2. (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 u 3: L} is the population growth rate. The government estabiishes a social security system that is a hybrid between a payasryougo (FAG) and a fullyfunded (FF) system. The system provides a pension (lumpsum) b to every old individual. The funding of the entire amount of pensions comes 50% from contributions of the current yolmg as in the FAG systemI and 5U% 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 FAG 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 sf. n which is assumed to be unaffected by the program. (a) [6 marks) What is the government budget constraint from running this hybrid social seciuity system? (b) [13 marks) What is the lifetime budget constraint for any individual born after the establishment of this hybrid social security system? Is this individual better or worse off with the introduction of the system? Use equations and graphs to show your answer. (c) [6 marks) Assume now that n = r, and that the mandated savings under the hybrid social security system are higher than what each individual wouid be picking in the absence of the system. In terms of welfareJ are individuals better off with this system? Explain