Suppose that Cook County in Illinois did not yet have a tax on sweetened beverages but was considering the introduction of a $0.20 tax per bottle. The economic advisers to the county estimate the supply and demand curves for sweetened beverages as: Qd = 200,000-25,000P and Qs = 40,000+75,000P, where Q = daily sales in bottles of sweetened beverages, and P= price per bottle. The county has hired you to provide the following information regarding the sweetened beverage 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).