Understanding Production Costs for Firms

We want to talk now about the costs of production. So what we're going to do for the next several chapters is we're going to think about how firms make decisions. Those decisions are going to be, the first decision is how much output to produce. And then we're going to think about situations where the firm has to decide on the price that they're going to charge. Now we know with a perfectly competitive market, the firm has no control over the price. Firms in that type of market don't get to pick the price, but other firms will have some control over the price. So we'll talk about those in later chapters when we talk about monopolistic competition and monopoly and oligopoly. But first we need to talk about how costs behave for firms. And so the nice thing about this chapter is the costs of the firm don't necessarily depend on the type of market that it's in. So the cost curves for... monopolistically competitive firm are going to be the same as the cost curves for a competitive firm or for an oligopoly. So this stuff that we're going to think about in this chapter will apply to the next four chapters that we do after this. So let's start by thinking about the objective of a business. And the objective that we're going to use is that firms seek to maximize the profit that they earn. Now sometimes, economists get criticized for that, people will say, you know what, all, what you're saying is that firms will do anything to make another dollar and it all boils down to just maximizing the pile of profit that they've got. And that's not what we're saying. We're saying that firms can have other objectives. Firms can have as an objective to be a responsible member of society or to, um, donate money to worthy causes or things like that, but they need to have as their primary objective to maximize profit. If they don't, they're typically going to be driven out of the market. So let's think about what profit looks like. If we think about profit, we're going to use Greek pi to stand for the word profit. Profit is going to be total revenue minus total cost. In this chapter, we're going to be focusing on the total costs of the firm. Now, once we move to the next few chapters, we're going to think about the total revenue of firms, and the total revenue of a firm will depend upon the type of market that it's in. So the total revenue, the way revenue behaves, is going to be different for a competitive firm than for an oligopoly, etc. So, this chapter we're going to think about how costs behave. And we want to look at, we want to understand the relationship between the costs for the firm and how much output they produce. So that's going to be our goal. Let's start by thinking about the difference between explicit and implicit costs. So if we think about, if I were to ask you to consider a business, and let's suppose that we... think about a business where we're making pizzas. Consider a pizza business. If I said, think about the costs that you're going to have to pay in running this business, then most of the ones that you would list, at least initially, would be what we would call explicit costs. So if I said, think of the costs, you would probably come up with things like raw materials. So to run a pizza business, you're going to have to buy things to make. the dough and you're going to have to buy sauce, the tomato sauce to put on it, and vegetables and meat and cheese and all of that stuff. And so those would be costs that you'd have to pay. Those would be raw materials. You'd probably also have to pay some wages to workers that you hire. There'd be other things. You'd have to pay for electricity and things like that. Those would all be what we would call explicit costs. So those are costs. that require you to pay money for them, money that's in your account and you pay for it. Some textbooks define them as costs that require a cash outlay. That doesn't mean that you're paying cash for them. That simply means that it's money in your account and then you pay for it. But if you think about the costs of running a pizza business, you'd also realize that there are some other costs that you're going to incur. And these will be different in nature from these explicit costs. So, for example, let's suppose you're going to run the business. If you're running a business, that means you can't be working some other job in the time that you're running the business. And whatever you could have earned in that other job, your next best employment alternative, you're giving that up to run the pizza business. That's a cost also. It doesn't require a cash outlay. So let's suppose that your next best employment alternative is to earn, I don't know, let's say $20 an hour doing something else. Well, if you're running the pizza business, that means you're giving up $20 an hour that you could have earned at your next best employment alternative. And that's a cost too, but it's different, right? It's dollars that never made it into your account because of this decision that you've made. So we call that an implicit cost. It doesn't require you to pay money that's already in your account, but the outcome is the same. The outcome is that you don't have the money. It just never, ever made it into your account. So it's an implicit cost. So this would be your next best employment alternative. That would be an example. Next best employment alternative. Now, when we think about how firms make decisions, we want to think about the explicit cost and the implicit cost. We don't want to ignore any of those because we're interested in understanding why people make the decisions that they do, why firms make the decisions that they do. And so we don't want to ignore some cost. Now, if we were thinking about the way that you would treat costs if you were an accountant, if you're an accountant, you need to ignore these implicit costs. So cost, total cost for accounting purposes would be just the explicit cost because those are dollars that are coming out of an account. Implicit costs would never be included. So for an accountant to do their job correctly, they need to ignore these costs right here, the implicit ones. For what we're doing, because we're trying to understand behavior, we can't ignore any cost. So. Let's think about, and we'll come back to that here in a second, we'll define what we mean by economic profit versus accounting profit. And it will have to do with this implicit versus explicit distinction. Before we do that, think about this, investment. There's an important... thing that you need to keep in mind and that is that investments are not going to be costs. So let's think about an example. Let's suppose that in the course of running your pizza business, you take a thousand dollars out of your savings account and you buy a pizza oven with that thousand dollars. And so right over here we've got our pizza oven and we're going to use that in our pizza business. Let's suppose that Had you left that $1,000 in your savings account, it would have earned some interest. Let's make it convenient and suppose that you're getting 10% on your savings. That means that had you left that $1,000 in the account, over the course of the next year, you would have earned $100 in interest income. But because you didn't leave it in there, you're giving that up. So that $100 of foregone interest... that you're not going to earn, that's going to be a cost associated with this buying of the pizza oven. And it's an implicit cost, right? It's not explicit because you never had that hundred dollars. Because of the decision you made, you're not going to get it. In the end, the outcome is the same. You don't have a hundred dollars that you could have had, but it was never in your possession. So it's an implicit cost. Let's think about the thousand dollars you spent on the oven itself. We would count that as an investment, but not a cost of production. Because what you've done is you've taken that $1,000 and you've put that into the form of an oven here. And that's fundamentally different from dollars that you spend on things like this. So let's suppose that you buy some raw materials. And so let's suppose we put our raw materials together in the form of a pizza. And then we put it in our oven and we bake it and we take the pizza out and our pizza is sitting right here. It's done. And let's suppose I think to myself, you know what, that was a bad decision. I'd like to undo that. Well, unfortunately, I can't undo that. I can't turn that baked pizza back into its raw materials, right? I can try to sell the pizza and get whatever I can out of it, but I can't undo the making of the pizza. If we think about this oven, Let's suppose at the end of a year I've used the oven, I've baked with it, and I want to undo that. Well, I can. It's fundamentally different from these raw materials. When I bake a pizza in my oven, a little piece of my oven doesn't somehow vanish. Right? I've still got the oven sitting there. And so let's suppose at the end of the year I want to undo that. I always ask my classes, face-to-face classes, well, if I want to sell that oven at the end of the year, What am I going to be able to sell it for? Am I going to be able to sell it for a thousand dollars or more than a thousand dollars or less than a thousand dollars? And without fail, people will say less than a thousand dollars. And then I will say, well, why? How do you know I'm going to be able to sell it for less than a thousand dollars? And they will say, because it's going to depreciate. Well, let's think about that for a second. The only reason that we depreciate anything on the books is because it provides us with a tax advantage. We can typically deduct depreciation from our taxes. And so that's not really the question I'm asking. I'm asking, what's this oven going to be worth if I sell it at the end of the year? Depreciation doesn't have anything to do with that. That's just an arbitrary rule determined by the tax code. What I want to know is, can I undo this pizza oven? Can I turn it back into purchasing power? And the answer is yes. Now, what's going to determine how much I can sell it for at the end of the year? Well, my hope is that someday my economics students will realize it doesn't have anything to do with depreciation. It has everything to do with demand and supply. It's demand and supply that's going to determine the price of that oven if I want to sell it. It could be that I haven't taken good care of the oven, and so there's really low demand for that oven at the end of the year, and so I'm not able to get much out of it. It could also be that that oven was the greatest oven ever made and that I've taken good care of it and people really like it, but at the end of the year demand is high and I get more than a thousand. It's demand and supply that's going to determine the price, but the point is that I can undo it. I can turn it back into purchasing power. So those are what we would call investments. That oven is an investment. We don't count that as a cost. And you might ask, well, okay, so why is this important? Well, it's important because on homework questions or maybe test questions, I'm going to have you calculate the costs of production. And I might give you some things in there that are investments. And you want to make sure that if it's an investment, you don't add that up as you're figuring out what your costs are going to be. So now, since we know a little bit about costs, we can think about what profit looks like. Let's think about what Economic profit is going to look like the way we're going to define economic profit. It's going to be total revenue minus total cost, but now this cost is going to be made up of explicit and implicit costs. So I'm going to put explicit, I'm running out of room here, and implicit costs. Draw a little line to distinguish between those. So, economic profit is total revenue minus your explicit costs and also minus your implicit costs. If we were thinking about accounting profit, well, accounting profit is going to be your total revenue minus just your explicit costs. Accountants need to ignore implicit costs. So, in an economics class, we define the word profit different for... differently from the way you think about it if you were in an accounting class. Now here's the problem with this. Your brain is going to want to think about profit as an accountant would. When you hear me talk about profit, this is going to be the thing that pops into your head. But this will be what I mean. And so there will be some points as we go through, especially the next chapter, where I'm going to give you some conclusions about the way a market works. And when I when you first hear those, you're going to say, oh gosh, that can't be right. That can't be right. And what will be happening is that you'll be thinking of profit like this, and I'll be talking about profit like this. The point is that accounting profit can be positive while economic profit is negative. They will be equal if implicit costs are zero, but implicit costs are almost never zero. If implicit costs are positive. then economic profit will always be less than accounting profit. So we'll come back to that. For what we want to do now, let's think about what we're going to call a production function. Production function. So a production function is going to show us the relationship between the amount of an input that we use and the amount of output that we can produce. So let's continue with our pizza example, and we'll think about a very simple situation where the number of We change the amount of pizza that we can produce by changing the amount of workers that we use. So let's start by thinking about a pizza business. In the short run, the only way that we're going to be able to change output is to change the amount of labor that we use. If we were talking about a long time horizon, then we could think about, let's suppose we have a pizza business. And somebody comes to us today and says, look, tomorrow I need you to make... 500 pizzas for me. And let's suppose 500 is more than we typically make. Well, what that means is I can't snap my fingers right now and double the size of my pizza kitchen. I can't all of a sudden just make there be twice as many ovens in my pizza kitchen. I'm stuck with what I've got in terms of the capital, the size of my kitchen and the number of ovens that I've got and the number of preparation tables that I've got there. I can't change that right now. I can. A month from now, later on I can, but not right now. But the one thing I can do is I can bring in more workers. I can buy more labor from workers. So in the short run, the only way I can change output is to change the amount of workers that I've got. I'm stuck with the capital that I've got. So let's suppose that we think about the number of workers that we're going to use. Number of workers. Let's make a column here also that gives me the number of ovens. Now we're going to hold that fixed. Let's suppose we've only got one oven. That's going to be a one. It's going to be a one regardless of whether we use zero workers or five workers or 20 workers. We're stuck with one oven. Let's think about the amount of output. So I'm going to call this Q. Let's just write here output. This is the number of pizzas that I can produce. And let's think about this as if this is pizzas per hour. Clearly, let's start by thinking about having no workers. If I have zero workers, then I'm going to be able to produce zero output. Let's think about having one worker. Suppose we now have one worker. We've still only got one oven, but now let's suppose that if we've got one worker, that worker can produce, let's say, 50 pizzas per hour. But we want to make more than 50 pizzas per hour. We can't change the number of ovens we've got, so the only thing we can do is bring another worker in. So let's suppose we bring another worker in. So now we've got two workers still stuck with one pizza oven. And let's suppose with those two workers... We can produce, let's say, 90 pizzas per hour. And you might wonder, well, so why didn't that go up to 100? And we'll talk about that. You can probably already tell that it's going to have to do with the fact that we're stuck with one oven. That's our bottleneck. Let's suppose we need more than 90 pizzas. So we bring in a third worker. We're still stuck with one oven. And so let's suppose that with a third worker we can make 120 pizzas per hour. We want more than that, so we bring in a fourth. Again, we're stuck with one oven. And let's suppose we can make 140 pizzas per hour. And with five workers and one oven, let's suppose we can make 150 pizzas per hour. So now we see the relationship between the number of workers that we've got and the amount of output that we can produce. And that's going to be what our production function tells us. It tells us the relationship between an input, workers, and an output, the thing that we're producing, pizzas. So let's draw this. I want to draw the relationship between the... the input and the output, I'm going to put the number of workers here on my horizontal axis. So this is workers. And I want to put output up here on my vertical axis. The number of workers goes up to five. So we'll put that down here. The number of units of output goes up to 150, but it doesn't go up by the same increment each time. It goes up first by 50, and then it goes up by a little less. That's 90, and then 120, and then 140, and then 150. So you don't want to space those out equally because clearly they shouldn't be. And if we graph the combination of points here... Between the number of workers and the amount of output, we get the production function. There's a point. With zero workers, we have zero units of output. With one worker, we have 50 units of output. There's a point. Two workers, we have 90 units of output. Three workers, we have 120. Four workers, we have 140. And with five workers, we have 150. And if you... Connect these, you get something that looks like that. It's not linear. You can see that because these distances are getting smaller, this thing starts to bend over. This is our production function. So that is a production function right there. Let's define a couple of definitions, and I want to put a couple more columns right here. that will help us understand something about the relationship between the number of workers and the amount of output. Let's define first what we call average product. Average product, we're going to call it AP, average product. Average product is just going to be the total product, total amount of output. this one, so it would be output or I'm going to call it total product, divided by the number of workers that we've got, number of workers that we're using. So average product, total product, divided by the number of workers. Let's put in another column right here where we've got average product. So we're going to be taking our quantity of output and dividing it by the number of workers. We can't divide by zero, so we're not going to calculate anything right there. If we have 50 units of output and we're using one worker, then 50 divided by one would be 50. On average, that worker's producing 50 pizzas per hour. If we're producing 90 pizzas per hour with two workers, then our average would be 45. On average, each of those workers is producing 45 in an hour. 120 divided by 3 would be 40. And you can see that this thing's going down by 5 each time. This one would be 35 and this one would be 30. So there's what our average product looks like. And what we can see is that as we increase the number of workers, on average, each of them is producing less pizzas per hour. Now we also want to talk about something that we're going to call marginal product. and it probably will not surprise you that we need a marginal measure. So marginal product we're going to abbreviate MP, marginal product. Marginal product is just the change in the out amount of output that you can produce when you hire one more worker. Okay so marginal product Marginal product is going to be the change in output. I'm going to just write it this way. Change in output when you change workers. And we're going to be thinking about changing the number of workers by one unit each time. So going from zero to one workers or one to two or two to three. So it's a change in output when you change workers. And again, if you've... stuck with me to this point in the class, you've heard marginal enough that you know what that is. You've heard it in the context of marginal cost and marginal benefit and those things. So let's calculate our marginal product. We need to go from 0 to 1, so I'm not going to calculate it for 0, but once we go from 0 to 1, we see that our... Total output goes from 0 to 50, so the marginal product of that first worker is 50. If we look at going from one worker to two, we see that output goes from 50 to 90, so the marginal product of that second worker, 40. If we go from 2 to 3, we see that output goes from 90 to 120, so the marginal product would be 30. That's how much output changes by. 120 to 140, it's going to be 20, and then 10. There's what marginal product looks like. And you can see that what happens is as we hire another worker, at the margin, the output that we get out of the workers is going down. Now, let's think about why marginal product declines. First, let's talk about how marginal product shows up on this picture. So if we look at this little line segment right here, the rise is 50 and the run is 1, so the slope of that little line segment right there would be 50. If we look at this little line segment, The rise is 40 and the run is 1. The slope of this little line segment right there would be 40. The slope of that little line segment would be 30. And the slope of this one would be 20. And the slope of that one is going to be 10. So what you see is that the marginal product shows up as the slope of the production function. Essentially, the production function shows us total product. It shows us the total amount of output we can produce with 1, 2, 3, up to 5 workers. But the slope of that total product curve represents the marginal product. So the question we want to think about is, well, why is this thing not linear? Why is it the case that when you hire a second worker, output only goes up by 40 units? And when you hire a third, output goes up by even less. It goes up by 30. Why is it that the marginal products here are declining as you increase the amount of output that you produce? And the reason that that happens is something that we call the law of diminishing marginal product. Let's write it right up here. The reason this thing is not linear, law of diminishing marginal product. That's why marginal product is declining here. It's diminishing as we increase the amount of output that we're producing. And we can see that visually as this production function starting to curve over. Eventually it would curve over and go back down to the horizontal axis. Let's talk about why. And this is something that probably at some point somebody has tried to teach you a lesson or... mention something to you about this. This is something that your mom probably understood. If your mom ever said something like, hey, we've got too many cooks in the kitchen. If your mom was an economist, she probably would have said, hey, the law of diminishing marginal product is setting in here. You need to get out. But the idea here is this. Let's suppose that we, let's suppose we've got our preparation table here and we're going to make pizzas right here. And then right over here is our oven. Right, we prepare the pizzas right here and then we put them in the oven. And let's suppose that I can make 50 pizzas in an hour. Suppose me, working by myself, I'm capable of producing 50 pizzas in an hour. And so I'm making pizzas, but let's suppose we want more than 50 pizzas per hour, so we bring in another person. And let's suppose that other person, by themselves, would also be able to make 50 pizzas per hour. Well, when we bring them in, now we've got a problem. By ourselves, working with whatever equipment we've got, we can each make 50 pizzas per hour. But if we've got two of us in here, now we've got to share space, we've got to share the equipment that we've got, we've got to share that oven. And so... Let's suppose that I've got my pizzas baking in the oven and the other person is making their pizzas, but because mine are in the oven, they've got theirs made, but they have to wait. They have to wait until mine get out of the oven. And so that bottleneck, the fact that we've got a limited amount of capital, that's going to cause productivity to decline, not just for the second worker that comes in, but also for me, because once I get my pizzas out of the oven and they put theirs in, Now I can put mine together, but now I've got to wait on theirs. And so when you get multiple workers sharing the same amount of capital, everybody's productivity goes down. And this is not some economic theory. This is just a fact of the world that we live in. If the law of diminishing marginal product wasn't a real thing, then you'd be able to grow the world's supply of tomatoes in one tomato pot, right? Let's suppose you've got a plant that's capable of producing, I don't know, let's say 10 pounds of tomatoes every summer. And you think, you know what, that plant's really productive. I'm going to plant another one in the same pot. Or maybe I'll plant two more in the same pot. And by planting two more, I'm going to be able to get... 30 pounds of tomatoes in the summer. What you'll find is you won't. You may get more than 10, but now all of a sudden those three plants in one pot are going to be competing with each other for water and for nutrients and for sun. And each of those plants is going to be less productive than if they were in that pot by themselves. And again, that's not an economic theory thing. That's just the world that we live in. So The law of diminishing marginal product is something that's just a real world phenomenon. We can have, at very low levels of output, you could actually for a little bit have increasing marginal product. So if we were to think about a production process like, let's suppose we're talking about framing a house. Well, one person trying to put up the frame for a house is probably going to be less productive than having it another person in there to help them. So if you bring that a second worker in, then maybe those two together would both be more productive than each of them just working by themselves. But then eventually, probably very quickly, the law of diminishing marginal product will set in. If you were to bring in a third worker or a fourth worker or a fifth worker and you've only got one hammer, well, the second worker is able to help. hold up the ends of boards to nail them in and things like that. That's probably helpful, but a third and a fourth and a fifth, you don't need a third person to hold up the other end of the board. So in any production process, the law of diminishing marginal product is eventually going to set in. And once it sets in, it's going to cause this production function to get flatter and flatter. You can have so many cooks in the kitchen that productivity goes down. You can have so many cooks in the kitchen that you don't get anything made. Okay, so what we need to do is clear this off and then we're going to talk about another example where we link this up with some costs of production. Let's take a look now at how we go from this amount of information or this type of information to linking it up with costs. So this is some of the information from the table I had right here. We've got the number of workers out. and then I went ahead and put marginal product. What we want to do is think about how the number of workers is going to translate into costs. We're really going to be interested in the link between output and costs, but let's start here. Let's think about the cost of the factory. So let's suppose that the cost of the factory, this is we've got everything per hour. Let's suppose you could think about the cost of the factory as something like the rent that you have to pay. Now the rent that you have to pay doesn't depend on the amount of output that you're producing. So it's not going to depend on whether we have zero workers producing zero output. Let's suppose it's $30 per hour. It's going to be the same if we've got five workers making 150 units of output. So it's going to be 30 on every row here. Let's think for a second. The story I just told you is that you're renting the building. Let's think about what it would look like if you owned it. Well, keep in mind that owning something doesn't make it free. If you own the building and you're not renting it out to somebody else, then that means you're giving up $30 of rent per hour. So the column here would not look any different if you owned the building than it would if you didn't and you were renting it from somebody else. If you're renting it from somebody else, it would be an explicit cost. If you own it and you're choosing to use it, instead of renting it to somebody else, it would be an implicit cost. But it would be $30 in either case. So that's what our cost of factory looks like. Let's think about our cost of workers. And let's suppose, just to make it convenient, let's suppose that the wage is $10 an hour. If we've got zero workers, then clearly the cost of workers is zero. If we've got one worker working for an hour to make 50 pizzas, then our cost of workers is going to be $10. If we've got two workers working for an hour, our cost is going to be $20. And this thing goes up by 10 each time, so it's $30. 40, 50. Let's pretend like, just to keep it simple, those are the only two costs that we've got. Now we can think about our total cost. Total cost of producing these pizzas. If we think about producing zero pizzas with zero workers, then we have zero cost of workers, but we still have that rent that we have to pay. And so our total cost would be 30 even if we produce no pizzas. If we produce 50 pizzas using one worker, then we've got our $30 cost of factory plus the $10 cost of workers. This would be 40. 30 plus 20 is 50. You can see that this is going up by 10 each time, so it's going to be 60, 70, and 80. So there's our total cost of producing this many pizzas right there. Now, in terms of what we're really interested in, it's the relationship between this column and this column. We want to understand how our costs of production change as we change the amount of output that we're producing. So what I'm going to do is I'm going to graph the relationship between these two. Let's put it right over here. And we're going to put the amount of output on our horizontal axis. We're going to put Q down here. We're going to... going to put total cost up here. I'm going to abbreviate it TC. Now our total cost is going up to 80 by 10. So we can space these out every 10 units. 10, 20, there would be 80. Here's 30. Our quantity though, we have to be careful as we space it out because the distances between each of these are not the same. So we've got 50, we've got 90, 120, 140, and that one is 150. So you have to be careful, just like we did on our production function. You have to be careful with the spacing of that horizontal axis. So now we can graph the combinations of points here. So if we... are producing zero units of output it costs us $30. There's a point on what's going to end up being our total cost curve. If we're producing 50 units of output our total cost is 40 so it's going to be right here. 90 units of output our total cost, let me fill these in, 40, 50, 60, 70. If we produce 90 units of output it's 50 that's going to be somewhere right here. 120. It's 60, that's somewhere in here. 140, it's going to be $70. And then 150, it's going to be 80. And if we connect these, you can see that this thing gets steeper and steeper. There's our total cost curve. Let's talk about why it gets steeper and steeper. And it has to do with something that we just talked about, and that is the law of diminishing marginal product. So if we want to produce more output, if we want to move out in this direction and produce more output, that means we have to use more workers. Now, when we bring in another worker, we don't get a break on how much we pay that worker. Every time we bring in another worker, we've got to pay them $10 an hour. The problem for us is that they're going to be less productive, not just them, but our prior workers that we've already got working. everybody's going to be less productive. So we bring in more workers. They have to share space and equipment. And so our costs aren't going down, but the amount of output that we're getting out of our workers is going down. And so that's causing our total cost to get steeper and steeper. Now, this is important. What this means is if costs increase linearly, then every unit would cost the same. number of dollars. Every next unit would cost the same number of dollars to make. But what we see is that as we produce more and more units, it gets more and more expensive at the margin to make another unit. You probably already can see that what we're going to do here in a little bit is we're going to talk about marginal cost. And the marginal cost will be the slope of the total cost curve. And our marginal cost is rising. This thing is getting steeper and steeper. So What we need to do is we need to think about some other measures of cost, but what I want to do is I want to... Change my table here. To think about marginal cost, what we need to do is think about how total cost changes when we change output by one unit. The problem with this table is that output is not changing by one unit. It's jumping from zero to 50 and 50 to 90. So I want to create another table where my output is changing by one unit. Remember the point of this table at first was to look at the impact that the number of workers has. So we've got workers changing by one unit. Now we want to shift and focus on output. So I'm going to clear this off and put another table up here, and then we'll take a look at that. Let's create another table here. I'm going to put quantity. We're going to have output here. This time we want our output not to jump by big chunks. We want it to just change by one unit each time. So I'm going to start output at zero and go up to, let's go up to 10. And we're going to fill in kind of a big table here. We're going to think about some other measures of cost. The next column I want to put up here is going to be total cost. And I'm just going to give you some total cost numbers, and then we'll kind of work backwards from what we did in the previous table. In the previous table, we started with output, and then we had a couple of categories of cost, and then we calculated total cost. Let's do it the other way. Let's suppose that... If we produce zero units of output, our total cost is $3. And then let me just fill in the rest of these. Let's suppose that then it's $3.30, $3.80, $4.50, $5.40, $6.50, $7.80, $9.30. $11, $12.90, and $15. I would encourage you to work. Don't just watch me do this. If you really want to understand how costs behave, I would write these down with me, draw these pictures with me, because it's going to be important that you have an understanding of why the cost curves look the way they do. So you might at this point be thinking, well, gosh, where did you get those numbers? Well... Well once we develop this you'll start to see where those numbers come from. So we need to talk about some different definitions that we're going to use that will be useful to us. Let's first just think about what this cost curve looks like. This is a total cost curve. Let me just kind of in a little small picture just kind of graph what that thing looks like. If we put total cost on the vertical axis and quantity on the horizontal axis. At zero units of output, our total cost is $3. At 10 units of output up here, it's $15. So it ends up right up there. And if you were to graph it, I'm not going to plot all those points, you'd see that our total cost curve looks something like that, just like the total cost curve that we had from our previous table. Now, let's think about types of costs. So... Total cost can be broken up into two different types of cost. We're going to be thinking about fixed costs. These are costs that do not depend on output. That is the definition. Don't depend on output. Let's put that in here. Don't depend on Q. It doesn't matter how many units of output you're producing. In the previous table that we had, our fixed cost was that cost of our factory, right? It was $30 per hour. It didn't matter whether we were producing zero pizzas or 150 pizzas. So if we want to understand, looking at this table, how to figure out what our fixed costs are, it's pretty easy because your fixed costs are going to be whatever your total cost is when output is zero. Right, that's how it looked in our previous table. So our fixed cost here is $3. And it's going to be $3 whether we're producing one unit of output or 10 units of output. So I'm just going to put a little quote line here on each of these just to remind you that it's $3 at every level of output. The second type of cost we're going to think about is what we call variable cost. These do depend on Q. These depend on the amount of output that you're producing. If you're producing zero units of output, your variable cost is zero. In our previous table, our variable cost was the cost of workers. And if we were producing zero units of output, we needed zero workers. So we didn't have any variable cost. So let's put up here what our variable cost is. So variable cost is zero when output is zero. And then if we look at our total cost of $3.30, and $3 of that is our fixed cost, then the rest of it has to be the variable cost. Here's the relationship. Total cost is equal to fixed cost plus variable cost. So... any cost is either going to be a fixed cost or it's going to be a variable cost. So the sum of these two have to add up to that. So this one's going to be 30 cents. And then if we look here, $3.80 of total cost, $3 of that is fixed cost. So 80 cents of that is going to be our variable cost. Here's what variable cost looks like for the rest of them. It's $1.50 and then $2.40. $3.50, $4.80, $6.30, $8, $9.90, and then $12. And you can verify that this plus that is going to add up to this one. $3 plus $12 adds up to $15. So now we understand the difference between a fixed and a variable cost. What we want to do now is think about some other definitions of cost that are going to be useful to us. And we're going to define something that we call average fixed cost. Average fixed cost. We're going to abbreviate it AFC. Average fixed cost is simply going to be fixed cost divided by Q. It tells us on average how much our fixed cost is per unit. Let's calculate that, our average fixed cost. We can't divide by Q, so we're not going to divide by zero. So we aren't going to calculate it for zero units of output. But if we take our fixed cost of $3 and we divide it by the one unit of output, Average fixed cost is $3. $3 divided by two units of output, it's $1.50. $3 divided by three units of output, it's $1. Here's what the rest of them look like. It's going to be 75 cents, 60 cents, 50 cents, 43 cents, 38 cents, 33, and then 30. Here's what... average fixed cost looks like. The next definition that we're going to think about is what we call average variable cost. And average variable cost, we will abbreviate AVC. It is going to be variable cost divided by quantity. So let's calculate that. Average variable cost. We're going to be taking our variable cost column, which is this one, and we're going to be dividing it by our quantity column. We can't divide by zero. So our variable cost here is 30 cents divided by one unit of output. That's 30 cents. Here with two units of output, our variable cost is 80 cents divided by two. That's 40 cents. $1.50 divided by 3, that's 50 cents. You can see that this is going up by a dime each time. So this is easy to fill in. It's going to go up to $1.20. Then we can calculate what we're going to call average total cost. Average total cost we abbreviate ATC. It's equal to total cost divided by Q. Let's calculate that. Average total cost. Again, can't divide by zero. We're going to take total cost and divide it by quantity. So total cost divided by $3.30 divided by 1 is $3.30. $3.80 divided by 2 is going to be $1.90. Here's what the rest of these look like. $1.50, $1.35, $1.30. $1.30 again, $1.33, $1.38, $1.43, and then $1.50. So this one starts at $3.30, it goes down for a little bit, and then it starts to come back up. We'll talk about why here in a little bit. The last thing we want to calculate is what we're going to call marginal cost. You've heard marginal cost before. Marginal cost is just how much your total cost changes when you change output by one unit. So our marginal cost is going to be equal to the change in total cost when you change output. And we're going to be thinking about our change in output of always being one unit. So our denominator there, how much Q changes by, is always going to be one. So our marginal cost... is just going to be the change in total cost. So you can see that if we go from, I'm not going to calculate it at zero because we need to go from zero to one. We need to change output. Total cost goes from $3 to $3.30. So our marginal cost of that first unit is $0.30. If we think about going from one unit to two units, we see that our... Total cost goes from $3.30 to $3.80. That's 50 cents. Changed by 50 cents. So you can see that this is going up by 20 cents each time. So it's easy to fill in. It goes up to $2.10. So the marginal cost is telling us if we produce another unit, one more unit of output, how much does that add to our total cost? So now what we want to do, there's a lot of numbers there. We're only going to use, really for what we're going to do, we're going to use these last few columns. Let me also identify what's going on here. Notice that your average total cost is equal to... Average fixed cost plus average variable cost. So this we can rewrite this way. Average total cost is equal to average fixed cost plus average variable cost. Now you need to make sure that you remember these definitions, all of these definitions that I've just given you right here. All of them are going to be very important along with the The little trick that we did here, it's not really a trick, it's just recognizing that when output is zero, variable cost is zero. All of those things are going to be important to remember, but they're fairly easy to remember because the average measures always just have Q in the denominator. So anytime you see average, you're going to be putting Q down there, at least when we're talking about costs. So these shouldn't be hard to... Remember, what I need to do is I want to clear off this part and then we're going to graph what these last few columns look like and take a look at kind of what the cost curves look like for a firm. Let's graph some of these and we're not going to plot them point by point. What I want to do is just kind of give you a rough idea of what these things look like. So we're going to put quantity on our horizontal axis. We're going to put our costs up here. Our quantity goes up to 10, so I'm going to just put some tick marks out here. So there's 10. That's really going to be the most important one. We'll put one on here, but like I said, we're not going to graph every point. So we're going to kind of graph the beginning and graph the end and then kind of sketch in what it looks like in the middle there. We're going to stick with this side, so really if you look at the... numbers here, the highest dollar number is $3.30. So I'm going to put $1 here. I'm going to put $2 here. $3 here, and then $3.30 would be right up here. Precision is not key here. We just want a rough idea of what these things look like. So let's start with average fixed cost. That one's easy. At one unit of output, average fixed cost is right up in here at $3. By the time we get to 10 units of output, average fixed cost is down here at 30 cents. It's somewhere right down here. And if you look at what it's doing, it falls very rapidly. By the second unit, it's cut in half. So it's going to be $1.50 at two units. And then it continues to fall, but it falls slower and slower. So this thing falls quick at first and then starts to slow down. There's what average fixed cost looks like. falls rapidly at first, and then it starts slowing down. Let's do our average, let's do average variable cost next. So average variable cost starts at 30 cents. It starts down here, and then it ends up at $1.20 up here at 10 units. So it ends up, here's $1.20 roughly, somewhere right in here. So it's gonna end up somewhere right up there, and it's linear. Right, average variable cost is going up by 10 cents each time. So this thing looks something like this. There's average variable cost. Average total cost, it starts out at $3.30. So average total cost starts out right up here. It ends up at $1.50, so it ends up right over here. But now notice what it does. Average total cost falls at first. It falls until it reaches $1.30, somewhere in the middle. So it's going to fall until it reaches somewhere right around in here, in the middle. And then it starts to go back up, right? And ends up at $1.50. So it's going to come down here. It's going to stop falling and then it's going to start going back up. There's average And then let's do marginal cost. So marginal cost starts at 30. It starts right down here. It ends up at 10 units at $2.10. So it ends up somewhere right up in here. And it's linear. It's going up by 20 cents each time. So it's twice as steep as the average variable cost curve. Now when you draw this, here's what I want you to do. And your point may not match up. But what we're going to see is that the marginal cost is going to come up right through the bottom of this average total cost curve. We'll talk about why here in a little bit. But this thing's going to come up linearly. It's going to go right through the bottom of that average total cost curve, and it goes right up to there. There's marginal cost. And if you didn't hit right on the bottom of your average total cost curve, it's not that critical. I mean, when we draw them from this point on, you want to try to do that. But it's kind of hard when you're just sketching these things out. So these curves here represent what's going on in this table. Let's talk about kind of the features of these cost curves. The first one is rising marginal cost. And remember that marginal cost rises. It gets more and more expensive at the margin to produce additional units because of the law of diminishing marginal product. We can also think about the average total cost curve, and we see that it's U-shaped. U-shaped average total cost. The reason it's U-shaped is this. Average total cost is equal to average fixed cost plus average variable cost. So the shape of the average total cost curve is going to be determined by what these two curves are doing. The sum of those two curves. Well, if we look at low levels of output, average variable cost is small and average fixed cost is big. So it's going to be at low levels of output. output is going to be the average fixed cost curve that really determines what's happening with average total cost. And since average fixed cost is falling rapidly, average total cost falls rapidly. But eventually, towards the middle, average fixed cost and average variable cost are about the same. And then from that point on, average variable cost is bigger than average fixed cost. And so average variable cost is going to determine what happens to average total cost. And since average variable cost is rising, it starts to push that average total cost curve back up. So it's U-shaped for two reasons, the shapes of those two curves. Now, let's talk for just a second about the average total cost curve and this bottom point. We've actually got a special name for the quantity where average total cost is at a minimum. So if we were to just draw the average total cost curve, it's U-shaped. It looks something like that. This point right here is Q. Here's cost, dollars. This point right here where average total cost is at a minimum. We call that the efficient scale. This quantity right there we call the efficient scale. Now this will come back in a later chapter. It's the efficient scale, the quantity of output that minimizes the firm's total cost on average. Let's talk for just a second about why the marginal cost curve has to intersect the average total cost curve at its minimum. That's true because of the mathematical nature. It's just a mathematical fact. Any marginal curve will intersect the average curve at its minimum. Let's draw another picture here where we just look at the average total cost curve and the marginal cost curve. So here's marginal cost. Here's average total cost. You can see that any time that... Marginal cost is below average total cost, the average total cost is falling. Anytime the marginal cost is above the average total cost, the average total cost is rising. Right there is the efficient scale of the firm, because that's the bottom of that average total cost curve. What's going on here is if you think about what's happening, let's suppose you've got people in a room, and we figure out the average age of the people in the room, and let's suppose the average age is 20. and then all of a sudden I walk into the room and I'm older than 20. Well, that's going to raise the average. I would be the marginal person that enters the room. And anytime the marginal is greater than the average, it's going to pull that average up. Let's suppose that the average age is 20 and then somebody who's 5 years old walks into the room. That's going to pull the average down a little bit. Well, anytime the marginal is below the average, it's going to pull the average down. So that's why anytime you draw an average curve and a marginal curve, the marginal curve is going to have to intersect at the bottom point of that average curve. What we need to do now is clear all of this off and draw just a picture of the typical cost curves that we're going to be thinking about. Because what we've done with all of this is really just give you an idea, hopefully, of why cost curves look the way they do. Once we start using the cost curves, we're not going to be going through all of this. We're just going to draw a picture of the cost curves. But you need to understand why the picture looks the way it does. So let's clear this off and then we'll take a look at kind of the typical cost curves. Let's draw a picture of the cost curves where we just focus on the main things that we're going to be interested in. So if we... Again, put quantity on the horizontal axis. We're going to put costs up here. It's just dollars. Let's start with average total cost. So the main thing that we get from that previous picture is that our average total cost is U-shaped. The way that I'm going to typically draw that is going to be like that. I'm not too worried. Our previous one was real high up here and it came down real steep and then kind of ended up over here. It's just U-shaped. So we're not going to worry about too much, anything more than it being U-shaped. Now, I'm going to go ahead and draw the marginal cost curve. Our marginal cost curve in the previous picture was linear. They're typically not linear. They're usually going to have some curvature to them. And remember that it's going to come up and go right through the bottom of that average total cost curve. So if it helps, think about where that bottom is, and then just draw your marginal cost curve so that it comes right up through the bottom there. There's what marginal cost looks like. We're also going to be interested in average variable cost. Now in our previous example, average variable cost was linear, and it just kind of came up like that. Typically, average variable cost is U-shaped. Now, it's an average curve, so the marginal cost comes up through the bottom of the average variable cost curve. So here's how I want you to do this. I want you to put a point over here a little bit below, quite a ways below your average total cost curve. Then your average variable cost is going to come down and hit a bottom somewhere right in here, and then it's going to go back up, and it's going to... Get kind of close to average total cost. I'll explain why, but it should look something like this. Come down, hit a bottom, and then start heading back up there. There's average variable cost. So that's the typical cost curves that we're going to think about. And we're going to draw that picture. We're going to use that picture a lot as we go throughout the next several chapters. All of the important... things that we talked about previously are in there. We've got rising marginal cost, we've got U-shaped average total cost, and our marginal cost curve is coming up through the bottom of those average curves. You might ask, well, in the previous picture we had average fixed cost. Why isn't that on there? Well, remember that average fixed cost, average total cost, is equal to average fixed cost plus average variable cost. Well, what that means is average fixed cost is equal to average total cost minus average variable cost. I just subtracted average variable cost from both sides. Well, what this means is that your average fixed cost is the difference between these two curves. It's the difference between average total cost and average variable cost. So this vertical distance right there represents average fixed cost. That's why I made these wide apart here. And then as we get, as quantity increases, they get closer and closer to each other. Because your average fixed cost starts out big and ends up small. So those are the typical cost curves that we're going to use. This is something you need to get used to drawing. You shouldn't have to stop and think whether the average total cost curve is on the top or the bottom. This should be automatic. Let's talk about the difference between costs in the short run. and the long run. So I've mentioned the short run. We talked about our pizza business and in the short run, the only way you can produce more pizza is to hire more workers. But at that point, we didn't talk about what we meant by the short run versus the long run. And so here's the main, here's how we define it. There are no fixed costs in the long run. No fixed costs in the long run. That's how we define the long run. The short run is defined as the period of time during which there is some fixed cost. So if you think about the fixed cost that we've talked about, we talked about your cost of your factory, your rent. Well, that's a fixed cost because presumably you've signed a lease that goes to a particular date. And so during that period of time, there's nothing you can do about it. contractually obligated to pay $30 an hour for your building. But once that lease is up, then you can make a decision about what you want your rent to be. You could move into a different building, bigger building, a smaller building. But during the time that that lease is in effect, you have a fixed cost. And so a fixed cost, fixed costs come from fixed inputs. So as long as there's some input that you can't change, then the cost associated with that input is fixed for you. So if we think about kind of what that looks like, let's think about what fixed costs would look like in the long run. I'm going to put quantity on my horizontal axis. I'm going to stretch this out a little bit. I'm going to put costs up here on my vertical axis. Let's think about... But... what your costs would look like if we were, let's suppose we're going to build a pizza restaurant, okay? And we haven't built it yet. Once we build it, we're stuck with the building that we've built, at least for a little while. That's, it would be a fixed input, and we would have fixed costs that are associated with it. But we haven't built it yet, so we can think about building a pizza restaurant where we would... produce small quantities of output. And we can think about the average total cost curve for a small plant. Let's suppose it looks something like this. This would be the average total cost for a small plant. I'm just going to put small. It's U-shaped. I'm not going to put the marginal cost curve or average variable cost. We're just going to think about average total cost. Then let's think about, you know, suppose we wanted to build a bigger restaurant than that. that would allow us to produce more pizzas per day. We could have a bigger building size. So let's think about an average total cost curve for, say, a medium-sized one. I'm going to put it a little bit lower, and we'll talk about why here in a second. This would be average total cost for a medium. restaurant size. But let's suppose we wanted a building where we could produce even more pizzas than that. We want to be able to produce a lot of pizzas. We could build a bigger building and it would have its own average total cost curve. Let's suppose we put it up here. And again, I'll explain why I made this one the lowest one. But let's make this the average total cost curve for a large plant, large pizza restaurant. Now, these are just three of the infinite number of building sizes that we could build. We could build one in between these two and it would look something like this and we could build one in between these two and it would look something like that. And you can see that if we were to fill in all of the possible plant sizes, this thing would start to just fill in and eventually if we filled them all in, it would start to just turn into a big blue boob. bowl-shaped thing. Well, if we were to draw a line that kind of represented the lower frontier, and I don't know if you can tell, I'm trying to draw this in a different color, but on the video it may not show up as a different color. That's that red frontier. That's what we would call the long-run average total cost curve. It's kind of what we would call an envelope. curve. It envelops all of the short-run average total cost curves. So all of these short-run average total cost curves have to lie above or they're going to touch in one spot. Each one's going to touch that long-run average total cost curve. But no part of any short-run average total cost curve is going to lie below the long-run average total cost curve. So our long-run average total cost curve is much... flatter than any particular short-run average total cost curve, and all of the short-run average total cost curves lie on or above the long-run average total cost curve. Now, let's think about how we're going to use this long-run average total cost curve. If I were to draw another picture here, again, I'm going to stretch my horizontal axis out. Here's costs. Let's draw a long-run average total cost curve that looks something like that. Long run average total cost. Here's Q down here. Ignore the cost. That goes with that picture. So let's suppose that this is our long run average total cost curve, but we have built a plant size, and it has a short run average total cost curve that goes with it. Suppose it looks like this. There's our short run average total cost curve for the plant that we have built. Let's think about how we use this long-run average total cost curve. Let's suppose we're producing this quantity. Well, if we're producing that quantity, let's suppose that's 10,000. If we are producing 10,000 units, we can go up to the average total cost curve and we can see what our costs are on average. Let's suppose they are $9 per unit. On average, each of those 10,000 units costs us $9 to produce. But let's suppose we want to produce more units than that. We want to move production up to 11,000. Suppose that's right here. Here's what this tells us. In the short run, we're stuck with our plant that we've got built. And if we want to produce 11,000 units in that plant size, in the plant we've got, our costs on average are going to go up. Let's suppose they go up to $13. Well, if we were just going to increase production to 11,000 for a short amount of time and then move it back down to 10,000, well, we're just kind of stuck paying that higher cost on average for a little while. But if we were going to continue producing 11,000 units from now on, then what this picture tells us is that we can do better than this. What it tells us is that we should build a bigger plant size. And if we build a bigger plant size, we could build a plant... with the appropriate average total cost to reduce our average total cost back down to nine. This would be short-run average total cost for a bigger plant than the one we've got. So what this allows us to do is see what our costs are going to be with the investment that we've got versus what they could be if we were to build a bigger building. This works whether we're talking about building a bigger building. Or if we were to reduce production below 10,000. If we were to reduce production to say 9,000, our costs would also go up. The short-run average total cost is U-shaped. If you start at the bottom and go in either direction, your costs will go up. So there may be a time if we wanted to decrease production to 9,000 that we build a smaller plant. Sometimes people have the mistaken belief that having too much space is not a problem. It's not nearly the same problem as having not enough space. Yeah, it is. If you have too much space that you're not using, you're bearing the cost of that. That's not free. Let's talk... here at the end of this about what causes the long run average total cost curve to look the way it does we've actually got some terminology and let's put one final picture in over here we've got quantity we've got uh costs up here let's draw an long run average total cost curve i'm going to put kind of a long flat portion on it So here's our long run average total cost. And let's suppose that we think about kind of dividing this up into some sections here. So if we look at it, it's decreasing up until right about here. And there, at that point on, it gets flat. And then starting somewhere right in here, it starts to go back up again. So we've got some names for different portions of this long run average total cost curve. Over this... range of output. What we see is that as we increase output, as the firm increases output, its costs on average are declining. We say that the firm is experiencing what we call economies of scale. I'm just going to write economies. From this point on, as the firm increases output, Nothing is happening to their costs. We would say that we have constant returns to scale, constant returns. And then from this point on, as the firm increases output, its costs start to go back up. And we would say that the firm is experiencing diseconomies of scale, diseconomies. So let's talk about what causes economies and diseconomies of scale and constant returns to scale. So if we think about what we've done with the short-run curves, we talked about why these curves look the way they do. And in a lot of cases, the answer was the law of diminishing marginal product. That's why the marginal cost curve looks the way it does. That's why it goes up. That's part of why the average total cost curve starts to go back up. It's the reason that the average variable cost curve eventually starts to go back up. So if you're ever asked why a cost curve looks the way it does and you don't have any idea, a really good guess is the law of diminishing marginal product. More times than not, you'll be right. Turns out, though, that the law of diminishing marginal product can't explain any of this. And the reason is we're talking about the long run. And remember that in the long run there are no fixed costs, right? So fixed costs, fixed inputs are what cause the law of diminishing marginal product. So the answer for what's going on here is something different. If you think about what's happening here, economies of scale, what's happening is that we increase the scale of our production process, we get decreases in the form of... Decreasing average costs. Well, what's happening there is that as you increase the scale of your production process, it allows your workers to specialize in tasks. Rather than doing multiple tasks, workers can specialize in a particular task. And so that allows them to get better. If you're the only one producing something like a car, let's take something simpler. If you're the only one producing something like a shoe, then you've got to do a lot of different tasks. If, on the other hand, you're going to increase the scale of your production process so that you're producing lots of shoes with lots of workers, then you can have each worker specialize in a particular part of the production process, and they'll get really good at it. And as they get good, that increase in productivity causes your costs to go down. Let's talk about diseconomies. Well, this is caused by... What's happening here is you've got a big production process and you're making it even bigger. What that means is that big production processes are difficult to manage. So if you've got a small production process and you can manage it yourself, Well, that's relatively easy, but as you get bigger and bigger, then you have to start hiring managers. And if you think about what a manager does, a manager comes in and they're not producing output, they're just managing people. And so that's adding costs of production without giving you more output. And so big production processes require lots more layers of management, and that's expensive. That drives your costs up on average. Constant returns, it's just the absence of economies or diseconomies. So hopefully this gives you an idea of how costs behave in the short run, what costs look like in the long run. We're going to use this picture a lot. What we're going to do now is we're going to combine this picture. Remember that profit is equal to total revenue minus total cost, right? We've just talked about... this. We've talked about how costs behave. What we need to do in our next chapters is talk about how revenue behaves. So we're going to combine this stuff with some new stuff in upcoming chapters, and then we'll be able to see what profit, how profit behaves for a firm, and how that firm is going to maximize profit. So I'll see you in a future video.

And then we're going to think about situations where the firm has to decide on the price that they're going to charge. Now we know with a perfectly competitive market, the firm has no control over the price. Firms in that type of market don't get to pick the price, but other firms will have some control over the price.

So we'll talk about those in later chapters when we talk about monopolistic competition and monopoly and oligopoly. But first we need to talk about how costs behave for firms. And so the nice thing about this chapter is the costs of the firm don't necessarily depend on the type of market that it's in. So the cost curves for...

monopolistically competitive firm are going to be the same as the cost curves for a competitive firm or for an oligopoly. So this stuff that we're going to think about in this chapter will apply to the next four chapters that we do after this. So let's start by thinking about the objective of a business. And the objective that we're going to use is that firms seek to maximize the profit that they earn.

Now sometimes, economists get criticized for that, people will say, you know what, all, what you're saying is that firms will do anything to make another dollar and it all boils down to just maximizing the pile of profit that they've got. And that's not what we're saying. We're saying that firms can have other objectives.

Firms can have as an objective to be a responsible member of society or to, um, donate money to worthy causes or things like that, but they need to have as their primary objective to maximize profit. If they don't, they're typically going to be driven out of the market. So let's think about what profit looks like. If we think about profit, we're going to use Greek pi to stand for the word profit. Profit is going to be total revenue minus total cost.

In this chapter, we're going to be focusing on the total costs of the firm. Now, once we move to the next few chapters, we're going to think about the total revenue of firms, and the total revenue of a firm will depend upon the type of market that it's in. So the total revenue, the way revenue behaves, is going to be different for a competitive firm than for an oligopoly, etc. So, this chapter we're going to think about how costs behave.

And we want to look at, we want to understand the relationship between the costs for the firm and how much output they produce. So that's going to be our goal. Let's start by thinking about the difference between explicit and implicit costs.

So if we think about, if I were to ask you to consider a business, and let's suppose that we... think about a business where we're making pizzas. Consider a pizza business. If I said, think about the costs that you're going to have to pay in running this business, then most of the ones that you would list, at least initially, would be what we would call explicit costs.

So if I said, think of the costs, you would probably come up with things like raw materials. So to run a pizza business, you're going to have to buy things to make. the dough and you're going to have to buy sauce, the tomato sauce to put on it, and vegetables and meat and cheese and all of that stuff. And so those would be costs that you'd have to pay. Those would be raw materials.

You'd probably also have to pay some wages to workers that you hire. There'd be other things. You'd have to pay for electricity and things like that. Those would all be what we would call explicit costs. So those are costs.

that require you to pay money for them, money that's in your account and you pay for it. Some textbooks define them as costs that require a cash outlay. That doesn't mean that you're paying cash for them. That simply means that it's money in your account and then you pay for it.

But if you think about the costs of running a pizza business, you'd also realize that there are some other costs that you're going to incur. And these will be different in nature from these explicit costs. So, for example, let's suppose you're going to run the business.

If you're running a business, that means you can't be working some other job in the time that you're running the business. And whatever you could have earned in that other job, your next best employment alternative, you're giving that up to run the pizza business. That's a cost also.

It doesn't require a cash outlay. So let's suppose that your next best employment alternative is to earn, I don't know, let's say $20 an hour doing something else. Well, if you're running the pizza business, that means you're giving up $20 an hour that you could have earned at your next best employment alternative. And that's a cost too, but it's different, right? It's dollars that never made it into your account because of this decision that you've made.

So we call that an implicit cost. It doesn't require you to pay money that's already in your account, but the outcome is the same. The outcome is that you don't have the money. It just never, ever made it into your account. So it's an implicit cost.

So this would be your next best employment alternative. That would be an example. Next best employment alternative. Now, when we think about how firms make decisions, we want to think about the explicit cost and the implicit cost. We don't want to ignore any of those because we're interested in understanding why people make the decisions that they do, why firms make the decisions that they do.

And so we don't want to ignore some cost. Now, if we were thinking about the way that you would treat costs if you were an accountant, if you're an accountant, you need to ignore these implicit costs. So cost, total cost for accounting purposes would be just the explicit cost because those are dollars that are coming out of an account. Implicit costs would never be included.

So for an accountant to do their job correctly, they need to ignore these costs right here, the implicit ones. For what we're doing, because we're trying to understand behavior, we can't ignore any cost. So.

Let's think about, and we'll come back to that here in a second, we'll define what we mean by economic profit versus accounting profit. And it will have to do with this implicit versus explicit distinction. Before we do that, think about this, investment.

There's an important... thing that you need to keep in mind and that is that investments are not going to be costs. So let's think about an example. Let's suppose that in the course of running your pizza business, you take a thousand dollars out of your savings account and you buy a pizza oven with that thousand dollars.

And so right over here we've got our pizza oven and we're going to use that in our pizza business. Let's suppose that Had you left that $1,000 in your savings account, it would have earned some interest. Let's make it convenient and suppose that you're getting 10% on your savings.

That means that had you left that $1,000 in the account, over the course of the next year, you would have earned $100 in interest income. But because you didn't leave it in there, you're giving that up. So that $100 of foregone interest... that you're not going to earn, that's going to be a cost associated with this buying of the pizza oven. And it's an implicit cost, right?

It's not explicit because you never had that hundred dollars. Because of the decision you made, you're not going to get it. In the end, the outcome is the same.

You don't have a hundred dollars that you could have had, but it was never in your possession. So it's an implicit cost. Let's think about the thousand dollars you spent on the oven itself. We would count that as an investment, but not a cost of production. Because what you've done is you've taken that $1,000 and you've put that into the form of an oven here.

And that's fundamentally different from dollars that you spend on things like this. So let's suppose that you buy some raw materials. And so let's suppose we put our raw materials together in the form of a pizza.

And then we put it in our oven and we bake it and we take the pizza out and our pizza is sitting right here. It's done. And let's suppose I think to myself, you know what, that was a bad decision.

I'd like to undo that. Well, unfortunately, I can't undo that. I can't turn that baked pizza back into its raw materials, right?

I can try to sell the pizza and get whatever I can out of it, but I can't undo the making of the pizza. If we think about this oven, Let's suppose at the end of a year I've used the oven, I've baked with it, and I want to undo that. Well, I can.

It's fundamentally different from these raw materials. When I bake a pizza in my oven, a little piece of my oven doesn't somehow vanish. Right? I've still got the oven sitting there. And so let's suppose at the end of the year I want to undo that.

I always ask my classes, face-to-face classes, well, if I want to sell that oven at the end of the year, What am I going to be able to sell it for? Am I going to be able to sell it for a thousand dollars or more than a thousand dollars or less than a thousand dollars? And without fail, people will say less than a thousand dollars. And then I will say, well, why?

How do you know I'm going to be able to sell it for less than a thousand dollars? And they will say, because it's going to depreciate. Well, let's think about that for a second.

The only reason that we depreciate anything on the books is because it provides us with a tax advantage. We can typically deduct depreciation from our taxes. And so that's not really the question I'm asking. I'm asking, what's this oven going to be worth if I sell it at the end of the year? Depreciation doesn't have anything to do with that.

That's just an arbitrary rule determined by the tax code. What I want to know is, can I undo this pizza oven? Can I turn it back into purchasing power? And the answer is yes. Now, what's going to determine how much I can sell it for at the end of the year?

Well, my hope is that someday my economics students will realize it doesn't have anything to do with depreciation. It has everything to do with demand and supply. It's demand and supply that's going to determine the price of that oven if I want to sell it.

It could be that I haven't taken good care of the oven, and so there's really low demand for that oven at the end of the year, and so I'm not able to get much out of it. It could also be that that oven was the greatest oven ever made and that I've taken good care of it and people really like it, but at the end of the year demand is high and I get more than a thousand. It's demand and supply that's going to determine the price, but the point is that I can undo it. I can turn it back into purchasing power.

So those are what we would call investments. That oven is an investment. We don't count that as a cost.

And you might ask, well, okay, so why is this important? Well, it's important because on homework questions or maybe test questions, I'm going to have you calculate the costs of production. And I might give you some things in there that are investments.

And you want to make sure that if it's an investment, you don't add that up as you're figuring out what your costs are going to be. So now, since we know a little bit about costs, we can think about what profit looks like. Let's think about what Economic profit is going to look like the way we're going to define economic profit. It's going to be total revenue minus total cost, but now this cost is going to be made up of explicit and implicit costs. So I'm going to put explicit, I'm running out of room here, and implicit costs.

Draw a little line to distinguish between those. So, economic profit is total revenue minus your explicit costs and also minus your implicit costs. If we were thinking about accounting profit, well, accounting profit is going to be your total revenue minus just your explicit costs. Accountants need to ignore implicit costs. So, in an economics class, we define the word profit different for...

differently from the way you think about it if you were in an accounting class. Now here's the problem with this. Your brain is going to want to think about profit as an accountant would. When you hear me talk about profit, this is going to be the thing that pops into your head.

But this will be what I mean. And so there will be some points as we go through, especially the next chapter, where I'm going to give you some conclusions about the way a market works. And when I when you first hear those, you're going to say, oh gosh, that can't be right.

That can't be right. And what will be happening is that you'll be thinking of profit like this, and I'll be talking about profit like this. The point is that accounting profit can be positive while economic profit is negative. They will be equal if implicit costs are zero, but implicit costs are almost never zero. If implicit costs are positive.

then economic profit will always be less than accounting profit. So we'll come back to that. For what we want to do now, let's think about what we're going to call a production function.

Production function. So a production function is going to show us the relationship between the amount of an input that we use and the amount of output that we can produce. So let's continue with our pizza example, and we'll think about a very simple situation where the number of We change the amount of pizza that we can produce by changing the amount of workers that we use.

So let's start by thinking about a pizza business. In the short run, the only way that we're going to be able to change output is to change the amount of labor that we use. If we were talking about a long time horizon, then we could think about, let's suppose we have a pizza business.

And somebody comes to us today and says, look, tomorrow I need you to make... 500 pizzas for me. And let's suppose 500 is more than we typically make.

Well, what that means is I can't snap my fingers right now and double the size of my pizza kitchen. I can't all of a sudden just make there be twice as many ovens in my pizza kitchen. I'm stuck with what I've got in terms of the capital, the size of my kitchen and the number of ovens that I've got and the number of preparation tables that I've got there. I can't change that right now. I can.

A month from now, later on I can, but not right now. But the one thing I can do is I can bring in more workers. I can buy more labor from workers. So in the short run, the only way I can change output is to change the amount of workers that I've got.

I'm stuck with the capital that I've got. So let's suppose that we think about the number of workers that we're going to use. Number of workers. Let's make a column here also that gives me the number of ovens.

Now we're going to hold that fixed. Let's suppose we've only got one oven. That's going to be a one. It's going to be a one regardless of whether we use zero workers or five workers or 20 workers. We're stuck with one oven.

Let's think about the amount of output. So I'm going to call this Q. Let's just write here output. This is the number of pizzas that I can produce. And let's think about this as if this is pizzas per hour.

Clearly, let's start by thinking about having no workers. If I have zero workers, then I'm going to be able to produce zero output. Let's think about having one worker. Suppose we now have one worker. We've still only got one oven, but now let's suppose that if we've got one worker, that worker can produce, let's say, 50 pizzas per hour.

But we want to make more than 50 pizzas per hour. We can't change the number of ovens we've got, so the only thing we can do is bring another worker in. So let's suppose we bring another worker in.

So now we've got two workers still stuck with one pizza oven. And let's suppose with those two workers... We can produce, let's say, 90 pizzas per hour. And you might wonder, well, so why didn't that go up to 100? And we'll talk about that.

You can probably already tell that it's going to have to do with the fact that we're stuck with one oven. That's our bottleneck. Let's suppose we need more than 90 pizzas. So we bring in a third worker.

We're still stuck with one oven. And so let's suppose that with a third worker we can make 120 pizzas per hour. We want more than that, so we bring in a fourth. Again, we're stuck with one oven. And let's suppose we can make 140 pizzas per hour.

And with five workers and one oven, let's suppose we can make 150 pizzas per hour. So now we see the relationship between the number of workers that we've got and the amount of output that we can produce. And that's going to be what our production function tells us.

It tells us the relationship between an input, workers, and an output, the thing that we're producing, pizzas. So let's draw this. I want to draw the relationship between the... the input and the output, I'm going to put the number of workers here on my horizontal axis.

So this is workers. And I want to put output up here on my vertical axis. The number of workers goes up to five. So we'll put that down here. The number of units of output goes up to 150, but it doesn't go up by the same increment each time.

It goes up first by 50, and then it goes up by a little less. That's 90, and then 120, and then 140, and then 150. So you don't want to space those out equally because clearly they shouldn't be. And if we graph the combination of points here...

Between the number of workers and the amount of output, we get the production function. There's a point. With zero workers, we have zero units of output. With one worker, we have 50 units of output. There's a point.

Two workers, we have 90 units of output. Three workers, we have 120. Four workers, we have 140. And with five workers, we have 150. And if you... Connect these, you get something that looks like that.

It's not linear. You can see that because these distances are getting smaller, this thing starts to bend over. This is our production function. So that is a production function right there.

Let's define a couple of definitions, and I want to put a couple more columns right here. that will help us understand something about the relationship between the number of workers and the amount of output. Let's define first what we call average product.

Average product, we're going to call it AP, average product. Average product is just going to be the total product, total amount of output. this one, so it would be output or I'm going to call it total product, divided by the number of workers that we've got, number of workers that we're using.

So average product, total product, divided by the number of workers. Let's put in another column right here where we've got average product. So we're going to be taking our quantity of output and dividing it by the number of workers. We can't divide by zero, so we're not going to calculate anything right there.

If we have 50 units of output and we're using one worker, then 50 divided by one would be 50. On average, that worker's producing 50 pizzas per hour. If we're producing 90 pizzas per hour with two workers, then our average would be 45. On average, each of those workers is producing 45 in an hour. 120 divided by 3 would be 40. And you can see that this thing's going down by 5 each time.

This one would be 35 and this one would be 30. So there's what our average product looks like. And what we can see is that as we increase the number of workers, on average, each of them is producing less pizzas per hour. Now we also want to talk about something that we're going to call marginal product. and it probably will not surprise you that we need a marginal measure.

So marginal product we're going to abbreviate MP, marginal product. Marginal product is just the change in the out amount of output that you can produce when you hire one more worker. Okay so marginal product Marginal product is going to be the change in output. I'm going to just write it this way.

Change in output when you change workers. And we're going to be thinking about changing the number of workers by one unit each time. So going from zero to one workers or one to two or two to three. So it's a change in output when you change workers.

And again, if you've... stuck with me to this point in the class, you've heard marginal enough that you know what that is. You've heard it in the context of marginal cost and marginal benefit and those things.

So let's calculate our marginal product. We need to go from 0 to 1, so I'm not going to calculate it for 0, but once we go from 0 to 1, we see that our... Total output goes from 0 to 50, so the marginal product of that first worker is 50. If we look at going from one worker to two, we see that output goes from 50 to 90, so the marginal product of that second worker, 40. If we go from 2 to 3, we see that output goes from 90 to 120, so the marginal product would be 30. That's how much output changes by.

120 to 140, it's going to be 20, and then 10. There's what marginal product looks like. And you can see that what happens is as we hire another worker, at the margin, the output that we get out of the workers is going down. Now, let's think about why marginal product declines. First, let's talk about how marginal product shows up on this picture. So if we look at this little line segment right here, the rise is 50 and the run is 1, so the slope of that little line segment right there would be 50. If we look at this little line segment, The rise is 40 and the run is 1. The slope of this little line segment right there would be 40. The slope of that little line segment would be 30. And the slope of this one would be 20. And the slope of that one is going to be 10. So what you see is that the marginal product shows up as the slope of the production function.

Essentially, the production function shows us total product. It shows us the total amount of output we can produce with 1, 2, 3, up to 5 workers. But the slope of that total product curve represents the marginal product. So the question we want to think about is, well, why is this thing not linear? Why is it the case that when you hire a second worker, output only goes up by 40 units?

And when you hire a third, output goes up by even less. It goes up by 30. Why is it that the marginal products here are declining as you increase the amount of output that you produce? And the reason that that happens is something that we call the law of diminishing marginal product.

Let's write it right up here. The reason this thing is not linear, law of diminishing marginal product. That's why marginal product is declining here.

It's diminishing as we increase the amount of output that we're producing. And we can see that visually as this production function starting to curve over. Eventually it would curve over and go back down to the horizontal axis. Let's talk about why.

And this is something that probably at some point somebody has tried to teach you a lesson or... mention something to you about this. This is something that your mom probably understood.

If your mom ever said something like, hey, we've got too many cooks in the kitchen. If your mom was an economist, she probably would have said, hey, the law of diminishing marginal product is setting in here. You need to get out.

But the idea here is this. Let's suppose that we, let's suppose we've got our preparation table here and we're going to make pizzas right here. And then right over here is our oven. Right, we prepare the pizzas right here and then we put them in the oven. And let's suppose that I can make 50 pizzas in an hour.

Suppose me, working by myself, I'm capable of producing 50 pizzas in an hour. And so I'm making pizzas, but let's suppose we want more than 50 pizzas per hour, so we bring in another person. And let's suppose that other person, by themselves, would also be able to make 50 pizzas per hour.

Well, when we bring them in, now we've got a problem. By ourselves, working with whatever equipment we've got, we can each make 50 pizzas per hour. But if we've got two of us in here, now we've got to share space, we've got to share the equipment that we've got, we've got to share that oven.

And so... Let's suppose that I've got my pizzas baking in the oven and the other person is making their pizzas, but because mine are in the oven, they've got theirs made, but they have to wait. They have to wait until mine get out of the oven.

And so that bottleneck, the fact that we've got a limited amount of capital, that's going to cause productivity to decline, not just for the second worker that comes in, but also for me, because once I get my pizzas out of the oven and they put theirs in, Now I can put mine together, but now I've got to wait on theirs. And so when you get multiple workers sharing the same amount of capital, everybody's productivity goes down. And this is not some economic theory. This is just a fact of the world that we live in. If the law of diminishing marginal product wasn't a real thing, then you'd be able to grow the world's supply of tomatoes in one tomato pot, right?

Let's suppose you've got a plant that's capable of producing, I don't know, let's say 10 pounds of tomatoes every summer. And you think, you know what, that plant's really productive. I'm going to plant another one in the same pot. Or maybe I'll plant two more in the same pot.

And by planting two more, I'm going to be able to get... 30 pounds of tomatoes in the summer. What you'll find is you won't.

You may get more than 10, but now all of a sudden those three plants in one pot are going to be competing with each other for water and for nutrients and for sun. And each of those plants is going to be less productive than if they were in that pot by themselves. And again, that's not an economic theory thing. That's just the world that we live in.

So The law of diminishing marginal product is something that's just a real world phenomenon. We can have, at very low levels of output, you could actually for a little bit have increasing marginal product. So if we were to think about a production process like, let's suppose we're talking about framing a house.

Well, one person trying to put up the frame for a house is probably going to be less productive than having it another person in there to help them. So if you bring that a second worker in, then maybe those two together would both be more productive than each of them just working by themselves. But then eventually, probably very quickly, the law of diminishing marginal product will set in. If you were to bring in a third worker or a fourth worker or a fifth worker and you've only got one hammer, well, the second worker is able to help.

hold up the ends of boards to nail them in and things like that. That's probably helpful, but a third and a fourth and a fifth, you don't need a third person to hold up the other end of the board. So in any production process, the law of diminishing marginal product is eventually going to set in. And once it sets in, it's going to cause this production function to get flatter and flatter.

You can have so many cooks in the kitchen that productivity goes down. You can have so many cooks in the kitchen that you don't get anything made. Okay, so what we need to do is clear this off and then we're going to talk about another example where we link this up with some costs of production. Let's take a look now at how we go from this amount of information or this type of information to linking it up with costs. So this is some of the information from the table I had right here.

We've got the number of workers out. and then I went ahead and put marginal product. What we want to do is think about how the number of workers is going to translate into costs. We're really going to be interested in the link between output and costs, but let's start here.

Let's think about the cost of the factory. So let's suppose that the cost of the factory, this is we've got everything per hour. Let's suppose you could think about the cost of the factory as something like the rent that you have to pay.

Now the rent that you have to pay doesn't depend on the amount of output that you're producing. So it's not going to depend on whether we have zero workers producing zero output. Let's suppose it's $30 per hour. It's going to be the same if we've got five workers making 150 units of output. So it's going to be 30 on every row here.

Let's think for a second. The story I just told you is that you're renting the building. Let's think about what it would look like if you owned it. Well, keep in mind that owning something doesn't make it free.

If you own the building and you're not renting it out to somebody else, then that means you're giving up $30 of rent per hour. So the column here would not look any different if you owned the building than it would if you didn't and you were renting it from somebody else. If you're renting it from somebody else, it would be an explicit cost.

If you own it and you're choosing to use it, instead of renting it to somebody else, it would be an implicit cost. But it would be $30 in either case. So that's what our cost of factory looks like.

Let's think about our cost of workers. And let's suppose, just to make it convenient, let's suppose that the wage is $10 an hour. If we've got zero workers, then clearly the cost of workers is zero.

If we've got one worker working for an hour to make 50 pizzas, then our cost of workers is going to be $10. If we've got two workers working for an hour, our cost is going to be $20. And this thing goes up by 10 each time, so it's $30.

40, 50. Let's pretend like, just to keep it simple, those are the only two costs that we've got. Now we can think about our total cost. Total cost of producing these pizzas. If we think about producing zero pizzas with zero workers, then we have zero cost of workers, but we still have that rent that we have to pay. And so our total cost would be 30 even if we produce no pizzas.

If we produce 50 pizzas using one worker, then we've got our $30 cost of factory plus the $10 cost of workers. This would be 40. 30 plus 20 is 50. You can see that this is going up by 10 each time, so it's going to be 60, 70, and 80. So there's our total cost of producing this many pizzas right there. Now, in terms of what we're really interested in, it's the relationship between this column and this column. We want to understand how our costs of production change as we change the amount of output that we're producing. So what I'm going to do is I'm going to graph the relationship between these two.

Let's put it right over here. And we're going to put the amount of output on our horizontal axis. We're going to put Q down here.

We're going to... going to put total cost up here. I'm going to abbreviate it TC.

Now our total cost is going up to 80 by 10. So we can space these out every 10 units. 10, 20, there would be 80. Here's 30. Our quantity though, we have to be careful as we space it out because the distances between each of these are not the same. So we've got 50, we've got 90, 120, 140, and that one is 150. So you have to be careful, just like we did on our production function. You have to be careful with the spacing of that horizontal axis. So now we can graph the combinations of points here.

So if we... are producing zero units of output it costs us $30. There's a point on what's going to end up being our total cost curve. If we're producing 50 units of output our total cost is 40 so it's going to be right here. 90 units of output our total cost, let me fill these in, 40, 50, 60, 70. If we produce 90 units of output it's 50 that's going to be somewhere right here.

120. It's 60, that's somewhere in here. 140, it's going to be $70. And then 150, it's going to be 80. And if we connect these, you can see that this thing gets steeper and steeper.

There's our total cost curve. Let's talk about why it gets steeper and steeper. And it has to do with something that we just talked about, and that is the law of diminishing marginal product.

So if we want to produce more output, if we want to move out in this direction and produce more output, that means we have to use more workers. Now, when we bring in another worker, we don't get a break on how much we pay that worker. Every time we bring in another worker, we've got to pay them $10 an hour.

The problem for us is that they're going to be less productive, not just them, but our prior workers that we've already got working. everybody's going to be less productive. So we bring in more workers.

They have to share space and equipment. And so our costs aren't going down, but the amount of output that we're getting out of our workers is going down. And so that's causing our total cost to get steeper and steeper.

Now, this is important. What this means is if costs increase linearly, then every unit would cost the same. number of dollars. Every next unit would cost the same number of dollars to make.

But what we see is that as we produce more and more units, it gets more and more expensive at the margin to make another unit. You probably already can see that what we're going to do here in a little bit is we're going to talk about marginal cost. And the marginal cost will be the slope of the total cost curve. And our marginal cost is rising. This thing is getting steeper and steeper.

So What we need to do is we need to think about some other measures of cost, but what I want to do is I want to... Change my table here. To think about marginal cost, what we need to do is think about how total cost changes when we change output by one unit. The problem with this table is that output is not changing by one unit. It's jumping from zero to 50 and 50 to 90. So I want to create another table where my output is changing by one unit.

Remember the point of this table at first was to look at the impact that the number of workers has. So we've got workers changing by one unit. Now we want to shift and focus on output.

So I'm going to clear this off and put another table up here, and then we'll take a look at that. Let's create another table here. I'm going to put quantity. We're going to have output here. This time we want our output not to jump by big chunks.

We want it to just change by one unit each time. So I'm going to start output at zero and go up to, let's go up to 10. And we're going to fill in kind of a big table here. We're going to think about some other measures of cost.

The next column I want to put up here is going to be total cost. And I'm just going to give you some total cost numbers, and then we'll kind of work backwards from what we did in the previous table. In the previous table, we started with output, and then we had a couple of categories of cost, and then we calculated total cost. Let's do it the other way. Let's suppose that...

If we produce zero units of output, our total cost is $3. And then let me just fill in the rest of these. Let's suppose that then it's $3.30, $3.80, $4.50, $5.40, $6.50, $7.80, $9.30.

$11, $12.90, and $15. I would encourage you to work. Don't just watch me do this. If you really want to understand how costs behave, I would write these down with me, draw these pictures with me, because it's going to be important that you have an understanding of why the cost curves look the way they do. So you might at this point be thinking, well, gosh, where did you get those numbers?

Well... Well once we develop this you'll start to see where those numbers come from. So we need to talk about some different definitions that we're going to use that will be useful to us. Let's first just think about what this cost curve looks like.

This is a total cost curve. Let me just kind of in a little small picture just kind of graph what that thing looks like. If we put total cost on the vertical axis and quantity on the horizontal axis.

At zero units of output, our total cost is $3. At 10 units of output up here, it's $15. So it ends up right up there.

And if you were to graph it, I'm not going to plot all those points, you'd see that our total cost curve looks something like that, just like the total cost curve that we had from our previous table. Now, let's think about types of costs. So...

Total cost can be broken up into two different types of cost. We're going to be thinking about fixed costs. These are costs that do not depend on output. That is the definition.

Don't depend on output. Let's put that in here. Don't depend on Q. It doesn't matter how many units of output you're producing.

In the previous table that we had, our fixed cost was that cost of our factory, right? It was $30 per hour. It didn't matter whether we were producing zero pizzas or 150 pizzas.

So if we want to understand, looking at this table, how to figure out what our fixed costs are, it's pretty easy because your fixed costs are going to be whatever your total cost is when output is zero. Right, that's how it looked in our previous table. So our fixed cost here is $3. And it's going to be $3 whether we're producing one unit of output or 10 units of output. So I'm just going to put a little quote line here on each of these just to remind you that it's $3 at every level of output.

The second type of cost we're going to think about is what we call variable cost. These do depend on Q. These depend on the amount of output that you're producing. If you're producing zero units of output, your variable cost is zero.

In our previous table, our variable cost was the cost of workers. And if we were producing zero units of output, we needed zero workers. So we didn't have any variable cost. So let's put up here what our variable cost is.

So variable cost is zero when output is zero. And then if we look at our total cost of $3.30, and $3 of that is our fixed cost, then the rest of it has to be the variable cost. Here's the relationship.

Total cost is equal to fixed cost plus variable cost. So... any cost is either going to be a fixed cost or it's going to be a variable cost. So the sum of these two have to add up to that. So this one's going to be 30 cents.

And then if we look here, $3.80 of total cost, $3 of that is fixed cost. So 80 cents of that is going to be our variable cost. Here's what variable cost looks like for the rest of them.

It's $1.50 and then $2.40. $3.50, $4.80, $6.30, $8, $9.90, and then $12. And you can verify that this plus that is going to add up to this one.

$3 plus $12 adds up to $15. So now we understand the difference between a fixed and a variable cost. What we want to do now is think about some other definitions of cost that are going to be useful to us. And we're going to define something that we call average fixed cost.

Average fixed cost. We're going to abbreviate it AFC. Average fixed cost is simply going to be fixed cost divided by Q. It tells us on average how much our fixed cost is per unit. Let's calculate that, our average fixed cost.

We can't divide by Q, so we're not going to divide by zero. So we aren't going to calculate it for zero units of output. But if we take our fixed cost of $3 and we divide it by the one unit of output, Average fixed cost is $3.

$3 divided by two units of output, it's $1.50. $3 divided by three units of output, it's $1. Here's what the rest of them look like.

It's going to be 75 cents, 60 cents, 50 cents, 43 cents, 38 cents, 33, and then 30. Here's what... average fixed cost looks like. The next definition that we're going to think about is what we call average variable cost.

And average variable cost, we will abbreviate AVC. It is going to be variable cost divided by quantity. So let's calculate that.

Average variable cost. We're going to be taking our variable cost column, which is this one, and we're going to be dividing it by our quantity column. We can't divide by zero.

So our variable cost here is 30 cents divided by one unit of output. That's 30 cents. Here with two units of output, our variable cost is 80 cents divided by two.

That's 40 cents. $1.50 divided by 3, that's 50 cents. You can see that this is going up by a dime each time. So this is easy to fill in. It's going to go up to $1.20.

Then we can calculate what we're going to call average total cost. Average total cost we abbreviate ATC. It's equal to total cost divided by Q. Let's calculate that.

Average total cost. Again, can't divide by zero. We're going to take total cost and divide it by quantity.

So total cost divided by $3.30 divided by 1 is $3.30. $3.80 divided by 2 is going to be $1.90. Here's what the rest of these look like. $1.50, $1.35, $1.30. $1.30 again, $1.33, $1.38, $1.43, and then $1.50.

So this one starts at $3.30, it goes down for a little bit, and then it starts to come back up. We'll talk about why here in a little bit. The last thing we want to calculate is what we're going to call marginal cost.

You've heard marginal cost before. Marginal cost is just how much your total cost changes when you change output by one unit. So our marginal cost is going to be equal to the change in total cost when you change output. And we're going to be thinking about our change in output of always being one unit. So our denominator there, how much Q changes by, is always going to be one.

So our marginal cost... is just going to be the change in total cost. So you can see that if we go from, I'm not going to calculate it at zero because we need to go from zero to one. We need to change output.

Total cost goes from $3 to $3.30. So our marginal cost of that first unit is $0.30. If we think about going from one unit to two units, we see that our...

Total cost goes from $3.30 to $3.80. That's 50 cents. Changed by 50 cents. So you can see that this is going up by 20 cents each time.

So it's easy to fill in. It goes up to $2.10. So the marginal cost is telling us if we produce another unit, one more unit of output, how much does that add to our total cost? So now what we want to do, there's a lot of numbers there. We're only going to use, really for what we're going to do, we're going to use these last few columns.

Let me also identify what's going on here. Notice that your average total cost is equal to... Average fixed cost plus average variable cost.

So this we can rewrite this way. Average total cost is equal to average fixed cost plus average variable cost. Now you need to make sure that you remember these definitions, all of these definitions that I've just given you right here. All of them are going to be very important along with the The little trick that we did here, it's not really a trick, it's just recognizing that when output is zero, variable cost is zero. All of those things are going to be important to remember, but they're fairly easy to remember because the average measures always just have Q in the denominator.

So anytime you see average, you're going to be putting Q down there, at least when we're talking about costs. So these shouldn't be hard to... Remember, what I need to do is I want to clear off this part and then we're going to graph what these last few columns look like and take a look at kind of what the cost curves look like for a firm.

Let's graph some of these and we're not going to plot them point by point. What I want to do is just kind of give you a rough idea of what these things look like. So we're going to put quantity on our horizontal axis.

We're going to put our costs up here. Our quantity goes up to 10, so I'm going to just put some tick marks out here. So there's 10. That's really going to be the most important one. We'll put one on here, but like I said, we're not going to graph every point.

So we're going to kind of graph the beginning and graph the end and then kind of sketch in what it looks like in the middle there. We're going to stick with this side, so really if you look at the... numbers here, the highest dollar number is $3.30.

So I'm going to put $1 here. I'm going to put $2 here. $3 here, and then $3.30 would be right up here.

Precision is not key here. We just want a rough idea of what these things look like. So let's start with average fixed cost.

That one's easy. At one unit of output, average fixed cost is right up in here at $3. By the time we get to 10 units of output, average fixed cost is down here at 30 cents. It's somewhere right down here.

And if you look at what it's doing, it falls very rapidly. By the second unit, it's cut in half. So it's going to be $1.50 at two units. And then it continues to fall, but it falls slower and slower. So this thing falls quick at first and then starts to slow down.

There's what average fixed cost looks like. falls rapidly at first, and then it starts slowing down. Let's do our average, let's do average variable cost next.

So average variable cost starts at 30 cents. It starts down here, and then it ends up at $1.20 up here at 10 units. So it ends up, here's $1.20 roughly, somewhere right in here.

So it's gonna end up somewhere right up there, and it's linear. Right, average variable cost is going up by 10 cents each time. So this thing looks something like this.

There's average variable cost. Average total cost, it starts out at $3.30. So average total cost starts out right up here.

It ends up at $1.50, so it ends up right over here. But now notice what it does. Average total cost falls at first.

It falls until it reaches $1.30, somewhere in the middle. So it's going to fall until it reaches somewhere right around in here, in the middle. And then it starts to go back up, right?

And ends up at $1.50. So it's going to come down here. It's going to stop falling and then it's going to start going back up. There's average And then let's do marginal cost.

So marginal cost starts at 30. It starts right down here. It ends up at 10 units at $2.10. So it ends up somewhere right up in here. And it's linear. It's going up by 20 cents each time.

So it's twice as steep as the average variable cost curve. Now when you draw this, here's what I want you to do. And your point may not match up.

But what we're going to see is that the marginal cost is going to come up right through the bottom of this average total cost curve. We'll talk about why here in a little bit. But this thing's going to come up linearly. It's going to go right through the bottom of that average total cost curve, and it goes right up to there.

There's marginal cost. And if you didn't hit right on the bottom of your average total cost curve, it's not that critical. I mean, when we draw them from this point on, you want to try to do that. But it's kind of hard when you're just sketching these things out. So these curves here represent what's going on in this table.

Let's talk about kind of the features of these cost curves. The first one is rising marginal cost. And remember that marginal cost rises. It gets more and more expensive at the margin to produce additional units because of the law of diminishing marginal product. We can also think about the average total cost curve, and we see that it's U-shaped.

U-shaped average total cost. The reason it's U-shaped is this. Average total cost is equal to average fixed cost plus average variable cost. So the shape of the average total cost curve is going to be determined by what these two curves are doing. The sum of those two curves.

Well, if we look at low levels of output, average variable cost is small and average fixed cost is big. So it's going to be at low levels of output. output is going to be the average fixed cost curve that really determines what's happening with average total cost.

And since average fixed cost is falling rapidly, average total cost falls rapidly. But eventually, towards the middle, average fixed cost and average variable cost are about the same. And then from that point on, average variable cost is bigger than average fixed cost.

And so average variable cost is going to determine what happens to average total cost. And since average variable cost is rising, it starts to push that average total cost curve back up. So it's U-shaped for two reasons, the shapes of those two curves.

Now, let's talk for just a second about the average total cost curve and this bottom point. We've actually got a special name for the quantity where average total cost is at a minimum. So if we were to just draw the average total cost curve, it's U-shaped.

It looks something like that. This point right here is Q. Here's cost, dollars.

This point right here where average total cost is at a minimum. We call that the efficient scale. This quantity right there we call the efficient scale. Now this will come back in a later chapter. It's the efficient scale, the quantity of output that minimizes the firm's total cost on average.

Let's talk for just a second about why the marginal cost curve has to intersect the average total cost curve at its minimum. That's true because of the mathematical nature. It's just a mathematical fact. Any marginal curve will intersect the average curve at its minimum. Let's draw another picture here where we just look at the average total cost curve and the marginal cost curve.

So here's marginal cost. Here's average total cost. You can see that any time that... Marginal cost is below average total cost, the average total cost is falling. Anytime the marginal cost is above the average total cost, the average total cost is rising.

Right there is the efficient scale of the firm, because that's the bottom of that average total cost curve. What's going on here is if you think about what's happening, let's suppose you've got people in a room, and we figure out the average age of the people in the room, and let's suppose the average age is 20. and then all of a sudden I walk into the room and I'm older than 20. Well, that's going to raise the average. I would be the marginal person that enters the room.

And anytime the marginal is greater than the average, it's going to pull that average up. Let's suppose that the average age is 20 and then somebody who's 5 years old walks into the room. That's going to pull the average down a little bit. Well, anytime the marginal is below the average, it's going to pull the average down.

So that's why anytime you draw an average curve and a marginal curve, the marginal curve is going to have to intersect at the bottom point of that average curve. What we need to do now is clear all of this off and draw just a picture of the typical cost curves that we're going to be thinking about. Because what we've done with all of this is really just give you an idea, hopefully, of why cost curves look the way they do.

Once we start using the cost curves, we're not going to be going through all of this. We're just going to draw a picture of the cost curves. But you need to understand why the picture looks the way it does.

So let's clear this off and then we'll take a look at kind of the typical cost curves. Let's draw a picture of the cost curves where we just focus on the main things that we're going to be interested in. So if we...

Again, put quantity on the horizontal axis. We're going to put costs up here. It's just dollars.

Let's start with average total cost. So the main thing that we get from that previous picture is that our average total cost is U-shaped. The way that I'm going to typically draw that is going to be like that. I'm not too worried. Our previous one was real high up here and it came down real steep and then kind of ended up over here.

It's just U-shaped. So we're not going to worry about too much, anything more than it being U-shaped. Now, I'm going to go ahead and draw the marginal cost curve.

Our marginal cost curve in the previous picture was linear. They're typically not linear. They're usually going to have some curvature to them. And remember that it's going to come up and go right through the bottom of that average total cost curve. So if it helps, think about where that bottom is, and then just draw your marginal cost curve so that it comes right up through the bottom there.

There's what marginal cost looks like. We're also going to be interested in average variable cost. Now in our previous example, average variable cost was linear, and it just kind of came up like that. Typically, average variable cost is U-shaped. Now, it's an average curve, so the marginal cost comes up through the bottom of the average variable cost curve.

So here's how I want you to do this. I want you to put a point over here a little bit below, quite a ways below your average total cost curve. Then your average variable cost is going to come down and hit a bottom somewhere right in here, and then it's going to go back up, and it's going to... Get kind of close to average total cost.

I'll explain why, but it should look something like this. Come down, hit a bottom, and then start heading back up there. There's average variable cost. So that's the typical cost curves that we're going to think about. And we're going to draw that picture.

We're going to use that picture a lot as we go throughout the next several chapters. All of the important... things that we talked about previously are in there. We've got rising marginal cost, we've got U-shaped average total cost, and our marginal cost curve is coming up through the bottom of those average curves. You might ask, well, in the previous picture we had average fixed cost.

Why isn't that on there? Well, remember that average fixed cost, average total cost, is equal to average fixed cost plus average variable cost. Well, what that means is average fixed cost is equal to average total cost minus average variable cost.

I just subtracted average variable cost from both sides. Well, what this means is that your average fixed cost is the difference between these two curves. It's the difference between average total cost and average variable cost.

So this vertical distance right there represents average fixed cost. That's why I made these wide apart here. And then as we get, as quantity increases, they get closer and closer to each other. Because your average fixed cost starts out big and ends up small. So those are the typical cost curves that we're going to use.

This is something you need to get used to drawing. You shouldn't have to stop and think whether the average total cost curve is on the top or the bottom. This should be automatic.

Let's talk about the difference between costs in the short run. and the long run. So I've mentioned the short run.

We talked about our pizza business and in the short run, the only way you can produce more pizza is to hire more workers. But at that point, we didn't talk about what we meant by the short run versus the long run. And so here's the main, here's how we define it.

There are no fixed costs in the long run. No fixed costs in the long run. That's how we define the long run. The short run is defined as the period of time during which there is some fixed cost.

So if you think about the fixed cost that we've talked about, we talked about your cost of your factory, your rent. Well, that's a fixed cost because presumably you've signed a lease that goes to a particular date. And so during that period of time, there's nothing you can do about it. contractually obligated to pay $30 an hour for your building.

But once that lease is up, then you can make a decision about what you want your rent to be. You could move into a different building, bigger building, a smaller building. But during the time that that lease is in effect, you have a fixed cost. And so a fixed cost, fixed costs come from fixed inputs. So as long as there's some input that you can't change, then the cost associated with that input is fixed for you.

So if we think about kind of what that looks like, let's think about what fixed costs would look like in the long run. I'm going to put quantity on my horizontal axis. I'm going to stretch this out a little bit.

I'm going to put costs up here on my vertical axis. Let's think about... But...

what your costs would look like if we were, let's suppose we're going to build a pizza restaurant, okay? And we haven't built it yet. Once we build it, we're stuck with the building that we've built, at least for a little while. That's, it would be a fixed input, and we would have fixed costs that are associated with it. But we haven't built it yet, so we can think about building a pizza restaurant where we would...

produce small quantities of output. And we can think about the average total cost curve for a small plant. Let's suppose it looks something like this. This would be the average total cost for a small plant. I'm just going to put small.

It's U-shaped. I'm not going to put the marginal cost curve or average variable cost. We're just going to think about average total cost.

Then let's think about, you know, suppose we wanted to build a bigger restaurant than that. that would allow us to produce more pizzas per day. We could have a bigger building size. So let's think about an average total cost curve for, say, a medium-sized one.

I'm going to put it a little bit lower, and we'll talk about why here in a second. This would be average total cost for a medium. restaurant size.

But let's suppose we wanted a building where we could produce even more pizzas than that. We want to be able to produce a lot of pizzas. We could build a bigger building and it would have its own average total cost curve.

Let's suppose we put it up here. And again, I'll explain why I made this one the lowest one. But let's make this the average total cost curve for a large plant, large pizza restaurant. Now, these are just three of the infinite number of building sizes that we could build. We could build one in between these two and it would look something like this and we could build one in between these two and it would look something like that.

And you can see that if we were to fill in all of the possible plant sizes, this thing would start to just fill in and eventually if we filled them all in, it would start to just turn into a big blue boob. bowl-shaped thing. Well, if we were to draw a line that kind of represented the lower frontier, and I don't know if you can tell, I'm trying to draw this in a different color, but on the video it may not show up as a different color.

That's that red frontier. That's what we would call the long-run average total cost curve. It's kind of what we would call an envelope. curve. It envelops all of the short-run average total cost curves.

So all of these short-run average total cost curves have to lie above or they're going to touch in one spot. Each one's going to touch that long-run average total cost curve. But no part of any short-run average total cost curve is going to lie below the long-run average total cost curve. So our long-run average total cost curve is much...

flatter than any particular short-run average total cost curve, and all of the short-run average total cost curves lie on or above the long-run average total cost curve. Now, let's think about how we're going to use this long-run average total cost curve. If I were to draw another picture here, again, I'm going to stretch my horizontal axis out.

Here's costs. Let's draw a long-run average total cost curve that looks something like that. Long run average total cost.

Here's Q down here. Ignore the cost. That goes with that picture.

So let's suppose that this is our long run average total cost curve, but we have built a plant size, and it has a short run average total cost curve that goes with it. Suppose it looks like this. There's our short run average total cost curve for the plant that we have built.

Let's think about how we use this long-run average total cost curve. Let's suppose we're producing this quantity. Well, if we're producing that quantity, let's suppose that's 10,000.

If we are producing 10,000 units, we can go up to the average total cost curve and we can see what our costs are on average. Let's suppose they are $9 per unit. On average, each of those 10,000 units costs us $9 to produce.

But let's suppose we want to produce more units than that. We want to move production up to 11,000. Suppose that's right here. Here's what this tells us.

In the short run, we're stuck with our plant that we've got built. And if we want to produce 11,000 units in that plant size, in the plant we've got, our costs on average are going to go up. Let's suppose they go up to $13.

Well, if we were just going to increase production to 11,000 for a short amount of time and then move it back down to 10,000, well, we're just kind of stuck paying that higher cost on average for a little while. But if we were going to continue producing 11,000 units from now on, then what this picture tells us is that we can do better than this. What it tells us is that we should build a bigger plant size.

And if we build a bigger plant size, we could build a plant... with the appropriate average total cost to reduce our average total cost back down to nine. This would be short-run average total cost for a bigger plant than the one we've got.

So what this allows us to do is see what our costs are going to be with the investment that we've got versus what they could be if we were to build a bigger building. This works whether we're talking about building a bigger building. Or if we were to reduce production below 10,000. If we were to reduce production to say 9,000, our costs would also go up. The short-run average total cost is U-shaped.

If you start at the bottom and go in either direction, your costs will go up. So there may be a time if we wanted to decrease production to 9,000 that we build a smaller plant. Sometimes people have the mistaken belief that having too much space is not a problem. It's not nearly the same problem as having not enough space. Yeah, it is.

If you have too much space that you're not using, you're bearing the cost of that. That's not free. Let's talk... here at the end of this about what causes the long run average total cost curve to look the way it does we've actually got some terminology and let's put one final picture in over here we've got quantity we've got uh costs up here let's draw an long run average total cost curve i'm going to put kind of a long flat portion on it So here's our long run average total cost. And let's suppose that we think about kind of dividing this up into some sections here.

So if we look at it, it's decreasing up until right about here. And there, at that point on, it gets flat. And then starting somewhere right in here, it starts to go back up again.

So we've got some names for different portions of this long run average total cost curve. Over this... range of output.

What we see is that as we increase output, as the firm increases output, its costs on average are declining. We say that the firm is experiencing what we call economies of scale. I'm just going to write economies. From this point on, as the firm increases output, Nothing is happening to their costs.

We would say that we have constant returns to scale, constant returns. And then from this point on, as the firm increases output, its costs start to go back up. And we would say that the firm is experiencing diseconomies of scale, diseconomies. So let's talk about what causes economies and diseconomies of scale and constant returns to scale.

So if we think about what we've done with the short-run curves, we talked about why these curves look the way they do. And in a lot of cases, the answer was the law of diminishing marginal product. That's why the marginal cost curve looks the way it does.

That's why it goes up. That's part of why the average total cost curve starts to go back up. It's the reason that the average variable cost curve eventually starts to go back up. So if you're ever asked why a cost curve looks the way it does and you don't have any idea, a really good guess is the law of diminishing marginal product. More times than not, you'll be right.

Turns out, though, that the law of diminishing marginal product can't explain any of this. And the reason is we're talking about the long run. And remember that in the long run there are no fixed costs, right? So fixed costs, fixed inputs are what cause the law of diminishing marginal product.

So the answer for what's going on here is something different. If you think about what's happening here, economies of scale, what's happening is that we increase the scale of our production process, we get decreases in the form of... Decreasing average costs. Well, what's happening there is that as you increase the scale of your production process, it allows your workers to specialize in tasks.

Rather than doing multiple tasks, workers can specialize in a particular task. And so that allows them to get better. If you're the only one producing something like a car, let's take something simpler.

If you're the only one producing something like a shoe, then you've got to do a lot of different tasks. If, on the other hand, you're going to increase the scale of your production process so that you're producing lots of shoes with lots of workers, then you can have each worker specialize in a particular part of the production process, and they'll get really good at it. And as they get good, that increase in productivity causes your costs to go down. Let's talk about diseconomies.

Well, this is caused by... What's happening here is you've got a big production process and you're making it even bigger. What that means is that big production processes are difficult to manage.

So if you've got a small production process and you can manage it yourself, Well, that's relatively easy, but as you get bigger and bigger, then you have to start hiring managers. And if you think about what a manager does, a manager comes in and they're not producing output, they're just managing people. And so that's adding costs of production without giving you more output. And so big production processes require lots more layers of management, and that's expensive.

That drives your costs up on average. Constant returns, it's just the absence of economies or diseconomies. So hopefully this gives you an idea of how costs behave in the short run, what costs look like in the long run.

We're going to use this picture a lot. What we're going to do now is we're going to combine this picture. Remember that profit is equal to total revenue minus total cost, right?

We've just talked about... this. We've talked about how costs behave. What we need to do in our next chapters is talk about how revenue behaves. So we're going to combine this stuff with some new stuff in upcoming chapters, and then we'll be able to see what profit, how profit behaves for a firm, and how that firm is going to maximize profit.

So I'll see you in a future video.

Transcript for:Understanding Production Costs for Firms

Transcript for:
Understanding Production Costs for Firms