Well, immediately you can see that since the numerator is fixed,

as I step along this axis to the right,

increasing output, this denominator is going to grow and this numerator

is constant which means this has to be a falling curve.

In fact, it falls in a very specific way.

It's not a straight line at all.

It's a curve that looks like this.

We'll call this curve, average fixed cost.

Think about it, as output gets very large,

let's go back to this picture, this ratio,

as output gets very large,

what's happening to this ratio?

It's getting very small but does it ever get to zero?

No, it asymptotically approaches the horizontal axis,

but it's never really going to touch the horizontal axis which would be zero-level.

Likewise, if output got very small and as you start reducing production a lot,

this thing would go up very very fast in a hurry.

In fact, if it went to zero,

this thing would not be defined; it's infinite.

Think about it, suppose I tell you that if you're going

to sell cars you got to put advertisements on TV.

Well, advertisements on TV cost a lot of money and you've got a $10 million ad campaign,

but you sell 10 million vehicles like a big company like General Motors,

well, it's about a buck a ca.

Okay, but if you have to spend the same $10 million that General Motors

spent to put your ads on TV and you're only going to sell a million cars,

the per car share of that fixed cost is now ten bucks a car, still not a big deal.

Suppose you're a boutique seller who only sells 250 thousand cars.

They're expensive, and part of the reason

they're expensive is because when you put the commercials on,

now the per car share is pretty high.

Okay. When you got to start making small numbers of cars,

and you still try and advertise those,

that average fixed cost is going to get pretty steep.

That's what this curve reflects.

If you showed this to somebody who was in a geometry class,

they'd say that's a rectangular hyperbola.

A rectangular hyperbola is exactly this.

It's a hyperbola; it's curved but it's curved in a special way.

If you were to take any point on this graph,

the rectangle defined by that point would be the same area.

That area, of course, as you can guess would be that constant fixed cost.

No matter what point you pick on this graph,

it will define a rectangle.

The area of that rectangle will be a constant equal to that.

All right, we're only halfway home.

You remember, we have to do this, and we have to do this.

The second one's a little bit harder than was before,

but we got through it, and we'll get through this one.

We draw another graph, another axis system.

Let me put dollars and cents on the vertical and we put output on the horizontal.

Now I want to think about

the average variable cost which is equal to the variable cost over output.

But when I did average fixed cost,

the ball game was easy because as I increased my output,

the denominator went up, but the numerator was constant.

Not the case anymore.

As I increase my output,

the denominator is going to grow,

but I also know the numerator is going to

grow because more output is going to be more costly.

There's no such thing as magic production.

If I want to put more output out there,

I know my variable costs are going to have to grow.

So, what's really interesting to me then is,

what's happening to the rate of change of these two?

What's happening to the rate of change of these two?

So, the way I'm going to think about this,

is I'm going to ask you to take a simple abstraction with me.

Let's go back and look at our variable cost curve.

The way we designed it earlier.

We had a variable cost curve that looked this, right?

I know that what I'm looking for today is something called the average variable cost,

which would be the ratio of the numerator,

which is variable cost to the denominator, which is quantity.

Well, suppose I've picked some amount here, right?

Right here. We'll call this q sub zero.

I know that at q sub zero,

variable cost would be equal to this height.

Let's call that vc at q zero.

That would be the variable cost at output level q zero.

But look what I'm asking. I've been asked to evaluate

a ratio that is essentially variable cost,

which is that height over output,

which is that length across the horizontal axis.

But, remember the old trick days,

that's opposite over adjacent.

If you take the opposite side of a triangle over the adjacent side of a triangle,

that's going to give you essentially the slope of that line.

As you can see, as we step out now,

if I were to take a different output level,