All the information and question is provided in the image attached.
Eleanor has difficulty finding parking if illegally parking on the sidewalk because of the opportunity cost of the time she spends searching for parking. On any given day, Eleanor knows she may or may not get a ticket, but she also expects that if she were to do it every day, the average amount she would pay for parking tickets should converge to the expected value. If the expected value is positive, then in the long run, it will be optimal for her to park on the sidewalk and occasionally pay the tickets in exchange for the benefits of not searching for parking.
Suppose that Eleanor knows that the fine for parking this way is $100, and her opportunity cost (OC) of searching for parking is $15 per day. That is, if she parks on the sidewalk and does not get a ticket, she gets a positive payoff worth $15; if she does get a ticket, she ends up with a payoff of $-85.
Given that Eleanor does not know the probability of getting caught, compute her expected payoff from parking on the sidewalk when the probability of getting a ticket is 10% and then when the probability is 50%.
Probability of Ticket: 10% 50%
EV of Sidewalk Parking (OC = $15)
Now, suppose Eleanor gets a new job that requires her to work longer hours. As a result, the opportunity cost of her time rises, and she now values the time saved from not having to look for parking at $30 per day.
Again, compute the expected value of the payoff from parking on the sidewalk given the two different probabilities of getting a ticket. Probability of Ticket: 10% 50% EV of Sidewalk Parking (OC = $30)
Based on the values you found in the first table, use the blue line (circle symbol) to plot the expected value of sidewalk parking on the following graph.
Value of sidewalk parking when the opportunity cost of time is $30.
Again, compute the expected value of the payoff from parking on the sidewalk given the two different probabilities of getting a ticket.
Probability of Ticket: 10% 50%
EV of Sidewalk Parking (OC = $30)
Based on the values you found in the first table, use the blue line (circle symbol) to plot the expected value of sidewalk parking on the following graph when the opportunity cost of time is $15. Based on the values you found in the second table, use the orange line (square symbol) to plot the expected value of sidewalk parking when the opportunity cost of time is $30.
60
40
EV when OC is $15
PARKING 20 ILLEGAL 10 EXPECTED VALUE 0 -40 40
EV when OC is $30
20 40 80 100 PROBABILITY OF TICKET
Despite Eleanor's uncertainty regarding the exact probability of being ticketed, suppose she decides to go ahead and park illegally every business day for two months (a total of 40 times). During the two months, she receives tickets on 9 days. If this is an accurate reflection of the overall probability of receiving a ticket, then there is a X% chance of receiving a ticket. Given this chance of getting ticketed, she Y% have parked illegally when the opportunity cost of searching was $15. Now that the opportunity cost of searching is $30, at the same chance of getting a ticket, she Z% park illegally.
