Total product, marginal product and average product | APⓇ Microeconomics | Khan Academy

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.

As we do that, we're going to 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: per day ice cream production.

Let me make a table here. In my 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. You could view this as workers per day. 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. 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. Let's just assume that this is our output 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 at our factory, we're going to produce 18 gallons a day. And if we have three workers at our factory, let's say we can produce 24 gallons a day. Fair enough?

Now, I'm going to introduce an idea, and you have seen this word "marginal" perhaps at other times in your life. I'm going to introduce the marginal product of labor. The way to think about marginal is 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 much more, how many more gallons of ice cream am I producing?

So, my marginal product of labor when I go from zero to one worker is 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 8 gallons per day.

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: your marginal product of labor will oftentimes go down the more and more people that you add.

You might say, "Why is that the case?" Well, they're just not going to be quite as productive. That second person might be waiting while the first person is using the mixer, and that third person is going to 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.

You can imagine you had four, five, six; at some point, you're not even going to be able to fit people into the factory. 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. This is average product as a function of labor, so A for average product. 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 today per day, our average product as a function of labor is going to be 18 divided by two, which is going to be nine gallons per worker per day on average. Then in this last situation, it's going to be 24 divided by three, which is eight gallons per worker per day on average.

You can see this visually as well. I can draw this on a curve. Let me do that. 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. On our vertical axis, I'll have our total output, so total product, I could say. Let's say that's 10, 20, and 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 going to be just like that. Notice the slope has gone down a little bit. We have a certain slope here, but it's a little less steep there.

That steepness of that line, of that curve, tells you about the marginal product. So it's a little bit less steep. Our marginal product of labor has gone down a little bit; we're having diminishing marginal returns. 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.

It gets even a little bit flatter. We go from 0 to one, we added +10, and you can see that there in the marginal product of labor. Then as we add one more person, it goes plus eight, and then we add another person, it goes 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 steep, well that tells you that your marginal product is going lower and lower, and you're getting diminishing marginal returns.