Question

I drive to school and am currently looking for a parking spot so I can walk to Jacob's. If I turn into a parking lot to look for a spot to park in that specific lot, the process of looking for a spot takes 1 minute of time whether I find a spot or not.  

Parking lot A is closest to Jacobs. If I get a spot here, it takes me 1 minute to walk into my class at the business school, however there is only a 10% chance I'll find a spot if I look.

Parking lot B is a 4-minute walk; if I pull in to look for a spot, there is a 30% chance I'll find a spot.

Parking lot C is an 8-minute walk; if I pull in to look for a spot, there is a 100% chance I will find a spot.  

Which strategy to find a parking spot is best for me (ie. which order should I check the parking lots for spots to park), assuming we are risk-neutral, and simply want to have the earliest expected arrival time to Jacob’s as possible? (Another way to say this is we want the smallest expected value of time spent getting to Hall).

Now, assume I am risk averse (let’s say that in this second case, my class starts in 10 minutes, and there is a large decrease in my utility if I am late for class). Is the best strategy the same as when I am risk-neutral, or has it changed?

Answer 1

Since, there  is a 100% chance to find a spot in Parking lot C, below are the possible orders with expected arrival time to Jacob’s are

(A, B, C) Expected arrival time = 0.1 * (1 + 1) + ( 1 - 0.1) * 0.3 * (4 + 2) + (1- 0.1) * (1 - 0.3) * 1 * (8 + 3) = 8.75 minutes

(A, C)   Expected arrival time = 0.1 * (1 + 1) + (1- 0.1) * 1 * (8 + 2) = 9.2 minutes

(B, A, C) Expected arrival time = 0.3 * (4 + 1) + ( 1 - 0.3) * 0.1 * (1 + 2) + (1- 0.1) * (1 - 0.3) * 1 * (8 + 3) = 8.64 minutes

(B, C) Expected arrival time = 0.3 * (4 + 1) + (1- 0.3) * 1 * (8 + 2) = 8.5 minutes

(C) Expected time = 1 * (8 + 1) = 9 minutes

So, the earliest expected arrival time to Jacob’s is 8.5 minutes for the order B, C

For risk neutral, the order to be followed - Parking lot B and Parking lot C

For risk averse, since there is a large decrease in my utility if you are late by 10 minutes, Parking lot C is preferred in which expected time to Jacob's is 9 minutes (8 minutes of walk + 1 minute to search for spot) So, the best strategy is changed.