00:01
So here we have an optimization problem, right? we know that the price is equal to 20.
00:05
We know that the cost function is equal to 200 plus 2q squared.
00:11
So what i want to do is set up a profit function and profit in general is equal to revenue, price times quantity minus costs.
00:19
Here, the price is 20 because we're operating in a perfectly competitive industry.
00:23
We get q as the number of units we produce, minus 200 fixed cost, minus.
00:30
Is two q squared variable costs.
00:33
I'm now going to take the derivative of profit with respect to quantity, right? the whole idea is that profit is the quadratic here.
00:40
It's got that squared term.
00:42
And i want to find where the slope is equal to zero to get the maximum, right? so a derivative of profit with respect to quantity is 20.
00:50
The 200 drops out.
00:51
That's my fixed cost.
00:52
It doesn't matter.
00:53
I get 4q...