Alexander Industries is considering purchasing an insurance policy for its new office building in St$.$ Louis, Missouri. The policy has an annual cost of $$10,000.$ If Alexander Industries doesn$$t purchase the insurance and minor fire damage occurs, a cost of $$100,000$ is anticipated; the cost if major or total destruction occurs is $$200,000.$ The costs, including the state$-$of$-$nature probabilities, are as follows:

Damage

None Minor Major

Decision Alternative s $1$ s $2$ s $3$

Purchase insurance, d $110,00010,00010,000$

Do not purchase insurance, d $20100,000200,000$

Probabilities $0\mathrm{.}940\mathrm{.}050\mathrm{.}01$

$($a$)$ Using the expected value approach, what decision do you recommend?

The best decision using the Expected Value approach is

not to purchase

insurance, with an expected cost of $

$7000$

$.$

$($b$)$ Using the indiffence probabilities below, calculate the utility for $$10,000$ and $$100,000.$ Let the utility of $$0$ be $10$ and the utility of $$200,000$ be $0.($Note: Because the data are costs, the best payoff is $$0.)$

Cost Indifference Probability

$10,000$ p $=0\mathrm{.}99$

$100,000$ p $=0\mathrm{.}70$

Cost Utility

$$010$

$$10,000$

$99$

$$100,000$

$221$

$$200,0000$

$($c$)$ Using the utilities and indifference probabilities for the insurance defined in part $($b$).$ What decision would you recommend?

purchase

$($d$)$ Which method would you recommend to a risk adverse decision maker? Why?

Use the

expected utility

approach. The other approach may result in a

high

$-$risk decision, where the decision maker is exposed to a $

loss.