The Filthy Chemical Company dumps 100 tons of pollutants every year in the Pristine Lake. The Trout Fishing Co., the only other user of the lake, estimates that if Q) tons of pollution were cleaned up every year its profits would rise according to the relation An = 10 Q - - Q2 Filthy estimates it can clean the pollutants at a constant average cost of $2 per ton. (a) In the interest of efficiency, how much pollution should be cleaned up every year? (b) Suppose Filthy bought the Trout Co. How much would it clean up? What if Trout bought Filthy? (c) State the Coase Theorem. Does your answer to (b) confirm or deny the theorem? Explain briefly