Okay, so remember, we're trying to figure out what does the average total cost curve look like? And last video, we figured out what this average fixed cost looks like. So now, we're almost home. Now, what we have to do is think about what's the average variable cost curve look like? This is going to be harder, okay? So bear with me, concentrate, we can make this work. First, we're going to draw our axes system, okay? And then, we're going to put dollars and cents on the vertical, and output on the horizontal. And we want to figure out what the average variable cost looks like. And we know average variable cost is definitionally variable cost over output. Now, as I increase my output, for increases in output what's happening? Well, one thing, this denominator is getting larger. But also, at the same time, what's happening in the numerator? Well, it's also getting larger. You cannot just wish for extra output. If you're going to get extra output, you have to have extra cost. So your variable costs are going to be going up, okay? Variable cost can't go down. I mean, imagine a production function where you went from six to seven and your costs drop. That's not going to happen, okay? So moving from output six to output seven requires you to spend more money. So the variable cost is going to be going up, too. So we've got both the numerator and the denominator getting larger. The only way we can figure out the ratio is we have to figure out which one goes proportionally faster. And to make that work, we're going to have to go back to our production function and think a bit about that production function, okay? Or think about over our cost function. So what I want to do here is I want to put one of those, I'm fond of putting one of these little, you know how in the cartoon character, the little thought bubble pops up out of their head and they start thinking about this stuff? I want you to recall what we did with our variable cost function. Our variable cost function looked like this. Remember, our variable cost function looked like this. And now, we're asking ourselves, in this particular lecture, we're asking ourselves to figure out this ratio, variable cost divided by output. Well, variable cost divided by output is pretty easy. Pick any given output point you want, just pick an arbitrary output point. I'm going to pick this one. You know my old joke. I've got the pen, right? I'm picking this one right here. We'll call that Q0. And at Q0, what is the variable cost? Say, I can read that off that axis, Larry, that graph. This height would be the variable cost at Q0. And this horizontal distance is Q0. So if I were to divide that vertical height, that's the numerator, if I divided that vertical height by this horizontal length, that's opposite over adjacent. We just know a little bit of trig or geometry to know that the slope of this line would give us average variable cost. The slope of this line tells us the ratio of variable cost over output. Well, let's try a different one. Let's try this one, q1. q1 gives us a variable cost of this. And so, the slope of that line has fallen. That means the ratio of variable cost over output is lower at q1 than it was at q0. I can do it again. q2. I could see it falls again. And eventually, I'm going to get to some point about right here, we'll call this q sub 6, where this line is just tangent to this curve. And as I keep adding output to q7, now I see that the slope is starting to rise back up again. So the slope, the line from the origin to the curve, for those of you who really like to talk about mathematics, that's called a ray. A straight line from the origin to the curve, the slope is going to keep increasing. Now, first of all, for those of you who are looking at this saying what in the heck is he doing here, if you don't really understand this because you forgot that part of analytical geometry, that's okay. I'm never going to ask you to reproduce this particular construction. But for those of you who think hard about this thing, you can see that what's actually happening as I increase my output, what's happening to this ratio, variable costs over quantity? Which is essentially the slope of the line from the origin to the curve. It's falling at low output points and then starts rising. That means that what we call this, economists call this Take a look at what it looks like here. The average variable cost is falling at low levels and then rising. And this is what economists refer to, when you read economics papers or textbooks, they'll talk about u-shaped average cost curves. And I'm going to talk about that a lot, too. Because the u-shaped average cost curves are essentially a creature of that law of diminishing marginal product. The law of diminishing marginal product, which we did four videos ago when we looked at the production function, told us that as you keep hiring more and more inputs, the successive inputs, the extra inputs will give you more output, but they give you a little bit less output on the margin than the previous ones did. And the result of that is, intuitively, you have a variable cost function that starts to kind of go up and flatten out, and then just go screaming north, okay? because it's really expensive to keep getting more output because you have to jam more and more workers into that factory to make it work. And so, our average variable cost curve is going to be what we call a u-shaped cost curve.