Re: Finding equilibrium price and quantity

Posted by Algaeconomics on Jun 12, 2017; 3:27am
URL: http://discussion-forum.276.s1.nabble.com/Finding-equilibrium-price-and-quantity-tp7605383p7605393.html

(a) Profit fn = (a-Q)*Q

Maximising we get a-2Q=0 or Q= a/2

Now P= a-Q = a-a/2= a/2

Therefore, if a>2000 then Q= 1000 and P= a-1000
                  a< 2000 then Q= a/2 and P= a/2

(b) Profit fn for firm 1= (a-Q)*q1
                              = (a- (q1+q2+...+q10))q1
           Maximizing we get
                                      (a-(q2+q3+..+q4))/2 = q1

Now by symmetry all the best response functions look the same so

 solving for q==q1=q2=...=q10
we get (a-9q)/2=q
or a=11q
or q= a/11
and p=(a-10*q)
= a-10/11a
= a/11

and since a>= 1100
q>= 1100/11 = 100
so they can and will sell q=100 and p= 100

(c) p= MC = 0
therefore a-Q=0
or Q=a