00:01
So here marginal revenue is the derivative of revenue with respect to quantity, which we sometimes proxy as the change in revenue with respect to quantity.
00:10
And revenue, of course, is just price times quantity.
00:15
So for each of these, all we need to do is construct a revenue function, price times quantity, substitute in for your price.
00:23
Here we have 100 minus 2q to the half times q.
00:28
Now take the derivative, right? and the derivative here is gonna be relying on the product rule and the chain rule.
00:35
So the one half power comes down, the interior is unchanged, that's your power rule.
00:43
Now your chain rule gives you this minus two, the other half is still unchanged.
00:47
Now we take the derivative of the other half, right? i'm taking the derivative of each side in turn with the power rule, and i simply get 100 minus 2q to the half.
00:58
There would be my marginal revenue curve...