00:01
Alright, so to find our maximizing prices and outputs, we need to find our marginal revenue for each.
00:06
This is found by taking the derivative of the total revenue with respect to the quantity.
00:13
So, taking our derivative for our first segment is going to be 500 minus 6p1.
00:24
And for our mr2, we're going to get 800 minus 8p2.
00:30
Then we want to set these equal to the marginal cost of 50.
00:34
So, we're going to get 500 minus 6p1 is equal to 50, which is going to give us that p1 is equal to 75.
00:45
And then we're going to set 800 minus 8p2 equal to 50 to get that p2 is equal to 93 .75.
00:55
Then we can substitute these back into our demand equation.
01:00
And we're going to get that our q1 is 275 and our q2 is 225.
01:09
Our firm's profit then, if we use our formula, is going to be 75 times 275 plus 93 .75 times 225, which is equal to $16 ,875.
01:30
Then for b, if we're forced to charge the same price, we need to find the price that maximizes the total profit...