Consider the Cournot model with n firms. The inverse linear market demand function is = a

Consider the Cournot model with n firms. The inverse linear market demand function is ρ = a – bQ. Each of the n identical firms has the same cost function C(q_i) = Aq_i + 1/2 Bq_i², where a > A. In terms of n, what is each firm’s Nash equilibrium output and profit and the equilibrium price? As n gets very large (approaches infinity), does each firm’s equilibrium profit approach zero? Why?