Lewit and Coate (1982) estimated that the price elasticity of demand for cigarettes is -0.42. Suppose that the daily market demand for cigarettes in New York City is Q = 20,000p-0.42 and that the inverse market supply curve of cigarettes in the city is p = 1.5pw, where pw is the wholesale price of cigarettes. (That is, the inverse market supply curve is a horizontal line at a price, p, equal to 1.5pw. Retailers sell cigarettes if they receive a price that is 50% higher than what they pay for the cigarettes so as to cover their other costs.)
a. Assume that the New York retail market for cigarettes is competitive. Calculate the equilibrium price and quantity of cigarettes as a function of the wholesale price. Let Q* represent the equilibrium quantity. Find dQ*/dpw.
b. Now suppose that New York City and State each impose a $1.50 specific tax on each pack of cigarettes, for a total of $3.00 per pack on all cigarettes possessed for sale or use in New York City. The retailers pay the tax. Using both math and a graph, show how the introduction of the tax shifts the market supply curve. How does the introduction of the tax affect the equilibrium retail price and quantity of cigarettes?
c. With the specific tax in place, calculate the equilibrium price and quantity of cigarettes as a function of wholesale price. How does the presence of the quantity tax affect dQ*/dpw?