Background: 
Q15(Not need to answer this question, just need to answer Q16-Q21)
Q16
Q17
Q18
Q19
Q20
Q21
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 , Ben's effort e, and the road condition . 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 O is 0 (unskilled) with probability 1/2 and 1 (skilled) with probability 1/2. The road condition 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. = = = = = = = 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 r z 3. O c. skilled for sure if r = 0, skilled with prob 1/2 if r = 1, and unskilled for sure if r = 2. = O d. skilled for sure if rs 2, and unskilled for sure if r 23 Following Q15, if Ben indeed drives very carefully (e = 2), what is Ben's expected payoff? = a. 3.5 O b. -4.5 C. 1.5 d. -0.5 Following Q15, what will happen if Ben drives normally (e = 1) instead of very carefully (e = 2)? a. If Ben happens to be a skilled driver and = 4, then insurance companies' belief will go down from q = 1 to q = 1/2 (r will go up from 1 to 2, and thus a goes down from 1/2 to 0) = = = O b. If Ben happens to be an unskilled driver and = 3, then insurance companies' belief will go down from q = 1/2 to q = 0 (r will go up from 1 to 2, and thus q goes down from 1/2 to 0) - = = O c. If Ben happens to be an unskilled driver and = 4, then insurance companies' belief will go down from q = 1/2 to q = 0 (r will go up from 2 to 3, and thus q is unchanged at 0) = = O d. If Ben happens to be a skilled driver and = 3, then insurance companies' belief will not change. (r will go up from 0 to 1, and thus q goes down from 1 to 1/2) Following Q15, does Ben have an incentive to drive normally instead of very carefully? a. Yes, because by driving normally instead of very carefully, Ben's payoff will go up by 0.5, given that the expected value of a goes down by only 3/8 , while cost of effort goes down by 3.5. O b. No, because by driving normally instead of very carefully, Ben's payoff will go down by 4.5, given that the expected value of a goes down by 1, while cost of effort goes down by 3.5. O c. No, because driving normally instead of very carefully will increase Ben's frequency of accidents. O d. Yes, because driving normally costs less than driving very carefully. Following Q15, what can be an equilibrium behavior? a. Ben will drive carelessly. b. Ben will drive very carefully. C. Ben will drive normally. d. None of the above is possible equilibrium behavior. Following Q15, suppose the car insurance companies are able to identify Ben's commuting route and also identify a big group of drivers who commute via the same route. Suppose all these drivers look ex ante the same as Ben. That is, the description we made about Ben applies to all these drivers. The data on the frequency of accidents for all these drivers gives the insurance companies better information about a. The road condition of Ben's commuting route. O b. Both (a) and (b) C. Ben's driving skill. O d. Neither (a) nor (b) Following Q15, suppose all the insurance companies are able to learn the road condition of Ben's commuting route. Suppose all the insurance companies believe that Ben drives very carefully. In the case where Ben's commuting route has = 3, how does insurance companies' belief about Ben's driving skill depend on Ben's accident frequency r? = = a. skilled for sure if r s 1, skilled with probability 1/2 if r = 2, and unskilled for sure if r z 3. b. skilled for sure if r s 1 and unskilled for sure if r > 2. O c. skilled for sure if r = 0 and unskilled for sure if r > 1. = d. skilled for sure if r s 2, skilled with probability 1/2 if r = 3, and unskilled for sure if r = 4. 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 , Ben's effort e, and the road condition . 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 O is 0 (unskilled) with probability 1/2 and 1 (skilled) with probability 1/2. The road condition 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. = = = = = = = 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 r z 3. O c. skilled for sure if r = 0, skilled with prob 1/2 if r = 1, and unskilled for sure if r = 2. = O d. skilled for sure if rs 2, and unskilled for sure if r 23 Following Q15, if Ben indeed drives very carefully (e = 2), what is Ben's expected payoff? = a. 3.5 O b. -4.5 C. 1.5 d. -0.5 Following Q15, what will happen if Ben drives normally (e = 1) instead of very carefully (e = 2)? a. If Ben happens to be a skilled driver and = 4, then insurance companies' belief will go down from q = 1 to q = 1/2 (r will go up from 1 to 2, and thus a goes down from 1/2 to 0) = = = O b. If Ben happens to be an unskilled driver and = 3, then insurance companies' belief will go down from q = 1/2 to q = 0 (r will go up from 1 to 2, and thus q goes down from 1/2 to 0) - = = O c. If Ben happens to be an unskilled driver and = 4, then insurance companies' belief will go down from q = 1/2 to q = 0 (r will go up from 2 to 3, and thus q is unchanged at 0) = = O d. If Ben happens to be a skilled driver and = 3, then insurance companies' belief will not change. (r will go up from 0 to 1, and thus q goes down from 1 to 1/2) Following Q15, does Ben have an incentive to drive normally instead of very carefully? a. Yes, because by driving normally instead of very carefully, Ben's payoff will go up by 0.5, given that the expected value of a goes down by only 3/8 , while cost of effort goes down by 3.5. O b. No, because by driving normally instead of very carefully, Ben's payoff will go down by 4.5, given that the expected value of a goes down by 1, while cost of effort goes down by 3.5. O c. No, because driving normally instead of very carefully will increase Ben's frequency of accidents. O d. Yes, because driving normally costs less than driving very carefully. Following Q15, what can be an equilibrium behavior? a. Ben will drive carelessly. b. Ben will drive very carefully. C. Ben will drive normally. d. None of the above is possible equilibrium behavior. Following Q15, suppose the car insurance companies are able to identify Ben's commuting route and also identify a big group of drivers who commute via the same route. Suppose all these drivers look ex ante the same as Ben. That is, the description we made about Ben applies to all these drivers. The data on the frequency of accidents for all these drivers gives the insurance companies better information about a. The road condition of Ben's commuting route. O b. Both (a) and (b) C. Ben's driving skill. O d. Neither (a) nor (b) Following Q15, suppose all the insurance companies are able to learn the road condition of Ben's commuting route. Suppose all the insurance companies believe that Ben drives very carefully. In the case where Ben's commuting route has = 3, how does insurance companies' belief about Ben's driving skill depend on Ben's accident frequency r? = = a. skilled for sure if r s 1, skilled with probability 1/2 if r = 2, and unskilled for sure if r z 3. b. skilled for sure if r s 1 and unskilled for sure if r > 2. O c. skilled for sure if r = 0 and unskilled for sure if r > 1. = d. skilled for sure if r s 2, skilled with probability 1/2 if r = 3, and unskilled for sure if r = 4
