The marginal private benefit (MPB) for loud parties is 120 − x, where x is the decibel level of the party. The cost of cranking up the stereo another decibel (the marginal private cost) is $20. For each additional decibel, another five neighbors must put in a pair of earplugs, and each pair of earplugs (a negative externality) costs $5. Given this information, answer the following questions.

a. Find the marginal social cost. Is it the same as the marginal private cost? Find the marginal social benefit. Is it the same as the marginal private benefit? Draw MSC and MSB on the graph.
b. In the absence of government intervention, how loud is the party (in decibels)?
c. What is the socially efficient level of noise? Suggest two ways to achieve the socially efficient level of noise.
d. If the government imposed a $10 tax on noise (i. e. a tax where a household pays $10 per decibel), how loud is the party? What if the tax was $20?
e. Find the tax policy that achieves the socially efficient level of noise. (This is the optimal Pigouvian tax.)
f. Instead of imposing tax, suppose the neighbors are given a legal right to peace and quiet, and the police will enforce that right. However, if partiers pay a certain amount, the neighbors will not call the police. What does the Coase theorem suggest will happen? Describe the bargaining process in detail - how loud will the party be, who will pay whom, and provide bounds on the transfer.
g. Suppose that the partiers have the right to be as loud as they want, and the police will not enforce any noise complaints. What does the Coase theorem suggest will happen? Describe the bargaining process in detail. Compare the result with part (f).
h. (Challenging) Go back to the situation in part (f). Suppose the government imposes the Pigouvian tax from (e) on the market described in part (f). What does the Coase theorem suggest will happen? (Hint: Think about the effect of the tax on partiers decision.) Can you achieve the socially efficient level of noise by imposing both the Pigouvian tax and the tradable permit? Explain.