Earlier in our videos, we discussed this issue of scarcity and has scarcity is fundamental to what gives economist their job thinking about allocation of scarce goods and services. And in order for it to work, we sort of got to this point where we understood that for the most part, Duke basketball games notwithstanding, we have markets that do the heavy lifting for us. Markets figure out through this tool called prices, figure out how to allocate these scarce goods and services. And so today we want to think about how this process works. We're going to venture into what will be the first of what you will probably end up thinking was 10 million graphs that we're going to do in this course. Well, we'll do a lot of graphs but this will be our first effort to go into it. And so what we're going to talk about today is equilibrium in a market, okay? And a market as we said is a place where buyers and sellers come together and we're going to put a little bit more of a formal definition on that right here. We're going to say, prices are determined by the interaction of two parties, okay? Right now for this lecture, we're doing two parties, okay, so we're going to live with two parties right now. And essentially what we're doing by this assumption is we're assuming for right now, no government intervention. See, the government gets involved in a lot of market behavior, sometimes for very good reasons, sometimes for not so good reasons. But we're going to talk about that when we move into the next module. Module 2 talks about government interaction and how it can change, in fact, it does change the equilibrium prices and quantities we find in the market, but for now, we're assuming just two parties. So, we're assuming away government to start with. And these two parties, for us we call these two parties buyers and sellers, okay? Buyers are people like you and I, we wade into a market, okay. We've got these little, if I can get that guy pocket here. We've got these little sheets of paper, right and we go out to the market with these little sheets of paper and we exchange them for goods and services, okay? Those are the sellers who are going to provide these to this. And so what we want to do is we want to figure out how this market works, okay? And so, what we're going to do is we're going to construct, Some curves, That are going to depict the behavior of these two groups. So we're going to start by depicting the behavior of consumers with something we'll call demand curves, and then we'll move into depicting the behavior of firms that is sellers by something we call supply curves. These curves are going to be abstract representations of how people really do behave when they get into a market, okay? And it's going to help us find something pretty cool. So we'll start by thinking about a demand curve. A demand curve is a locus, let's look at this definition, a locus of points showing how much consumers wish to purchase at different prices. The demand curve tells us how much do people wish to purchase when prices vary, okay. So we're going to draw this graph and to draw this graph, what I want to do is I'm going to get my black pen on here. And I got a horizontal axis and the vertical axis. And on the vertical axis, I'm going to put price, which from now on I'm just going to use P, okay, for the rest of the course. I'm just going to use P and on the horizontal axis, we're going to measure quantity of whatever this good or service is, gallons of gasoline, barrels of oils, apples. Whatever the product is you're buying only, we're going to again abbreviated from now on with Q. We'll change Q at various points from lowercase q to uppercase Q, but that's all will depend on where we are as we meander through thinking about how markets work in this course. Right now, we're just going to start with an uppercase Q which refers to us as market output, okay. And what we're saying here is that demand is some function of price. Demand is some function of price and that function is in general. It has this sort of shape, okay. And I'm going to redraw that because it cut a little bit too far down on the axis. There, okay, and so this curve, we're going to call the demand curve, okay? I'll write it out once and then from then on, I'm just going to call it D and I'll probably put D sub zero a lot, which means it's the original demand curve. Because we're going to have to figure out how things change when something comes along and moves the demand curve when consumers interest and taste for this product change, okay? Now this is the demand curve. The demand curve slopes down, it has that downward slope. Now, we have to talk about several issues about this demand curve, okay. First, those of you who are engineers and I know there are a lot of you out there who have a formal classical chaining in let's say, mathematics are looking at this and you say, Larry, that's kind of like wrong. If you're going to have quantity is equal to function of price, let me just add an extra slide here, okay? And in this slide, I'm going to introduce a little, how when you read the comic books, sometimes over somebody's head, there's a little bubble. It's a cloud, that's what the person is thinking, he doesn't really say that he's in, yeah. So I want you to remember, essentially if I were to write quantity is a function of price which is kind of explaining what that function says, a locus of points showing how much people want to buy for different puzzle prices, you change price around. I'll tell you how much I want to buy. Well, you were good, you should if you are properly trained say Larry, that curve should be like this price and Q. Because in fact, if you were to step back to your algebra class and say, y is equal to some function of x, you know that you would put x on the horizontal axis and y on the vertical axis, and then you would come up with some functional form. Okay, and that's right. Unfortunately, that's right. But in the vast history of economics, one of the great founding fathers decades ago, Marshall who wrote the first real tree to study economics. Marshall through the curve like this and then put the demand curve on there, even though the mathematical form looks like this, he put it on the axes that are inverse. So in fact, this is really the inverse demand curve but economists being lazy mathematicians never really used the word inverse. We just call it demand curve. So those of you who are a little bit offended by that, suck it up. From now on in this course, we're going to put price on the vertical axis and quantity on the horizontal axis, even though all we're doing is drawing the inverse demand curve, but that's okay. Second thing to note about this is, the curve of course is downward-sloping and that kind of makes sense because what that means is, that if in fact this is the original price. This point alpha, you read off the demand curve and say, you know what, consumers want to buy Q sub 0. So at that price P sub 0, consumers want to buy Q sub 0 and if you lower the price to some amount, I don't know why but suppose price went down to P1. What's going to happen in the marketplace? Well, you can see if price goes down. Consumers are going to want to buy more, okay? And we'll call that P1 Q1, it moves out the beta. That's the fundamental law of demand in the sense that would you lower price more, people will want to buy this product or people who already buy the product will want to buy even larger quantities of product. That's why firms have sales. They put a sign on the door that says 25% off sale, not because they just want to give their products away from lower prices. It's because they know that when by getting lower prices, more people will come across their doorstep in to buy their product in this case. So demand curve is inversely related, quantity demanded is inversely related to price. At higher prices, let's just pick an arbitrary price up here, P2. It says higher price P2, okay. We'll call this gamma. At gamma, consumers don't want to buy as much as they used to because it's too expensive. Remember, what we talked about last video, when we did the the opportunity cost and I said, you know what, this little sheet of paper, what it's good for? Well, it's good to us because you know it has embodied value, okay? You can't eat this but you know what you're in your head, you have a calculus that tells you what this thing is really worth, okay. And what happens here is that when the price goes up, you got to give more of these sheets of paper. And giving more sheets of paper means you're giving up more and more of that next best alternative, whatever the opportunity cost to this. I know what I could buy with this if I had just gone over to that product, but now this product is getting more expensive, I got to give it more green sheet of paper. I'm not going to buy as much as I used to. The question for you is, why did I draw it linear? Why is demand drawn linear? Do you think it's really linear in the real world? Well, the answer is probably not, okay. The answer is probably not but the good news is, linearity doesn't matter, okay? Being nonlinear, that is if I draw it as a curve. In fact, maybe a little bit more accurate representation and we'll get to that when we look at the next video is where that might come from. But it doesn't get us any extra mileage, it doesn't help us. It just makes the problem more intractable. You have to learn, if I give you a supply curve and demand curve and say find the equilibrium which I will, it's pretty easy for you to find the equilibrium of two straight lines, two linear functions. But if they're nonlinear, then you've got to get this thing out that you've already forgotten about unless you're a real hardcore engineer. It's called the quadratic rule, which is how you solve a quadratic nonlinear function so that you can find the exact outcome on that, if you were to do something like this. I'm going to add another one of those videos, or another one of those axis system here. And suppose this was price and this is quantity, and the demand curve looked like this, which it might, and the supply curve looked like this, which it might. Well then I say, tell me what the equilibrium price and quantity as you say Larry, I can do it graphically, there it is, equilibrium price and quantity. But solving it would require didn't do some pretty advanced math techniques. So, even here at Illinois, when I got my PhD at Cornell and when we teach PhD students here in economics, you spend four, five, six years to get your PhD and you're doing lots of hairy problems with demand and supply. But we still use linear because you don't get any extra miles just like, there's no reason to beat people up and make them figure out how to solve those all the time because the intuition is what we want. So first of all, I'm sorry that we have the axes upside down, but that's what we're going to live with. Secondly, we're just going to use linear demand curves here because it makes life easier and it doesn't cost us anything, okay? It makes the tractability, and the third thing is some of you are asking yourself right now, Larry, how did you know it was right there? Maybe it's out here or maybe it's back here, and the answer is, I got the pen. Okay, I got the pen, I get to draw it where I want. All I need is for that demand curve to have downward slope, the inverse relationship between price and quantity is what's necessary and all it needs is downward slope. So let's make life simple and do linear, and I just put it there and when you draw yours, you're going to put it someplace too, okay. Unless I tell you explicitly if I give you a straightforward linear function, then you'll actually have to plot it out and get the right numbers on the axes and stuff like that. All right, good.
