You have been appointed head of university parking enforcement. Your mission is to eliminate illegal parking. Car drivers are completely rational expected utility maximizes. They have utility functions given by u=x(1/2) where x is $ of consumption on things other than parking. But of course, everyone must park, whether legally or illegally. People start with $144. A legal parking permit costs $63, and if you catch someone parking illegally you are allowed to fine them $80.
a) If university is able to catch illegal parkers half the time, will people buy permits? Draw the picture and show your math.
b) Catching illegal parkers is expensive. Exactly how often do you have to catch illegal parkers, before they will buy the $63 parking permit instead? (Hint: Set EU legal = EU illegal and solve for p, the probability that you catch them).
c) Now go back to catching illegal parkers the time. Assume you are also in charge of selling legal parking permits so the price is no longer fixed at $63. If you can raise the price of a ticket for illegal parking from $80 to $108, how high can you set the price of a parking permit to park legally? Do the math and explain.
d) The Prospect Theory in the De Martino neuroscience paper argued that many people are actually risk loving over losses they prefer the risk of a big loss to the certain expected value of the loss. If this is true, what effect will it have on your explanation in a) about stopping illegal parkers using fines? Explain