A city must decide whether to build a downtown parking garage and what rate to charge. It is

Question

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 given by 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 $0.62 million (regardless of the number of cars utilizing it) over its estimated 40-year life. The city's discount rate is 8%.
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
facility be built? If so, which of the two rates should be charged?
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).

Answer 1

a) The demand curve is given by Q = 900 - 300P, where Q is the number of cars in the garage each hour and P is the hourly rate.

Under the flat $1.50-per-hour rate, the total benefits would be equal to the consumer surplus plus revenue, which is equal to (900 - 300*1.50)*1.50 = $1125. Under the all-day rate averaging $1 per hour, the total benefits would be equal to (900 - 300*1)*1 = $600.

Given that the capital cost of the garage is estimated to be $20 million and its annual operating cost to be $0.62 million, the facility should be built. The all-day rate averaging $1 per hour should be charged, as it yields higher total benefits than the flat $1.50-per-hour rate.

b) A private developer could profitably build and operate the garage. It would set the all-day rate averaging $1 per hour, as it yields higher total benefits than the flat $1.50-per-hour rate.