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[music] Very well. So, we are at the point of this lesson in

which we have to come up with that actual numerical example to understand some of

the other stuff we're going to talk about this week.

So, that's what we're going to do now. And we're going to continue to use the

example of Black Dog, our barbecue sandwich shop to illuminate some of this,

we're going to give you some actual numbers, hypothetical numbers, but numbers

that in some way recreate reality a little bit.

But before that, let's hear the setup of the issue by, here from Mike which is the

owner of the Black Dog, what is the main issue he has that is related to what we're

going to talk about. So let's hear from him first and then

we'll come back here. >> We decide, well, we need this many

people to serve this many this many customers.

And then, as we got busier, we realized we could divide the restaurant up into three

sections. We need three servers all the time.

Sometimes, we need to add a fourth. It's just based on how busy we are.

And that's just the number of people that can work in here efficiently, without

being too crowded. If we had try to add more people in, you

certainly get to a point where it doesn't work anymore.

You get, people are just getting in each other's way.

And so that's kind of worked out where each server gets about four, four to five

tables. And then we know that we need them all the

time. And it's just the demand in the business

and how many people are showing up and, and as far as producing the food, we

started with two cooks in our, on our serving line, and we realized at a certain

point if we had added a third cook, that we would be able to produce the food

faster, and be able move more people in and out.

And so, the third cook was more efficient but we can't add any more than that

because there's not enough space. So, that's sort of the maximum that we

reached there. And then, we ended up adding some people

in the back because we needed to be able to um,do the prep work and get everything

prepared so the people on the line can do their work faster.

And so it's kind of a limitation, or an equation between the space, amount of

available space, and the number of people that we need to do the work.

>> Okay, so essentially, what Mike was saying is that the problem he has is that

the kitchen is too small for the number of cooks that he would like to have.

So, there's too many cooks in the kitchen. This is very related to what we have been

talking about this week, which is this idea of as you increase the number of

workers with a fixed input, you run into limitations for that fixed input and your

workers become to be more unproductive. So, let's see if we can come up with an

actual numerical example for barbecue sandwiches, which is the example we are

using, that kind of recreate, recreates this idea of diminishing marginal returns

to the variable input. So, here's what I have.

Suppose that this was the production function for barbecue sandwiches for Black

Dog, which is our store. They make a lot of other stuff, but we're

going to focus on the sandwiches themselves.

So, when they have no cooks, they have no sandwiches.

When they have one cook, now they can make any sandwiches, and they have a total of

40 sandwiches. When they have two cooks that have 90

sandwiches so that's the first cook brought 40 additional sandwiches, the

second cook added 50 additional sandwiches.

The third cook increases up to 120, that means 30 more.

The fourth cook to 135, that's 15 more. The fifth cook 140 which is 5 more.

And the last cook or the sixth cook increases to 142, which is 2 more.

So if we put this in a diagram, we can see that the curve we actually have is what we

call the total product curve. And when we simply put the information we

have in those two columns. In a diagram, with number or workers, on

the horizontal axis and the output that they produced together in the vertical

axis. And you'll see what you get is a curve

that is increasing at a decreasing rate. And that makes sense, because the slope of

that curve, which is, this tells you how many more work, how many more sandwiches

each additional worker is bringing to the operation.

So, you, each worker is, is by, I, every time you add a worker, your, your number

of sandwiches increases, but it increases by a smaller number than when you brought

the worker before. That is particularly after the second

worker. In fact, if you actually take the slope of

that curve and graph it out on the vertical axis we call that the marginal

product of labor. The slope of this total product curve,

which is a change in output every time you add one more worker, is called the

marginal product of labor. And if you actually graph that against the

number of workers, what you get is, at the beginning, your productivity of workers is

increasing. Then after you add more workers, they

start to decrease. Now, we can also see that on the table.

Here's the same table with one additional column that actually calculates the

marginal product of labor. And again, the equation I'm using to

calculate that additional column is what we call the marginal product of labor

which is the variable input, in this case, and that is going to be the additional

output each additional worker brings. So, to calculate it you can just simply

say, a change in output every time you change your workers, right?

That's how you calculate. So, the first one is the change in output,

it's going to be 40. And workers are changing one-to-one.

So, the marginal product of the first worker is 40.

The marginal product of the second worker, marginal product of labor of the second

worker is going to be what the second worker increase up to, from 40 to 90,

which is 50 more. Again, one worker.

So, this will be 50. But when you add the third worker, that

third worker increases output from, from 90 to 120, which is only 30 more, compared

to 50, which is the increase of the worker before that.

So, you see that at that point, the change in the increasing output starts to go

down. And that is why we, what we call

diminishing margin of product for the variable input.

That's what we have in the discussion. So, you see that this example for this

hypothetical example for the Black Dog case, recreates what we know about

reality, which, which, which is that you increase the variable inputs with a fixed

input, the variable inputs become more productive, and also recreates what Mike's

problem is having. Which is that at some point, you have too

many cooks in the kitchen, and they start running into each other.

Okay. So, now that we have the example, we can

use the same example at an, at the cost to that equation and that's what we're going

to do in the next section. [MUSIC]Produced by OCE Atlas digital

media, at the University of Illinois, Urbana-Champaign