Suppose the market demand function is Qd = 6I − 1.2P2 − 0.4P where I is income in $1,000. At what price is demand unit elastic if I = $57,000? A competitive firm has the following quadratic cost function: TC = aQ2 + bQ + 100 Determine a and b if the following two conditions are satisfied: I. When the market price is 60, the profit maximizing level of output is 15. II. When the market price is 40, the break-even level of output is 10.