Ben just bought a car and signed a car insurance contract. In a year, this contract will expire and Ben will move across

[answerhappygod]

Ben Just Bought A Car And Signed A Car Insurance Contract In A Year This Contract Will Expire And Ben Will Move Across 1 (353.42 KiB) Viewed 28 times

Ben Just Bought A Car And Signed A Car Insurance Contract In A Year This Contract Will Expire And Ben Will Move Across 2 (21.18 KiB) Viewed 28 times

Ben just bought a car and signed a car insurance contract. In a year, this contract will expire and Ben will move across the country. Suppose, when he is in the market for a new car insurance contract next year after he moves, the potential insurance companies can all see the number r of car accidents Ben has been involved in this year. This number r depends on Ben's driving skill 8 , Ben's effort e, and the road condition ε. More specifically, r = € - 0 - e. Ben's driving skill O is unknown to both Ben and all potential car insurance companies. All believe that Ben's driving skill Ở is 0 (unskilled) with probability 1/2 and 1 (skilled) with probability 1/2. The road condition ε is 3 with probability 1/2 and 4 with probability 1/2. Ben can choose to drive very carefully (e = 2), normally (e = 1) or carelessly (e = 0). But none of the potential car insurance companies observe Ben's effort choice. The potential car insurance companies will offer the car insurance contract that best matches Ben's driving skill. The more likely they think Ben is skilled, the lower the insurance premium they would charge. Ben wants to minimize the insurance premium, but driving carefully is costly. In particular, given the potential insurance companies' belief that Ben is skilled with probability q, Ben's payoff is equal to 89 - c(e), where c(e) = 0 if e = 0, c(e) = 1 if e = 1 and c(e) = 4.5 if e = 2. Use the above information to answer all of the following question. Suppose car insurance companies believe that Ben drives carelessly. How does their belief about the probability Ben is a skilled driver (0 = 1) depend on Ben's number of accidents r? - = a. skilled for sure if r s 1, skilled with probability 1/2 if r = 2, and unskilled for sure if r> 3. O b. skilled for sure if r = 0, skilled with probability 3/4 if r = 1, skilled with probability 1/2 if r = 2, skilled with probability 1/4 if r = 3, and unskilled for sure if r z 4. = O c. skilled for sure if r s 2, and unskilled for sure if r 2 3. O d. skilled for sure if r s 2, skilled with probability 1/2 if r = 3, and unskilled for sure if r =4.
Following Q11, if Ben indeed drives carelessly, what is Ben's expected payoff? a. 8 O b. 2 c. O d. 4
Following Q11, what will happen if Ben drives normally instead of careless? a. If Ben happens to be a skilled driver and ε = 4, then insurance companies' belief will go up from q = 1/2 to q = 1 (r will go down from 3 to 2, and q up from 1/2 to 1.) = = = O b. If Ben happens to be a skilled driver and ε = 3, then insurance companies' belief will go up from q = 1/2 to q = 1 (r will go down from 2 to 1, and q = 1 to q = 1) = c. If Ben happens to be an unskilled driver and ɛ 4, then insurance companies' belief will go up from a O to q = 1 (r will go down from 4 to 3, and thus q from 0 to 1/2) d. If Ben happens to be an unskilled driver and ɛ 3, then insurance companies' belief will go up from q = 0 to q = 1/2 (r will go down from 3 to 2 and thus q from 1/2 to 1)
Following Q11, does Ben have an incentive to drive normally instead of carelessly? a. Yes, because driving normally will reduce Ben's frequency of accidents. O b. Yes, because by driving normally instead of carelessly, Ben's payoff will go up by 2, given that the expected value of a goes up by 3/8 , while cost of effort goes up by only 1. C. No, because by driving normally instead of carelessly, Ben's payoff will go down by 1, given that the expected value of q does not change, while cost of effort goes up by only 1. q d. No, because driving normally costs more than driving carelessly.
Following Q11, suppose car insurance companies believe that Ben drives very carefully. That is, e = 2. How does their belief about the probability Ben is a skilled driver ( 0 = 1) depend on Ben's number of accidents r? = a. skilled for sure if r s 2, skilled with probability 1/2 if r = 3, and unskilled for sure if r = 4. O b. Skilled for sure if r s 1, skilled with probability 1/2 if r = 2, and unskilled for sure if rz 3. C. Skilled for sure if r = 0, skilled with prob 1/2 if r = 1, and unskilled for sure if r = 2. = d. skilled for sure if rs 2, and unskilled for sure if r 23