0:00
Hi there.
00:01
In the question is given that the demand equation for the product is q is equal to 3 ,600 minus 3p square where p is the unit price and we have to find price intervals where demand is elastic and inelastic and the price resulting to the maximum revenue and at last the maximum revenue.
00:18
Let's see how we'll do it.
00:21
First we'll find the price intervals in which the demand is elastic and inelastic.
00:28
Demand is elastic if e of p is greater than one and demand is inelastic.
00:32
If e of p less than 1 and e of p is equal to negative p divided by q multiplied by dq over d.
00:45
So here q is equal to 3 ,600 minus 3p square.
00:49
So we'll be having dq over dp is equal to d over dp of 3 ,600 minus 3p square and that is equal to 0 minus 2 in 2 multiple.
01:04
Multiplied by 3p and that is equal to negative 6p.
01:11
So e of p is equal to negative p divided by q multiplied by dq over dp.
01:19
And that is equal to negative p divided by q.
01:23
In place of q we can write 3 ,600 minus 3p square multiplied by negative 6p.
01:34
And that will result into 6p square divided by 3 ,600 minus 3p square.
01:41
So we got the e of p.
01:44
Now demand is elastic if e of p is greater than 1.
01:50
So we'll be getting the inequality that e of p greater than 1 implies 6p squared divided by 3 ,600 minus 3p square is greater than 1.
02:02
And that implies 6p square is greater than 3 ,600 minus 3p square.
02:10
And that again implies 9p square is greater than 3 ,600.
02:17
And that implies p square greater than 400 and which implies p p is greater than 20 or p is less than negative 20.
02:31
So here, since we are dealing with unit price, we'll go with p.
02:34
Greater than 20.
02:35
So the interval will be, the interval will be p should belong to the interval 20 infinity.
02:49
So demand is elastic in price interval 20 infinity.
02:55
Now demand is inelastic if e of p is less than one.
02:59
That is we'll be getting 6p squared divided by 3 ,600 minus 3 p square is less than one.
03:07
And that implies 6p square less than 3 ,600 minus 3p square.
03:13
And that implies 9p square less than 3 ,600.
03:18
And again, implies p square less than 400...
