00:01
So here we have a firm that's trying to minimize costs.
00:03
It's hiring a labor and capital.
00:05
So i'm going to call w the wage.
00:07
So it hires l units at w each and then hires k units of capital and pays the rate of rental rate of capital earn.
00:15
So this is total costs.
00:18
But when firms are optimizing, what should they do? well, just like when they're utility maximizing, we can't get these sorts of rules of thumb that say, look, a cost minimizing firm should set the dollars per return from each of the two units equal.
00:36
And we can summarize that as saying the marginal product of labor over the wage has to equal the marginal product of capital over the rental rate of capital, right? and this is sort of saying cost per unit of labor.
00:56
And this is therefore saying cost per unit of labor.
00:57
Say cost per unit of capital, right? so if the average work, if the last worker gives me 10 units and i have to pay them say $30 an hour, i am in some sense getting a, right, a third of a unit per dollar from labor.
01:18
But if the marginal product of capital is 20 and the rental fee on capital is 50, then in some sense i am getting 0 .4 units of output per dollar spent renting capital.
01:33
So now this equation has to balance.
01:35
This is just our simple optimality condition for a cost minimizing firm.
01:39
And we're told that the price of labor is going to go up.
01:44
So the price of labor is going to go up and this thing needs to keep balanced.
01:51
So there's two ways this equation can balance, right? r is not a variable.
01:57
The firm can control, this is an aggregate variable, the rental rate...