Question

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:

	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

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.

Profit	Utility
$0	10
$10,000
$100,000
$200,000	0

Answer 1

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