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Consider an individual that lives for at most two periods. The probability that she survives until period 2 is 0.8. Initial weal is $10,000 and, if she is alive in period 2, she will then receive a Social Security check for $4,600 and no additional inoon Suppose that the price of private annuity is aetuarially fair, the interest rate is mro and that the person chooses to have t] same level of oonsumption in the two periods by appropriately annuitizing (so that there is no saving from period one to peric two, other than through the annuity that is purchased). What is that level of consumption? 1 5. Consider an individual that lives for at most two periods. The probability that she survives until period 2 is 0.8. Initial wealth is $10,000 and, if she is alive in period 2, she will then receive a Social Security check for $4,600 and no additional income. Suppose that the price of private annuity is actuarially fair, the interest rate is zero and that the person chooses to have the same level of consumption in the two periods by appropriately annuitizing (so that there is no saving from period one to period two, other than through the annuity that is purchased). What is that level of consumption?.Il TMobile '3' 1226 PM The policy paid for upfront, benefits conditional on survival D Without annuities. consumers risk running out of their resources if they live too long > Two periods. the probability of survival until period 2 is 1/2. Initial resources of $100, no further income, no interest. How much can be consumed in the second period? The straightforward solution: $100 Under this solution, $100 is left behind in the case of death... How much would an insurer provide if paid $100? VVVV If the insurance company pays 3 when the individual survives, on average it pays 3/2. Therefore, $100 can finance benefits of B*/2 = 100 2 8* = 200. Private markets for annuities V It is possible to buy private annuities but they are overpriced V Estimates of the \"money's worth of annuities": 0.75-0.93 a dollar invested in a private annuity pays on average 75 to 93 cents. > Adverse selection in annuity markets annuitants live longer than non-annuitants > From the point of view of an insurance company, bad risks are those who will live long how to identify them? > Example: driving a fast car V Note asymmetry between annuities and life insurance m I'D E Dashboard Calendar To Do Notifications Inbox