I am confused on how to actually find the utility, can someone help me? Alexande

Question

I am confused on how to actually find the utility, can someone help me?

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:

What lottery would you use to assess utilities? (Note: Because the data are costs, the best payoff is $0.) Round your answer in one decimal place.

None Minor Major Decision Alternative s1 s2 s3 Purchase insurance, d1 10,000 10,000 10,000 Do not purchase insurance, d2 0 100,000 200,000 Probabilities 0.96 0.03 0.01

Explanation / Answer

Expected values for eah decision alternative are

EV (d1) = 10000 (0.96) + 10000 (0.03) + 10, 000 (0.01) = 10, 000

EV (d2) = 0 (0.96) + 100, 000 (0.03) + 200, 000 (0.01) = 5000

So best expected decision is d2. Donot purchase insurance,

Lottery use to assess utilities

The best outcome is 0

Worst outcome -200, 000

Lottery is an investment alternative with a probability p of obtaining the best payoff and a probability of 1-p of obtaining the worst payoff.

Lottery: Probability p for 0, and (1-p) = 0*p +200000*(1-p) = 200000 - 200000p

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