The private marginal benefit associated with a product's consumption is PMB = 630 - 6Q, and the private marginal cost associated with its production is PMC = 3Q, where Q is measured in thousands.Further, the marginal external damage associated with this good's production is MD = $45 for every unit.

Use the equations for PMB, PMC, and MD to answer the questions below.

(a) What is the equilibrium market quantity and price?

(b) What is the allocatively efficient quantity in this market?

(c) What is the deadweight loss associated with this externality?

(d) The government decides to impose a tax of TP dollars per-unit produced to correct for the externality. To correct for the externality, the government decides to impose a tax of T dollars per unit sold.