This was a tough one. College Board, "You bastards"
2004 AP Micro FRQ#1
Answer from the college board
As MSC > than MPC, the externality is a negative production externality.
At a quantity of Q2, MSB = MSC at a price of $12.
The government can incentivise the monopolist to produce more by providing a subsidy. A subsidy should be provided to the point where the monopolists MC (MPC) curve will be reduced until it intersects with the MR (MPB) curve at Q2 (social optimal quantity)
A Perfectly competitive firm would produce an overproduction of a negative production externality. Its market price is where MPC = MPB and this is at the price of $7 and at a quantity of Q3. To get the perfectly competitive firm to produce less a per-unit tax must be levied against the (industry). As the firm has no control over price (price-takers) the industry must have the tax imposed upon it. At a tax of $5 the price would rise to $12 and the quantity would be reduced to Q2. Or what I believe to be the socially optimal quantity and price.
Students were asking why the government would subsidise a monopoly to create more negative goods,,, I believe the answer is to recognise that even a negative production externality has a benefit to society. Pollution might be the problem,, but no pollution means no production and this would be much worse than the externality. So government recognises that there is a benefit in the production of the good.
Understand that the marginal benefit should equal the marginal cost. (MB = MC) or the MSC = MSB.
We could spend trillions of dollars to clean all of the rivers and lakes but then the MSC > MSB. Society would have pristinely clean rivers but not much of anything else.
Thank you Michelle for bringing this to my attention,,
Such fun I've had today,, trying to figure this out.