Greetings, last time we looked at the relationship of marginal cost to average total cost, we understood both of those of U shaped and we understood that the marginal cost curve has to go right through the minimum of the average total cost curve. But we've got lots of curves we need to think about, so I'm going to make this really messy for you, okay? I know you're going to appreciate it. But I told you you wouldn't really like this module, costs theory, but it's really important. So we got output on the horizontal axis and I want to put on here our average fixed cost curve a, AFC. Remember that curve, it's a rectangular hyperbola. You don't need to remember that, it's a curve that asymptotically vanishes as output gets very large or as output gets very small and asymptotically explodes, okay? And then we had something called the average variable cost curve. And it looks something like this, and then we had the sum of those two and that was called the average total cost curve And that looks something like this and recall, we know that that average total cost curve and the average variable cost curve are going to asymptotic approach each other. Because at extremely high output levels this curve, the average fixed cost curve gets down to infinitesimally small, okay? Never really goes to 0, but it's going to asymptotically get really close to that axis. Which means these two curves never really touch, but they get remarkably close to each other. And now I have to put the marginal cost curve on here. The marginal cost curve is itself u-shaped, where does it go? Well, I'm not sure where it goes, I know its u-shaped. I am Pretty sure where it goes given this family, I'm going to put it in. Little label a couple points before we get started this point, this is the output that minimizes average total cost. And by the way, as we get farther onto the course, I mean weeks away yet, but minimizing average total cost turns out to be a really good thing in terms of evaluating properties, that means that you're producing at the cheapest per unit cost. You can possibly get, remember average total cost was defined as per unit cost. If your production point is right there, it minimizes the per-unit cost. That's a very efficient thing. Now that doesn't mean you're always going to be there. The profit maximizing point may be for you to be away from that. I mean, because prices could be so high you just really producing a lot and your average cost is going up because at the higher output levels you just going to experience that but it might be optimal for you to do that given the current price. We don't know yet. That's what that's more of the fun that will come. This output point, we're going to call Q sub minimum average variable cost. And finally, we're going to put in blue on here are our marginal cost curve. You may note that the marginal cost curve itself is U and it's u-shaped, but it goes through the minimum of average total cost curve which you proved in the previous video. But it also goes through the minimum of the average variable cost curve through a proof that is something the same thing we would do. I'm not going to repeat it here, but you can do the same intuitive logic of thinking that out. Or better yet if you knew calculus, you could make that proof very quickly by just taking the total cost curve, take the derivative and you have marginal cost. And then take create an average total cost curve and create average variable cost curves and take what those two look like when they're minimized and you can see that the two will be equal. So the average marginal cost curves goes through there. I've got to ask a question though, and I'll label this point alpha. Now this is, call this point alpha. Alpha is where marginal cost hits average fixed cost. And the question is where is that point? I've drawn it the way I've drawn it point alpha. What is its significance? Is there some systemic point where that supposed to hit and the answer is no, no, no, no, okay? There's absolutely nothing at all associated with this. If you think about this little, we'll come back to this picture. Let's just think about this little thought bubble and this thought bubble we think about the fact that total cost is equal to fixed cost plus variable cost. And so marginal cost which was equal to the derivative of total cost with respect to output, would be equal to the derivative of fixed cost with respect to output plus the derivative of variable cost with respect to output, but what is this term? Well, this term is non existence, it's not defined. There is no such thing as the derivative of fixed cost fixed cost can never change, by definition fixed cost is a constant. There is no such thing as a div, so this is not defined, okay? It's a zero, so since fixed costs and variable costs, that means fixed cost and marginal cost have absolutely no relationship, none, zero. I could go back to this picture, suppose now something came along that changed fixed cost. Suppose that there's a giant increase in fixed costs, the city put a new $10,000 tax on every establishment in town regardless to how big or small you are because they have to help pay for a for redoing the streets or something like that, okay? Well, if it's a giant increase in fixed costs, what's going to happen average fixed cost? Well, average fixed cost is going to shift out, right? So average fixed cost might go clear out to here. This is would be average fixed cost under the new world. Now if average fixed cost shifts out there, what's going to change to average variable cost? Nothing, average variable cost has no relationship to average fixed cost, what's going to happen to marginal cost? Nothing, marginal cost has no relationship to fixed cost. So it has no relationship to average fixed cost. What's going to happen to average total cost? Well, it's going to go up a lot because average total cost is the sum of average fixed cost plus average variable cost. And so if this average fixed cost jumps up, even if average variable cost doesn't move, the new average total cost is going to be something way out here. It's still going to have its minimum. It's still going to have its minimum on the marginal cost curve, okay? But again, all of a sudden now marginal cost hits average fixed cost out here. This is our marginal cost curve and we were asking with that earlier question is, where is this point alpha where marginal cost hits average fixed cost? It's irrelevant, it makes nothing, it means nothing to anything else you would never do and we can't really predict where it is. We could calculate where it is, okay, if we knew the numbers, but it's irrelevant to us. All the really matters to us is that in our family of cost curves, our u-shaped average variable cost and u-shaped average total cost the marginal cost hits both of them at their respective minimums. That's all that's key to us, thanks.