. let's call this section in here this,

this entire area right in here. right after this price per unit, so this

box that I'm tracing out right now. Let's call the area of that rectangle B.

Just call it B for a second. And then for this triangle over here that

I'm tracing out right now. All the way down.

From price per unit, all the way down to where the demand curve hits zero over

here. We're going to call that A.

So, there's this area right here, we'll call A.

So, we have B, and we have A. So, let's make this look a little more

pronounced. That right there.

Okay. So.

The first thing is. What is the price that the user's

going to have to pay? Okay.

So, we have a given price per unit. We know what quantity he's going to

consume. Right?

So, from the price per unit that's being charged, assume we know that's whatever

it is 10 dollars per gigabyte. We know what quantity it is that he's

going to consume. So, how much does he have to pay?

Well it's pretty simple math. We, we did, read an example right before.

We multiplied $10 per gigabyte times how ever many gigabytes he was consuming,

right. So really the multiplication of price per

unit and quantity is going to give us the amount that the person's going to have to

pay or the price. And that is just the area of this

rectangle right here, right. So, because, you know, we're just, we're

just basically multiplying the length and the width of a rectangle.

You know, without going into the mathematics or the calculus of it.

that's all we're doing. So the, the price that the user's

going to have to pay is going to be this quantity B right here.

Just this rectangle right in here. [SOUND] Now what about the utility?

Well, what's the users utility? Well, without going into large detail,

really the utility is just the total area down here, right.

So, he's consuming this much of a quantity, it doesn't depend upon the

price obviously, right the utility doesn't depend on the price that's being

offered. the quantity depends on the price, but

utility indirectly depends on price not directly.

So the utility the persons going to get is going to be this whole area in here,

all the way out to the end of this demand curve.

And we won't go into mathematical detail on that, but this entire area then is

going to be utility, so we're going to get A+B for the utility, right.

Everything down to this line over here from this line.

7:53

And we're going to subtract out B from that because that's the price we're

paying. So, the payoff is going to be A, right.

So, the person's payoff or the payoff that they're getting is really just this

fun rectangular region over in here. This is the, this is the added benefits

over A. This is what the person's taking.

This is what the person's taking, so this is what the person is taking home at the

end of the day. This area A in here, right.

B as we said is the price the person is going to have to pay this area.

The area A plus B is the utility. And the payoff is the area A.

So, these types of graphical analysis are going to be really important in help with

us going forward. So, the next question is well why does

the user actually consume based upon the demand curve, right.

So, this is great and if the users actually did and do conform to this then

it is easy to see. and for usage based pricing, right, where

we have a certain price per unit that we're charging the person, right.

We can tell they're, the client, they're going to pay and then we can figure out

what their payoff's going to be. But the question's why does the person

consume based on the demand curve, right? Why wouldn't he go, either higher or

lower and try to get more utility out of it.

And we'll look at that right now as to why it's the case.

That they do consume exactly the quantity given at the price per unit.