3. The total benefit (measured in dollars) that a musician gets from making music is Bm = 25 ln D, where D denotes the decibels involved. A sleeper lives next door. The total benefit that she gets is Bs = 20 ln (20 − D), where 20 is the loudest sound technically possible.

a. Find the level of sound that maximizes total benefits for musician and sleeper.

b. Suppose no ordinance about noise exists. What will happen if the two can bargain freely? Is this efficient?

c. The city adopts an ordinance forbidding noise levels above 5 decibels.

Being drawn and quartered is the penalty for violating the ordinance, but the city has hired no one to enforce the ordinance. It will respond only to complaints.What will happen? Is this efficient?

d. The city revises the ordinance. The penalty for violating the ordinance is now $1 for each decibel over 5. Enforcement is by inspectors who are perfectly effective, omnipresent, and absolutely incorruptible. Complaints have no standing—the ordinance will be enforced whether or not the neighbors complain. What will happen? Will this be efficient? How does this compare with the situation in part c? If you were on the city council, would you support the revised ordinance?