A competitive firm's short run total cost function is given by _ 3 2 TCq 16q +100q+120 (a) Calculate the profit maximizing output and the resulting profit when price is $30. (b) Calculate the profit maximizing output and the resulting profit when price is $80. 2. In a perfectly competitive industry each producer has a long run total cost function given by LTC= q3 24q2 +200q where q denotes the output of the individual firm. The market demand for the product is Q = 1480 SP where Q and P denote the market output and price respectively. (a) Calculate the optimal output produced by each firm at the long run competitive equilibrium (LRCE). (b) Calculate the market price and market output at the LRCE. (c) Calculate the number of firms at the LRCE. 3. A monopolist produces a product in one central production facility using the cost structure: TC = and sells it in two different markets with the following 20 Q + 90 demand functions: Market 1: |\"1 = 50 501 Market 2: , P2 = 100 1002 where o=01+02