00:01
So let's go over this question.
00:13
We're given demand as price is equal to 120 minus 0 .25 times q.
00:21
Marginal cost is equal to 2q plus 5.
00:27
The marginal cost needs to have a positive slope, so therefore there's a typo in the question.
00:36
So we have demand, marginal revenue, and marginal cost.
00:47
So our profit maximizing quantity is where marginal cost is equal to marginal revenue.
00:56
And then we draw a line up to the demand curve.
01:00
And this is our consumer surplus, this is our producer surplus, and then this is our deadweight loss.
01:08
So now to calculate this, first of all, we need to find total revenue, that's price times quantity.
01:17
So plug in the price based off of the demand.
01:28
And then we find marginal revenue, which is going to be the derivative.
01:36
So then we're going to set marginal revenue equal to marginal cost.
01:48
Then we're going to solve for q.
02:10
So we have 46.
02:13
So then we're going to plug the quantity back into the demand function.
02:20
And then we need to find the price.
02:39
And then we're going to set quantity equal to 0 so that we can figure out where the demand curve crosses the vertical axis.
02:51
So we see that from marginal cost, it's going to cross the vertical axis at 5.
03:14
And then what we need to do is we need to plug the quantity back into marginal revenue or marginal cost.
03:39
So now we can find consumer and producer surplus.
03:44
So we find the area of the triangle.
03:47
Then for producer surplus, find the area of the top rectangle.
04:30
And then find the area of the bottom triangle.
04:47
Now add these two together...