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# Marginal cost, average variable cost, and average total cost

AP.MICRO:
PRD‑1 (EU)
,
PRD‑1.A (LO)
,
PRD‑1.A.5 (EK)

## Video transcript

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 a met or measure based on how our business is running and then we're going to be able to figure out some other things based on this data so 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 five thousand dollars a month then you have your labor units and for the sake of this this model will 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 every full 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 in 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 cost 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 cost or based on our fixed and variable costs now what we have here are other things that we would want to look at if we really want to 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 cost and then you have your average total costs so like always pause this video and try to fill out what these values would be for even one row of this table and then I'll do it with you all right 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 are we how much more are we able to produce and so we'd have to start at the second one because we have to think about an incremental labor you so as we go from one to two labor units we were able to go from ten to twenty five total output so we were able to produce fifteen more watches I could just type in 15 but 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 want to find the difference in my total output so 25 that cell minus this cell so that's saying hey look I was able to grow 15 output or increase my output by 15 when I increased labor by 2-1 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 when 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 way a lot of businesses or factories work which is initially you're getting the benefits of specialization where an 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 and fit the gears on your watches and 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 in 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 trends go in the other direction is the marginal product of labor so marginal cost is just for every for a sir increment increment an output how much is that costing us so for example if we are going from ten to fifty five output for that 15 incremented output how much is that costing us and I would say costing us on average but I don't want to get confused we're not talking about average variable cost or average fixed cost or average total cost but that would be well see our costs went from 7,000 to 11,000 US will 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 or extend to that formula and you can see this trend that as the marginal product of labor is increasing your marginal cost is decreasing that makes sense where in some ways we're getting more efficient through the specialization 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 variable cost well 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 we talk about the fixed component well that's just going to be our fixed cost divided by our total units and then our average total cost well that's going to 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 going to 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 your 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 will see when we graph it the point at which marginal cost intersects with the average variable costs that's when you have that change in direction of average variable costs and the same thing is true of when marginal costs intersects with average totals and costs 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 as spread up spread amongst more and more output so that's just going to keep asymptoting downward and the next video will actually graph that and see these trends visually