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Main content
Current time:0:00Total duration:8:33
AP.MICRO:
PRD‑1 (EU)
,
PRD‑1.A (LO)
,
PRD‑1.A.1 (EK)

Video transcript

you will hear the term production function thrown around in economics circles and it might seem a little intimidating and a little mathy at first but as you're about to see it's a fairly basic idea it's this idea that you could have these various inputs let's call this input number one and then you have input number two and you can keep going and then you put them in their inputs into some type of process and then that function let's just call that F that's going to describe how much output you can get given that input we can also describe it a little bit more mathematically those of you who remember your algebra 2 might recognize this where we could say the output it's often use the letter Q in economic circle it's going to be a function it's going to be a function of the various inputs so I'll put input number one input number two and you could go you could have as many inputs as is necessary to produce that good and these inputs if you wanted to categorize them these are the classic factors of production that we would have talked about before these would be these would be your land labor capital and entrepreneurship and it doesn't have to be all of them but each of these inputs would likely be factored as one of these now this might still seem very abstract and very mathy so to make things very tangible let's let's give a well let's give a tangible example let's say that we're trying to make a bread toasting operation so what we need to do is we take bread we stick it in a toaster and then once it's toast we're done and so what are our inputs there well you're definitely going to need some bread so let me draw some bread right over here my best attempt at drawing bread so that right over there that is bread you could call that input number one now you're also going to need a toaster at least one toaster or toasters I should say and let's say the toasters that we use for this operation they can toast four pieces of bread at a time and it takes 10 minutes to do that for slices in 10 minutes now you might say well aren't those going to be all of our inputs but then the obvious question is that bread isn't just going to jump into the toaster on its own and then jump back out someone there's going to be needs to be some labor to operate this operation so we're going to need some toaster operators and let's say that they can they can process they can process one slice per minute one slice per minute I know many of you all are thinking that you could do better than that but try to do it all day one slice per minute now based on this if these are really all of the three inputs into producing the output boosted piece of bread we could try to construct a production function here so let's do that so let's say then the output is going to be the number of slices slices of toasted toasted bread and it's going to be equal to and I'm gonna write this as I'm gonna make our production function as being the minimum of of several values and what you're going to see it's going to be based on what's going to be our rate limiting factor and I want to get too much in the weeds with you on this but just to help us understand so it's going to be the minimum of well the amount of bread you have so slices of bread slices of bread and why does that make sense well you're only the amount of toasted bread you can produce is always going to be limited by the amount of untoasted bread that you put into your process if you only have 60 that's going in per hour here well then you can only produce a maximum of 60 right over here and this is going to be per hour per hour so there's gonna be the slices of bread per hour now our other input how much toast can one toaster toast in one hour well if they do four slices in ten minutes we'll multiply that time six to get to an hour that's gonna be 24 slices per hour so we could do 24 times the number of toasters times the toasters and then last but not least how much bread or how many slices can one person process per hour well it's going to be 60 slices per hour so it do 60 times times let's call them workers I was going to call them toasters but we are using that for the equipment times the number of workers and so it's worth at this point just pause this video and really process what's going on what are the inputs here and what are the outputs well the inputs are right over here this is the number of slices of bread per hour the number of toasters we have at our disposal the number of workers toasters you could view as capital workers you could view as labor and now another interesting thing to think about and we will talk a lot about this in economics is what's going on in the long run and the short run and production functions are useful for thinking about the long run in the short run because the short run is defined the short run is defined as the situation in which at least one of your inputs is fixed let me write this down at least at least one input is fixed now what does that mean in our bread toasting example right over here well let's just say that we can it's very easy to get slices of bread if we if we have the capacity and we want to produce more bread the slices of bread are let's say it's just never our rate limiting factor so that part isn't fixed but to get a new toaster let's say these are special toasters and you got to order them and it takes a month so let's say that there's a one-month lead time on this input one month lead time and let's say for workers there's just not a line of people ready to toast toast you have to put a job posting out there and you're going to have to interview people and also let's say that it takes two weeks to hire someone so two weeks to hire or I guess you could also say two weeks to hire or to fire someone if you want to reduce capacity in let's say it takes one month to either get a toaster or to remove a toaster well in that case the short-run in this situation is a time period where at least one of the inputs is fixed so pause this video and think about what would be the short-run in our situation well the short-run in our situation the number of toasters we're going to have is going to be fixed for at least a month so our short-run in this situation is up to a month so up to up to a month and then the other side of it what would the long-run be well in the long run by definition none of your inputs are fixed you can change the number you have of any of these things so our long-run is going to be greater than one month in this example now it's really worth noting that was just for this example if we were talking about some type of automobile factory and the output is the number of automobiles produced per day or per month and then you have all these inputs you would have your metal you would have your labor and then you would have the equipment for the factory itself well there the long run it might take another year or even two years or five years to build a factory in that case the long run would be the time period greater than it amount it takes to build another factory usually capital is the thing that is most fixed for the longest period of time and that's why I made it hard for us to get our toasters so I will leave you there this is just an introduction to the idea of a production function but hopefully with our bread toasting example it is not so intimidating
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