Problem 2. Basketball Production Balding is a Basketball producing firm that has seen better days. Its technology is old and expensive. Total costs of the old basketball-producing technology are given by = 50 + 2 + 0.52, where Q is balls produced per hour. The Balding managers are thinking about investment in a new technology. Total costs would then be given by: = 100 + 0.12 Balding is producing for the low-quality end of the market, and its basketballs are undifferentiated. The typical price for a ball is $10, and you may take this as given. a) Under the old technology, what is the profit-maximizing output of Balding? What are profits at this output? 2 b) If Balding cannot avoid paying the fixed cost of the old technology, should it continue to produce basketballs? c) If Balding operated only the new technology, what would be the optimal output, and what would be its profits? d) If Balding cannot avoid paying the fixed costs for the old plant (e.g., you can think of these as payments to the bank for the original loan for the old plant), should it still build the new plant? If so, what would be the optimal total output and total profits? [Note: check whether, after building the new plant, Balding would still want to produce in the old plant].