Question 6: [10 points] Assume you are interested in buying a used vehicle C₁. You are also considering of taking it to

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Question 6 10 Points Assume You Are Interested In Buying A Used Vehicle C You Are Also Considering Of Taking It To 1 (218.29 KiB) Viewed 32 times

Question 6: [10 points] Assume you are interested in buying a used vehicle C₁. You are also considering of taking it to a qualified mechanic and then decide whether to buy it or not. The cost of taking it to the mechanic is $100. C₁ can be in good shape (quality q+) or bad one (quality q¯). The mechanic might help to indicate what shape the vehicle is in. C₁ costs $3,000 to buy and its market value is $4,000 if in good shape; if not, $1,400 in repairs will be needed to make it in good shape. Your estimate is that C₁ has a 70% chance of being in good shape. Assume that the utility function depends linearly on the vehicle's monetary value. a. Calculate the expected net gain from buying C₁, given no test. b. We also have the following information about whether the vehicle will pass the mechanic's test: P(pass(c₁)|q+(c₁)) = 0.8 P(pass(C₁)|q (C1)) = 0.35 Use Bayes' theorem to calculate the probability that the car will pass/fail the test and hence the probability that it is in good/ bad shape given what the mechanic will tell you. [Hint: Compute the four probabilities: P(q+|Pass), P(q¯|Pass), P(q+|¬Pass), P(q¯|-Pass)] c. What is the best decision given either a pass or a fail? What is the expected utility in each case? [Hint: Use the probabilities from the previous question.] d. What is the value of optimal information for the mechanic's test? Will you take C₁ to the mechanic or not? [Hint: You can easily answer this based on the answers from questions a) and c).]