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Total product, marginal product, and average product

The short-run production function describes the relationship between output and inputs when at least one input is fixed, such as out output varies based on the amount of labor used. We can use this production function to find the total product of labor, the marginal product of labor, and the average product of labor.

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Video transcript

- [Instructor] In previous videos, we introduced the idea of a production function that takes in a bunch of inputs. Let's call this input one, input two, input three. And that based on how much of these various inputs you have, your production function can give you your output. In this video, we're going to constrain all of the inputs but one, to really take it down to how does our output vary as a function of one input. And as we do that, we're going be able to understand these ideas of total product, marginal product, and average product. So, to give you a tangible example, let's say that we are running an ice cream factory and we care about how much our ice cream production per day varies as a function of the number of people working in the factory. So, let me write this down. So, per day ice cream, ice cream production, production. And so, let me make a table here. So, in our first column, I am going to put our labor, which you could view as the input that we're going to see how does that drive output. So, I will put Labor. So, you could view this as workers per day. Workers. And we're going to see how our output varies whether we have zero workers, one worker per day, two workers per day, or three workers per day. Now, our next column would just be our output, and we'll say that's our total product as a function of labor. TP standing for total product. And let's say that we know, if we have zero people working in our ice cream factory, well then, we're going to produce zero gallons of ice cream, and let's just assume that our output is in gallons, and it's gallons per day. If we have one worker at our factory, well then, we're going to be able to produce 10 gallons a day. If we have two workers in our factory, we're going to produce 18 gallons a day. And if we have three workers in our factory, let's say we can produce 24 gallons a day. Fair enough. Now, I'm going to introduce an idea, and you've seen this word marginal, perhaps, in other times in your life. I'm going to introduce marginal product of labor. And the way to think about marginal, that's how much for every increment of one thing, how much more of the other thing do you get? So here, our marginal product of labor says, for each incremental unit of labor, for each incremental person working there per day, how many more gallons of ice cream am I producing? So, my marginal product of labor, when I go from zero to one worker, I'm able to produce 10 more gallons from that first worker. Now, what about when I go from one worker to two workers? Well then, I go from 10 to 18 gallons. So, that second person gets me an incremental eight gallons per day. And then as I go from two people working there to three people working there, well, my total product goes up by six. So, my marginal product of labor for that third worker is going to be six. Now, there's something interesting that you're immediately seeing here, and this is actually pretty typical, is that your marginal product of labor will oftentimes go down the more and more people that you add. And you might say, why is that the case? Well, they're just not gonna be quite as productive. That second person might be waiting while the first person is using the mixer and that third person is gonna be waiting while the first person and the second person, maybe they're using the restroom or something and the third person has to go. And you can imagine, you add four, five, six, at some point, you're not even be able to fit people into the factory, and so you're going to have what's known as a diminishing marginal return, and you see that right over here. As you're adding more and more labor, your marginal return is getting smaller and smaller, so this is a diminishing marginal return. Now, the last concept I'm going to introduce you to in this video is that of average product, and this is average product as a function of labor. So, AP for average product. And all that is, is our total product divided by our labor. So over here, when we have one worker, our total product is 10 gallons, and we're going to divide that by one worker. So, our average product per worker is going to be 10 gallons. Now, when we have two people working per day and we're producing 18 gallons per day, our average product as a function of labor is gonna be 18 divided by two, which is gonna be nine gallons per worker per day on average. And then in this last situation, it's going to be 24 divided by three, which is eight gallons per worker per day on average. And you can see this visually as well. I can draw this on a curve. Let me do that. So, if on our horizontal axis, I have our labor units, which is workers per day, so one, two, and three. So, this is labor right over here. In our vertical axis, I'll have our total output. So, total product, I could say. So let's say that's 10, 20. Let's say that is 30 right over there. Well, this first one right over here, when we have one person working in the factory, we produce 10 gallons per day. And this is total product right over here. When we have two people working in our factory, we produce 18 gallons a day. So, it's gonna be just like that. And notice, the slope has gone down a little bit. We have a certain slope here, but it's a little less steep there. And that steepness of that line or of that curve, that tells you about the marginal product. So, it's a little bit less steep, so our marginal product of labor has gone down a little bit. We're having diminishing marginal returns. And then last but not least, when we have three people working, we're able to produce 24, so three and 24 might be right over there. And once again, we can see our diminishing returns gets even a little bit flatter. We go from zero to one, we added plus 10, and you can see that there in the marginal product of labor. And then as we add one more person, it goes plus eight. And then we add another person, it guess plus six. So in general, if you see total product as a function of labor, or total output as a function of labor, and the curve is getting less and less and less steep, well, that tells you that your marginal product is going lower and lower and you're getting diminishing marginal returns.