00:01
So here we're talking monopoly, right? we have a demand function which is 304 minus q and it says q1 but there's only one q here so i'm just going to call it q.
00:11
We have a cost function of 500.
00:14
Sorry that's not my best little bit of pen drag there.
00:17
500 plus q plus 8q squared if i'm reading this correctly.
00:26
So my idea is first i'm going to reverse this, right? to maximize profit what you do is you set marginal revenue equals to marginal cost.
00:38
So revenue is equal to price times quantity so this would be 304 minus q times q.
00:44
Marginal revenue is therefore 304, stupid pen drag, 304 minus 2q.
00:54
Marginal cost is just the derivative of cost with respect to quantity is equal to 1 plus 16q.
01:02
I want to set these equal.
01:04
I get 304 minus 2q is equal to 1 plus 16q.
01:10
I get 303 is equal to 18q.
01:14
I get q is equal to, appealing to my calculator, 16 .83 and this gives me price equal to 304 minus 16 .83 which is equal to 287 .17, right? and that's the basic idea.
01:42
Monopolist wants a high price to make profits...