– [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.