Two students live next door to each other. One likes to play loud music. The other likes her space to be quiet. Each person has $100 in a piggy bank, and then gets additional total benefits depending on how much music is played (see table below). Total wealth is the sum of the two amounts.

 

Amount of music (hours)	0	1	2	3
Music player's extra total benefit	$0	$30	$50	$60
Neighbor's extra total benefit	$35	$30	$20	$0

 

a. What is the efficient amount of music to be played?

b. If the music player has the right to play as much music as she wants, how much will she play without negotiating?

c. What is the maximum amount of money the neighbor would be willing to pay the music player to get to the efficient outcome?

d. What is the smallest amount of money the music player would accept to agree to the efficient outcome?

a. The music must be played as long as the marginal benefit is greater than the marginal cost. Thus, the efficient amount of music is 2.

b. She would play the music as long as the marginal benefit of playing is positive (i.e., the total benefit is increasing). So, she will play 3 music if she has the right for playing that

c. The maximum amount of money the neighbor would be willing to pay the music player to get to the efficient outcome is $20. This is because if the player plays 3 music, the neighbor gets $0 benefit. Any number between $10 to $20 will induce the player to play 2 music (i.e, the efficient level). By paying $20 the net benefit to the neighbor remains unchanged at $0. Any value less the $20 is in favor of the neighbor.

d. The smallest amount of money the music player would accept to agree to the efficient outcome is $10. Because without any agreement she will play 3 music as get $60 benefits. At the efficient level, she gets $50 benefit. Thus, she is willing to receive at least $10 to play 2 music.