Your neighbor likes to blast 1970's rock music and the louder the better.The loud music imposes a cost on you because it disrupts your study of economics.Let D stand for the volume of his music in decibels,B for his benefits and C for your costs,where B and C are in dollars.For any given volume,D,your neighbor's benefit is and your cost is With an efficient Pigouvian tax,what noise level will your neighbor choose?

Question

Your neighbor likes to blast 1970's rock music and the louder the better.The loud music imposes a cost on you because it disrupts your study of economics.Let D stand for the volume of his music in decibels,B for his benefits and C for your costs,where B and C are in dollars.For any given volume,D,your neighbor's benefit is  and your cost is  With an efficient Pigouvian tax,what noise level will your neighbor choose?

Quizplus · Accepted Answer

In order to determine the optimal level of noise, we need to find the level of noise where the marginal social cost equals the marginal social benefit. The marginal social cost is the cost imposed on you by the neighbor's noise, which is given as C = 10D. The marginal social benefit is the benefit received by the neighbor from listening to music, which is given as B = 11D.

To find the efficient Pigouvian tax, we need to find the difference between the marginal social cost and the private cost (the cost borne by the neighbor). The private cost of playing music is zero, so the Pigouvian tax is equal to the marginal social cost, which is C = 10D.

Now we can set the marginal social benefit equal to the Pigouvian tax:

B = 10D
11D = 10D
D = 0

This implies that there should be no noise at all! But in reality, some level of noise is inevitable. The next best option is to choose the level where the marginal social benefit equals the Pigouvian tax. Plugging in D = 95, we get:

B = 11(95) = 1045
C = 10(95) = 950

So at a noise level of 95 decibels, the neighbor's benefit is $1045 and the cost imposed on you is $950, which are exactly equal. Therefore, the neighbor should choose to play music at a volume of 95 decibels, which is option B.

Your Neighbor Likes to Blast 1970's Rock Music and the Louder