Suppose that Cook County decided to introduce a temporary $0.42 tax per gallon of gasoline to discourage unnecessary travel. The economic advisers to the county estimate the demand and supply curves for gasoline as:QD=200100PandQS=8+20Pwhere Q = daily sales of gasoline (in units of 10,000), and P = price per gallon. The county has hired youto provide the following information regarding the gasoline market and the proposed tax.

a. What are the equilibrium values (price and quantity) in the current environment with no tax?

b. What price and quantity would prevail after the imposition of the tax? What portion of the tax would be borne by buyers and sellers respectively?

c. Calculate the elasticities of supply and demand at the original (pre- tax) equilibrium and verify that the relative elasticities of demand and supply are consistent with your answer to (b) (i.e. the group with higher elasticity pays a lower share of the tax).