Question

1. Imagine that you pulled over for speeding.  You are given a choice of either paying $150 on the spot or hiring a lawyer to appeal the ticket which has a 90% success rate. If you win the appeal, then the court pays your legal fees. If you lose the appeal, then your total cost of the ticket and lawyer is $1000.

What is the expected value of appealing the ticket? (Note: this will be a negative number). Please show your work.

What should you do according to the expected value rule?

(Continued ). Now suppose that you focus on the utilities rather than dollar amounts and that you are weighing losses more than gains. Let’s assume that every loss hurts twice as much as it’s dollar amount suggests (i.e. a loss of $100 is associated with -200 utility units).

What is the expected utility associated with appealing the ticket? Please show your work.

What should you do according to the expected utility rule?

Answer 1

Let Event A be winning the appeal

Event B be losing the appeal

Expected outflow of cash if appeal is won (Event A)= NIL

Expected outflow of cash if appeal is lost (Event B)= $ 1000

Expected value of appealng

= -$1000 X Probability of losing+$0 X Probability of winning

=(-$1000 X 0.10)+($0 X 0.90)

=-$100

Since the expected value of appealing is $100 i.e lower than the cost of paying the fine, therefore appealing is advisable.

Part(b)

If loss is associated with double the pain, then the expected value of loss becomes

(-$1000 X 0.10 X 2) +($0 X 0.90)

=-$200 utility loss

Since, now expected loss is higher than the cost of paying on the spot, appealing is not advisable.