There are two identical firms in the industry which set

Question

Consider the following Cournot oligopoly:

• There are two identical firms in the industry, which set their quantities produced simultaneously.
• The two firms face a market demand curve, Q = 120 - P, in which Q = q1 + q2.
• Each firm's cost function is ci(qi) = qi2.
• Each firm acts to maximize its own profit.

1. Write down each firm's profit function.
2. From the profit functions, derive a best response rule for each player.
3. From the best response rules, find the Nash Equilibrium in this market.