Marginal cost, average variable cost, and average total cost

- [Instructor] Let's say that we run ABC Watch Factory and we want to understand the economics of our business. So, what we have in this table is some data that we've already been able to estimate or measure based on how our business is running and then we're gonna be able to figure out some other things based on this data. This first column is fixed costs, our monthly fixed costs, so these are the things that we can't really change in the short run regardless of how many people we hire or how many units we produce, so that might be the rent on our facilities or the cost of renting the equipment and so, for us that's $5,000 a month. Then you have your labor units and for the sake for this model, we'll say that a labor unit is a full-time employee who's at the factory working every working day in a month and so, you can see, we can go from one person working full time every working day in a month, all the way up to six. Now, this is the variable cost and for simplicity, this is mainly driven by the labor units and a real-world example would be driven by the labor units, it would be driven by how much material we're using to produce the watches but we have our variable cost right over here. And then we have our total cost which is just simply the fixed costs plus the variable cost for any given level of labor units and then we know how many watches we can produce in a month based on our number of labor units or you could view it as based on our total costs or based on our fixed and variable cost. Now, what we have here are other things that we would wanna look at. If we really wanna understand how our factory works. So, this is the marginal product of labor, MPL for short, then you have your marginal cost, then you have your average variable cost, then you have your average fixed costs and then you have your average total costs, so like always, pause this video and try to fill what these values would be for even one row of this table and then I'll do it with you. Now let's do it together. Let's start with marginal product of labor. Let's remind ourselves what that is. That says for every incremental labor unit, how much more are we able to produce? And so, we'd have to start at the second one 'cause we have to think about it incremental labor unit. So, as we go from one to labor units, we were able to go from 10 to 25 total output, so we were able to produce 15 more watches. I could just type in 15 but it's even better to do it with a formula so I can just scroll it down the rest of the rows. So, in this formula, I wanna find the difference in my total output, so 25, that cell minus this cell, that that's saying hey look, I was able to grow 15 output or increase my output by 15 when I increase labor by two minus one. And then I got my marginal product of labor is 15 when I went from one employee to two and then I can just figure that out for the other rows, that's the value of using a spreadsheet. My marginal product of labor when I went from two employees to three employees is 20, so that means by adding that third employee, I'm able to produce 20 more watches per month and so, you might be noticing two interesting trends here. Initially my marginal product of labor seems to be increasing and then it seems to be decreasing. And that's consistent with the way a lot of businesses or factories work which is initially you're getting the benefits of specialization where if you only have one person working in your factory, they have to do everything, they have to polish the glass and bring in the boxes and talk to your suppliers and fit the gears on your watches and whatever and do the wiring while as you add more people, they can start to specialize. One person can specialize on assembly. Another person can specialize on bringing the boxes in and so, initially you have these benefits of specialization and so, people can focus on just one skill and do it well but then you start getting diminishing returns, the office starts getting crowded, people are waiting for different supplies, they have to get out of each other's way and so, then you see this diminishing return trend where the marginal product of labor starts going down for those incremental labor units. Next, we'll think about marginal cost and as we'll see, the marginal cost trend's going the other direction as the marginal product of labor. So, marginal cost is just for every, for a certain increment and output, how much is that costing us? So, for example, if we are going from 10 to 25 output, for that 15 increment and output, how much is that costing us and I would say costing us on average but I don't want you to get confused, we're not talking about average variable cost or average fixed cost or average total cost but that would be, let's see our costs went from 7,000 to 11,000, so we'll do 11,000 minus 7,000. That is our change in cost divided by our change in total output. So, that's going to be divided by the 25 minus the 10. And we could just scroll this down, we'll extend that formula and you can see this trend that is as the marginal product of labor is increasing, your marginal cost is decreasing and it makes sense, in some ways we're getting more efficient through the specialization and what else but then once you have diminishing returns, diminishing marginal returns, your marginal cost is going up. And now we can do the, I guess you could say the average cost. So, first average of variable cost. That's just taking your variable cost and dividing it by your total output. And so, for at least those first 25 units, they cost on average or just the variable component, you have to be careful is $240. If you talk about the fixed component, well, that's just gonna be our fixed cost divided by our total units and then our average total cost, that's gonna be our total cost divided by those 25 units and so, you can see, our average total cost for those first 25 units is $440 and then it can be broken up between how much of that $440 is variable versus fixed and then we can just extend these formulas down, the magic of spreadsheets and what's interesting here and it's not gonna be going to be so obvious just looking at this spreadsheet is something interesting is happening when marginal cost seems to intersect either your average variable cost or your average total cost that at some point you're average variable cost, you see that same trend, it's trending down and then it starts to trend up again. Average total cost is trending down but then it trends up again and as we'll see when we graph it, the point at which marginal cost intersects with the average variable cost, that's when you have that change in direction of average variable cost and then same thing is true of when marginal cost intersects with average total cost. That's when you have that change in direction. Average fixed cost just continues to go down because those fixed costs aren't going up as you have more and more output, so you have those same fixed costs, you could view it has spread amongst more and more output, so that's just going to keep asymptoting downward. In the next video, we'll actually graph that and see these trends visually.