Introduction to production functions | APⓇ Microeconomics | Khan Academy


– [Instructor] You will hear
the term production function thrown around in economic 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 Two might recognize this. Or 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 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, four 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 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
toasted 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 of toasted bread. And it’s going to be equal to, and I’m gonna write this as, well, I’m gonna make
our production function as being the minimum 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 this is 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 10 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 we’ll do 60 times, times, let’s call them workers, I was gonna call ’em 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 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 gotta 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 so 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. 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 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 it made it hard
for us to get our toasters. So I will leave ya 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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