What marginal tax per decibel emitted does government

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Reference no: EM131160496

A factory and an amusement park are both located next to a residential neighborhood, creating a noise problem that the local government is considering regulating. The amusement park’s total cost function for reducing the noise level by D decibels is TCa = (4/3)D2 . The factory’s total cost function for noise reduction is TCf = 4D2 . The social marginal benefit of noise reduction is SMB = 40 – 2D. a. What is the socially optimal level D* of total noise reduction? Find the amount of noise reduction done by the factory (Df* ) and by the amusement park (Da*) at the optimal outcome. b. How much noise reduction (Df’) will the factory undertake in the absence of any intervention? How much noise reduction (Da’) will the amusement park undertake? c. The government decides to mandate that each firm reduce noise by ½D*. Indicate clearly on a diagram all DWL in the presence of this regulation. Calculate the amount of deadweight loss there is under this regulatory regime. Is society better or worse off than with no regulation at all? 2 d. The government decides to mandate that each firm reduce noise by ½D*, but then allows the firms to trade noise reduction as long as the total amount of noise reduction remains at D*. Which firm will pay the other to do more noise reduction than ½ D*? Why? e. Now imagine that the government knows the marginal costs of noise reduction with certainty, but does not know the marginal damage of noise (i.e., the social marginal benefit of noise reduction) with certainty. The true SMB of reducing noise is 40 – 2D, as in the rest of this problem, but the government’s best guess is that the marginal damage of one decibel of noise is constant and equal to 8. The government decides to address the externality problem with a tax per unit of noise, rather than regulation. What marginal tax per decibel emitted does the government choose, and why? How much do the factories reduce noise when faced with this tax? f. Indicate clearly on a diagram all DWL in the presence of the tax regime in e).

Reference no: EM131160496

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