4. The Commonwealth of Pennsylvania is the monopoly retailer of wine in that state. Suppose that Quaker Cabernet has no close substitutes and that the statewide inverse demand function for this wine is p=5-0.001Q. The state purchases the wine on the wholesale market for $2 per bottle, and the state-operated liquor stores incur no other expenses to sell this wine.
a. Find the state’s profit- maximizing price and quantity.
b. Neighboring New Jersey permits private retailers to sell wine. They face the same statewide demand curve as in Pennsylvania. No interstate wine trade is permitted. Suppose the New Jersey market for Quaker Cabernet is perfectly competitive. Find the corresponding equilibrium price and quantity.
c. New Jersey taxes wine sales. While the retailers pay the taxes on wine sales, they may pass on some or all of these taxes to consumers by raising prices. Identify the specific tax (tax per bottle sold) for which New Jersey’s equilibrium market price and quantity equal the Pennsylvania monopoly price and quantity. Given the quantity tax, show that New Jersey’s tax revenue equals Pennsylvania’s profit.