00:01
So here we have a cost minimization problem with some very special preferences, right? and this min function in the preferences means that we can't use our normal tools of calculus because the minimum function is not differentiable.
00:14
It's not a function that you can differentiate.
00:17
It doesn't have the right properties to be differentiable.
00:20
So i want to just sort of show off first that there are some very basic rules for dealing with this minimum function, right? so consider that we used four capital and for labor.
00:33
Then the quantity would be minimum of two times four, four, which is the minimum of eight and four, which is four.
00:46
We say, look, this is kind of weird.
00:49
The labor and the capital are sort of are not really relevant in the same way.
00:54
The labor input here determined the level of output, but the capital didn't.
00:59
So what happens if we reduce capital? right.
01:02
I reduce capital to three...