Leslie Knope at the Parks and Recreation Department of Pawnee is considering whether to impose subsidies or quantity restrictions to curb the noise pollution of their environ- ment. The subsidies, {1:5, r3) , would be Pigouvian subsidy on the marginal unit of noise reduction that each club emits. The quantity restriction, (2'5, 25) , would be a lower bound on the amount of noise reduction for each club. For example, the Snakehole Lounge must reduce noise pollution by at least is. d. What is the optimal Pigouvian subside on the Snakehole Lounge, 1:5, and the Bulge, T3, to achieve the social optimum? Underline your answer. Hint: With subsidy, the Snakehole Lounge solves maximizes 1523 c, (as) . {4 points} e. What is the optimal quantity restriction on the Snakehole Lounge, 25, and the Bulge, 23, to achieve the social optimum? Underline your answer. (4 points} f. Do optimal Pigouvian tax policies achieve the same noise reduction as the optimal quantity restrictions in this setting? Please explain why in one sentence. (6 points) Suppose Leslie Knope knows that one of the clubs has cost $22 and the other has $22, but she does not know which club has the high cost and which one has the low cost. Hence, she can only impose the same Pigouvian tax, r5 2 TB, and quantity restriction, 25=ZB=%(-l-%). g. Are Pigouvian taxes equivalent to quantity restrictions in this case? Which policy is preferred? Please show your work. (6 points}