Your mission is to eliminate illegal parking. Car drivers are completely rational expected utility maximizers. 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.
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).
Similar question with answer for your use (this one has probability, but asks you to find x):
You have $64 and the utility function U = x^(1/2) where x is money. Jimmy, a well known bully, comes up and says "Guess which hand I am holding my knife in. If you guess right you can keep all your money. If you guess wrong, I will take $60. Or, if you give me enough money right now, I'll just walk away and let you keep the rest."
Using certainty equivalents, show and calculate how much money you are willing to give Jimbo to get him to leave you alone.
w= 64
u(x)= √x
Certainty equivalent:
EUG = EUC
1/2 √4+ 1/2 √64=1*√(64-J)
1+4=√(64-J)
5^2=64-J
25=64-J
EU_G= $25
25=J
Certainty Equivalent = $39