Question

Suppose that a market is described by the following supply and demand equations:

QS= 2P

QD = 300P

a. Solve for the equilibrium price and the equilibrium quantity.

b. Suppose that a tax of T is placed on buyers so the new demand equation is QD = 300 (PT). Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold?

c. Tax revenue is T×Q. Use your answer to part (b) to solve for tax revenue as a function of T. 
d. The deadweight loss of a tax is the area of the triangle between the supply and demand curves. Recalling that the area of a triangle is , solve for deadweight loss as a function of T. 

(Hint: Looking sideways, the base of the deadweight loss triangle is T, and the height is the difference between the quantity sold with the tax and the quantity sold without the tax.)