Q$4$:

Marks $15$

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 destruction occurs

is $$200,000.$ The costs, including the state$-$of$-$nature probabilities, are as

follows:

Decision Alternative

Purchase insurance, $d_1$

Do not purchase insurance, $d_2$

Probabilities

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

b$.$ What lottery would you use to assess utilities? $($Note: Because the data

are costs, the best payoff is $$0.)$

c$.$ Assume that you found the following indifference probabilities for the

lottery defined in part $($b$)$ What decision would you recommend?

Cost Indifference Probability

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

$100,000,p=0\mathrm{.}60$

d$.$ Do you favor using expected value or expected utility for this decision

problem? Why?

e$.$ By drawing the utility profile, can you explain the nature of the industry?