00:01
In this video, we're going to be dealing with the concepts of average cost and marginal average cost.
00:06
And for those of you that need a refresher, we know that if we're given our total cost function or our c of x, our average cost is just going to be c bar of x, which is just c of x over x.
00:18
We also know that our marginal average cost is just the derivative of our average cost function.
00:23
So we will call this c bar prime of x.
00:28
In this question, we are given the total cost function, c of x is equal to 100.
00:33
X plus 200 ,000, where x is equal to the number of their senior executive model that they produced.
00:41
For part a, what they want us to do is fairly simple.
00:44
They just want us to draw upon our definition of average cost to develop our average cost function, c bar of x.
00:54
If we apply our definition, we know that c bar of x is just going to be c of x over x.
01:04
And if we plug in our c of x, we know that this is going to become 100x.
01:09
Plus 200 ,000 all over x and that if you want to simplify this some more we can rewrite it as 100x over x plus 200 ,000 over x we simplify this out some more we get 100 plus 200 ,000 over x and that because this can't be simplified anymore this is our c bar of x and that our episode part a and part b what they want us to do is to use our c bar of x to develop our marginal average cost function, c bar prime of x.
02:03
And as you remember, this is just the derivative of our c bar of x.
02:11
So when we first apply our sum rules, and we want to find the derivative of the 100, we know that the derivative of a constant is simply zero, so there's no need to carry that over.
02:21
And we also know that the derivative of 200 ,000 over x, that for those of you who are a bit confused by this, we can write this as 200 ,000 times x to the power of negative 1.
02:33
So if we just apply our power rule and our constant multiple rule, what we're going to be left with is negative 200 ,000 times x to the power of negative 2...