00:01
So here we have ap equals l squared minus 200l plus 10 ,000.
00:08
We also have mp equals 3l squared minus 400l plus 10 ,000.
00:15
At the amount of labor input where the firm's average and marginal product of labor are highest and equal, we get ap equals mp.
00:24
I'm going to go ahead and substitute ap is l squared minus 200l plus 10 ,000 equals mp, which is 3l squared minus 400l plus 10 ,000.
00:37
I'm going to go ahead and move everything to the right, and i'm doing this so that my l squared stays positive.
00:43
So i'm going to subtract l squared from both sides.
00:46
I'm going to add 200l to both sides, and i'm going to subtract 10 ,000 from both sides.
00:53
I want to be able to set this equation equal to zero so that we can solve for l.
00:58
L squared minus l squared is 0, negative 200l plus l is, or negative 200 l plus 200 l ,000, plus 200 l, is zero and 10 ,000 minus 10 ,000 is zero.
01:09
On the right hand side i also have at the end here the 10 ,000 minus 10 ,000...