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

P = 12 3QD

P = 2 + 2QS

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

P + T = 12 3QD

Solve for the new equilibrium. Solve for the price received by sellers, the price paid by buyers, and the quantity sold after the tax T is imposed.

c. Tax revenue is TQ. Use your answer to part (b) to solve for tax revenue as a function of T. Graph this relationship for T between $0 and $10.

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 baseheight, solve for deadweight loss as a function of T. Graph this relationship for T between $0 and $10.

e. The government now levies a tax on this good of $8 per unit. Is this a good policy? Why or why not? Can you propose a better policy? (Hint: Propose a different tax that incurs lower deadweight loss, but raises tax revenue.)

f. Assume that T=$5. What is the loss of consumer surplus associated with some buyers dropping out of the market as a result of the tax?What is the loss of producer surplus for those sellers of the good who continue to sell it after the tax is imposed?