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# Long-run average total cost curve

AP.MICRO:
PRD‑1 (EU)
,
PRD‑1.A (LO)
,
PRD‑1.A.10 (EK)
,
PRD‑1.A.11 (EK)
,
PRD‑1.A.9 (EK)

## Video transcript

we've talked about the idea of average total cost in several videos so far where it was the sum of your average variable cost and your average fixed cost but when we're talking about fixed costs by definition that means we're talking about things in the short-run remember the short-run is defined as the amount of time over which at least one of your inputs is fixed but if we talk about longer term so let's say you're running a factory and in the short-run the short-run would be how long it takes to build another factor or how long it takes to close down or sell another factory but in the long run you can always add more factories or shut down factories so in the long run everything is variable so what we're gonna do in this video is think about how the average total cost that we've studied in previous videos which were actually short-run average total costs how those relate to the long-run average total cost so let's imagine that we are trying to open up a food truck business and let's say that each food truck so each food truck and let's say we're going to sell tacos so these are taco food trucks and so each food truck can optimally optimally I'll just write it like that serve serve 100 tacos per day and we haven't started our business yet but we have to decide how many food trucks to buy and we do some market research and we feel pretty confident that we are going to be able to sell 200 tacos 2 per day so we're going to target target 200 tacos tacos per day now in this world what you would want to do is optimize your fixed costs to minimize your average total cost for 200 tacos per day remember your fixed cost is essentially going to be let's say it's just your food truck and then you're going to have a variable cost it might be the staff that's that's making the tacos it might be the supplies for the tacos things like that and so you might have an average total cost curve that looks like this let me make some axes here so this is going to be quantity of tacos per day quantity of tacos this is going to be per day and then in the vertical axis this is going to be cost per taco cost per taco and let's say since you're optimizing for 200 tacos today you want to minimize your cost per taco 200 tacos per day that happens with two food trucks so if we're at 200 tacos per day let me put it right over there 200 tacos per day we get to a cost per taco average total cost per taco let's say that is 50 cents so that is 50 cents right over there but the actual number of sales the actual number of tacos that you might have to produce in a given day might vary from that and that will actually help construct your average total cost curve and so your average total cost curve might look something like this it might look might look something like this we've seen curves like this in the past and we would have call this our average total cost but now because we're differentiating between our short-run and long-run let's make this very clear this is our short-run average total cost and this is a situation where we have two of our food trucks per day two food trucks now what if instead of 200 tacos per day it ends up that we only have to produce a hundred tacos per day because that's how many people are demanding so let's say this is 100 right over here well if we keep our the number of trucks we have constant so we don't change our fixed cost well then our cost per taco is going to be higher let's say that this right over here is let's say this is 70 cents 70 cents per taco and then there's the other scenario let's say that our tacos sell better than expected let's say that we need to somehow produce hundred tacos per day well if we can't change our fixed cost which is by definition what the short-run is well then we might be at say this point it looks like it would be about let's just call that 80 cents 80 cents per taco as our short-run average total cost now in either of these situations let's say that we have the more pessimistic scenario actually happens that there's only demand for a hundred tacos per day well in that world the rational thing would be hey let's sell one of those trucks we're only at 50% utilization at a hundred tacos per day let's sell one of those trucks to lower our average total costs and so in the long run you can adjust your fixed cost so with one truck what a curve that looks like this so at a hundred at a hundred tacos per day our costs are 60 cents per taco and the curve might look something like something like this so if things were to get even worse than that our cost would go up and if for some reason the market were to actually go back to what we expected or even beyond then our cost would go even higher so this cost curve which is based on one truck so let me call this our short-run average total cost and this is for one truck this would be suboptimal if we actually do have 200 sold 200 units being produced today or 300 units produced per day but it is optimal for 100 units per day now things could go the other way you might start with those two trucks that are optimal for 200 units per day 200 tacos per day but you're in the world where people want to buy 300 tacos per day and 300 tacos with two trucks is not optimal so in the long run you order another truck and maybe it takes a couple of months for it to show up and be outfitted whatever but once you get that third truck now you can optimally serve 300 tacos per day and so you might be in this situation so at if you get another truck you could have another run average total cost curve that looks something like this right over here so this is our short-run average total cost curve and so this is when we have three trucks and remember the short-run is when at least one of your inputs is fixed and in this one for the simplified model we're assuming that input is the truck that everything else is a variable expense now when you look at this it helps us think about a long-run average total cost what would that be well in the long run we can change the number of trucks we have and if we can in the long run we can change the number of trucks we have we would always be picking the optimal number of trucks for the quantity we're producing so in the long run we would want to be at that point so if there's only a hundred that we need to produce a day we would only use one truck if there's 200 produce a day we would use two trucks and be at that point if we need to produce 300 we would have three trucks and be on that point and so your long-run average total cost curve would be connecting these dots and so it would look something it would look something like this and some of you might be thinking well but this situation right over here is where you have one and a half trucks what's the deal with that but in the long run you might be able to get a custom truck size that is one and a half times as big as your typical truck or two and a half a times as big as your typical truck but the big takeaway here is that your long-run average total cost curve you can view as the envelope of all of the minimum points of all of your various short-run average total cost curve because at any given for any given quantity you want to optimize your fixed cost which puts you at the minimum point of one of these short-run average total cost curves