00:01
So here we've got the idea of production equilibrium and production costs.
00:05
We're given a production function, y is equal to 1 .5, k to the 0 .3, l to the 0 .7, so classic cobb douglas style.
00:15
We're told that k is 343 and that l is equal to 512.
00:19
Now, in equilibrium, the whole point here is that firms will set the marginal product of capital equal to the rental rate and the marginal product of labor equal to the wage, right? you hire capital up until the return on capital is equal to the rate, and you hire labor up until the point at which those things are equal, right? because if you got $20 of value out of a unit of labor, which costs you 16, you're leaving $14 on the table by not hiring the extra person.
00:48
So we need to take the marginal products.
00:51
Well, those are just the derivatives of y with respect to the factors.
00:55
So when we take the derivative with respect to k, we get the marginal product of capital, which looks like 0 .45k to the minus 0 .7, l to the 0 .7...