II: Moral hazard Assume for this part that all individuals are like student 2. Suppose that the probability of being employed depends on the effort the individual makes to either find a job or remain employed. Assume that individuals dislike making efforts and thus their utility levels are lower when they exert effort. Also assume that the insurance company cannot observe whether an individual exerts effort. Assume then that the utility is given by: U = (1/a when individuals exert no effort, in which case probability of being unemployed is still p U = (1/a 0.75 when individuals exert effort (efforts lowers their utility by 0.75), in which case the probability of being unemployed is p= 0.25 * p a. Suppose there is no insurance. What will student 2's utility be if they do not exert effort? If they do exert effort? Will they choose to exert effort? b. What is the cost of actuarially fair full insurance if the insurance company assumes that all individuals will make efforts to get/retain their job? Will an individual like student 2 buy this insurance if offered? Will they choose to exert effort if they buy the insurance? c. What is the cost of actuarially fair full insurance if the insurance company assumes that no one will exert effort to get/retain their job? Will an individual like student 2 buy this insurance if offered? Will they choose to exert effort if they buy the insurance? d. Would other values for the cost of effort, which is set to 0.75, lead to different results for (c)? Provide support for your answer. (Assume that the cost cannot be less than zero) You can provide support by showing a specific value that changes the results or by showing the results don't change even if you try extreme values (e.g., if you get the same results if effort costs ( as when the cost of effort is very large) e. Is there an actuarially fair incomplete insurance contract that the individual buys and that leads them to exert effort? If so, then provide an example and show that the individual will choose to exert effort. If not, then show that there is not (to show that there is not it is sufficient if you show that an individual is not willing to exert effort even if they have no insurance) f. Suppose the insurance company develops the technology to observe if an individual exerts effort and can offer two types of actuarially fair full insurance contracts - one for individuals exerting effort and one for individuals not exerting effort. Will an individual like student 2 choose to buy insurance and exert effort? Has the technology made individuals better off or worse off when compared to the case when the insurance company cannot observe effort and can only offer one actuarially fair full insurance plan to all individuals? III: Adverse selection O Suppose that individuals receive 75% of their normal income from severance if they become unemployed. Suppose the insurance company offers full insurance to replace the other 25% of income that is missing and cannot charge separate prices to different individuals. Assume that 60% of individuals are like student 1, 30% are like student 2 and 10% are like student 3. a. If the insurance company charged one actuarially fair price to the entire pool of students, what would the price be if they all bought the insurance? b. Is a pooling equilibrium feasible? Why or why not? c. Can your answer to (b) change based on the share of students? Show either that it can or cannot change. To show it can you just need to give one example that changes the result To show it cannot you can either test several very different sets of shares and verbally argue that it cannot or If pooling equilibrium was feasible in (b) then you can show can show everyone is still willing to buy insurance at the maximum potential actuarially fair price (as the shares change the actuarially fair price changes so some set of shares give higher possible prices) if they are willing to all buy at this price then they are willing to buy at all lower insurance prices If the pooling equilibrium was not feasible then you can show that not everyone is willing to buy insurance at the minimum potential actuarially fair price - if they won't all buy at this price then they won't all buy at any higher insurance prices d. If the government mandates all individuals to buy this insurance, would this constitute a Pareto improvement? Why or why not? e. Suppose 50% of individuals are like student 1 and 50% are like student 2. Suppose also that the company now offers two separate plans; 100% insurance (25% of income) and 50% insurance (12.5% of income) and can only charge one price for each plan. Is a separating equilibrium feasible where individuals like student 1 purchase one insurance plan and individuals like student 2 purchase the other insurance plan at actuarially fair prices? Provide support for your answer. II: Moral hazard Assume for this part that all individuals are like student 2. Suppose that the probability of being employed depends on the effort the individual makes to either find a job or remain employed. Assume that individuals dislike making efforts and thus their utility levels are lower when they exert effort. Also assume that the insurance company cannot observe whether an individual exerts effort. Assume then that the utility is given by: U = (1/a when individuals exert no effort, in which case probability of being unemployed is still p U = (1/a 0.75 when individuals exert effort (efforts lowers their utility by 0.75), in which case the probability of being unemployed is p= 0.25 * p a. Suppose there is no insurance. What will student 2's utility be if they do not exert effort? If they do exert effort? Will they choose to exert effort? b. What is the cost of actuarially fair full insurance if the insurance company assumes that all individuals will make efforts to get/retain their job? Will an individual like student 2 buy this insurance if offered? Will they choose to exert effort if they buy the insurance? c. What is the cost of actuarially fair full insurance if the insurance company assumes that no one will exert effort to get/retain their job? Will an individual like student 2 buy this insurance if offered? Will they choose to exert effort if they buy the insurance? d. Would other values for the cost of effort, which is set to 0.75, lead to different results for (c)? Provide support for your answer. (Assume that the cost cannot be less than zero) You can provide support by showing a specific value that changes the results or by showing the results don't change even if you try extreme values (e.g., if you get the same results if effort costs ( as when the cost of effort is very large) e. Is there an actuarially fair incomplete insurance contract that the individual buys and that leads them to exert effort? If so, then provide an example and show that the individual will choose to exert effort. If not, then show that there is not (to show that there is not it is sufficient if you show that an individual is not willing to exert effort even if they have no insurance) f. Suppose the insurance company develops the technology to observe if an individual exerts effort and can offer two types of actuarially fair full insurance contracts - one for individuals exerting effort and one for individuals not exerting effort. Will an individual like student 2 choose to buy insurance and exert effort? Has the technology made individuals better off or worse off when compared to the case when the insurance company cannot observe effort and can only offer one actuarially fair full insurance plan to all individuals? III: Adverse selection O Suppose that individuals receive 75% of their normal income from severance if they become unemployed. Suppose the insurance company offers full insurance to replace the other 25% of income that is missing and cannot charge separate prices to different individuals. Assume that 60% of individuals are like student 1, 30% are like student 2 and 10% are like student 3. a. If the insurance company charged one actuarially fair price to the entire pool of students, what would the price be if they all bought the insurance? b. Is a pooling equilibrium feasible? Why or why not? c. Can your answer to (b) change based on the share of students? Show either that it can or cannot change. To show it can you just need to give one example that changes the result To show it cannot you can either test several very different sets of shares and verbally argue that it cannot or If pooling equilibrium was feasible in (b) then you can show can show everyone is still willing to buy insurance at the maximum potential actuarially fair price (as the shares change the actuarially fair price changes so some set of shares give higher possible prices) if they are willing to all buy at this price then they are willing to buy at all lower insurance prices If the pooling equilibrium was not feasible then you can show that not everyone is willing to buy insurance at the minimum potential actuarially fair price - if they won't all buy at this price then they won't all buy at any higher insurance prices d. If the government mandates all individuals to buy this insurance, would this constitute a Pareto improvement? Why or why not? e. Suppose 50% of individuals are like student 1 and 50% are like student 2. Suppose also that the company now offers two separate plans; 100% insurance (25% of income) and 50% insurance (12.5% of income) and can only charge one price for each plan. Is a separating equilibrium feasible where individuals like student 1 purchase one insurance plan and individuals like student 2 purchase the other insurance plan at actuarially fair prices? Provide support for your