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 marginal cost to you at the socially efficient noise level?

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Quizplus · Accepted Answer

To find the marginal cost (MC) at the socially efficient noise level, we first need to determine the socially efficient level of noise. This is where the marginal benefit (MB) equals the marginal cost (MC). The marginal benefit to your neighbor from the music is the derivative of B with respect to D, and the marginal cost to you is the derivative of C with respect to D.Given B = 0.63D - 0.002D^2 and C = 0.06D + 0.001D^2, let's find the derivatives:MB = dB/dD = 0.63 - 0.004DMC = dC/dD = 0.06 + 0.002DSetting MB = MC to find the socially efficient level of D:0.63 - 0.004D = 0.06 + 0.002D0.57 = 0.006DD = 95 decibelsNow, plug D = 95 back into the MC equation to find the marginal cost at this level:MC = 0.06 + 0.002(95) = 0.06 + 0.19 = $0.25.

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