Consider the following overlapping generations model where each generation lives two periods. Population size evolves as follow: N'/N=(1+n) with n=0.1. The consumer will choose c=c' whenever is possible. The income of a consumer when young is y= 150. The consumer has no income when old: y'=0. The interest rate is r=0. 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 to each old consumer. There are no other taxes or government expenditures in this economy.

a) Find out the optimal consumption allocation in terms of t,

b).Suppose that the government levies a 20% social security tax on young, determine the social security benefit that would balance the social security budget. Note: the number of old people is different from the number of young people

c) Calculate lifetime wealth, optimal consumptions and savings under the social security system as in (b).

d) What would be lifetime wealth, consumptions and savings in this economy without social security?

e) EXPLAIN the impact of social security on welfare, consumption and savings in this model.