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. 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. 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. And the payoff, as we said is the utility, really, minus the price that the person's going to have to pay. Right? This is utility, this is the price paid or the total price, total price paid. So, the payoff is going to be the utility, which is A plus B. 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.
