Two polluting utility companies offer power at a regulated price of $3 per unit but have different cost functions. The first company produces a cheaper but more polluting energy at cost TCd=2 - qd+0.5q2d, with emissions ed=2qd. The second company produces a less polluting energy, but at a higher cost, TCc=4 - qc+q2c, with emissions ec=qc. (a) Find the amount of energy and emissions that each firm will produce if left unregulated. (b) If the external cost of pollution is E =12(ed+ec)2(the regulator cannot directly measure each firm's emissions, but can measure total emissions), find the socially optimal amount of output from each firm. (c) Is it possible to find a single emissions fee t that would induce the market to produce at the social optimum?