Consider a scenario where you work for a firm (B) that has only one competitor firm (C) in the market. Firm C is identical to firm B. Let qb = Firm B's output, and qb + qc = Q. Assume a production cost function of TC = 8Q2 + 5 and a market demand function of P = 100 - 2Q.
1. If firm B's reaction is qb = 5 - 0.8qb, then what is firm C's reaction function?
2. How many units of output should each firm produce to maximize profit?