[music]. .

So let's focus now on that marginal cost. So first let's figure out how to calculate

it. So here's the table again.

But this time I'm adding a one more column, which is the marginal cost.

And the way I'm calculating that Is the, let's call that marginal cost is MC.

It's going to be the change in the total cost every time you increase your output

by 1. So we can calculate it by the following

equation, the changing total cost over the change In output.

So, for instance, when you have, when you go from 0 sandwiches, to 40 sandwiches,

right? So the marginal cost, of the 40th

sandwich, is going to be the change in total cost, over the change in output of

that sandwich. And the change in total cost, well, the

total cost went from 100 to 180 and the change in sandwiches was from 0 to 40.

So when you calculate that, you actually get the marginal costs of the 40th worker,

of the 40th sandwich which was $2. So there, when you make the 40th sandwich,

that sandwich added $40 of cost to your operation.

You can calculate the marginal cost of the 90th sandwich in the same way.

It will be the change in total cost of that sandwich over the change in output,

and that's going to be well, the change in total, the cost went from 180 to 260,

minus 180, and the output went from 40 to 90.

90 minus 40, so that's going to be 80, divided by 50.

And again, that's going to be equal to marginal costs of $1.60, so the marginal

cost went down. So the second, the second worker, when you

hire the second worker, the second worker decreased the cost of operation.

Now, I think you could suspect why is that.

It's because the second worker, the first worker, you paid him $80, but they

increase output by 40, but the second worker, you pay him the same money, $80,

but they brought 50 units of output. So the second worker is a much better deal

to you than the first worker, because the second worker increased productivity by

more. Because if you're them paying the same,

your cost per unit your, your changing costs are going down, your, your cost of

operation are going down. Now the, the third worker is a whole

different story. The third worker increased output to 120,

so what is the cost of making that 120th sandwich?

Again, it will be the change in total cost over the change in output.

And now, your output went up from 340 from one, from 260.

I'm sorry, your costs. And your output went up from 90 to 120.

So again, this is 80, again. You're always paying, you're increasing

output by one worker, and you're paying all the workers $80, so your change in

cost is always $80. And then the increase in output is worth

30. So now with the third worker, the cost of

the, of the 120th units was actually $2.67.

So now your costs are increasing at a increasing rate.

So the, we can see this very easily, is the third worker increase productivity by

less than the first work, than the second worker, and you're paying the third worker

the same amount of money. Now, in the previous session we said that

that's because of the diminishing, the marginal product of labor.

And we can see this clear now. You see that, every time we're increasing,

we're calculating the marginal costs, we always dividing 80, which is the wage, by

the marginal product of that worker, that created that output.

50 is the marginal product of the second worker, that created the additional 50

units. And 30 is the marginal product of the

third worker that brought that increase in output.

So basically, the way we calculate marginal cost every time, is the, the

change in, in total cost, which is, happens to be the wage over the marginal

product of labor of that additional worker that creates that output.

So clearly, since a marginal product of labor, at some point is going to start to

decrease, this number is going to start to increase.

So, this is a mathematical proof of what we know, by intuition, which is the reason

why your costs of operation eventually start to increase at an increasing rate

and get really high really rapidly, because you're paying the workers the

same, but each, but each additional worker is bringing less, because there's too many

cooks in the kitchen. This is a problem, Mike knows this.

And this is I don't if you heard this already, but at some point in the

interview with him, he actually tells you that at some point he had to stop hiring

work cooks. It doesn't make sense.

Even though hiring more cooks will increase the number of sandwiches, since

he has to pay them some money, it doesn't make any economic sense to, for him to

continue to hire cooks. Okay, so we have one more thing left on

this lesson. And that is to take all this cost measure,

divide them by output to get a per unit cost, and then see how all this costs look

in the diagram in what we call the cost curves.

So I, that's what we're going to do next. .

[music]. Produced by OCE, Atlas Digital Media at

the University of Illinois, Urbana-Champaign.