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 measured in dollars.For any given volume,D,your neighbor's benefit is B = 0.63D - 0.002D² and your cost is C = 0.06D + 0.001D².With an efficient Pigouvian tax,how much will your neighbor pay in noise taxes?

Question

Quizplus · Accepted Answer

To find the efficient Pigouvian tax, we need to equate the marginal social cost (MSC) to the marginal social benefit (MSB). The MSC is the derivative of the cost function, and the MSB is the derivative of the benefit function. The cost function is C = 0.06D + 0.001D^2, and the benefit function is B = 0.63D - 0.002D^2. Taking derivatives gives us the marginal cost (MC) = 0.06 + 0.002D and the marginal benefit (MB) = 0.63 - 0.004D. Setting MC = MB to find the efficient level of D, we get 0.06 + 0.002D = 0.63 - 0.004D, which simplifies to 0.006D = 0.57. Solving for D gives D = 95 decibels. The tax per unit of D should be equal to the marginal external cost at the efficient level of D, which is the difference between the marginal cost and the marginal benefit at D = 95. Plugging D = 95 into the MC formula gives MC = 0.06 + 0.002(95) = 0.25. The tax is the difference between the MC and the benefit at this level, but since we're looking for the total tax paid, we calculate the total external cost at the efficient level, which is the cost function at D = 95: C = 0.06(95) + 0.001(95)^2 = 5.7 + 9.025 = 14.725. However, the correct approach to find the tax is to calculate the marginal external cost at the efficient quantity and multiply by the quantity. The calculation provided does not directly lead to the correct answer due to a misunderstanding in the application of the Pigouvian tax principle. The correct approach involves setting the marginal benefit equal to the marginal cost and then calculating the tax based on the difference between the social and private costs or benefits at the margin, not the total cost.

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