00:01
For part a, we have to maximize profit revenue with the constant of selling only 400 tickets.
00:15
So, we need to determine the optional allocation of tickets between the two market segments.
00:22
So, market segment 1 is for regular adults.
00:40
So, demand is set to be p1 which is 600 minus q1.
00:49
And then market segment 2 is for students and senior citizens.
01:15
So, the demand is denoted as p2 which is 400 minus q2.
01:25
Then total ticket constants here is q1 plus q2 which is equal to 400.
01:44
So, we have to find the profit maximizing allocation.
01:49
So, we need to equate the marginal revenue to 0 in each market segment.
01:55
Then market segment 1 mr1 is equal to 600 minus 2qi equal to 0.
02:14
Then the value of 2qi is equal to 600.
02:19
So, q1 will be 300.
02:23
Further for market segment 2 mr2 is equal to 400 minus 2q2 which is equal to 0.
02:46
Then 2q2 is equal to 400.
02:51
The value of q2 then is 200.
02:55
So, we can say that the optimal ticket allocation is 300 tickets in segment 1 and 200 tickets in segment 2.
03:04
So, now determining the price.
03:06
So, for market segment 1 price p1 is equal to 600 minus q1.
03:21
So, putting in the value 600 minus 300 we get it as 300.
03:28
And for market segment 2 price p2 is evaluated as 400 minus q2.
03:42
Putting in the values 400 minus 200 we get it as 200.
03:49
So, we can say that therefore the optimal price in segment 1 is 300 dollars and in segment 2 it is 200 dollars.
04:28
Now for part b firstly we will evaluate the revenue maximizing quantity and price in market p1.
04:40
So, over here demand in market 1 is p1 is equal to 360 minus q1.
04:56
So, evaluating mr1 as 360 minus 2q1 which is equal to 0.
05:05
Then 2q1 is equal to 360.
05:08
Q1 then will be 180.
05:12
Now price is evaluated as p1 is equal to 360 minus q1.
05:19
Putting in the values 360 minus 180 we get it as 180.
05:26
So, we can say over here that the revenue maximizing quantity in market 1 is 180 units and the price is 180 dollars...