A firm's marginal product revenue curve

Narrator: What we're going to do in this video is dig a little bit deeper into labor markets. It's really not going to be any fundamentally new concepts. We're really just going to reapply concepts that we've already seen before and maybe use slightly different words, but the reason why labor is interesting is labor is one of the factors of production. It's one of the inputs you need for firms to produce whatever they do produce. Unlike in most markets, if we're talking about the computer markets, let me write over here. In the computer market, the demand is coming from individuals. It's coming from, I'll just call it, individual people while the supply is coming from firms, is coming from firms. In the labor market it's the other way around. In the labor market the demand is coming from firms, these are the people who need labor, who are hiring the labor, so this is coming from firms and the supply is coming from individual people. So, it's coming from individual people. What's interesting about that is because the demand is coming from firms, in the past, when the supply was coming from firms, we could look at a firms cost structure and we could come up with a supply curve from that. Now that the demand is coming from firms, we can look at a firms, essentially their revenue structure, how much incremental revenue do they get per extra employee and we could actually generate a demand curve, their marginal benefit curve, by looking at their business a little bit closer. That's essentially what we're going to be doing in this video. These aren't any fundamentally new ideas, we just applying them in a slightly different way and we'll use slightly different words. Now, let's assume, for the sake of this video that I run a car wash, a car wash. It is a competitive car wash. It is a competitive car wash. I have to be a price taker. I do not have a monopoly, or an oligopoly. I'm not even a monopolistic competitor. There are many car washes in this city. We are undifferentiated. We are all offering the same service. So, I'm going to be a price taker. Let's say the equilibrium price in this market for competitive car washes is $5 per car wash, $5 per car wash. Just as a little bit of review, that also means, remember, this is a competitive firm, not a monopoly, that my marginal revenue is equal to a constant $5 per car wash. If I do 1 car wash I'll get $5, 2 car washes, $10 3 car washes, $15. In a monopoly, the marginal revenue would change. Let's think about how much benefit I would get from each incremental employee. First, I'll do a ... let's make this column right over here, let's take this L for labor. This is going to be the quantity of labor. I'm going to think what I hire, what zero people, 1, 2, 3, 4, or 5 people. Let's think about how much that we can produce when I hire these amounts of people. I'll call that total product, or we could call it total product of labor. It's essentially saying, how many cars can I wash? This is going to be car washes per hour, so cars washed per hour. How many cars can I wash per hour with a different number of people here? Well, if I have zero people, I'm going to wash zero cars. Let's say that I find if I have one person that person can wash 5 cars per hour by him or herself. Two people can wash 9 cars together. Three people can do 12 cars. Four people can do 14 and 5 people can do 15 cars together. We can plot this. Let's actually plot this on a graph just to see what's going on. It always helps to visualize things, so that is going to be our total product. That is going to be our total product and this is going to be our quantity of labor. The quantity of labor we can have 1, 2, 3, 4, or 5 people and this is actually zero people right over here and my total product goes all the way up to 15. Let's say that this is 15, this would be 10 and this would be 5, 5, 10 and 15. So we can plot these points right over here. What is the total product? Well, this is zero/zero. Zero people, I'm not washing any cars per hour. Total product is in cars washed per hour. If I have 1 person, I can wash 5 cars per hour. If I have 2 people I can wash 9 cars per hour, 2 people I can wash 9 cars per hour, 3 people, I can was 12 cars per hour, 3 people I can wash 12 cars, that's about right there. Four people, I can wash 14 cars per hour, 4 people, 14 is right about there and then finally I will do this ... well let's see. I'm already using a lot of my colors. Let's see, pink. Five people, I can wash 15 cars per hour, 5 people I could wash 15 cars per hour. So, total product is a function of quantity of labor it will look like a curve that looks something like this. I could just connect the dots or I could make it look a little bit more curvy, so it's going to look something like that. One way that we should think about it, as you'll see in economics when you always want to think about how much you want to produce or how much you want to hire, you always want to think about how much benefit are you getting for that incremental thing when you're thinking about your cost structure. How much cost for that incremental unit? When you're thinking about your benefits or your demand, you're thinking, how much benefit am I getting from that incremental unit? Let's view this as the marginal ... Let's write marginal product, MP. Sometimes in some economics text books I've seen this referred to as MPL, marginal product of labor. Actually, I'll just write the L there to make this clear. This is the marginal product of labor. So, when we go from zero people to 1 person, on average between those 2 points over there, we're able to ... our delta, our change. Delta is just the Greek letter that symbolizes change. Our change in total product is 5. We can view that as the average marginal product, or you can kind of view that as marginal product halfway between these or you could view that as the average marginal product between those two points right over there. That's why I wrote it in a row. That it is in between these two points. It's taking us from zero to 1. Actually, let me plot these while I calculate what they are. So, I'll draw this one a little bit more flat, so I have space, which I can scroll down a little bit. So, in this axis I'm going to do marginal product of labor and then on this axis I'm going to have the quantity of labor. This is 1, this is 2, this is 3, 4 people and 5 people. So, this point right over here, this point right over here, that's the marginal product of labor, halfway. You could view this as a slope halfway between zero and 1 or you could view this as the average slope from zero to 1. So, I'll plot it right over here. I'll view it and actually I haven't labeled these axis. This is, let's call this 5, 4, 3, 2, 1. So, halfway between zero and 1 my marginal product of labor is 5, right over there. Then halfway between 1 and 2, my marginal product of labor, I go from 5 cars washed per hour to 9, so my marginal product of labor is 4. So, between 1 and 2 my marginal product of labor is 4 and then between 2 and 3, my marginal product of labor, I go from 9 car washes, cars washed per hour to 12. So, I have 3 incremental cars washed by adding that third person, so the average that you could view that as the slope right over there is going to be 3. So, the slope right over there is going to be 3. I didn't make this completely to scale and then, these are a little bit more bunched up down here, but let's just keep going. Then from going from 3 to 4, the marginal product of labor, I'll go from 12 cars washed to 14, so I get 2 extra cars washed by adding that fourth person, so between 3 and 4 I get an incremental, on average, 2 cars for that extra person and then finally between 4 and 5, I get one extra car. So, between 4 and 5 I get exactly 1 extra car. I'm going to get, it looks a little bit like a curve here because I bunched up the measurements, but this really should be a line. This really should be a line. Maybe I'll ... Well, that's my best. I don't want to have to re-plot all the points, but this should be a line like that. Every time we moved up 1, we went down 1. Every time we moved up 1, we moved down 1. We see that over here. We went to 5, 4, 3, 2, 1. So, this is 5, 4, 3, 2, 1. This really should be a straight line. This is essentially plotting the slope of this curve at any point. Now, what we can think about is, because this by itself, this is telling us the marginal benefit in terms of cars washed, but this doesn't tell us the marginal benefit in terms of dollars. To do that we need the marginal product revenue or you could call it the value of the marginal product of labor. Let me write that over here. We could call this the MPR, for marginal product revenue or we could view that as the value of the marginal product of labor, but essentially we're saying okay, if we're washing 5 extra cars from that first person and I'm going to get $5 per car wash. I have a constant marginal revenue. I am a price taker. Then I'm going to make $25 on those incremental 5 cars and if I wash 4 more cars, 4 times 5, I'm going to make $20 extra dollars. If I wash 3 extra cars, I'm going to make $15 extra dollars. Two extra cars, $10 extra dollars. I'm just multiplying by 5 every time. This is times 5, times 5, times 5, times 5 and if I wash one extra car, times $5 per car, I'm going to make $5 extra. So, essentially we could take every point on this curve and we could multiply it by 5 to get our marginal product of revenue or marginal product revenue. I have to be careful where I say the 'of's'. So let me plot that and I'll try to plot that a little bit neater so it's clear that this is a line. That's my marginal product revenue. You could also view that as the marginal benefit calculated in terms of dollars. You could view this as a marginal benefit in terms of cars washed. This is the marginal benefit in terms of dollars. Right over here we're going to have the quantity of labor. So, 1, 2, 3 ... Actually, I want them to line up a little bit better. So, 1 is right over there, 2 is right over there, 3 is there, 4 is there, and 5 is there. 1, 2, 3, 4, 5 Let me just go down a little bit. This is my quantity of labor and the marginal product revenue goes up to 25. Let's say this is 5, 10, 15, 20 and 25. Halfway between zero and 1 person, so this is 25 right over here. I am producing $25, or I get an incremental revenue of $25 halfway on average. You could view this point right over here. I multiply it by 5. I'm getting $25 on average for that incremental person. Then, when we go to this point right over here we're getting $20. That's this right over there. Then when we go to this point in orange, if we multiply it times five, we get $15 dollars. So, this is 5, 10, 15. So that's halfway between 2 and 3. Our marginal product revenue is $15, so that is ... I'm going to make it clear. This is 15 right over there and then halfway between 3 and 4 people it's $10, halfway between 3 and 4 it is $10, so it's going to look something like this and then halfway between, finally between 4 and 5, it is $5, it is $5. So, we're just picking points along here. We picked kind of the mid-point, the slope at those points or the average slope between zero and 1, but if you assume this curve has a continuous slope the slope changes continuously, then this will be a line and then this will be a line as well. So, our line will look something like that and what's neat about this line is essentially, this is the marginal benefit curve. Marginal benefit curve for this firm as it gets more and more labor. So, it's essentially the demand curve for this firm. If you wanted to find the demand curve for the market you could just take the demand curve for each of these competitive firms and then you would just add them all together.