00:01
So here we have a bunch of questions about monopoly.
00:03
And remember that the golden rule of monopoly is marginal revenue is equal to marginal cost, right? so for a, we have price is equal to 55 minus q, which means that revenue, which is equal to price times quantity, is equal to 55 minus q times q.
00:23
So marginal revenue, which is the derivative of revenue with respect to quantity, is 55 minus 2.
00:30
2q, right? we are also told that total cost is equal to 5q plus 20.
00:38
So marginal cost, which is the derivative of total cost with respect to quantity, is equal to five, right? so now marginal revenue is equal to marginal cost, 55 minus 2q is equal to 5, q is equal to 25.
00:55
Now you subcue back into the demand function, right? so price is equal to 55 minus q is equal to 30.
01:05
So that would be the profit maximizing price, which is a.
01:09
We move on to b.
01:12
So for b, we are doing something else.
01:16
We have a different demand curve.
01:17
P is equal to 100 minus q over 2, right? so we'll do revenue is equal to price times quantity.
01:25
100 minus q over 2 times q.
01:28
Marginal revenue is then equal to 100 minus q.
01:35
We're again told that total cost is equal to 10 q plus 1 ,500.
01:41
Marginal cost is therefore equal to 10 if q is greater than zero...