In this lesson, we're going to further explore the demand curve. If you recall, the demand curve was our abstraction to give us consumer behavior. I'm going to remind us of that by putting up this simple device. It said that if we put quantity on the horizontal axis, it's here and we put price on the vertical axis, which is here, the demand curve is a relationship that tells us that from consumers point of view, price and quantity are inversely related. If the price goes up, consumers can't buy as much as they did before. They may like it, but it's too expensive in terms of the opportunity cost of what they have to give up. The price goes down, consumers may be convinced that they could go ahead and afford a few more of that unit. That's the general indirect relationship between price and quantity. We can say that quantity demanded is some function of the price. So, again, that Q is quantity and that P is price and f is just some functional operator that translates price into different levels of quantity demanded that consumers wish to purchase. Now, as you know, we're abstracting to linearity for the demand curve. That doesn't really hurt us anything in the intuition. It saves us all a little bit intractability. We don't have to worry about quadratic equations to solve problems out and and we still get all of the horsepower with this curve. But one of the things we've also not gotten clear enough about is what's really underneath that demand curve. So, the way we're going to think about that is to bring a different picture to bear. Here, I'll draw all those same axes, price and quantity. A firm has a choice. Firm says, if I offer a price, let's just pick a price out. We'll, call this price P_0. At this price, the firm says, "Why don't we try this price?" They do these things, and they do these marketing tricks. They know that along that price line, consumers are actually going to be distributed along something that looks kind of like the normal distribution. The normal distribution says that, they don't know for sure how many people were going to buy the product. They say, if we quote a price here, I know that it's very unlikely that only this amount will be sold. It's very unlikely that this amount will be sold. As we get over here, we see that the amount that we think is the best estimate of what will be sold would be the peak of that normal distribution. Now, it's up to the firm to sort of tinker around with prices and say, well, at different possible prices, how much will people actually want to purchase? They know that if they lower the price to say P_1, that along that possible price, the distribution, consumer purchases will probably look something like this. Again, it's still a normal distribution. It's just that the mean of that distribution has shifted to the right. Along that price vector, there's a small probability that this amount will be purchased. There's a higher probability that this amount will be purchased and as well out here, but the most likely amount is right here, the center of that distribution. Not to belabor the point too much longer, but we could do one more possible price. At this lower price, the distribution for consumers would look something like this. Again, for us, the mean of that, that is the most likely amount of sales, would be right here. So, from the first of view, for different possible prices, they can discover this sort of this locus of expected sales points and this we would call our demand curve. Now, how did they find these? Well, they hire statisticians, they have people who go out and look at the data, they look at their sales, they do gimmick tricks, they'll mail out certain discount cards. So, some people will have a discount of $0.20, another one with a discount of two dollars, and another one with a discount of four dollars, and then get an idea of how much does a lower price really spur more purchases? They'll get an idea of how they can actually figure out what this distribution of consumption patterns is all about for the prices for their product. So, what we see then, is that we'll end up with a product that we'll call a market demand curve. The market demand curve is basically the summation of all of the demands of the individual consumers. Some people really like this product. As price goes up, they don't cut back their purchases very much at all. Some people, the product's okay. If the price goes up, they'll cut back a little more. From the point of view of the firm, the firm aggregates those by thinking about those probability functions and understanding for different possible prices, what's their expected amount of sales. For us, that locus of those expectation points gives us what we estimate to be the demand curve. In this course, we'll use these expected value operators, understanding that actually there's a little uncertainty there. The firm doesn't know for sure how many people are going buy it if they quote a price of P_0 but they have a pretty good idea of the distribution to consumers and say the expected sales at that price P_0. They know the expected sales if they raise the price to some higher level P_1. They know the expected sales, they've put it down. We are gathering those expected amounts and putting them down as this representation of what we expect the demand curve to be.