00:01
So here we're going to do some simple optimization.
00:03
Benefits are equal to 100 plus 36 q plus 4q squared.
00:11
That means that, oh, we're told the marginal benefit is therefore 36 plus 8q, the power rule derivative.
00:19
The costs are equal to 80 plus 12q, and that means the marginal cost is equal to 12, right? so a net benefits is equal to benefits minus costs, which would be equal to if we group these things together, 20, 100 minus 80, plus 24 q, right, because we've got 36 plus 12, plus 4q squared, right? those are the net benefit.
00:52
Oh, sorry, minus 4q squared, minus 4q squared.
00:56
That's an important catch.
00:57
Minus 4 q squared right we are subtracting the costs from the benefits um we now want to think about so when b the net benefit at q equals to one will be 20 plus 24 minus 4 is equal to 40 the net benefit at q equals to 5 is equal to 20 plus again just plugging in for five, 120 minus 100 is equal to 40.
01:35
Look at that.
01:35
We have the exact same net benefits, right? c, because we've got a quadratic.
01:42
So you know, you're gonna have two cues which correspond to any given level.
01:46
Marginal net benefits is equal to the marginal benefit minus the marginal cost, which is 24 plus eight q, right? that is the marginal net...