Average Variable Cost and Average Fixed Cost (AVC, AFC)

Just one more quick thing before we move on. It’s small, but I’ll need it later.

I want to break STC apart like this:

STC = FC + VC

So short-run total cost = fixed cost + variable cost. Standard stuff.

Now divide both sides by $Q$:

$$\frac{STC}{Q} \quad = \quad \frac{FC}{Q} \quad + \quad \frac{VC}{Q}$$

Obviously this still holds.

And that gives us:

$$SAC \quad = \quad AFC \quad + \quad AVC$$

(Average Fixed Cost and Average Variable Cost, respectively.)

OK, so what does AFC look like? Here’s FC:

AFC is the slope from the origin to a point on this graph, so plotting that out, you get:

There it is.

Same deal for AVC. Here’s the VC curve:

AVC = slope from the origin to a point on the VC curve, which gives us:

There.

So the SAC graph we drew earlier? It’s literally just the sum of these two:

The SAC curve we sketched without thinking — it decomposes cleanly into AVC + AFC!!!!

OK so why am I bothering with this little aside? Because it’s going to come back and bite us in a sec.

Specifically: we already know SMC passes through the minimum of SAC. But — SMC also passes through the minimum of AVC (average variable cost).

And you can prove this in like, two lines of math:

OK OK so let me throw this onto the picture too:

There we go.

This is going to show up immediately in the very next thing we do, so — heh heh heh — don’t forget it.

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Originally written in Korean on my Naver blog (2016-07). Translated to English for gdpark.blog.