00:01
Okay, so in a stack over competition, one firm chooses its output first and then the other firm chooses its output after observing the leader's decision.
00:10
And the one that chooses first is the firm 1 and the one that chooses the second is the firm 2.
00:16
So, we'll solve for the equilibrium quantities for both farms given the market demand, p equals 100 minus 4 q, and constant marginal cost of 20 for each farm.
00:34
Here q is the total quantity produced by both farms, q1 plus q2.
00:43
Now first thing you want to do is to determine the follower's reduction function, or reaction function.
00:51
So, farm2 will choose q2 to maximize its profit given the output q1 of farm1.
00:58
The profit function for farm2 is pi2 equals 100 minus 4 times q1 plus q2 minus 20 q2.
01:12
Now, now solving for farm 2's profit maximizing output q2 in terms of q1 involves taking the derivative of pi2 with respect to q2, which gives 100 -4q1 -8q2 -20, which we set equal to 0, and we're gonna solve for q2 here.
01:47
Here.
01:49
So q2 is equal to 80 minus 4q1 over 8, or 10 minus 0 .5q1...