Suppose that the supply curve (private marginal cost) for a manufactured good is given bys=1/2and that the demand for the product is given byd= 14 . Environmental damage is represented by the functionMD= 1+Q.

a) What is the optimal Pigouvian tax to address the externality?

b)After the tax is imposed, what are the levels of CS, PS, environmental damage, and tax revenue?

c) In a sentence or two explain why the Pigouvian tax in this case depends on knowing both PMC and demand. If total damages are linear, do we still need to know PMC and demand in order to set the optimal tax? Explain why or why not.