(25 marks) Consider an overlapping generations economy in which individuals live for two periods. Each individual has an endowment y when young and y' when old. In each period there are N old individuals and N ' = (1 + n)N young individuals alive, where n > 0 is the population growth rate. The government establishes a social security system that is a hybrid between a payasyougo (PAG) and a fullyfunded (FF) system. The system provides a pension (lump-sum) b to every old individual. The funding of the entire amount of pensions comes 50% from contributions of the current young as in the PAC system, and 50% from the investment of what the old contributed when they were young, as in the FF system. Denote the contribution of a young individual to the PAG component of the system as t and to the funded component as tF. There are no other government expenditures or taxes in any period. All agents face the same interest rate r