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Tutorial 3.SOLUTIONS

# Tutorial 3.SOLUTIONS - Tutorial 3 Solutions Problem 1/1...

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Tutorial 3 Solutions Problem 1. ( /1/ , p173, ex2).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 Decision Alternative None s 1 Minor s 2 Major s 3 Purchase insurance, d 1 10,000 10,000 10,000 Do not purchase insurance, d 2 0 100,000 200,000 Probabilities 0.96 0.03 0.01 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 = 0.99 100,000 p = 0.60 d. Do you favor using expected value or expected utility for this decision problem? Why? Prompting: a. Expected values for each decision alternative are 000 , 5 ) 01 . 0 ( 000 , 200 ) 03 . 0 ( 000 , 100 ) 96 . 0 ( 0 ) ( 000 , 10 ) 01 . 0 ( 000 , 10 ) 03 . 0 ( 000 , 10 ) 96 . 0 ( 000 , 10 ) ( 2 1 = + + = = + + = d EV d EV So, 2 d - best expected decision b. The best outcome is 0, the worst-200,000. Lottery: probability p for 0, and (1- p ) for 200,000. Expected value for the lottery is p p p 000 , 200 000 , 200 ) 1 ( 000 , 200 0 - = - + c. The Table of utilities is Damage Decision Alternative None s 1 Minor s 2 Major s 3 Purchase insurance, d 1 0.99 0.99 0.99 Do not purchase insurance, d 2 1 0.6 0 Probabilities 0.96 0.03 0.01 Expected utilities for each decision alternative are 978 . 0 ) 01 . 0 ( 0 ) 03 . 0 ( 6 . 0 ) 96 . 0 ( 1 ) ( 99 . 0 ) 01 . 0 ( 99 . 0 ) 03 . 0 ( 99 . 0 ) 96 . 0 ( 99 . 0 ) ( 2 1 = + + = = + + = d EU d EU

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So, 1 d - best expected utility decision Problem 2. ( /1/ , p174, ex4).Two different routes accommodate travel between two cities.
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