Re: economics question

Posted by Anviksha on May 30, 2015; 5:41am
URL: http://discussion-forum.276.s1.nabble.com/economics-question-tp7597253p7597254.html

1..
P= 100-Q
i th firm maximizes its profit given others quantity.
πi = qi(1000-Q)
   =1000qi-Qqi
   = 1000qi-qi(qi+summation qi but not i )
    = 1000qi-qi^2-qi( summ other qi)
First order condition:
1000-2qi- summ other qi=0
Since production cost is zero and same for all.. Each firm priduces same quantity in equilibrium..(symmetric firms).
And in equilibrium foc is also satisfied.
Thus all qi* are same..
Using this in foc: 1000-2qi-3qi=0
Thys, 5qi=1000 and qi*= 200
Q= 4x200 = 800
Hence P = 1000-800= 200