Greetings. In our last video, we laid out the formal definition of the marginal cost curve. I gave it a lot of props. I said this is really important curve and it is. It's really an important curve for us, and so obviously, as we've done when I did the total cost curve, I figured out how to drought. When I showed you the average total cost curve, I figured out how to drought. Now, we're going to figure out how to draw the marginal cost. Let's recall what the definition of the marginal cost is. The marginal cost is the change in total cost for a change in output also known as aka the slope of the total cost curve. So we're going to have to draw that. Let's start with our axes. The dollars on the vertical axis, output on the horizontal axis. Let's draw our total cost function. We remember from two videos, three videos, four videos ago, the total cost function was the sum of a horizontal line we called fixed cost. Fixed cost at some level F0 and this curve that we called variable cost which is a curve that's always going up but it starts to flatten out earlier and then it starts to scream up as we get into this region of the law of diminishing marginal product. It's getting more and more expensive for the firm to make more output because each extra input that's puts in, while it's productive is not quite as productive as the previous input. Remember, this is not a feature of the fact that maybe they're just hiring bad workers out of the working pool. No, it's because the engineers know the underlying polynomial that is the production function and they know that for the fixed capital, which was what we got in the short run, the brick and mortar, there's an optimal amount of the variable input labor. You can squeeze more out by putting more of that in there. But as you put more and more of that variable input to the fixed component of that complex polynomial that was a production function, it's just not kicking out as much extra output each time. That's the problem. You're over utilizing labor relative to the pool of capital. Let's add these two up and this gives us our total cost curve. Okay, good. All we have to do now is think about what our definition is. The change in total cost or change in output, otherwise known as the slope of the total cost curve. Well, we can figure that out right now. At low output points, let's try this output point, Q0. At Q0, the slope of the total cost function would be the slope of that line that's tangent to the total cost function right there. If we're to increase output to say Q1, the slope of the total cost function out here is now a little bit flatter, okay? If we were to increase output a little bit more out here to Q2, I'm just arbitrarily picking these, you can see that in fact, the slope of the line that is just tangent to the curve is now flatter again and we can continue that process every time it's getting a little bit flatter up to you get to some famous point and that famous point is referred to as the inflection point. After that inflection point as we continue to add more output, oops, that was a poorly drawn Q. As we continue to add more output, we'll call this Q7. You can see the slope of the total cost curve is now starting to get deeper again and we go out here to Q8 and the slope or the total cost curve at Q8 is getting steeper and Q9, wow, really, marginal cost is pretty high out here. This curve is getting really steep. The slope of the total cost function is marginal cost and as you can see, it's always a positive number. Think about that, you can't have negative marginal cost. What a great world that would be. Every time you produce an extra jar of mayonnaise, your costs go down. Fun world, but that's not the way the world works. If you're going to produce an extra jar of mayonnaise, it's going to cost you some extra money. So marginal cost is going to be a positive number, it's just that the value of marginal cost is falling over this range. The marginal cost which is the slope of this curve is going down. It's still positive, but it's going down and then after this inflection point, it's not only still positive but now, it's starting to scream up. So the general shape of the marginal cost curve is going to be positive, is going to fall over one region and go up as we get to higher output. What's that remind you of? Well, of course, that is another in the family of what we call U-shaped cost curves. There's a U-shaped marginal cost. So we already had U-shaped average cost curve last time, right? Average total cost and the average variable cost were U-shaped. We did those in some previous videos and now, we see the marginal cost itself is U-shaped.