Greetings, last video, we talked a bit about distinguish that economists make about the difference between the short run and the long run. We have a production function. And we said output was a function of inputs. In this particular case, our inputs were labor and capital and we said that in the short run, capital is fixed. We're going to put here capital is fixed in the short run and labor was variable input, variable in the short run. Remember the example we were dealing with was thinking about making mayonnaise at the Kraft plant. Now mayonnaise, I've got two inputs here, labor and capital. We know mayonnaise, there's lots of inputs. There's glass jars, there's eggs, there's milk. There's all sorts of things that go into their function of mayonnaise besides workers and the factory. But we have condensed those down to thinking all those variables, all those inputs that can vary on a daily basis. Things like the number of jars, the amount of eggs they have, all of those things and workers. Versus those that they can't change on a daily basis, for example, brick-and-mortar. They can't change the number of assembly lines inside that plant. It's a big plant, there's lots of assembly lines and they could add an assembly line, but they can't do it today. They can't get it done in a week. It takes a while to bring in a new assembly line, get it all bolted down to the floor and make sure it's all operational. Some inputs can't be changed in a short run. That's what we're talking about here with this production function. What I want to do is I want to actually draw a short run production function for us. I'm getting a new axes here, on the vertical axis, I'm going to put output and on the horizontal axis, I'm going to put Inputs. in this case, the inputs are L because we've lumped everything into this thing called Labor, which is a variable input. What we're interested in thinking about is what does the production function look like? The general shape of this production function looks like this. Production function says quantity is some function of Labor and capital. Notice, I used a semicolon there which is a typical mathematical notation to mean that everything to the right of the semicolon is parametric. It's fixed right now, you can't change it. You can vary L, if you're running this company, you can vary L all you want but in the short run, you can't change K. So it will remind us that capital is fixed in the short run. I should have written this across the top. So we'll just make sure we have it. So it's in your notes. We're looking at short run production function. That's the exercise that we're working on right now. Now one thing you should note about this curve is that the curve in the beginning for low input levels. As you increase inputs, look what's happened to the curve. The curve is actually getting steeper, see how the curve is getting up? The slope of the curve is going up. It's getting steeper as you go out. After some point, which if you've have a strong math background, you know there's some point about right here called an inflection point. After that point, as you continue to keep adding inputs, this curve is flattening out. We're going to segment this curve into two parts. This part is the part where it's growing up, it's getting faster and this part is the part where it's flattening out. The slope of that curve is beginning to flatten out. This production function is really a generalized production function. Let me give you a hint about the idea of where this comes from. Think about if you have an assembly line suppose, you're making automobiles. suppose you're at a big automobile production facility and they've got an assembly line and you have one worker. Now bear with me, this is a silly example, but think about this. Because what I want you to think deep and hard about what happens at low levels of inputs, low levels of workers into this. Levels of workers that are way too low and economically a bad idea, but still we want to map those points out because they're possibilities. Think about that example, if you have only one worker. That worker is going to have to jump from the right side of the car to the left side of the car, from the left side of the car back to the right side of the car. So if you could add a second worker so that one worker would only be on the driver's side of the car and the other worker would be on the passenger side of the car. They'd be a lot more efficient than having them hop back and forth across the assembly line. But maybe you should have to workers on each side. So one worker could work on the upper body and one could work on the lower body of the driver's side. And the other side, the passenger side, one could work on the lower body and one could work on the upper body. In instances like that, you can see these situations where this curve as you add more inputs, outputs are growing at a faster rate than inputs are growing. That's a good thing for the company, adding extra workers is growing up on the rate that's proportionately faster. But after some point, this goes away. Economists have a special special term to describe this, the law of diminishing marginal product. After some point, extra inputs will raise output less than the previous ones did. What's happening on here in terms of the fundamental geometry is that for these low levels of inputs. As you add extra inputs, output is proportionally growing faster than the growth in inputs. But after this thing called an inflection point, as you keep adding inputs, the extra inputs are indeed growing output. Putting extra workers in will increase inputs and that will increase outputs. This thing is going up but it's going up at a slower and slower and slower rate. Throughout the rest of this course and in any other thing you do read, I'm going to insert a little page here just so we can think about this issue. Another one of these little thought bubbles and that is economists use the word marginal to mean change. If you're comfortable with calculus, marginal is the derivative of anything. So if we have a cost function, the marginal cost function is the derivative of the total cost function. If we have a revenue function, the marginal revenue function is the derivative of accelerated function. Or if you don't like calculus, it's the slope, the rate of change. All those things mean the same thing, just different levels of technical. In this case, the law of diminishing marginal product says that while it may be that as you increase labor, you're getting more output out of that. All we're saying is that the extra output, the change in output from the tenth worker is less than it was from the ninth worker. That's all we're saying. That's why this curve begins to flatten out. Now the most important thing about this is the following, this word right here. This word right here is law and law means something really important to a economists. Law means we know of no known counterexample. The law of diminishing marginal product means it's a law because everybody is subject to it. No production function, we've never seen a production function for anything. Whether it's consulting services, building automobiles, making Style I for people to mark being a barista at a coffee shop. We've never seen any counterexample yet. In fact, if you think you know of a counterexample, get ready to start polishing up your Nobel Prize speech. Because you can win a Nobel Prize in economics if you could actually figure out a counterexample to the law of diminishing marginal product. You won't, there is no known example of this. This is a short run phenomena. Let me repeat that, it's a short run phenomena. It's due to the fact that we're fixed the amount of capital and then we're just changing the other input. Essentially, we're over utilizing the other input relative to this one input. Engineers would go don't do that, change or capital labor, as if you'd change capital or labor, both at 7%, it'll be. You're right. That's a long run thing, but in the short run, I'm stuck with my fixed capital. I'm stuck with the brick-and-mortar and the assembly lines. I have to change the number of workers that come in on a daily basis or don't come in on a daily basis to change my output. Because in the short run, by definition, I have no ability to change that, that capital is fixed. Given that it's fixed, the more of this we try to squeeze into that, they're going to be less and less efficient. Indeed, it turns out that if we were to somehow extend this picture farther out, it's actually going to go down. The production function will actually start going downhill. Now that would be a very, very bad place to be. If you're the manager of the firm and you hire extra workers and those extra workers mean you get less output than before. How can that be? I know people would never do that but we're thinking through the theoretical position here. Think about that Kraft plant on the edge of town, it's a big plant. But if you try and put 30,000 workers in there, they're going to be bumping shoulders with each other. You can't get too many workers in there or no work is going to get done. They're going to be knocking jars of mayonnaise over and breaking them. Everything will be in a bad situation. So we could get way out here, but that would be really, really over using labor. Remember the production function, quantity is some function of Labor and a fixed capital. If you've got a fixed capital there, like this fixed dimensions of the Kraft plant and you just keep piling workers in there. You're really going to get yourself it in a bad problem. One last thing, it's true that the law of diminishing marginal product says every firm will be subject to this. But it also says that for low levels of input, you can have some increasing part. It's just eventually the diminishing part is going to set in. Also the case that you can think of industries where there are some industries where if this is output and this is input, L for us. There's some industries that start out from the get-go with only having diminishing marginal returns. They don't have the luxury of experiencing any of this nice range here. Where the curve is growing proportionately faster than the inputs that you're hiring. This is a really wonderful place to be because you keep hiring workers and the extra workers are putting piling proportionately more and more output. This is a really attractive thing, but you're going to soon get past that over here. Some production functions start off from the very beginning already in the law of diminishing marginal returns. There's no increase in return segment for them to enjoy to start with. And some Industries have a larger one of these. No more graphs, I just wanted to say something here. If I were you and I was taking this course for the first time, I'd be sitting there and I'd say who does this guy think he is? You want to sit there and tell me that you just draw this general shape and tell me this is the shape of production for everything? And the answer is yeah, I am. I realize that the production function for a 737 is going to look remarkably different scale. Than the production function of my tree-trimming service or the production function of my tax accountant. But every single one of those entities is subject to the law of diminishing marginal product. And because of that even though the scale may be bigger, the numbers may be much bigger than my little tree-trimming business. There are all going to have this general shape. It's just like earlier, when I just drew the demand curve as downward sloping and said I put it here to work it out. In the real world, you might be able to find the real numbers for it. But in the real world, when we generate the real numbers for the production functions, which they do. Economists can estimate these, engineers can help help us find them, they look just like this. Sometimes they're on our really grand scale. Sometimes they're very small, but they all have the same general curvature. Because again, they're all subject to this magic word. The law of diminishing marginal product. Technology is Delta stat hand. Thanks.
