00:01
So here we are thinking about the production, right? at the production.
00:04
So we have a production function q is equal to 2 l to the 0 .5 k to the 0 .5.
00:11
For part a we want the marginal products.
00:14
So the marginal product of labor is dq dl, and this is equal to therefore l to the minus 0 .5 k to the 0 .5.
00:25
Now we need to evaluate this at the optimum, right? so if we plug in our numbers here for 100 workers and 25 units of capital, we get a hundred to the minus 0 .5, 25 to the 0 .5, that's equal to five over 10 is equal to 0 .5.
00:43
And that would be the marginal productivity of labor.
00:46
Now the marginal product of capital is the derivative with respect to k.
00:51
This gives us l to the 0 .5 k to the 0 .5 in general.
00:58
But if we plug in the numbers, we again get a hundred to the 0 .5 oops, missed my negative sign, divided by, or sorry, multiplied by 25 to the negative 0 .5.
01:11
So that would be 10 over five is equal to two.
01:15
Great...