Marginal cost, average variable cost, and average total cost | APⓇ Microeconomics | Khan Academy

Let’s say that we run ABC Watch Factory and we want to understand the economics of our business. So, what we have in this table is some data that we've already been able to estimate or measure based on how our business is running, and then we're going to be able to figure out some other things based on this data.

So, this first column is fixed cost or monthly fixed costs. These are the things that we can't really change in the short run, regardless of how many people we hire or how many units we produce. So, that might be the rent on our facilities or the cost of renting the equipment. For us, that's five thousand dollars a month.

Then you have your labor units, and for the sake of this model, we'll say that a labor unit is a full-time employee who's at the factory working every working day in a month. You can see we can go from one person working every full working day in a month all the way up to six. Now, this is the variable cost, and for simplicity, this is mainly driven by the labor units. In a real-world example, it would be driven by the labor units, it would be driven by how much material we're using to produce the watches. But we have our variable cost right over here, and then we have our total cost which is just simply the fixed cost plus the variable cost for any given level of labor units.

Then we know how many watches we can produce in a month based on our number of labor units, or you could view it as based on our total cost, or based on our fixed and variable costs. Now, what we have here are other things that we would want to look at if we really want to understand how our factory works. So, this is the marginal product of labor (MPL for short). Then you have your marginal cost, then you have your average variable cost, then you have your average fixed cost, and then you have your average total cost.

So, like always, pause this video and try to fill out what these values would be for even one row of this table, and then I'll do it with you. All right, now let's do it together. Let's start with marginal product of labor. Let's remind ourselves what that is. That says for every incremental labor unit, how much are we able to produce?

So, we'd have to start at the second one because we have to think about an incremental labor unit. As we go from one to two labor units, we were able to go from 10 to 25 total output, so we were able to produce 15 more watches. I could just type in 15, but it's even better to do it with a formula. So, I can just scroll it down the rest of the rows.

In this formula, I want to find the difference in my total output. So, 25 that cell minus this cell. So, that's saying, "Hey look, I was able to grow 15 output or increase my output by 15 when I increased labor by 2 minus 1." And then I got my marginal product of labor is 15 when I went from 1 employee to 2. Then I can just figure that out for the other rows. That's the value of using a spreadsheet.

My marginal product of labor when I went from two employees to three employees is 20. So, that means by adding that third employee, I'm able to produce 20 more watches per month. You might be noticing two interesting trends here; initially, my marginal product of labor seems to be increasing, and then it seems to be decreasing.

That's consistent with the way a lot of businesses or factories work, which is initially you’re getting the benefits of specialization. If you only have one person working in your factory, they have to do everything. They have to polish the glass, bring in the boxes, talk to your suppliers, fit the gears on your watches, and whatever, and do the wiring. While as you add more people, they can start to specialize. One person can specialize in assembly, another person can specialize in bringing the boxes in.

So initially, you have these benefits of specialization, and people can focus in on just one skill and do it well. But then you start getting diminishing returns. The office starts getting crowded; people are waiting for different supplies; they have to get out of each other's way. So then, you see this diminishing return trend where the marginal product of labor starts going down for those incremental labor units.

Next, we'll think about marginal cost, and as we'll see, the marginal cost trends go in the other direction as the marginal product of labor. So, marginal cost is just for every certain increment in output, how much is that costing us? For example, if we are going from 10 to 25 output for that 15 increment in output, how much is that costing us?

And I would say costing us on average, but I don't want to get confused. We're not talking about average variable cost or average fixed cost or average total cost. That would be, let's see, our costs went from 7,000 to 11,000. So, we'll do 11,000 minus 7,000; that is our change in cost divided by our change in total output. So, that's going to be divided by the 25 minus the 10.

We could just scroll this down or extend that formula, and you can see this trend that as the marginal product of labor is increasing, your marginal cost is decreasing. That makes sense, or in some ways, we're getting more efficient through the specialization. What else? But then once you have diminishing returns, diminishing marginal returns, your marginal cost is going up.

Now we can do the, I guess you could say, the average cost. So first, average variable cost. Well, that's just taking your variable cost and dividing it by your total output. For at least those first 25 units, they cost on average or just the variable component. You have to be careful; it is $240.

If we talk about the fixed component, well, that's just going to be our fixed cost divided by our total units. And then our average total cost, well that's going to be our total cost divided by those 25 units. You can see our average total cost for those first 25 units is $440.

Then it can be broken up between how much of that $440 is variable versus fixed, and then we can just extend these formulas down the magic of spreadsheets. What's interesting here, and it's not going to be so obvious just looking at this spreadsheet, is something interesting is happening when marginal cost seems to intersect either your average variable cost or your average total cost.

At some point, your average variable cost, you see that same trend; it's trending down and then it starts to trend up again. Average total cost is trending down, but then it trends up again. As we'll see when we graph it, the point at which marginal cost intersects with the average variable cost, that's when you have that change in direction of average variable cost.

The same thing is true when marginal cost intersects with average total cost; that's when you have that change in direction. Average fixed cost just continues to go down because those fixed costs aren't going up as you have more and more output. You have those same fixed costs. You could view it as spread amongst more and more output, so that's just going to keep asymptoting downward. In the next video, we will actually graph that and see these trends visually.