00:01
Hi, in this question we are given with the firm that has the total cost function that is equals to 1 by 3 qq minus 7 q squared plus 111 q plus 50.
00:16
Also we are given with the demand function q that is equals to 100 minus.
00:22
For the first part, we need to check does the total cost function satisfy the coefficient restriction for acd is greater than 0, b is less than 0 and b squared is less than 3a c.
00:37
Now here if we can see a is equals to 1 by 3 which is greater than 0, b is equals to minus 7 which is less than 0, c is equals to 1111 which is greater than 0.
00:49
D is equals to 50 which is greater than 0.
00:53
So from here we can see that a, c, d are greater than 0, b is less than 0.
01:02
Checking for b square that is equals to minus 7 square and this will be equals to 49 and it should be less than 3 times a which is 1 by 3 times c which is 1111.
01:15
This and this will get cancel and we get this to be equals to 49 less than 111...