Two Firms Produce a Homogenous Product

Essay

Two firms produce a homogenous product. Let p denote the product's price. The output level of firm 1 is denoted by q₁, and the output level of firm 2 by q₂. The aggregate industry output is denoted by Q with Q = q₁
+q₂. The aggregate industry (inverse)demand is given by p = 10 - Q. The cost functions of the two firms are
c₁(q₁)= 4q₁ and c₂(q₂)= 4q₂.
i)Assume that the firms choose their output levels simultaneously (i.e., we have Cournot competition). What are the equilibrium output levels and profits of each firm in this case?
ii)Suppose that firm 2 finds a cheaper way to produce the same product. The new cost function of firm 2 is c₂(q₂)= q₂. Assuming that the firms choose their output levels simultaneously, find the equilibrium output levels and profits of each firm.