Question 4: Social Security (25 marks Consider the following overlapping generations model where people live two periods. Each generation has the same number of people. Consumers prefer- ences over current and future consumption (c and c) are U(c, c)- log(c) +log(c) The income of a consumer when young is y-150. The consumer has no income when old: y0. The interest rate is r- 0.1. It can be shown that the optimal consumption allocation is 2 we we is the lifetime wealth. There is a Pay-As-You-Go Social Security system funded by a tax t on the young. Retirements benefits are given out as a fixed amount b 110 to each old consumer. There are no other taxes nor government expenditures in this economy (a) Determine the lump sum tax rate t that would balance the social security budget. (5 marks) (b) Calculate optimal consumptions and savings. (5 marks) (c) What would be the consumption in this economy without social security? (5 marks) (d) The US savings rate has been declining with the increase in the generosity of the social security. Explain why the results of this exercise are consistent with this fact. (5 marks) (e) Explain why replacing a Pay-As-You-Go Social Security system by a sys- tem without social security poses a problem of transition. (5 marks) Question 4: Social Security (25 marks Consider the following overlapping generations model where people live two periods. Each generation has the same number of people. Consumers prefer- ences over current and future consumption (c and c) are U(c, c)- log(c) +log(c) The income of a consumer when young is y-150. The consumer has no income when old: y0. The interest rate is r- 0.1. It can be shown that the optimal consumption allocation is 2 we we is the lifetime wealth. There is a Pay-As-You-Go Social Security system funded by a tax t on the young. Retirements benefits are given out as a fixed amount b 110 to each old consumer. There are no other taxes nor government expenditures in this economy (a) Determine the lump sum tax rate t that would balance the social security budget. (5 marks) (b) Calculate optimal consumptions and savings. (5 marks) (c) What would be the consumption in this economy without social security? (5 marks) (d) The US savings rate has been declining with the increase in the generosity of the social security. Explain why the results of this exercise are consistent with this fact. (5 marks) (e) Explain why replacing a Pay-As-You-Go Social Security system by a sys- tem without social security poses a problem of transition