How costs change when fixed and variable costs change | APⓇ Microeconomics | Khan Academy

In the last few videos, we were studying our watch factory, ABC Watch Factory. Based on some data, knowing what our fixed costs are, our labor units, our variable cost, our total cost, and then our total output, and that would be for different amounts of labor, we were able to calculate marginal product of labor, marginal cost, average variable cost, average fixed cost, and average total cost.

What we're going to do in this video is start to explore how these various calculations will change and, eventually, how these curves will change based on changes in cost and productivity. So, let's say our rent has gone up by two thousand dollars a month, and we have to pay that extra rent regardless of what our output is. So, what's going to do to marginal product of labor, marginal cost, average variable cost, average fixed cost, and average total cost?

Pause this video and think about what's going to happen before we actually model it in the spreadsheet by raising our fixed costs, our monthly fixed costs. So, we are going to go from five thousand dollars a month of fixed cost to seven thousand dollars a month of fixed cost. So it's going to be seven thousand, but we're not done yet. We want to scroll all the way down, and so what changed from what I had before?

Well, if you're paying close attention, your marginal product of labor hasn't changed. Your marginal cost hasn't changed. Your average variable cost hasn't changed. Your average fixed and average total cost did change, and that should hopefully make intuitive sense. If you look at the formulas for these things, for example, the marginal product of labor, you would see that it involves total output and the labor units; it doesn't involve the fixed costs at all.

So, if the fixed costs change, you wouldn't expect our marginal product of labor to change. When you look at marginal cost, you are involving total cost and you say, "Hey, is the fixed cost part of total cost?" But remember, fixed cost is the seven thousand dollars is part of the thirteen thousand, and it's part of this nine thousand right over here.

So when you take the thirteen thousand minus the nine thousand, which we do in the numerator right over here, we're doing our change in total costs over our change in output. Those seven to seven thousand dollars cancel out; the fixed costs cancel out, and so your marginal cost is not dependent on your fixed cost. Similarly, your variable cost is separate; you can view it in a lot of ways from your fixed costs.

So your average variable costs aren't going to be affected by fixed costs, and of course, you would expect your average fixed cost to change because that is directly derived from your fixed costs and your output. Then, average total costs are also derived from total cost; it's not a change between total cost and that total cost has the fixed cost in it.

So you might be asking yourself, "Well, what would change your marginal product of labor, your marginal cost, your average variable cost, or your average total cost?" Well, think about a change in labor productivity. Let's say that each person—there's some magical new device that allows a new process that allows them to be a little bit more productive.

Well then one person, instead of producing ten, let's say they now produce eleven. And let's say two people—not instead of twenty-five—can now produce twenty-seven. Let's say three people, instead of forty-five, can now produce forty-seven. And now four people, and I'm making these numbers up, they can now produce fifty-nine. Let me say that this is sixty-six, and then let's say that this is seventy-two.

And so notice that did change our marginal product of labor. Once again, marginal product of labor is based on the difference in total output as we have a difference in our labor units. That change in productivity—it might be more pronounced in the way I just happened to pick the numbers—it was more pronounced when you had fewer people, and then it got more diminished as you had more and more people.

But when you had that change in productivity, you might have noticed that that changed our marginal cost, and that changed our average variable cost because, once again, your marginal cost, if we look at it right over here, is calculated by looking at your change in total cost divided by your change in total output. And when we had this productivity improvement, our change in total output improved.

Now, there could be a situation where you have a productivity improvement, but the change in total output from one person to the next might not change, so it's not always going to change either the marginal product of labor or the marginal cost. But changes in productivity will often change those two things. Similarly, if you look at your average variable cost, it is based on your variable cost and your output. When you have this productivity improvement, that's going to improve your output for any given amount of variable cost, and so that's going to have an effect on your average variable cost.

Then your average total cost is, of course, based in part on your total variable cost, which is driven by that productivity improvement. Similarly, you could have changes in variable cost. Let's say all of the people who work at your factory have gotten together and said, "We want a raise," and you give in and you give a raise. Well, now instead of two thousand dollars per worker, it's going to cost twenty-two hundred dollars per worker. You gave a ten percent raise per month.

So let me get that all the way down, and notice the things that you would have expected to change did change. Your marginal product of labor didn't change because marginal product of labor is not driven by cost; it only looks at the labor units and the total output. But your marginal cost did change, even though our output for every incremental person did not change because the underlying cost of the people changed.

Similarly, the average variable cost, you would of course expect it to change because our variable costs all went up by 10. Your average fixed cost isn't going to be affected because we changed the variable cost, not the fixed, and the total costs were, of course, affected because the average variable costs were affected.