00:01
Okay, so the market price is given by the inverse demand function.
00:03
P equals 51 minus 9 times q, q1 plus nqf.
00:12
And profit for a follower is pi -f equals pqf minus a cqf, which is equal to a 51 minus 9, q1 plus nqf, which is equal to a 51 minus 9, q1 plus n qf times qf minus 8 plus 10 qf you can take the derivative or pi f with respect to qf and set it equal to 0 so pi f is equal to negative 9 n times qf plus 51 minus 9 minus 9 x plus 51 minus 9 q1 plus nqf minus 10, set it equal to 0.
01:20
And then you have negative 9 and qf plus 51 minus 9 9 q1 minus 9 and q1 minus 9 and qf.
01:47
So you have a qf, excuse me, negative nqf.
01:52
And qf equals 10, excuse me, negative 41 minus 9 q1 or plus q1, q1, q times, excuse me, 9 times q1.
02:20
And then qf is equal to 41 minus 9 q1 over 18n.
02:27
And then you need to determine the leader's optimal quantity q1.
02:37
So the leader anticipates the followers ' response and chooses q1 to maximize its profit...