00:01
So i'm going to do this question in reverse.
00:03
You see how the second part says identical to the profit maximizing firm, right? so if you are profit maximizing, you are first thinking about profits.
00:12
Profit is equal to revenue minus cost, which is equal to price times quantity minus cost, right? that's the definition of profit.
00:27
So now a profit maximizing firm is thinking about setting the wage equal to the value of the marginal product.
00:39
Right.
00:40
So what is the firm doing here? so we have to put some more structure here, right? the price is how much the firm gets per unit.
00:49
The quantity that the firm produces is usually thought of as a function of capital and labor.
00:56
Right this is is simply you know what the firm is is producing so it uses capital and labor to produce output that's sometimes called the production function the cost is my w times my labor my cost of capital is the rental rate of capital times the amount of capital so now i want to take the first order conditions like usual i want to and you know first order conditions say keep doing something as long as the change increases profit.
01:31
So if i take the derivative of profit with respect to labor, i get price times the derivative in q with respect to labor minus w is equal to zero, right? we are setting this equal because if we think of profit over the choice of workers, we want to set the slope equal to zero, right? you should keep hiring hiring more workers, hiring more workers, until the workers no longer contribute to profit, until the slope of profit with respect to workers is equal to zero, right? that's the traditional first order condition logic.
02:12
This here is equal to the price times the marginal product of labor, right? this is equal to this...