Consider the market for Widgets:

The demand for widgets is given by: QD=1300-10P

Supply of widgets is given by: QS=2P-20

Production of widgets causes an externality with marginal damage given by: MD=(0.6)Q

(Hint: Convert the demand and supply functions into PMB and PMC functions. Include a graph to show the intuition behind your equations.)

1. Calculate the free market equilibrium price and quantity for widgets.
2. Graphically illustrate total surplus. Calculate the total surplus and total welfare (total surplus less negative externality) at the free market equilibrium price and output.
3. Calculate the socially quantity for widgets.
4. Calculate the per-unit Pigouvian tax which leads to the socially optimal quantity.
5. Calculate total revenue generated by the Pigouvian tax.