The supply curve for coal is: P=0.5Qand the demand for coal is: P=1000?2Q

a.Find the equilibrium price and quantity of coal traded in this market. Find consumer surplus and producer surplus at this equilibrium.

b. Because coal production pollutes the environment, the government would like no more than 380 units of coal to be produced, so it sets an output quota of 380 units. What price must coal be sold for in order for there to be no surplus or shortage?

c. If the lowest-cost coal producers produce the coal, what is the minimum price would they need to receive in order to be willing to produce 380 units of coal? How much extra money do they earn because of the output quota?

d. If the government instead decides to tax coal in order to limit coal production to 380 units, how big would the tax need to be? What price would buyers pay for coal? What price would sellers receive? How much tax revenue would the government collect?

e. Explain in words why the total welfare from a tax like this may be higher than at the original market outcome. What can the government do with the tax revenue in order to increase welfare more?