|
it is like a generalisation to cournot duopoly model..with n firms.You can take the case of 2 firms..with homogeneous cost function (as given in this question)
let there be 2 firms.market demand ; p=a-bq and each faces a cost function c=cq
solving for profit maximisation of both the firms we get
q1=q2=(a-c)/b(n+1) that is q1=q2=(a-c)/2b ( as here n=2)
so if there are 4 firms and cost function is homogeneous then q1=q2=q3=q4 = (a-c)/(n+1)b
that is q1=q2=q2=q4= (100-40)/5= 12 (as a=100 c=MC=40 and b=1)
total output =q= 4*12= 48
price=100-48=52
|