CFAI text Vol 2, in the middle on P. 174
It stated : Because q2 = q1 under Cournot’s assumption… .
Is this the necessary assumption for a two-firm duopoly market in which : q2 + q1 = Q(D)?
Q(D) : Total quantity of market demand.
If both firms face the same cost and the same demand curve then yes q2 = q1.
And for cournot q1+q2 will always be Q(D). Just think that both firms will produce a total output that fully satisfies the demand.
In a duopoly it is not necessary that the two firms have the same market share; that’s a consequence on an assumption that Cournot made to symplify the analysis: that the firms have the same cost structure. With the same cost structure, if firm A is producing more than firm B, firm B’s marginal cost is less than firm A’s, so firm B can reduce its price and increase its market share. The equilibrium point is that A and B will each have 50% of the market.
If the cost structures aren’t the same, then the equilibrium point won’t be a 50/50 split: the firm with the lower costs will have a higher market share. But we cannot say exactly what share of the market each firm will have unless we know a lot more details about their cost structures; therefore, the important conclusion that the firms will gravitate to an equilibrium market division is obscured by unimportant details. Cournot’s assumption frees the analysis from these unnecessary complications. (Later, one can relax the assumption and see what effects that has on the conclusions, an analysis made easier by first having a solid understanding of the simplified model.)
S2000magicain & eho70 :
Thank you for your responses !
My pleasure.