Expected Utility Theory: Utility Theory and Moral Hazard

An insurance company has to decide whether to sell an auto insurance policy to one person.

This person is a risk-averse person whose utility function is

U (W)= W.

This person claims to be a good risk because his driving record is excellent.

The person can also choose to be either a careful driver or a not-so-carefuldriver.

1. Solve the case of Moral Hazard and Uncertainty. See table below:

The person faces the following loss distribution:

2. Make cases when insurance is or is not included. Analyzethe results.

3. For both cases, change the probabilities of having an accident or not having an accident if one drives with care or not. Specifically, the probability of having an accident if one drives carefully is 30% and the probability of not having an accident if one drives with care is 70%. Inverse these percentages if one drives without care.

4. Do the initial results change, in other words, if the person having insurance has an inducement to drive without caution?

\begin{tabular}{|c|l|l|l|l|} \hline Drives & \multicolumn{2}{c|}{ Whit care } & \multicolumn{2}{|c|}{ without care } \\ \hline & & & & \\ & Probabilities & Loss (EV) & Probabilities & Loss (EV) \\ \hline & & & & \\ accident & 0.25 & $10,000 & 0.75 & $10,000 \\ \hline & & & & \\ \hline No accident & 0.75 & 0 & 0.25 & 0 \\ \hline \end{tabular} \begin{tabular}{|c|l|l|l|l|} \hline Drives & \multicolumn{2}{c|}{ Whit care } & \multicolumn{2}{|c|}{ without care } \\ \hline & & & & \\ & Probabilities & Loss (EV) & Probabilities & Loss (EV) \\ \hline & & & & \\ accident & 0.25 & $10,000 & 0.75 & $10,000 \\ \hline & & & & \\ \hline No accident & 0.75 & 0 & 0.25 & 0 \\ \hline \end{tabular}