Buchanan Industries receives profits from polluting according to the formula Profits = = 10Q - Q2,

Question:

Buchanan Industries receives profits from polluting according to the formula Profits = π = 10Q - Q2, where Q = pollution emitted (in tons), and profits are measured in dollars. Marginal benefits (MB) of polluting, derived from this function, are MB = 10 - 2Q. The damages associated with pollution from this facility are estimated as Damages = D = Q2 + 2Q, where damages are measured in dollars. The marginal damages (costs) associated with that function are MD = 2Q + 2.
(a) Draw a graph with the marginal benefits and marginal damage curves. Be sure to label the axes.
(b) If Buchanan Industries could ignore the damages it caused, how much Q would it produce? How much profit would it earn at this level of production? How much would total damages be? What would be the net benefits, the difference between profits and damages?
(c) What is the efficient Q for this industry? How much profit would Buchanan Industries earn at this level of production? How much would total damages be? What would be the net benefits, the difference between profits and damages?
(d) Deadweight loss is the difference between the net benefits with the efficient level of pollution and net benefits with another level of pollution. What is the deadweight loss associated with Buchanan Industries ignoring damages that its production causes? Show the deadweight loss on your diagram. If Buchanan Industries would not on its own produce at the efficient Q, is it acting contrary to its own best interests by producing at the level in (c)?
(e) Those who live near Buchanan Industries propose that Buchanan Industries produce no more than Q = 1. What is the deadweight loss associated with this level of production? If Q = 1 is an inefficient level of production, are those who live near the factory acting contrary to their own best interests by pushing for Q = 1?
(f) Who benefits from reducing Q from the initial level in (a) to the efficient level in (b)? Who bears the costs? Is this change Pareto improving?