13. The loud music coming from the sorority next to your dorm is a negative externality that can be directly quantified. The following table shows the marginal social benefit and the marginal social cost per decibel (dB, a measure of volume) of music.
| Volume of music (dB) |
Marginal social benefit of dB |
Marginal social cost of dB |
| 90 | ||
| $36 | $0 | |
| 91 | ||
| 30 | 2 | |
| 92 | ||
| 24 | 4 | |
| 93 | ||
| 18 | 6 | |
| 94 | ||
| 12 | 8 | |
| 95 | ||
| 6 | 10 | |
| 96 | ||
| 0 | 12 | |
| 97 |
Draw the marginal social benefit curve and the marginal social cost curve. Use your diagram to determine the socially optimal volume of music.
Only the members of the sorority benefit from the music, and they bear none of the cost. Which volume of music will they choose?
The college imposes a Pigouvian tax of $3 per decibel of music played. From your diagram, determine the volume of music the sorority will now choose.