Question

You are planning to rent a car for a one-week vacation. You have the option of buying an insurance that costs $80 dollars for a week. If you do not purchase insurance, you would be personally liable for any damages. You anticipate that a minor collision will cost $2,000, whereas a major accident might cost $16,000 in repairs.

1. Develop a payoff table for this situation. What decision should you make using each strategy?

1. Aggressive (Optimistic)
2. Conservative (Pessimistic)
3. Opportunity Loss

1. You have recently read in a magazine that that the probability of a major accident is 0.05% and that the probability of a minor collision is 0.16%. Construct a decision tree and identify the best expected value decision.

Answer 1

a. i) ii) iii)

For All three pessimistic, Optimistic and Opportunity loss decision criteria we can see buying insurance is the best decision.

Optimistic decision - chooses best of the best payoffs. Best payoff is the minimum payoff as we are dealing with payoff (cost)

Pessimistic decision - chooses best of the worst payoffs. Worst payoff is the maximum payoff as we are dealing with payoff (cost)

Payoff (cost)

Formula

Decision tree

Expected value at node 3 = Expected value (Do not buy insurance) = 0.05%*16000+0.16%*2000+99.79%*0 = 11.2
Expected value at node 2 = Expected value (Buy insurance) = 0.05%*80+0.16%*80+99.79%*80 = 80

So according to Decision tree and expected value decision, best decision is "Do not Buy insurance"