Transcription
How's the class? So today, we're going to be working on chapter 22, which has to do with costs for a firm. Now, if you recall, I mentioned in a couple, I think a couple chapters ago, where we were looking at utility from a consumer's perspective, which is generally a very comfortable perspective for students at this level because most of them work on the consumer side. I mean, they operate on the consumer mindset, but not many happen to be working on the firm side, the business's perspective. And so, this sometimes takes a little bit of shifting gears in your head to try to make sure that you've got the right perspective.
So now, you've got to think like a firm and look at how costs are affecting you and how you're going to be managing your inputs and so forth, all for the goal of maximizing profits, which we start to get to for the next chapter, as well as well as the following, when we start covering market structures. But first, before we, uh, uh, get into input costs a little bit more in depth, let's look at the concept of the time frames that in economics classes, generally, you'll be, uh, thinking about. The first one is going to be the short run, and the second one is the long run. And a lot of times, we, we ask ourselves, what is the specific time frame for a short run versus a long run? And we can't really say what the time frame is in terms of months, days, years. It's, uh, it's really how flexible you can be in that given time frame, how, how much you can change your situation.
So, look at the short run. The short run is a time frame in which at least one input cannot be changed. So, in the short run, you're stuck with one input, and it typically, in economics, it's going to be your plant size. Uh, in the long run is a time frame in which all factors can be varied. Uh, you're not locked into anything. You have the ability to expand your type, your plant size, or other facilities or inputs that you may need to be expanding, or you can contract them as well. You can even go and go ahead and shut down if necessary, if that's the right choice. So, again, the short run versus the long run, the, the essential idea is that inputs are either variable or you're fixed in at least one sense.
So, the simplification that you should be aware of is essentially we're breaking down our inputs for a firm into two simple things: labor and physical capital, L and K. Now, that's generally what you're going to be considering, not just for this class, but moving forward. And of course, it does get more, more complicated than that. You have, uh, you actually have your raw material inputs, based on if you're making furniture, you're gonna need wood, you're gonna need nails, you're gonna need glue, and all that, and other types of things going into that. You're also going to need electricity, you're going to be paying rent, and all these other costs and inputs that you can be applying. But these simplifications are usually good enough to get across the ideas that you need to be considering and the way of thinking, uh, in terms of when you manage your, your resources, your inputs, and your costs. Now, of course, the other things come into play and complicate things, but if you have the general idea of how to approach the process of decision making, then that should be good.
So, as we push forward and looking at labor and physical capital, we're going to be looking at how these two inputs interact and how they, uh, can constrain the productivity of one versus the other, or how they can, how you'll see also gains and benefits given under circumstances where they interact with each other. Now, in terms of adding the concept, the short run and the long run, the labor is going to be your variable input in the short run. You're generally fixed in the long run with regards to physical capital, like we mentioned, the plant size. So, as you want to increase your output and expand, maybe what your productivity is, labor is going to be the first thing that you're going to be looking to expand in the short run. Now, it's possible that you're going to decide that in the long run, you're going to want to increase overall, almost on a semi-permanent sense. So, in that case, in the long run, you might expand, you will expand your physical capital, and of course, you're going to be adjusting your labor throughout to optimize your profit situation.
So, when it comes to the physical capital aspect, this is going to be my representation of physical capital. This is going to be representing workstations or workspace or plant size or whatever. And what I have here is, uh, set up two workstations in this scenario. Now, what we were going to be doing, we're fixed with this in the, in the short run. And as we add laborers, that's going to be our variable input in the short run. If we want to expand, as we have zero workers, we're gonna have zero output. But as we add workers, then as they utilize this physical capital, then what you're gonna see is the output is gonna increase. But what we're also gonna be looking at is how the output increases in terms of numbers, uh, as we increase workers, given this fixed workstation in the short run.
So, what we're going to do is add some numbers to this in terms of how many laborers. So, number of L was in this first column. So, we're going to look at a situation where we have zero workers. We're going to add workers as we go incrementally, and this marginal decision-making method, we're going to be thinking of adding in terms of one. And so, we're going to see how this works as we add workers incrementally throughout.
So, looking at the second and the third column, we have MPL and TPL. So, marginal product of labor. So, marginal, that word, additional product, output, and L is going to be the labor that we add, the labor that we add. And total product of labor is essentially the total output of our workers combined as we go. So, we're going to be looking at two, uh, perspectives of adding laborers: the incremental changes that each one adds, which is the marginal product of labor, and then the cumulative amount that they add as a sum total of workers. So, if we're going with the first value of zero, we have zero workers to work our physical capital, so it stands to reason that we're gonna have zero total product of labor.
Now, when it comes down to the marginal product, marginal product is the incremental change. So, it's really going from zero to one. So, oftentimes, we add this marginal product sort of as a staggered kind of an in-between stage between zero and one. Sometimes you'll see that represented specifically in your textbooks or literature, whichever textbook it may be. And sometimes they don't. They place it, uh, it right next to that, the the value of labor, even though it's kind of an incremental change, and it's best suited between zero and one, or one and two, and two and three. But you'll see it, you'll see various looks at it in that case.
So, let's look at the situation where we add one worker and we look at what this one worker adds in terms of the additional output of this worker, additional marginal output product, this worker labor, so the marginal product of labor. So, let's just say, and I'm making up these numbers, but let's just say that this one worker adds five units of output. So, at one worker, we have a total product of labor, now total output of five. Now, as we add our second worker here, going from one to two, which is kind of again, the incremental step, let's say now we have total output of 12 with that second worker. Sorry, that's written a little funny, 12. So, that's saying that we went from 5 to 12, so the additional output of that second worker was seven units. Now, if you notice, it increased. Why did this second worker increase the amount that he could crank out relative to the first one, who could only get five? Well, we have two workstations here. So, as we add the second worker, we are now taking advantage more appropriately of the two spaces of physical capital, the two workstations of physical capital. And now we are sort of, it's like where it's more and it's ideally engineered for not one worker, but more like two workers. And therefore, because, remember this idea of comparative advantage and specialization and how we increase output, now we have two workers where we can actually take advantage of that specialization and comparative advantage. And therefore, that second worker now contributes more output relatively compared to the first one.
And of course, we can still add another worker. Now, this workstation is not ideally completely set up for three, because there's only two workstations. But this third one can contribute. He can assist the first worker, and he can assist the second worker. So, even though he might not be as productive as adding that second worker, who gave us seven, maybe he will be, or he or she will be, uh, productive as to get maybe from 12 to 17, which is now a marginal product, the additional output of that worker of five. And then so forth and so on, as we add our fourth worker, as we add our fifth worker, and as we add our sixth worker, to all kind of increase output. So, maybe we're seeing high demand for our product, we want to respond as soon as we can, so we start hiring more workers, uh, to work our physical capital and get more output. But as we add them, we're going to be now seeing our additional workers straining the ability to produce of our physical capital, our limited physical capital in the short run.
So, now, as you can see, as we add our fourth worker, we now, that fourth worker does contribute more. Our total output went from 17 to 21. That fourth worker added four units of labor. And as we add the fifth one, they are adding to our total output, we went from 21 to 23, but as you can see, they only added two. Now, as we add our sixth worker, maybe there's only so much, uh, room to maneuver. And, uh, now maybe there's, if you've ever worked in an office, you'll know that the more workers you have, oftentimes the more chatting that goes on in between as people move and deliver things from one station to another. They stop, they chat, and actually, what might happen is that sixth worker, we might get into the negative. They become more, uh, deleterious to your goals of increasing output, and now they become a negative one. That's, they start removing productivity. So, if you notice, our total product of labor went from 23 to 22 as we added that sixth worker. So, there was a point where it just wasn't worth it. They actually became more of a hindrance to our production than helping.
Here we have another chart looking at the product production function and marginal product. Uh, this is a hypothetical case we're looking at. Again, in the first column, the labor. We have this time, we have total output in that next column. And then in the fourth column, we have the marginal output, the additional output that each worker adds. So, I had my columns reversed for those two. And then the third column is another one, the average physical product of labor. And that's simply looking at the average, looking at relative to how the output relative to how many workers you have. And that, that's also good to see. But like I mentioned before, we are a marginal decision-making science, so we're going to really be focusing on the marginals, the marginal values as we go in terms of determining how much we're going to produce.
So, taking a look at the total output function, the labor input, as you go, as you add labor on the horizontal axis, you can see the output going up. But as you can see, this negative parabolic looking function, sort of, it maxes out at some point under 60, and then it starts to go negative. It's such a downturn. And that was a situation, like I said, for my made-up situation, as we added the sixth worker, they started getting in the way too much and started reducing overall productivity, which is different because everyone's marginal product was going down, but we were still increasing our total product. So, they were contributing to the total, but they were contributing less as we go. Now, there's a point in the downturn up here, after the minimum, and we start to go down. They're not just contributing less, they're actually contributing negative. So, that's, that's a little different from what I just said a few seconds ago. So, like I mentioned, this is the total function that you can look at.
And here's another look. We're looking at the marginal function. So, what we're looking at is on the horizontal axis, we're looking at the amount of workers. As we add a worker, we're seeing that there's a positive contribution to each additional worker. But as we go for after the first and going to the second, you can see after that, it starts to really go down. What that's saying is that each one is still contributing, as long as we are in this range here, above the horizontal axis, each one is contributing to our total, but they're contributing less and less. There's a point though, like we, like I said, that we start getting to the negative because they become deleterious to our goals. So, if we were to, uh, combine those two to show how they relate, this is how they actually interact with each other. You can see on the bottom one, you can see the contributions, the positive contributions that occur here in the marginals, right? We're going into in-between states. So, actually, this is a situation that I'm going to erase some of these. This is a situation where actually these points selected here are actually, like I mentioned, the marginal concept in between stages, sorry, in between stages as we go, because again, we're going from zero, one, one to two. So, that's kind of how it's supposed to be. Even though it's hard to see, it's supposed to be staggered relative to the total up here, which is the actual increments instead of the between the one and two and so forth. But again, what we're saying is this positive amount, right? So, this is between right about here, that's about 10 right there, and that's that 10 here. And then over here, it contributes over here. So, going to this, it's going to be above. Looks about 27. So, over here looks like about 16, so 26 and so forth. And so, that's how we're gonna be interacting here. And at this point, going from seven to eight, it starts to contribute zero. So, we max out as, uh, going from there. And as we go beyond that, now the additional becomes negative. What they start to now bring down our total output.
Okay, so looking at the short-run cost of the firm, we're going to have total costs, the sum of total fixed costs and total variable costs. And then we're going to break down the fixed costs and variable costs. Fixed costs: costs do not vary with output and are fixed for a certain time period. So, for example, rent on a building. And then the variable cost: costs that vary with the rate of production. So, as you increase production, you might hire more workers, you might need more materials for your output, and so forth. So, the ver, they vary with the output that you have. You're going to have more workers, so it's the wages you pay. You're going to need more materials to produce, so there you go, it's another variable cost. You're going to increase that. So, the equation at the bottom: Total Cost is equal to TC, total, total fixed cost plus total variable cost. So, these, these equations that you're seeing here and the following are going to be very important for you to remember because these are such basic, easy equations, especially when we get to averages as well. It's simply dividing it by the quantity. But, you know, sometimes they get overlooked and, uh, it's not your first go-to, uh, rule to help answer the questions. But remembering these, uh, these equations is gonna really make answering questions or gathering your bear, getting your bearings in an idea in a question in the scenario, it's going to help you focus hopefully easier.
So, ATC, the average total cost, also called the average per unit total cost. ATC is going to equal to your total cost divided by the quantity, just like any average, right? Average, uh, your free throw percentage and so forth, that's your average divided by the quantity of free throws you take, that's an example. Your average variable cost, AVC. AVC is going to be TVC divided by Q, or your total variable cost divided by quantity. Your average fixed cost is your total fixed cost, TFC, divided by your quantity, your output as well. Okay. And then here's the very important marginal one: marginal cost. The change in total cost is due to a one-unit change in output or your production rate. So, oftentimes, marginal cost is going to be represented as: Marginal Cost is equal to the change in total cost divided by the change in quantity.
So, this next slide here is, uh, throwing everything in. And what's, while it looks like a, a bunch, an imposing set of numbers, actually, it can be, uh, it helps just to kind of take a look at it and and remember what you're looking at and what each column entails. And of course, it's laid out here for you. It shows you like for column two is total fixed cost, column three is total variable cost. And then you, if you go over, you're gonna see column five, average fixed cost, average variable cost. And then, you know, they're giving you an idea, for example, for column five, it's going to show you that it's column two divided by column one. Uh, so, uh, these are one of the, it's kind of, uh, useful to kind of take a look at this and see how they interact and play off of each other. Um, and I think a lot of it is just taking the time to kind of orient yourself with these ideas and kind of see how they interact. If you just neglect that and just take a look at this, I think not seeing, at least taking a look and making sure you understand it as you look at it, maybe not have to memorize everything, uh, at the moment, but if you can kind of understand how everything interacts, I think it'll be useful and it will hopefully get you over some sticky points, uh, when you are having to analyze a situation for your homework sets, for example.
Now, taking a look at a visual look at your, uh, at your different costs here, we have incorporated in here, we have fixed costs and variable costs. So, over here at 10. So, this is the amount of fixed cost that a firm has. It carries with it irrespective of what it produces. So, for example, in the short run, you're stuck with your factory, your workstations, your, your machinery, and whatever. So, generally, let's just say you're paying rent on it. So, whether or not you produce zero or 11 units of whatever, whatever this boring secure digital cards per hour, very old technology in a sense, but let's just say you're stuck with 10 in term, 10 dollars in terms of your total fixed cost. Now, we're also adding the variable costs as well, which is this red function here. So, at zero, you're producing nothing, so your variable costs are zero, but they're gonna vary with production. So, as you increase output, you're gonna start incurring labor's wages, you're gonna start incurring costs of your output, and your variable costs start to go up. So, that red function there is going to show you, separated from fixed costs, your variable cost. Now, if we want to combine it, we have our total cost, that black function above it. And all it does is it adds the total fixed cost to the variable cost. So, it just, the function, the red function just shifts upward by that fixed cost amount to 10. And then the very variable cost and total fixed cost, I mean, yeah, fixed costs are included, and now you have your total cost function there.
Now, this is a jumbled mess of all of our cost functions together, and a lot of people can get very, uh, intimidated by this. But if you stop to kind of pick things out, uh, and just kind of go from there, it really does help to kind of stop and think about these different curves. And you're going to be using all of these curves for analyzing market structures and making decisions in terms of maximizing profit using these diagrams. Uh, so please take the time to to to kind of focus and add some some concentration power to this and try to sift through this.
So, let's take a quick minute or two to kind of discuss, maybe probably a little more, but to discuss how these curves can be kind of looked at, methodically, to kind of get past that big mess of spaghetti noodles that looks like cost curves up there. So, I'm going to start with the average total cost curve. It's going to be this parabolic looking function, and, um, it's going to have a minimum. As you can see, it drops with a minimum there. And as we talked about earlier, it's going to be comprised of total, is going to be comprised of your fixed and your variable cost. So, first thing I'm going to do is do your, our average fixed cost. Now, the average fixed cost is just going to continue as we increase our quantity because it's fixed, it's not changing. It's going to be reducing the amount because the numerator is going to remain constant as fixed, but as you increase in terms of the denominator, the quantity of our output, as we crank out more surfboards, you're going to see that the fixed costs become spread out over more and more surf, surfboards. So, on average, our fixed cost is just going to decrease. Unlike our variable cost, our average variable cost is going to be going down. Why does it go down? At first, it starts to go down at first because of the specialization, our workstations, where we had two ideal workstations and we added additional workers, they were able to take advantage of their comparative advantage. And so, what happens is we increase our output because the workers are becoming more productive as we go, the cost, the variable cost is decreasing at first. But at some point, as we add additional workers, we said that each worker does contribute positively, but less and less. So, then in terms of the surfboards that we're creating, the variable cost starts to increase. And then now we're going to add our very important marginal cost curve, which also dips down at first. And why does it dip down at first? Same reason that I just mentioned before, is that the additional workers, the change in our total cost with respect to the change in output, as we're increasing output, we have a situation where workers are becoming more productive. So, the additional cost, uh, per surfboard, as we increase our output, is going down for each, for each surfboard because we're seeing these gains from specialization and comparative advantage. But almost immediately, in my example, we saw that starting to go away. So, our marginal cost, the additional costs, uh, starts to increase. And so, here we have our marginal cost curve that swoops up through it all. And one of the important concepts about the marginal cost related to the average total cost curve is that it intersects at the minimum of the average total cost curve. So, that's actually a very important reference point. The minimum of this average total cost curve is where you're going to see the marginal cost curve sliced through it. So, we're going to be using the average variable cost, uh, a lot as well in our decision making. The one that we don't think about too much in our, in our analysis, this one, average fixed cost, starts to go away. We don't look at it too much because it's, it's a fixed cost. It goes to the idea of of, um, of a sunk cost, or that concept that we said before of, don't cry over spilled milk in economics, because it's gone. Fixed costs are fixed. You know, if you're losing money and you're trying to decide whether or not to stay in business and shut down, it's all about the marginals. It's the fixed stuff you don't think about it anymore because it's already a sunk cost, it's gone. Uh, so anyway, this one starts to go away. So, we're gonna actually take a look at all this again without the fixed cost, most of the time, and just looking at either average total cost with marginal cost. And we're again going to add average variable cost, in particular, in chapter 23, when we talk about shutdown points for a firm.
Let's also spend a brief minute talking about the relationship of the marginal and the average total cost curve. Now, what's important to note is that the marginal pulls the average. Now, if it helps, maybe you can think about it in terms of basketball. So, when a basketball player goes up to take his free throw shot, the marginals are going to be the additional shots that that player takes. And then, of course, you know, the average. So, as this player takes his, let's just say it's a two-pointer, and they're gonna take two shots. If they make both shots, they're gonna have a hundred percent free throw, uh, a hundred percent of their marginal shots made at the line when they go up. If they make both, so what happens to the average? Well, as you know, it doesn't necessarily show on the numbers because when you see it on the screen during a game, the numbers thrown are so high that, you know, it gets lost. But if you could go down to the to the many, many decimal places to see what change, two made free throw shots, a hundred percent of the marginal shots made at each trip to the free throw line, it will actually pull up the average. Now, if this person goes up to the line and misses them both, then that marginal trip to the line, they made zero, right? Not a hundred percent of them. And so, now that marginal trip will pull down the average as well. Okay. So, that's kind of the relationship of the marginal to the average. The marginal will pull the average. So, as we see here, the marginal fall is below. This is an individual who is shooting below their normal average free throw percentage. And so, as they throw below it, it's going to be pulling down their average. Now, the marginal is going to intersect at the minimum. And as soon as the marginal is above the average, the average will start to rise. So, that's an important relationship that oftentimes you're tested on or you have homework questions on, um, and not just here, but in future economics classes. So, be aware of the marginal pulling the average.
So, hopefully, what we just covered slightly demystifies a little bit of this jumbled mess of curves, and you can kind of start to parse through them with a little bit more clarity. Why they're shaped, they look a little bit randomly shaped, but I think as you kind of understand these cost curves a little more, you're going to see that the decreases and the increases and sometimes the intersections are very, very important and things to understand and be familiar with. So, this is just matching up the the cost, uh, curves, the various looks, fixed cost, variable costs, averages and marginals, totals, and so forth. And you can kind of see how they match up with the actual curve. So, these are all, these two, the left and the right, are actually relatively matched up. So, if you want to kind of parse through it and kind of look through it and see, see if everything matches what you understand it to be, then that's probably a good thing to do.
Now, the next thing we're going to look at is something called the planning horizon. We looked at the short-run cost curves, that was what all that was. Now, we're going to be shifting our perspective to the long run. So, the long run, uh, happens to be our planning horizon because we can plan where we actually want to compete. Suppose, do we want to compete at the Walmart level, uh, in terms of, uh, retail, uh, where we have massive amounts of of physical capital locations, for example? We also have a, a complicated and and comprehensive network of shipping and inputs and so forth. Do we want to compete at that level where we have a lot of cost benefits, so we can sell things at a really cheap price? Or are we going to be competing at a mom-and-pop retail store level where we're very small, we don't get to take advantage of a lot of the, the cost advantages that a large company gets to, and therefore we tend to charge more? That's why when you go to a mom-and-pop store at the corner to pick up whatever Tylenol or a six-pack of beer or whatever, you're going to be paying higher prices.
So, this long-run average cost curve, it represents the locus of points representing the minimum unit cost of producing any given rate of output, given current technology and resource prices. So, taking a look at this preferable plant size and the long-run average cost curve. Now, the left diagram is going to be looking at the short-run average cost curves. Now, a small component about why we call it the short-run average cost curve, not calling it average total cost or average variable cost, why do we not specify that? Because remember, this is the long-run planning horizon, and now we don't have anything that is fixed. Everything is variable. So, we just call it short-run average cost. We don't have to call it average total cost or average variable cost because in the long run, everything is variable, including our plant size. And that's the point we're going to be looking at, where do we want to compete, in a sense? What are the long-run plans? We can choose to operate with the short-run average cost curve one or two or three or four or whatever. And the thing is, is that all those options laid before us on the right side is where we could choose to operate under. And just skimming the boundaries, what they call the envelope of those short-run cost curves will give us this long-run average total cost curve.
Now, taking a look at that long-run average cost curve, if you notice that green curve, obviously, just like our regular average total cost curve in the short run, decreases up to a point, it hits a minimum, and then it starts to increase again. So, the portion where the long-run average cost curve is decreasing, that's that situation you've probably heard of of economies of scale. So, economies of scale meaning you have benefits to the scale that you're operating under. So, if we're talking about Walmart, their economies of scale, their lower costs that they get to enjoy come from a situation where they have their own trucking system, they have their own storage systems along the way, they have a vast network that helps reduce their input costs. Instead of paying profits to other vendors, other intermediate providers, they do it a lot themselves because they've created a network that allows them to do that. And so, they enjoy lower costs, and the larger their, the larger their scale, they get benefits up to a certain point. But if you also notice on the right side of the minimum, this portion right here, you're going to see your cost start to increase. And that's a situation where the firm gets so large that it's kind of like they become inefficient, they inefficiently large. The, it's like the left hand doesn't know what the right hand is doing, uh, and that's that's an issue as well when firms, when firms grow, uh, too large. So, these are the types of things that you should be aware of regarding the average, uh, long-run average cost curve, the economies of scale versus the diseconomies of scale, where the firm gets too large and becomes inefficient, and then the costs start to rise.
So, this is a general look at the input costs, considering the short run and long run, and how the curves interact. And I hope this was helpful. If you guys have questions, please let us know, and we look forward to talking to you soon. Take care. Aloha.