Adding demand curves

>>In the last few videos, we constructed a marginal product revenue curve for our little competitive car wash, and we essentially figured out how this is really just the demand curve for labor from this firm. I talked about on the very first video that if you know the demand curve for, in a certain market, and this is the market for labor of a certain kind, maybe the type of labor that would work at a car wash, then if you knew it from one firm and all of the other firms in the market for that type of labor, you could add their demand curves to get the entire market demand for that type of labor, for that good or service. What I want to do in this video is to make sure you understand what it means to add demand curves. It's, on one level, straightforward, but on another level, a little non-intuitive because of the ways that the axes are defined in economics, that the price axis is the vertical axis. Let's draw the demand curve for two firms. I'll do simplified versions. I won't use this one right over here. I'll just do two simplified demand curves. This doesn't apply just to labor markets. This applies to any demand curve. If I want to add two demand curves, this is one entity's demand, so this is one firm's demand. That's price, and this is quantity. This is quantity. Let's say at a price of 10, they demand nothing, if that's the hourly wages, and if the price were 0, they would essentially get up to they would demand 10 people. And so you have a situation. You have a demand curve that would look something, a demand curve that would look something like that, a dot, a demand curve that would look like that. I'll do one other point on the demand curve. At a price of 5 a quantity, or $5 per hour, this firm would demand, if we're thinking of it in terms of labor, at a price of $5 per hour of labor, this firm would demand 5 people per hour. Obviously, what I'm going to do is general to any demand curve, but we'll just keep it in the labor mindset. This is Firm 1. This is a firm's demand. Firm 1. If we're talking about this as demand for oranges, then this wouldn't be a firm. This would be a consumer or maybe a wholesaler or something like that. This is Firm 1's demand for labor. Let's say Firm 2's demand looks something like this. I'll try to align them. Firm 2's demand looks something like this. The axes are going to have the exact same labels. This is Quantity. This is Price right over here. This is 5. This is 10. Then this is 15. Let's say that this is 5, and let's say this is 6 right over here. Their demand curve looks like this. It looks like that. Let me make it a little bit neater. That looks less neat. It looks something like that. I could put some extra points here. At a price of 10, this firm will demand 2 units. If we're thinking of labor, $10 per hour, they'll get 2 people per hour. At a price of 5, they will demand 4. They will demand 4 units. These are all ... We've looked at a couple of points on this demand curve. Now we are ready to add them together. This is Firm 2, Firm 2's demand for labor. Let's add these two curves. When I said it's unintuitive, we're actually going to look at ... For a given price, how much total quantity of labor is now demanded? We're going to essentially add it horizontally, and you're going to see what I'm talking about in a second. When I add them together, I add them together, I'm going to have the same axes. Let's say this is 5. This is 10. Actually, let me get a little bit further on this axis, on this second axis. The second axis, I'll make it as straight as possible. Let's say that this is 5, 10, 15, 5, 10, 15, and this is 5, 10, 15. I'm doing my best to align it horizontally, that this 15 is this 15, that this 10 is with this 10, is with that 10, and that 5 is with that 5 and with that 5. At a price of 15 in the market, what is the total quantity demanded? It's still going to be 0 because even this firm is still demanding 0. But then if we go to a price of 10, this firm, the Firm 1 is demanding 0, but Firm 2 over here is demanding 2. So we're going to go 10. It's going to be right over there. This is right about 2. That distance is right about 2. Then if we go to 5, at a price of 5, Firm 1 is going to demand 5. Firm 2 is going to demand 4 units of labor. At a price of 5, you're going to have 5 plus 4. At a price of 5, you're going to have 5 plus 4 or 9 units of labor, 9 units of labor. Then at a price of 0, if labor is free, this firm would demand 10 units, and this firm would demand 6 units. You add them together, you get 16 units. You'd get 16 units. The combined demand for labor curve will look something like ... I'll do it in ... or actually, I'll do it in blue. The combined demand for labor curve will look like this. Between $15 and $10, only Firm 1 is interested in getting any labor. So this part right over here will look just like that. But then after that point, you're going to essentially add Firm 1 to the mix, and then Firm 1, maybe I'll do that part in a different color, it will look something like ... it will look something like that. We have essentially added, we've horizontally added this line to this line. You could imagine taking this line, and at any given point, so at 5 right over here, you're taking its value and quantity and adding to this quantity here. The reason why I said this is a little bit nonintuitive is this would have been easier at least for me to add with the background of the traditional algebraic conventions we're used to. We're used to adding vertically. If we were to flip price and quantity, then we could stack these on top of each other and add them vertically. That's why it's a little nonintuitive. But hopefully, this makes sense. We're just looking at each of their demand curves at any given price, and we're saying, "OK, what is the demand from Firm 2? "What is the demand from Firm 1?" and we're adding them together, and then we get this. We get this combined market demand curve, Firm 1 plus Firm 2.