00:01
So here we're talking optimization, right? and we have a production function, 5l to the half, m to the half.
00:08
Now we also have prices, right? the cost of labor, which we usually call the wage, is 9, and the cost of using machines, which we call the rental rate or the interest rate, is 64.
00:20
And we want to set the output equal to 12, right? that's the goal.
00:24
So our goal is to minimize the cost.
00:28
We want to minimize the cost, and the cost is going to be 9 times the labor plus 64 times the capital, subject to 12 is equal to 5l to the half, m to the half, right? so really, this is just a pretty straightforward calculus problem.
00:50
The first thing i want to do is rearrange the constraint a little bit, right? so if i get 12 over 5 and i square both sides, i get l times m.
01:02
We're equipped...
01:04
Sorry, it's machines here, not capital.
01:08
Gotta be careful.
01:09
Usually it's k, not m...