00:01
So here, the firm is trying to maximize profit.
00:03
So we need to write a profit function.
00:06
And a profit function is revenue, what you bring in minus cost, what you spend.
00:11
But revenue is always price times quantity.
00:14
Cost is just total cost.
00:16
We know the price, and we also know the total cost function, right? so i just need to plug those two things in.
00:25
Now what i do is i take a derivative with respect to q and i want to set it equal to zero.
00:31
Right if you think of say the profit function looking like this i'm looking for the point where the slope is equal to zero right because where the slope is equal to zero tells me where the maximum of the function is so my derivative here is 10 minus 2 minus 0 .2 q i set that equal to 0 i get 8 is equal to 0 .2q.
00:56
That gives me q is equal to 400.
00:59
So that would be the profit maximizing level with the corresponding price, right, and so the price is 10...