00:01
So here we have a optimization problem.
00:03
And what i want to do is calculate a profit function, right? because profits represent net benefits for the firm, right? we are thinking about our revenues versus our costs.
00:14
That's what we call profits.
00:15
Now, if you want to call that net benefits, it's the same thing, right? so profits are revenues minus costs.
00:23
And we're given some nice functional forms.
00:25
Revenues are 30 ,000 q minus 80 ,000.
00:31
Q squared and costs will be minus 1 ,000 minus 20 q squared, right? so the maximum level, if we think of profits, you can see that profits here are a parabola and profits look something like this.
00:49
We want to find the point where the slope is equal to zero.
00:53
So i want to take the derivative of profits with respect to q to find out where that slope is equal.
01:01
Is equal to zero.
01:03
So this will give me 30 ,000 minus 160 q minus 40 q is equal to zero.
01:13
This gives me 30 ,000 equals to 200 q and that tells me that q is equal to 150, right? so that would be the maximum net benefits for the quantity of research that we're doing, right? b is now a little bit, right? so this is a.
01:40
B is a little bit unclear.
01:43
What is the marginal benefit? i would say that the marginal benefit is equal to the marginal revenue, right? we want to think about how much extra money will bring in when we increase q just a little bit...