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...

Extracted text: 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, Q = q1 + q2. The aggregate industry demand curve for this product is given by p = 200 – Q. a. Assuming that firms are homogeneous with cost function C(qi) = 2qi, derive the best response function for each firm. Show that Cournot-Nash equilibrium output for each firm is symmetric. Find the Cournot-Nash equilibrium aggregate output and price. Verify that given similar cost functions, equilibrium profits for each firm is symmetric as well.