A city must decide whether to build a downtown parking garage (for up to 750 cars) and what rate to charge. It is considering two rates: a flat $1.50-per-hour rate or an all-day rate averaging $1 per hour (based on a $10 daily rate and an average 10-hour stay). Parking demand is Q = 900 - 300P, where Q is the number of cars in the garage each hour and P is the hourly rate. The capital cost of the garage is estimated to be $20 million and its annual operating cost to be $.62 million (regardless of the number of cars utilizing it) over its estimated 40-year life. The city’s discount rate is 8 percent. At 8 percent, $1 per year for 40 years has a present value of $11.90. (Use the factor of 11.9 to multiply yearly net benefits to obtain a present value.)
a. Sketch the demand curve (per hour) and calculate total benefits—the sum of consumer surplus and revenue—from the garage under either rate. (Multiply by 10 hours per day and 260 working days per year to find annual values.) Should the city build the facility? If so, which of the two rates should it charge?
b. Could a private developer profitably build and operate the garage? Which of the two rates would it set? (Assume it faces the same demand, costs, and discount rate as the city.)