Suppose that the demand equation: P = 12 - Q and supply equation: P =2 Q.

a. Calculate the equilibrium price and quantity.

b. Calculate the consumer surplus, producer surplus and total surplus at equilibrium.
c. Suppose the government imposes a tax of $3 for each unit bought. Derive the new price that consumers pay, the price that firms receive, and quantity.

d. Calculate the deadweight loss of this tax.

e. In a diagram, show the equilibrium in part a and the equilibrium in part c; and the areas that you computed in part b and d.