The director of a theater company in a small college town is considering changing the way he prices tickets. He has hired an economic consulting firm to estimate the demand for tickets. The firm has classified people who go to the theater into two groups and has come up with two demand functions. The demand curves for the general public (Qgp) and students (Qs) are given below:
Qgp = 500 -5P
Qs = 200 -4P
a. Graph the two demand curves on one graph, with P on the vertical axis and Q on the horizontal axis. If the current price of tickets is $35, identify the quantity demanded by each group.
b. Find the price elasticity of demand for each group at the current price and quantity.
c. Is the director maximizing the revenue he collects from ticket sales by charging $35 for each ticket? Explain.
d. What price should he charge each group if he wants to maximize revenue collected from ticket sales?