In this lesson, we actually want to construct cost curves. We want to think about curves that explain cost. Now, in the last lecture, our lesson was to think about production functions, and there we had inputs on this axis. And on this axis we had output. We want to get output on the horizontal axis, because output was on the horizontal axis when we were dealing with demand curves. So we'd like to have it on the horizontal axis here with our production function so we can construct a supply curve that will fit right on that demand axis system. We're going to start with some definitions. We're going to say that total cost is equal to the sum of fixed cost plus variable cost. Now, again, because I don't want to write this all the time, I'm going to use TC as shorthand for total cost. And as shorthand for fixed cost, I'll use FC, and you can predict what I'm going to call this, VC, it means variable cost. So I can rewrite this much more simplified as total cost is equal to the sum of fixed cost plus variable cost. Fixed cost are the cost associated with the our fixed input back up on top here. I'm going to put, just to remember where we are, I'm going to say we're talking about short run costs. The fixed cost are those cost associated with the fixed input. And the variable cost are those costs associated with the variable input, in this case labor, because we've kind of simplify it down to just K and L, even though you know that L captures sort of several different variable inputs it takes to make whatever product we're producing in this particular factory. So, I want to graph these, I want to draw pictures for these. And the first one's pretty easy. This we'll put on as axis $, and on this axis we'll put quantity. And if I want to draw the fixed cost, I know the fixed cost is just a horizontal line, why? Well, that's what it means, it's fixed. Fixed cost don't vary with output, there are constant level. Let's just label that F0. F0 is the amount of fixed cost it takes when you're producing this product. It's the cost associated with the fixed input that don't change in the short run. Since it don't change, it's the same, whether you're producing 10,000 jars of mayonnaise or 0 jars of mayonnaise, you still have to pay for that plant and equipment, it's the same across there, that's an easy one. The next one's not going to be so easy, we want to look at variable cost, okay? Because we know that, in order for me to increase output, I have to put more inputs in. There's no magic production fairies that make it overnight while you're sleeping, you actually have to hire workers' byproduct and put them into that brick and mortar and then more output will come out. So if I want to go across this horizontal axis- Going have to increase, I'm going to get increasingly expensive to do that. And so the way to think about that is to recall- That we had a production function. And the production function said, we're hiring extra workers, these are the inputs, we got extra output. And the production function had this characteristic shape, there was a region of increasing returns on the margin, and there was a region of diminishing marginal returns. Well, this is pretty helpful for us, because what this is telling us is, essentially it's a functional operator that says output is some function of labor. When you took your algebra class, you know that that f means that you tell me the amount of labor and I'll tell you the output that comes out. Now if we were to do something clever and that is to invert this, if we inverted the function, that is solve for L equals instead of q equals, it would be L is equal to f to the -1(q), that's the inverse of f. Algebraically, it's just moving one, it's moving labor over to the left-hand side rather than starting with quality on the left-hand side. Graphically, that would be like me grabbing this axes system and flipping it. If I grab the axis and flipped it, I would have something that tells me, in English, tell me the amount of output you want and I'll tell you what labor you have to put in. See, the original function says, tell me the amount of labor you're throwing in the factory and I'll show you the output that comes out. If you invert it, you're answering the question of, tell me what type of output you want to come out of the factory and I can tell you how much labor you got to put in, that's what the inverse of the tells you. Well, the cool thing about that is, by inverting it, we now know, we have this F to the minus 1, the inverse of F tells us how many workers we have to hire for any level of production we want to make. If I know what I have to pay the workers, not too hard to get it, there's a union contract, I can see what the hourly wage is, I know exactly what it's going to cost me for each and every extra jar of mayonnaise or whatever the product is you're producing. It would be the inverse of this. And, again, graphically, it'd be like grabbing the axes and flipping it. And I'm going to back to this picture and say, what that would look like is that it would look like this, and we're going to call this the variable cost. As you can see, if this really was, for example, just a plastic overhead projector acetate and I could grab it and flip it over, you'd see that flipping it, it would look just like that production function that had that region of increasing returns then it started to flattening out. Here, that region of increasing returns is shown by this region where for low levels of output, I can increase output and cost don't go up very fast, cost are actually slowing down, they're not going down, I can't get something for nothing, I'm still going to have to lay some money out to get it. But I don't really have to lay out much extra money at this region because I'm capturing those, the region of increasing marginal returns. But after some point, as I want to get more output, those extra output are going to require more and more workers than the previous ones because of the law of diminishing marginal product. And what that means is that this cost function is going to start screaming up. Again, keep in mind that supply curve. This is why firms have to have more money if they want to put more output out because it's just getting increasingly expensive to produce this product. And that cute little three letter word law says that pretty much everybody lives with these problems. Okay, so now I've shown two curves and let's put them together. On this axis we'll measure dollars and cents, and on this axis we have output. And I know I have to add fixed cost to variable cost. Well, let's draw fixed cost. We found out it looks something like this, and our variable cost looked something like this. And total cost is the sum of fixed cost plus variable cost. So I want to add those two. And by adding those two, I'm basically going to get a curve that looks like this. Total cost is just variable cost plus an additional fixed amount. So it's vertically displaced the variable cost. What that says is, is that any output level you choose, the slope of this curve is the same as the slope of this curve because it just got shifted vertically up. So the slope along this curve at any output will be the exact slope along this curve at any output. So now, when we want to think about total costs and total revenue, we can. We've got ourselves a cost curve that tells us total cost of production. It factors in the fixed cost of our plant and equipment, that's that F. And it factors in the hand that technology dealt us in terms of the production function, how we combine expensive inputs to get outputs out of that factory backdoor, okay? We're only partly done. We have to continue thinking about other ways to slice and dice these cost curves.