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.What is the efficient Pigouvian tax?

Question

Quizplus · Accepted Answer

The efficient Pigouvian tax is calculated as the marginal external cost at the optimal level of the activity. Here, the marginal external cost is the difference between the marginal cost (MC) to you and the marginal benefit (MB) to your neighbor for each additional decibel of music. The marginal cost to you is the derivative of C with respect to D, which is MC = 0.06 + 0.002D. The marginal benefit to your neighbor is the derivative of B with respect to D, which is MB = 0.63 - 0.004D. The Pigouvian tax should be set equal to the marginal external cost, which is MC - MB = (0.06 + 0.002D) - (0.63 - 0.004D) = 0.06 + 0.002D - 0.63 + 0.004D = 0.006D - 0.57. However, without the specific value of D to calculate the exact tax per decibel, we look for the conceptual answer, which involves setting the tax equal to the difference in marginal benefits and costs. The correct calculation involves recognizing that the tax equals the difference in the coefficients of D in the marginal benefit and marginal cost equations, which is $0.006. This discrepancy suggests a mistake in the calculation process provided, as the correct approach is to equate the marginal external cost directly, which typically involves the difference in derivatives of the cost and benefit functions. Given the options, the closest to the conceptual explanation provided is $0.25 per decibel, acknowledging an error in the detailed calculation process.

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