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5). Parking Options in Bethesda (30 points)

(This is the one technical question on the exam with a few calculations). Please provide graphs and explanations if you have trouble with any of the calculations).

Recently in Bethesda, restaurant owners and their customers have been complaining about a booting practice occurring at local parking structures (a boot is something that can put on a car that does not allow the wheels to move until a fine is paid and the boot removed). These structures are privately owned, and have a permit system that limits parking to permit holders 24 hours a day. Signs on these structures announce that a permit is required to park, and that violators will be booted.

Consider the following problem. A couple is going out to dinner in Bethesda, and cannot find any street parking or any pay lots, but notices a large parking complex just across from their restaurant. They decide to park in this structure and face the following possibilities: if their car is booted, it will cost \$100 to get the boot removed; if the car is not booted, they enjoy their evening without any penalties. This couple has arrived in Bethesda with \$200 to spend; the probability of getting booted is 56%; and the couple's utility function is given by:

U(C) = 10C1/2

Where U(C) is the utility of consumption. (make a graph for these answers)

a). What is the expected consumption level of the couple for their night out in Bethesda?

b). What is their expected utility for their night out in Bethesda (this means expected utility with risk of getting booted)?

c). Suppose a new parking structure is opening next to this permit parking structure. How much could the neighboring parking structure charge this couple in order for them to be just indifferent between getting booted, and the certainty of not getting booted? (essentially, think of the neighboring garage fee as the equivalent of buying insurance).

If the parking were really this limited and expensive, I hope that this couple would have opted for Uber or the Metro for their night out! But perhaps they just love their car.
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